RD18-4 Reliability Standard PRC-025-2 (Exhibit A)

Exhibit A
Proposed Reliability Standard PRC-025-2 – Generator Relay Loadability

PRC-025-2 - Clean Version

PRC-025-2— Generator Relay Loadability

A. Introduction
1.

Title:

Generator Relay Loadability

2.

Number:

PRC-025-2

3.

Purpose: To set load-responsive protective relays associated with generation
Facilities at a level to prevent unnecessary tripping of generators during a system
disturbance for conditions that do not pose a risk of damage to the associated
equipment.

4.

Applicability:
4.1.

4.2.

5.

1

Functional Entities:
4.1.1.

Generator Owner that applies load-responsive protective relays 1 at
the terminals of the Elements listed in 4.2, Facilities.

4.1.2.

Transmission Owner that applies load-responsive protective relays1
at the terminals of the Elements listed in 4.2, Facilities.

4.1.3.

Distribution Provider that applies load-responsive protective relays1
at the terminals of the Elements listed in 4.2, Facilities.

Facilities: The following Elements associated with Bulk Electric System (BES)
generating units and generating plants, including those generating units and
generating plants identified as Blackstart Resources in the Transmission
Operator’s system restoration plan:
4.2.1.

Generating unit(s).

4.2.2.

Generator step-up (i.e., GSU) transformer(s).

4.2.3.

Unit auxiliary transformer(s) (UAT) that supply overall auxiliary power
necessary to keep generating unit(s) online.2

4.2.4.

Elements that connect the GSU transformer(s) to the Transmission
system that are used exclusively to export energy directly from a BES
generating unit or generating plant, except that Elements may also
supply generating plant loads.

4.2.5.

Elements utilized in the aggregation of dispersed power producing
resources.

Effective Date: See Implementation Plan

Relays include low voltage protection devices that have adjustable settings.

These transformers are variably referred to as station power, unit auxiliary transformer(s) (UAT), or station service
transformer(s) used to provide overall auxiliary power to the generator station when the generator is running. Loss of these
transformers will result in removing the generator from service. Refer to the PRC-025-2 Guidelines and Technical Basis for more
detailed information concerning unit auxiliary transformers.

2

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6.

Background: After analysis of many of the major disturbances in the last 25 years on
the North American interconnected power system, generators have been found to have
tripped for conditions that did not apparently pose a direct risk to those generators and
associated equipment within the time period where the tripping occurred. This tripping
has often been determined to have expanded the scope and/or extended the duration
of that disturbance. This was noted to be a serious issue in the August 2003 “blackout”
in the northeastern North American continent. 3
During the recoverable phase of a disturbance, the disturbance may exhibit a “voltage
disturbance” behavior pattern, where system voltage may be widely depressed and
may fluctuate. In order to support the system during this transient phase of a
disturbance, this standard establishes criteria for setting load-responsive protective
relays such that individual generators may provide Reactive Power within their dynamic
capability during transient time periods to help the system recover from the voltage
disturbance. The premature or unnecessary tripping of generators resulting in the
removal of dynamic Reactive Power exacerbates the severity of the voltage disturbance,
and as a result changes the character of the system disturbance. In addition, the loss of
Real Power could initiate or exacerbate a frequency disturbance.

7.

Standard Only Definition: None.

B. Requirements and Measures
R1.

Each Generator Owner, Transmission Owner, and Distribution Provider shall apply
settings that are in accordance with PRC-025-2 – Attachment 1: Relay Settings, on each
load-responsive protective relay while maintaining reliable fault protection. [Violation
Risk Factor: High] [Time Horizon: Long-Term Planning]

M1. For each load-responsive protective relay, each Generator Owner, Transmission Owner,
and Distribution Provider shall have evidence (e.g., summaries of calculations,
spreadsheets, simulation reports, or setting sheets) that settings were applied in
accordance with PRC-025-2 – Attachment 1: Relay Settings.

C. Compliance
1.

Compliance Monitoring Process
1.1.

Compliance Enforcement Authority: “Compliance Enforcement Authority”
means NERC or the Regional Entity, or any entity as otherwise designated by
an Applicable Governmental Authority, in their respective roles of monitoring

Interim Report: Causes of the August 14th Blackout in the United States and Canada, U.S.-Canada Power System Outage Task
Force, November 2003 (http://www.nerc.com/docs/docs/blackout/814BlackoutReport.pdf).
3

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and/or enforcing compliance with mandatory and enforceable Reliability
Standards in their respective jurisdictions.
1.2.

Evidence Retention: The following evidence retention period(s) identify the
period of time an entity is required to retain specific evidence to demonstrate
compliance. For instances where the evidence retention period specified
below is shorter than the time since the last audit, the Compliance
Enforcement Authority may ask an entity to provide other evidence to show
that it was compliant for the full time period since the last audit.
The applicable entity shall keep data or evidence to show compliance as
identified below unless directed by its Compliance Enforcement Authority to
retain specific evidence for a longer period of time as part of an investigation:
•
•

The Generator Owner, Transmission Owner, and Distribution Provider
shall retain evidence of Requirement R1 and Measure M1 for the most
recent three calendar years.
If a Generator Owner, Transmission Owner, or Distribution Provider is
found non-compliant, it shall keep information related to the noncompliance until mitigation is complete and approved or for the time
specified above, whichever is longer.

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Violation Severity Levels
R#

R1

Violation Severity Levels

Lower VSL

N/A

Moderate VSL

N/A

High VSL

Severe VSL

N/A

The Generator Owner,
Transmission Owner, and
Distribution Provider did not
apply settings in accordance
with PRC-025-2 –
Attachment 1: Relay
Settings, on an applied loadresponsive protective relay.

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D. Regional Variances
None.

E. Associated Documents
NERC System Protection and Control Subcommittee, “Considerations for Power Plant and Transmission System Protection
Coordination,” technical reference document, Revision 2. (Date of Publication: July 2015)
NERC System Protection and Control Subcommittee, “Unit Auxiliary Transformer Overcurrent Relay Loadability During a
Transmission Depressed Voltage Condition.” (Date of Publication: March 2016)
IEEE C37.102-2006, “IEEE Guide for AC Generator Protection.” (Date of Publication: 2006)
IEEE C37.17-2012, “IEEE Standard for Trip Systems for Low-Voltage (1000 V and below) AC and General Purpose (1500 V
and below) DC Power Circuit Breakers.” (Date of Publication: September 18, 2012)
IEEE C37.2-2008, “IEEE Standard for Electrical Power System Device Function Numbers, Acronyms, and Contact
Designations.” (Date of Publication: October 3, 2008)

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Version History
Version

Date

Action

1

August 15,
2013

Adopted by NERC Board of Trustees

1

July 17, 2014

FERC order issued approving PRC-025-1

2

April 19, 2017

SAR accepted by Standards Committee

2

February 8,
2018

Adopted by NERC Board of Trustees

Change
Tracking

New

Project 2016-04
Revision

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PRC-025-2— Generator Relay Loadability

PRC-025-2 – Attachment 1: Relay Settings
Introduction

This standard does not require the Generator Owner, Transmission Owner, or Distribution
Provider to use any of the protective functions listed in Table 1. Each Generator Owner,
Transmission Owner, and Distribution Provider that applies load-responsive protective relays on
their respective Elements listed in 4.2, Facilities, shall use one of the following Options in Table
1, Relay Loadability Evaluation Criteria (“Table 1”), to set each load-responsive protective relay
element according to its application and relay type. The bus voltage is based on the criteria for
the various applications listed in Table 1.
Generators

Synchronous generator relay setting criteria values are derived from the unit’s maximum gross
Real Power capability, in megawatts (MW), as reported to the Transmission Planner, and the
unit’s Reactive Power capability, in megavoltampere-reactive (Mvar), is determined by
calculating the MW value based on the unit’s nameplate megavoltampere (MVA) rating at rated
power factor. If different seasonal capabilities are reported, the maximum capability shall be
used for the purposes of this standard as a minimum requirement. The Generator Owner may
base settings on a capability that is higher than what is reported to the Transmission Planner.
Asynchronous generator relay setting criteria values (including inverter-based installations) are
derived from the site’s aggregate maximum complex power capability, in MVA, as reported to
the Transmission Planner, including the Mvar output of any static or dynamic reactive power
devices. If different seasonal capabilities are reported, the maximum capability shall be used for
the purposes of this standard as a minimum requirement. The Generator Owner may base
settings on a capability that is higher than what is reported to the Transmission Planner.
For applications where synchronous and asynchronous generator types are combined on a
generator step-up transformer or on Elements that connect the generator step-up (GSU)
transformer(s) to the Transmission system that are used exclusively to export energy directly
from a BES generating unit or generating plant (except that Elements may also supply generating
plant loads), the setting criteria shall be determined by vector summing the setting criteria of
each generator type, and using the bus voltage for the given synchronous generator application
and relay type.
Transformers

Calculations using the GSU transformer turns ratio shall use the actual tap that is applied (i.e., in
service) for GSU transformers with de-energized tap changers (DETC). If load tap changers (LTC)
are used, the calculations shall reflect the tap that results in the lowest generator bus voltage.
When the criterion specifies the use of the GSU transformer’s impedance, the nameplate
impedance at the nominal GSU transformer turns ratio shall be used.
Applications that use more complex topology, such as generators connected to a multiple
winding transformer, are not directly addressed by the criteria in Table 1. These topologies can

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result in complex power flows, and may require simulation to avoid overly conservative
assumptions to simplify the calculations. Entities with these topologies should set their relays in
such a way that they do not operate for the conditions being addressed in this standard.
Multiple Lines

Applications that use more complex topology, such as multiple lines that connect the generator
step-up (GSU) transformer(s) to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant (except that Elements may also
supply generating plant loads) are not directly addressed by the criteria in Table 1. These
topologies can result in complex power flows, and it may require simulation to avoid overly
conservative assumptions to simplify the calculations. Entities with these topologies should set
their relays in such a way that they do not operate for the conditions being addressed in this
standard.
Exclusions

The following protection systems are excluded from the requirements of this standard:
1. Any relay elements that are in service only during start up.
2. Load-responsive protective relay elements that are armed only when the generator is
disconnected from the system, (e.g., non-directional overcurrent elements used in
conjunction with inadvertent energization schemes, and open breaker flashover
schemes).
3. Phase fault detector relay elements employed to supervise other load-responsive phase
distance elements (e.g., in order to prevent false operation in the event of a loss of
potential) provided the distance element is set in accordance with the criteria outlined in
the standard.
4. Protective relay elements that are only enabled when other protection elements fail (e.g.,
overcurrent elements that are only enabled during loss of potential conditions).
5. Protective relay elements used only for Remedial Action Schemes that are subject to one
or more requirements in a NERC or Regional Reliability Standard.
6. Protection systems that detect generator overloads that are designed to coordinate with
the generator short time capability by utilizing an extremely inverse characteristic set to
operate no faster than 7 seconds at 218% of full load current (e.g., rated armature
current), and prevent operation below 115% of full-load current. 4
7. Protection systems that detect overloads and are designed only to respond in time
periods which allow an operator 15 minutes or greater to respond to overload conditions.
8. Low voltage protection devices that do not have adjustable settings.
Table 1

Table 1 below is structured and formatted to aid the reader with identifying an option for a given
load-responsive protective relay.

4

IEEE C37.102-2006, “Guide for AC Generator Protection,” Section 4.1.1.2.

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The first column identifies the application (e.g., synchronous or asynchronous generators,
generator step-up transformers, unit auxiliary transformers, Elements that connect the GSU
transformer(s) to the Transmission system that are used exclusively to export energy directly
from a BES generating unit or generating plant). Dark blue horizontal bars, excluding the header
which repeats at the top of each page, demarcate the various applications.
The second column identifies the load-responsive distance or overcurrent protective relay by
IEEE device numbers (e.g., 21, 50, 51, 51V-C, 51V-R, or 67) according to the application in the first
column. This also includes manufacture protective device trip unit designations for long-time
delay, short-time delay, and instantaneous (e.g., L, S, and I). A light blue horizontal bar between
the relay types is the demarcation between relay types for a given application. These light blue
bars will contain no text, except when the same application continues on the next page of the
table with a different relay type.
The third column uses numeric and alphabetic options (i.e., index numbering) to identify the
available options for setting load-responsive protective relays according to the application and
applied relay type. Another, shorter, light blue bar contains the word “OR,” and reveals to the
reader that the relay for that application has one or more options (i.e., “ways”) to determine the
bus voltage and setting criteria in the fourth and fifth column, respectively. The bus voltage
column and setting criteria columns provide the criteria for determining an appropriate setting.
The table is further formatted by shading groups of relays associated with asynchronous
generator applications. Synchronous generator applications and the unit auxiliary transformer
applications are not shaded. Also, intentional buffers were added to the table such that similar
options, as possible, would be paired together on a per page basis. Note that some applications
may have an additional pairing that might occur on adjacent pages.

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Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Setting Criteria

1a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output –100% of the maximum gross Mvar
output during field-forcing as determined by simulation

OR
Synchronous
generating unit(s),
including Elements
utilized in the
aggregation of
dispersed power
producing resources

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system

1b

OR

1c

The same application continues on the next page with a different relay type

Calculations using the generator step-up (GSU) transformer turns ratio shall use the actual tap that is applied (i.e., in service) for GSU transformers with de-energized tap
changers (DETC). If load tap changers (LTC) are used, the calculations shall reflect the tap that results in the lowest generator bus voltage. When the criterion specifies the use of
the GSU transformer’s impedance, the nameplate impedance at the nominal GSU turns ratio shall be used.

5

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Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Setting Criteria

2a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

2b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

2c

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner or, and
(2) Reactive Power output –100% of the maximum gross Mvar
output during field-forcing as determined by simulation

3

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

Voltage control setting shall be set less than 75% of the
calculated generator bus voltage

OR

Synchronous
generating unit(s),
including Elements
utilized in the
aggregation of
dispersed power
producing resources

Phase overcurrent
relay (e.g., 50, 51,
or 51V-R – voltagerestrained)
OR

Phase time
overcurrent relay
(e.g., 51V-C) –
voltage controlled
(Enabled to
operate as a
function of
voltage)

A different application starts on the next page

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

4

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The impedance element shall be set less than the calculated
impedance derived from 130% of the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

5a

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

5b

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The lower tolerance of the overcurrent element tripping
characteristic shall not infringe upon the resource capability
(including the Mvar output of the resource and any static or
dynamic reactive power devices) See Figure A.

6

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

Voltage control setting shall be set less than 75% of the
calculated generator bus voltage

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system

Asynchronous
generating unit(s)
(including inverterbased installations),
including Elements
utilized in the
aggregation of
dispersed power
producing resources

Phase overcurrent
relay (e.g., 50, 51,
or 51V-R – voltagerestrained)

Phase time
overcurrent relay
(e.g., 51V-C) –
voltage controlled
(Enabled to
operate as a
function of
voltage)

OR

Setting Criteria

A different application starts on the next page

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Setting Criteria

7a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

7b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

7c

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR

Relays installed on
generator-side 6 of the
Generator step-up
transformer(s)
connected to
synchronous
generators

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system
OR

The same application continues on the next page with a different relay type

6

If the relay is installed on the high-side of the GSU transformer, use Option 14.

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Setting Criteria

8a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

8b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

8c

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR
Relays installed on
generator-side 7 of the
Generator step-up
transformer(s)
connected to
synchronous
generators

Phase overcurrent
relay (e.g., 50 or
51)
OR

The same application continues on the next page with a different relay type

7

If the relay is installed on the high-side of the GSU transformer use, Option 15.

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Setting Criteria

9a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

9b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

9c

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR
Relays installed on
generator-side 8 of the
Generator step-up
transformer(s)
connected to
synchronous
generators

Phase directional
overcurrent relay
(e.g., 67) –
directional toward
the Transmission
system
OR

A different application starts on the next page

8

If the relay is installed on the high-side of the GSU transformer use, Option 16.

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type
Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system 9

Relays installed on
generator-side of the
Generator step-up
transformer(s)
connected to
asynchronous
generators only
(including inverterbased installations)

Phase overcurrent
relay (e.g., 50 or
51) 10

Phase directional
overcurrent relay
(e.g., 67) –
directional toward
the Transmission
system 11

Option

Bus Voltage 5

10

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The impedance element shall be set less than the calculated
impedance derived from 130% of the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

11

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer for overcurrent relays
installed on the low-side

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

12

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

Setting Criteria

A different application starts on the next page

If the relay is installed on the high-side of the GSU transformer, use Option 17.
If the relay is installed on the high-side of the GSU transformer, use Option 18.
11 If the relay is installed on the high-side of the GSU transformer, use Option 19.
9

10

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Unit auxiliary
transformer(s) (UAT)

Relays installed on the
high-side of the GSU
transformer, 12 including
relays installed on the
remote end of line, for
Elements that connect
the GSU transformer(s)
to the Transmission
system that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant
(except that Elements
may also supply
generating plant loads)
– connected to
synchronous
generators

12

Relay Type
Phase overcurrent
relay (e.g., 50 or
51) applied at the
high-side terminals
of the UAT, for
which operation of
the relay will cause
the associated
generator to trip

Option

Bus Voltage 5

13a

1.0 per unit of the winding nominal
voltage of the unit auxiliary
transformer

The overcurrent element shall be set greater than 150% of the
calculated current derived from the unit auxiliary transformer
maximum nameplate MVA rating

Unit auxiliary transformer bus
voltage corresponding to the
measured current

The overcurrent element shall be set greater than 150% of the
unit auxiliary transformer measured current at the generator
maximum gross MW capability reported to the Transmission
Planner

0.85 per unit of the line nominal
voltage at the relay location

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 120% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

Simulated line voltage at the relay
location coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit of the line nominal
voltage at the remote end of the
line prior to field-forcing

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR
13b

14a
Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system

OR

14b

Setting Criteria

The same application continues on the next page with a different relay type

If the relay is installed on the generator-side of the GSU transformer, use Option 7.
17 of 115

PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on the
high-side of the GSU
transformer, 13 including
relays installed at the
remote end of the line,
for Elements that
connect the GSU
transformer(s) to the
Transmission system
that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant
(except that Elements
may also supply
generating plant loads)
– connected to
synchronous
generators

13

Relay Type
Phase
instantaneous
overcurrent
supervisory
element (e.g., 50) –
associated with
current-based,
communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
and/or phase time
overcurrent relay
(e.g., 51)

Option

15a

Bus Voltage 5

Setting Criteria

0.85 per unit of the line nominal
voltage at the relay location

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 120% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

Simulated line voltage at the relay
location coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit of the line nominal
voltage at the remote end of the
line prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR

15b

The same application continues on the next page with a different relay type

If the relay is installed on the generator-side of the GSU transformer, use Option 8.

18 of 115

PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Relays installed on the
high-side of the GSU
transformer, 14 including
relays installed at the
remote end of the line,
for Elements that
connect the GSU
transformer(s) to the
Transmission system
that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant
(except that Elements
may also supply
generating plant load.)
–connected to
synchronous
generators

Phase directional
instantaneous
overcurrent
supervisory
element (e.g., 67) –
associated with
current-based,
communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
directional toward
the Transmission
system and/or
phase directional
time overcurrent
relay (e.g., 67) –
directional toward
the Transmission
system

Option

16a

Bus Voltage 5

0.85 per unit of the line nominal
voltage at the relay location

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 120% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

Simulated line voltage at the relay
location coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit of the line nominal
voltage at the remote end of the
line prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR

16b

Setting Criteria

A different application starts on the next page

14

If the relay is installed on the generator-side of the GSU transformer, use Option 9.

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Relays installed on the
high-side of the GSU
transformer, 15 including
relays installed on the
remote end of line, for
Elements that connect
the GSU transformer(s)
to the Transmission
system that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant
(except that Elements
may also supply
generating plant loads)
–connected to
asynchronous
generators only
(including inverterbased installations)

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system

15

Option
17

Bus Voltage 5
1.0 per unit of the line nominal
voltage at the relay location

Setting Criteria
The impedance element shall be set less than the calculated
impedance derived from 130% of the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

The same application continues on the next page with a different relay type

If the relay is installed on the generator-side of the GSU transformer, use Option 10.

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PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Relays installed on the
high-side of the GSU
transformer, 16
including, relays
installed on the remote
end of the line, for
Elements that connect
the GSU transformer(s)
to the Transmission
system that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant
(except that Elements
may also supply
generating plant loads)
– connected to
asynchronous
generators only
(including inverterbased installations)

Phase
instantaneous
overcurrent
supervisory
element (e.g., 50) –
associated with
current-based,
communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
and/or Phase time
overcurrent relay
(e.g., 51)

16

Option

18

Bus Voltage 5

1.0 per unit of the line nominal
voltage at the relay location

Setting Criteria

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

The same application continues on the next page with a different relay type

If the relay is installed on the generator-side of the GSU transformer, use Option 11.

21 of 115

PRC-025-2— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Relays installed on the
high-side of the GSU
transformer, 17 including
relays installed on the
remote end of the line,
for Elements that
connect the GSU
transformer(s) to the
Transmission system
that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant
(except that Elements
may also supply
generating plant loads)
–connected to
asynchronous
generators only
(including inverterbased installations)

Phase directional
instantaneous
overcurrent
supervisory
element (e.g., 67) –
associated with
current-based,
communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
directional toward
the Transmission
system and/or
Phase directional
time overcurrent
relay (e.g., 67)

17

Option

19

Bus Voltage 5

1.0 per unit of the line nominal
voltage at the relay location

Setting Criteria

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

End of Table 1

If the relay is installed on the generator-side of the GSU transformer, use Option 12.

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PRC-025-2— Generator Relay Loadability

Overload Area
Exclusion 7

1000
900

100

Protective Element
Time Tolerance

Protective Element
Operate Area

0.1

Asynchronous
Resource
Capability

Time (s)

10

1

Option 5b – The lower
tolerance of the
overcurrent element
tripping characteristic shall
not infringe on the resource
capability

Protective Element
Pick Tolerance

Protective
Element Non
Operate Area

.01

Current
Figure A

This figure is for demonstration of Option 5b and does not mandate a specific type of
protective curve or device manufacturer.

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PRC-025-2 — Application Guidelines

PRC-025-2 Guidelines and Technical Basis
Introduction

The document, “Considerations for Power Plant and Transmission System Protection
Coordination,” published by the NERC System Protection and Control Subcommittee (SPCS)
provides extensive general discussion about the protective functions and generator performance
addressed within this standard. This document was last revised in July 2015. 18
The basis for the standard’s loadability criteria for relays applied at the generator terminals or
low-side of the generator step-up (GSU) transformer is the dynamic generating unit loading
values observed during the August 14, 2003 blackout, other subsequent system events, and
simulations of generating unit response to similar system conditions. The Reactive Power output
observed during field-forcing in these events and simulations approaches a value equal to 150
percent of the Real Power (MW) capability of the generating unit when the generator is operating
at its Real Power capability. In the SPCS technical reference document, two operating conditions
were examined based on these events and simulations: (1) when the unit is operating at rated
Real Power in MW with a level of Reactive Power output in Mvar which is equivalent to 150
percent times the rated MW value (representing some level of field-forcing) and (2) when the
unit is operating at its declared low active Real Power operating limit (e.g., 40 percent of rated
Real Power) with a level of Reactive Power output in Mvar which is equivalent to 175 percent
times the rated MW value (representing some additional level of field-forcing).
Both conditions noted above are evaluated with the GSU transformer high-side voltage at 0.85
per unit. These load operating points are believed to be conservatively high levels of Reactive
Power out of the generator with a 0.85 per unit high-side voltage which was based on these
observations. However, for the purposes of this standard it was determined that the second load
point (40 percent) offered no additional benefit and only increased the complexity for an entity
to determine how to comply with the standard. Given the conservative nature of the criteria,
which may not be achievable by all generating units, an alternate method is provided to
determine the Reactive Power output by simulation. Also, to account for Reactive Power losses
in the GSU transformer, a reduced level of output of 120 percent times the rated MW value is
provided for relays applied at the high-side of the GSU transformer and on Elements that connect
a GSU transformer to the Transmission system and are used exclusively to export energy directly
from a BES generating unit or generating plant.
The phrase, “while maintaining reliable fault protection” in Requirement R1, describes that the
Generator Owner, Transmission Owner, and Distribution Provider is to comply with this standard
while achieving its desired protection goals. Load-responsive protective relays, as addressed
within this standard, may be intended to provide a variety of backup protection functions, both
within the generating unit or generating plant and on the Transmission system, and this standard
is not intended to result in the loss of these protection functions. Instead, it is suggested that the
http://www.nerc.com/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20SPCS%2020/SPCS%20
Gen%20Prot%20Coordination%20Technical%20Reference%20Document.pdf.

18

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PRC-025-2 — Application Guidelines

Generator Owner, Transmission Owner, and Distribution Provider consider both the requirement
within this standard and its desired protection goals, and perform modifications to its protective
relays or protection philosophies as necessary to achieve both.
For example, if the intended protection purpose is to provide backup protection for a failed
Transmission breaker, it may not be possible to achieve this purpose while complying with this
standard if a simple mho relay is being used. In this case, it may be possible to meet this purpose
by replacing the legacy relay with a modern advanced-technology relay that can be set using
functions such as load encroachment. It may otherwise be necessary to reconsider whether this
is an appropriate method of achieving protection for the failed Transmission breaker, and
whether this protection can be better provided by, for example, applying a breaker failure relay
with a transfer trip system.
Requirement R1 establishes that the Generator Owner, Transmission Owner, and Distribution
Provider must understand the applications of Attachment 1: Relay Settings, Table 1: Relay
Loadability Evaluation Criteria (“Table 1”) in determining the settings that it must apply to each
of its load-responsive protective relays to prevent an unnecessary trip of its generator during the
system conditions anticipated by this standard.
Applicability

To achieve the reliability objective of this standard it is necessary to include all load-responsive
protective relays that are affected by increased generator output in response to system
disturbances. This standard is therefore applicable to relays applied by the Generator Owner,
Transmission Owner, and Distribution Provider at the terminals of the generator, GSU
transformer, unit auxiliary transformer (UAT), Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant, and Elements utilized in the aggregation of dispersed power producing
resources.
The Generator Owner’s interconnection facility (in some cases labeled a “transmission Facility”
or “generator leads”) consists of Elements between the GSU transformer and the interface with
the portion of the Bulk Electric System (BES) where Transmission Owners take over the
ownership. This standard does not use the industry recognized term “generator interconnection
Facility” consistent with the work of Project 2010-07 (Generator Requirements at the
Transmission Interface), because the term generator interconnection Facility implies ownership
by the Generator Owner. Instead, this standard refers to these Facilities as “Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant” to include these Facilities when they are
also owned by the Transmission Owner or Distribution Provider. The load-responsive protective
relays in this standard for which an entity shall be in compliance are dependent on the location
and the application of the protective functions. Figures 1, 2, and 3 illustrate various generator
interface connections with the Transmission system, and Figure 4 illustrates examples of
Elements utilized in the aggregation of dispersed power resources that are in scope of the
standard.
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PRC-025-2 — Application Guidelines

Figure 1

Figure 1 is a single (or set) of generators connected to the Transmission system through a radial
line that is used exclusively to export energy directly from a BES generating unit or generating
plant to the network. The protective relay R1 located on the high-side of the GSU transformer
breaker CB100 is generally applied to provide backup protection to the relaying located at Bus A
and in some cases Bus B. Under this application, relay R1 would apply the loadability requirement
in PRC-025-2 using an appropriate option for the application from Table 1 (e.g., Options 14
through 19) for Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant.
The protective relay R2 located on the incoming source breaker CB102 to the generating plant
applies relaying that primarily protects the line by using line differential relaying from Bus A to B
and also provides backup protection to the transmission relaying at Bus B. In this case, the relay
function that provides line protection would apply the loadability requirement in PRC-025-2 and
an appropriate option for the application from Table 1 (e.g., 15a, 15b, 16a, 16b, 18, and 19) for
phase overcurrent supervisory elements (i.e., phase fault detectors) associated with currentbased, communication-assisted schemes (i.e., pilot wire, phase comparison, and line current
differential) where the scheme is capable of tripping for loss of communications. The backup
protective function would apply the requirement in the PRC-025-2 standard using an appropriate
option for the application from Table 1 (e.g., Options 14 through 19) for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy directly
from a BES generating unit or generating plant.
Since Elements that connect the GSU transformer(s) to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant are applicable
to the standard, the loadability for relays applied on these Elements as shown in the shaded area
of Figure 1 (i.e., CB102 and CB103) must be considered. If relay R2 or R3 is set with an element
directional toward the transmission system (e.g., Buses B, C and D) or are non-directional, the
relay would be affected by increased generator output in response to system disturbances and
must meet the loadability setting criteria described in the standard. If relay R2 or R3 is set with
an element directional toward the generator (e.g., Bus A), the relay would not be affected by
increased generator output in response to system disturbances; therefore, the entity would not
be required to apply the loadability setting criteria described in this standard.

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Transmission System

PRC-025-2 — Application Guidelines

Bus C

Bus A

UAT
CB101

CB102

CB103
Bus B

CB100

R3

R1

Relays subject
to PRC-025

Transmission System

GSU

R2

Bus D

Figure 1: Generation exported through a single radial line
Figure 2

Figure 2 is an example of a single (or set) of generators connected to the Transmission system
through multiple lines that are used exclusively to export energy directly from a BES generating
unit or generating plant to the network. The protective relay R1 on the high-side of the GSU
transformer breaker CB100 is generally applied to provide backup protection to the Transmission
relaying located at Bus A and in some cases Bus B. Under this application, relay R1 would apply
the loadability requirement in PRC-025-2 using an appropriate option for the application from
Table 1 (e.g., Options 14 through 19) for Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant.
The protective relays R2 and R3 located on the incoming source breakers CB102 and CB103 to
the generating plant applies relaying that primarily protects the line from Bus A to B and also
provides backup protection to the transmission relaying at Bus B. In this case, the relay function
that provides line protection would apply the loadability requirement in PRC-025-2 and an
appropriate option for the application from Table 1 (e.g., Options 15a, 15b, 16a, 16b, 18, and 19)
for phase overcurrent supervisory elements (i.e., phase fault detectors) associated with currentbased, communication-assisted schemes (i.e., pilot wire, phase comparison, and line current
27 of 115

PRC-025-2 — Application Guidelines

differential) where the scheme is capable of tripping for loss of communications. The backup
protective function would apply the requirement in the PRC-025-2 standard using an appropriate
option for the application from Table 1 (e.g., Options 14 through 19) for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy directly
from a BES generating unit or generating plant.

Transmission System

Since Elements that connect the GSU transformer(s) to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant are applicable
to the standard, the loadability for relays applied on these Elements as shown in the shaded area
of Figure 2 (i.e., CB102, CB103, CB104, and CB105) must be considered. If relay R2, R3, R4, or R5
is set with an element directional toward the transmission system (e.g., Buses B, C and D) or are
non-directional, the relay would be affected by increased generator output in response to system
disturbances and must meet the loadability setting criteria described in the standard. If relay R2,
R3, R4, or R5 is set with an element directional toward the generator (e.g., Bus A), the relay would
not be affected by increased generator output in response to system disturbances; therefore,
the entity would not be required to apply the loadability setting criteria described in this
standard.

Bus C

Bus A
UAT

CB102
CB101

R2

CB104
R4

Bus B

GSU

R1

CB103
R3

Relays subject
to PRC-025

CB105
R5

Transmission System

CB100

Bus D

Figure 2: Generation exported through multiple radial lines

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PRC-025-2 — Application Guidelines

Figure 3

Figure 3 is example a single (or set) of generators exporting power dispersed through multiple
lines to the Transmission system through a network. The protective relay R1 on the high-side of
the GSU transformer breaker CB100 is generally applied to provide backup protection to the
Transmission relaying located at Bus A and in some cases Bus C or Bus D. Under this application,
relay R1 would apply the applicable loadability requirement in PRC-025-2 using an appropriate
option for the application from Table 1 (e.g., Options 14 through 19) for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy directly
from a BES generating unit or generating plant.

Transmission System

Since the lines from Bus A to Bus C and from Bus A to Bus D are part of the transmission network,
these lines would not be considered as Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant. Therefore, the applicable responsible entity would be responsible for
the load-responsive protective relays R2 and R3 under the PRC-023 standard. The applicable
responsible entity’s loadability relays R4 and R5 located on the breakers CB104 and CB105 at Bus
C and D are also subject to the requirements of the PRC-023 standard.

Bus C
R4

CB104

Bus A
UAT

CB102
R2

CB101

CB102

CB100
R3

R1

Relays subject
to PRC-025

Transmission System

GSU

CB105
R5

Bus D

Figure 3: Generation exported through a network

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PRC-025-2 — Application Guidelines

This standard is also applicable to the UATs that supply station service power to support the online operation of generating units or generating plants. These transformers are variably referred
to as station power, unit auxiliary transformer(s), or station service transformer(s) used to
provide overall auxiliary power to the generator station when the generator is running. Inclusion
of these transformers satisfies a directive in FERC Order No. 733, paragraph 104, which directs
NERC to include in this standard a loadability requirement for relays used for overload protection
of the UAT(s) that supply normal station service for a generating unit. The NERC System
Protection and Control Subcommittee addressed low-side UAT protection in the document called
Unit Auxiliary Transformer Overcurrent Relay Loadability During a Transmission Depressed
Voltage Condition, 19 March 2016.
Figure 4

Elements utilized in the aggregation of dispersed power producing resources (in some cases
referred to as a “collector system” or “feeders”) consist of the Elements between individual
generating units and the common point of interconnection to the Transmission system.

http://www.nerc.com/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20SPCS%2020
/NERC%20-%20SPCS%20UAT%20-%20FEB_2016_final.pdf.

19

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PRC-025-2 — Application Guidelines

To GSU

Included in PRC-25-2
as collector system or
feeders
Low Voltage
Molded Case
Circuit Breaker
Circuit Breaker,
other than
To other DR
Molded Case
Circuit Breaker

To other DR

DR

DR

DR

DR

DR

DR

DR

Figure-4: Elements utilized in the aggregation of dispersed power producing
resources (DR)
Synchronous Generator Performance

When a synchronous generator experiences a depressed voltage, the generator will respond by
increasing its Reactive Power output to support the generator terminal voltage. This operating
condition, known as “field-forcing,” results in the Reactive Power output exceeding the steadystate capability of the generator and may result in operation of generation system loadresponsive protective relays if they are not set to consider this operating condition. The ability of
the generating unit to withstand the increased Reactive Power output during field-forcing is
limited by the field winding thermal withstand capability. The excitation limiter will respond to
begin reducing the level of field-forcing in as little as one second, but may take much longer,
depending on the level of field-forcing given the characteristics and application of the excitation
system. Since this time may be longer than the time-delay of the generator load-responsive
protective relay, it is important to evaluate the loadability to prevent its operation for this
condition.

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PRC-025-2 — Application Guidelines

The generator bus voltage during field-forcing will be higher than the high-side voltage due to
the voltage drop across the GSU transformer. When the relay voltage is supplied from the
generator bus, it is necessary to assess loadability using the generator bus voltage. The criteria
established within Table 1 are based on 0.85 per unit of the line nominal voltage. This voltage
was widely observed during the events of August 14, 2003, and was determined during the
analysis of the events to represent a condition from which the System may have recovered, had
other undesired behavior not occurred.
The dynamic load levels specified in Table 1 under column “Setting Criteria” are representative
of the maximum expected apparent power during field-forcing with the Transmission system
voltage at 0.85 per unit, for example, at the high-side of the GSU transformer. These values are
based on records from the events leading to the August 14, 2003 blackout, other subsequent
System events, and simulations of generating unit responses to similar conditions. Based on these
observations, the specified criteria represent conservative but achievable levels of Reactive
Power output of the generator with a 0.85 per unit high-side voltage at the point of
interconnection.
The dynamic load levels were validated by simulating the response of synchronous generating
units to depressed Transmission system voltages for 67 different generating units. The generating
units selected for the simulations represented a broad range of generating unit and excitation
system characteristics as well as a range of Transmission system interconnection characteristics.
The simulations confirmed, for units operating at or near the maximum Real Power output, that
it is possible to achieve a Reactive Power output of 1.5 times the rated Real Power output when
the Transmission system voltage is depressed to 0.85 per unit. While the simulations
demonstrated that all generating units may not be capable of this level of Reactive Power output,
the simulations confirmed that approximately 20 percent of the units modeled in the simulations
could achieve these levels. On the basis of these levels, Table 1, Options 1a (i.e., 0.95 per unit)
and 1b (i.e., 0.85 per unit), for example, are based on relatively simple, but conservative
calculations of the high-side nominal voltage. In recognition that not all units are capable of
achieving this level of output Option 1c (i.e., simulation) was developed to allow the Generator
Owner, Transmission Owner, or Distribution Provider to simulate the output of a generating unit
when the simple calculation is not adequate to achieve the desired protective relay setting.
Dispersed Generation

This standard is applicable to dispersed generation such as wind farms and solar arrays. The
intent of this standard is to ensure the aggregate facility as defined above will remain on-line
during a system disturbance; therefore, all output load-responsive protective relays associated
with the facility are included in PRC-025.
Dispersed power producing resources with aggregate capacity greater than 75 MVA (gross
aggregate nameplate rating) utilizing a system designed primarily for aggregating capacity,
connected at a common point at a voltage of 100 kV or above are included in PRC-025-2. Loadresponsive protective relays that are applied on Elements that connect these individual
generating units through the point of interconnection with the Transmission system are within
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PRC-025-2 — Application Guidelines

the scope of PRC-025-2. For example, feeder overcurrent relays and feeder step-up transformer
overcurrent relays (see Figure 6) are included because these relays are challenged by generator
loadability.
In the case of solar arrays where there are multiple voltages utilized in converting the solar panel
DC output to a 60Hz AC waveform, the “terminal” is defined at the 60Hz AC output of the
inverter-solar panel combination.
Asynchronous Generator Performance

Asynchronous generators will not respond to a disturbance with the same magnitude of apparent
power that a synchronous generator will respond. Asynchronous generators, though, will support
the system during a disturbance. Inverter-based generators will provide Real Power and Reactive
Power (depending on the installed capability and regional grid code requirements) and may even
provide a faster Reactive Power response than a synchronous generator. The magnitude of this
response may slightly exceed the steady-state capability of the inverter but only for a short
duration before limiter functions will activate. Although induction generators will not inherently
supply Reactive Power, induction generator installations may include static and/or dynamic
reactive devices, depending on regional grid code requirements. These devices also may provide
Real Power during a voltage disturbance. Thus, tripping asynchronous generators may
exacerbate a disturbance.
Inverters, including wind turbines (i.e., Types 3 and 4) and photovoltaic solar, are commonly
available with 0.90 power factor capability. This calculates to an apparent power magnitude of
1.11 per unit of rated MW.
Similarly, induction generator installations, including Type 1 and Type 2 wind turbines, often
include static and/or dynamic reactive devices to meet grid code requirements and may have
apparent power output similar to inverter-based installations; therefore, it is appropriate to use
the criteria established in the Table 1 (i.e., Options 4, 5, 6, 10, 11, 12, 17, 18, and 19) for
asynchronous generator installations.
Synchronous Generator Simulation Criteria

The Generator Owner, Transmission Owner, or Distribution Provider who elects a simulation
option to determine the synchronous generator performance on which to base relay settings
may simulate the response of a generator by lowering the Transmission system voltage at the
remote end of the line or at the high-side of the GSU transformer (as prescribed by the Table 1
criteria). This can be simulated by means such as modeling the connection of a shunt reactor at
the remote end of the line or at the GSU transformer high-side to lower the voltage to 0.85 per
unit prior to field-forcing. The resulting step change in voltage is similar to the sudden voltage
depression observed in parts of the Transmission system on August 14, 2003. The initial condition
for the simulation should represent the generator at 100 percent of the maximum gross Real
Power capability in MW as reported to the Transmission Planner. The simulation is used to
determine the Reactive Power and voltage at the relay location to calculate relay setting limits.
The Reactive Power value obtained by simulation is the highest simulated level of Reactive Power

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achieved during field-forcing. The voltage value obtained by simulation is the simulated voltage
coincident with the highest Reactive Power achieved during field-forcing. These values of
Reactive Power and voltage correspond to the minimum apparent impedance and maximum
current observed during field-forcing.
Phase Distance Relay – Directional Toward Transmission System (e.g., 21)

Generator phase distance relays that are directional toward the Transmission system, whether
applied for the purpose of primary or backup GSU transformer protection, external system
backup protection, or both, were noted during analysis of the August 14, 2003 disturbance event
to have unnecessarily or prematurely tripped a number of generating units or generating plants,
which contributed to the scope of that disturbance. Specifically, eight generators are known to
have been tripped by this protection function. These options establish criteria for phase distance
relays that are directional toward the Transmission system to help assure that generators, to the
degree possible, will provide System support during disturbances in an effort to minimize the
scope of those disturbances.
The phase distance relay that is directional toward the Transmission system measures impedance
derived from the quotient of generator terminal voltage divided by generator stator current.
Section 4.6.1.1 of IEEE C37.102-2006, “Guide for AC Generator Protection,” describes the
purpose of this protection as follows (emphasis added):
“The distance relay applied for this function is intended to isolate
the generator from the power system for a fault that is not cleared
by the transmission line breakers. In some cases this relay is set
with a very long reach. A condition that causes the generator
voltage regulator to boost generator excitation for a sustained
period may result in the system apparent impedance, as monitored
at the generator terminals, to fall within the operating
characteristics of the distance relay. Generally, a distance relay
setting of 150% to 200% of the generator MVA rating at its rated
power factor has been shown to provide good coordination for
stable swings, system faults involving in-feed, and normal loading
conditions. However, this setting may also result in failure of the
relay to operate for some line faults where the line relays fail to
clear. It is recommended that the setting of these relays be
evaluated between the generator protection engineers and the
system protection engineers to optimize coordination while still
protecting the turbine generator. Stability studies may be needed
to help determine a set point to optimize protection and
coordination. Modern excitation control systems include
overexcitation limiting and protection devices to protect the
generator field, but the time delay before they reduce excitation is
several seconds. In distance relay applications for which the voltage
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regulator action could cause an incorrect trip, consideration should
be given to reducing the reach of the relay and/or coordinating the
tripping time delay with the time delays of the protective devices in
the voltage regulator. Digital multifunction relays equipped with
load encroachment binders [sic] can prevent misoperation for these
conditions. Within its operating zone, the tripping time for this
relay must coordinate with the longest time delay for the phase
distance relays on the transmission lines connected to the
generating substation bus. With the advent of multifunction
generator protection relays, it is becoming more common to use
two-phase distance zones. In this case, the second zone would be
set as previously described. When two zones are applied for backup
protection, the first zone is typically set to see the substation bus
(120% of the GSU transformer). This setting should be checked for
coordination with the zone-1 element on the shortest line off of the
bus. The normal zone-2 time-delay criteria would be used to set the
delay for this element. Alternatively, zone-1 can be used to provide
high-speed protection for phase faults, in addition to the normal
differential protection, in the generator and iso-phase bus with
partial coverage of the GSU transformer. For this application, the
element would typically be set to 50% of the transformer
impedance with little or no intentional time delay. It should be
noted that it is possible that this element can operate on an out-ofstep power swing condition and provide misleading targeting.”
If a mho phase distance relay that is directional toward the Transmission system cannot be set
to maintain reliable fault protection and also meet the criteria in accordance with Table 1, there
may be other methods available to do both, such as application of blinders to the existing relays,
implementation of lenticular characteristic relays, application of offset mho relays, or
implementation of load encroachment characteristics. Some methods are better suited to
improving loadability around a specific operating point, while others improve loadability for a
wider area of potential operating points in the R-X plane. The operating point for a stressed
System condition can vary due to the pre-event system conditions, severity of the initiating event,
and generator characteristics such as Reactive Power capability.
For this reason, it is important to consider the potential implications of revising the shape of the
relay characteristic to obtain a longer relay reach, as this practice may result in a relay
characteristic that overlaps the capability of the generating unit when operating at a Real Power
output level other than 100 percent of the maximum Real Power capability. Overlap of the relay
characteristic and generator capability could result in tripping the generating unit for a loading
condition within the generating unit capability. The examples in Appendix E of the Considerations
for Power Plant and Transmission System Protection Coordination technical reference document
illustrate the potential for, and need to avoid, encroaching on the generating unit capability.

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Phase Instantaneous Overcurrent Relay (e.g., 50)

The 50 element is a non-directional overcurrent element that typically has no intentional time
delay. The primary application is for close-in high current faults where high speed operation is
required or preferred. The instantaneous overcurrent elements are subject to the same
loadability issues as the time overcurrent elements referenced in this standard.
Phase Time Overcurrent Relay (e.g., 51)

See Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document for a detailed discussion of this protection function.
Note that the setting criteria established within the Table 1 options differ from the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document. Rather than establishing a uniform setting threshold of 200 percent of the
generator MVA rating at rated power factor for all applications, the Table 1 setting criteria are
based on the maximum expected generator Real Power output based on whether the generator
is a synchronous or asynchronous unit.
Phase Time Overcurrent Relay – Voltage-Restrained (e.g., 51V-R)

Phase time overcurrent voltage-restrained relays (e.g., 51V-R), which change their sensitivity as
a function of voltage, whether applied for the purpose of primary or backup GSU transformer
protection, for external system phase backup protection, or both, were noted, during analysis of
the August 14, 2003 disturbance event to have unnecessarily or prematurely tripped a number
of generating units or generating plants, contributing to the scope of that disturbance.
Specifically, 20 generators are known to have been tripped by voltage-restrained and voltagecontrolled protection functions together. These protective functions are variably referred to by
IEEE function numbers 51V, 51R, 51VR, 51V/R, 51V-R, or other terms. See Chapter 2 of the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document for a detailed discussion of this protection function.
Phase Time Overcurrent Relay – Voltage Controlled (e.g., 51V-C)

Phase time overcurrent voltage-controlled relays (e.g., 51V-C), enabled as a function of voltage,
are variably referred to by IEEE function numbers 51V, 51C, 51VC, 51V/C, 51V-C, or other terms.
See Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document for a detailed discussion of this protection function.
Phase Directional Overcurrent Relay – Directional Toward Transmission System
(e.g., 67)

See Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document for a detailed discussion of the phase time
overcurrent protection function. The basis for setting directional and non-directional overcurrent
relays is similar. Note that the setting criteria established within the Table 1 options differ from
of the Considerations for Power Plant and Transmission System Protection Coordination
technical reference document. Rather than establishing a uniform setting threshold of 200
percent of the generator MVA rating at rated power factor for all applications, the Table 1 setting

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criteria are based on the maximum expected generator Real Power output based on whether the
generator is a synchronous or asynchronous unit.

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Table 1, Options
Introduction

The margins in the Table 1 options are based on guidance found in the Considerations for Power
Plant and Transmission System Protection Coordination technical reference document. The
generator bus voltage during field-forcing will be higher than the high-side voltage due to the
voltage drop across the GSU transformer. When the relay voltage is supplied from the generator
bus, it is necessary to assess loadability using the generator bus voltage.
Relay Connections

Figures 5 and 6 below illustrate the connections for each of the Table 1 options provided in PRC025-2, Attachment 1: Relay Settings, Table 1: Relay Loadability Evaluation Criteria.

2000/1

To 345 kV system
GSU Data
903 MVA
345 kV / 22 kV
X = 12.14%

2000/5
Options 14a and 14b
2000/5

21
21T

GSU

Options 16a and 16b
67

Options 7a, 7b, and 7c

50/51

67
Options 15a and 15b
25000/5

21

50/51

5000/5

UAT

Options 9a, 9b, and 9c

Options 8a, 8b, and 8c

200/1
50/51

To auxiliary
loads

Options 13a and 13b

Options 1a, 1b, and 1c
25000/5

21
50/51

51 V-R 51 V-C

Option 3

Generator Nameplate
903 MVA @ 0.85 pf
22 kV

Options 2a, 2b, and 2c

Figure 5: Relay Connection for corresponding synchronous options

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To 345 kV system

2000/1

GSU Data
150 MVA
346.5 kV / 22 kV
X = 12.14%

300/5
Option 17
300/5

21
21T

Option 19

67

GSU

Option 10

50/51

Option 12
67

Option 18

5000/5

Option 11

200/1

21

50/51

5000/5

UAT

Aggregated
Mvar
15 Mvar

To auxiliary
loads

50/51

Options 13a and 13b
22 kV / 12 kV
Aggregated MVA
3-40 MVA @ 0.85 pf
1-5 Mvar

50/51

50/51

Options
4, 5, & 6
21
51 V-C 51 V-R

21

50/51

5000/5

5000/5
Option 5

Option 5

21

5000/5

Options
4, 5, & 6 51 V-R

51 V-C 51 V-R

51 V-C

5 Mvar

Figure 6: Relay Connection for corresponding asynchronous options including
inverter-based installations
Synchronous Generators Phase Distance Relay – Directional Toward Transmission
System (e.g., 21) (Options 1a, 1b, and 1c)

Table 1, Options 1a, 1b, and 1c, are provided for assessing loadability for synchronous generators
applying phase distance relays that are directional toward the Transmission system. These
margins are based on guidance found in Chapter 2 of the Considerations for Power Plant and
Transmission System Protection Coordination technical reference document.
Option 1a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.

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Option 1b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on a 0.85 per unit nominal voltage at the high-side terminals of the GSU
transformer as well as the turns ratio and impedance. The actual generator bus voltage may be
higher depending on the GSU transformer impedance and the actual Reactive Power achieved.
This calculation is a more in-depth and precise method for setting of the impedance element than
Option 1a.
Option 1c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more
involved, more precise setting of the impedance element overall.
For Options 1a and 1b, the impedance element shall be set less than the calculated impedance
derived from 115 percent of both: the Real Power output of 100 percent of the maximum gross
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 150 percent of the MW value, derived from the generator nameplate MVA rating at
rated power factor.
For Option 1c, the impedance element shall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the maximum gross MW
capability reported to the Transmission Planner, and the Reactive Power output that equates to
100 percent of the maximum gross Mvar output during field-forcing as determined by simulation.
Synchronous Generators Phase Overcurrent Relay – (e.g., 50, 51, or 51V-R – Voltage
Restrained) (Options 2a, 2b, and 2c)

Table 1, Options 2a, 2b, and 2c, are provided for assessing loadability for synchronous generators
applying phase overcurrent relays (e.g., 50, 51, or 51V-R – voltage-restrained). These margins are
based on guidance found in Chapter 2 of the Considerations for Power Plant and Transmission
System Protection Coordination technical reference document.
Option 2a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Option 2b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on a 0.85 per unit nominal voltage at the high-side terminals of the GSU
transformer as well as for the turns ratio and impedance. The actual generator bus voltage may
be higher depending on the GSU transformer impedance and the actual Reactive Power achieved.

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This calculation is a more in-depth and precise method for setting of the overcurrent element
than Option 2a.
Option 2c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more
involved, more precise setting of the overcurrent element overall.
For Options 2a and 2b, the overcurrent element shall be set greater than 115 percent of the
calculated current derived from both: the Real Power output of 100 percent of the maximum
gross MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 150 percent of the MW value, derived from the generator nameplate MVA rating at
rated power factor.
For Option 2c, the overcurrent element shall be set greater than the calculated current derived
from 115 percent of both: the Real Power output of 100 percent of the maximum gross MW
capability reported to the Transmission Planner, and the Reactive Power output that equates to
100 percent of the maximum gross Mvar output during field-forcing as determined by simulation.
Synchronous Generators Phase Time Overcurrent Relay – Voltage Controlled (e.g.,
51V-C) (Option 3)

Table 1, Option 3, is provided for assessing loadability for synchronous generators applying phase
time overcurrent relays which are enabled as a function of voltage (“voltage-controlled”). These
margins are based on guidance found in Chapter 2 of the Considerations for Power Plant and
Transmission System Protection Coordination technical reference document.
Option 3 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation that
approximates the stressed system conditions.
For Option 3, the voltage control setting shall be set less than 75 percent of the calculated
generator bus voltage. The voltage setting must be set such that the function (e.g., 51V-C) will
not trip under extreme emergency conditions as the time overcurrent function will be set less
than generator full load current. Relays enabled as a function of voltage are indifferent as to the
current setting, and this option simply requires that the relays not respond for the depressed
voltage.
Asynchronous Generators Phase Distance Relay – Directional Toward Transmission
System (e.g., 21) (Option 4)

Table 1, Option 4 is provided for assessing loadability for asynchronous generators applying
phase distance relays that are directional toward the Transmission system. These margins are

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based on guidance found in Chapter 2 of the Considerations for Power Plant and Transmission
System Protection Coordination technical reference document.
Option 4 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation that
approximates the stressed system conditions.
Since the relay voltage is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant. Therefore, the generator bus voltage can be conservatively
estimated by reflecting the high-side nominal voltage to the generator-side based on the GSU
transformer’s turns ratio.
For Option 4, the impedance element shall be set less than the calculated impedance derived
from 130 percent of the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Asynchronous Generators Phase Overcurrent Relay – (e.g., 50, 51, or 51V-R – Voltage
Restrained) (Options 5a and 5b)

Table 1, Option 5a is provided for assessing loadability for asynchronous generators applying
phase overcurrent relays (e.g., 50, 51, or 51V-R – voltage-restrained). These margins are based
on guidance found in Chapter 2 of the Considerations for Power Plant and Transmission System
Protection Coordination technical reference document.
Option 5a calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation that
approximates the stressed system conditions.
Since the relay voltage is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant. Therefore, the generator bus voltage can be conservatively
estimated by reflecting the high-side nominal voltage to the generator-side based on the GSU
transformer’s turns ratio.

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For Option 5a, the overcurrent element shall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
For Option 5b, the overcurrent element shall be set to exceed the maximum capability of the
asynchronous resource and applicable equipment (e.g., windings, power electronics, cables, or
bus). This is determined by summing the total current capability of the generation equipment
behind the overcurrent element and any static or dynamic Reactive Power devices that
contribute to the power flow through the overcurrent element. The lower tolerance of the
overcurrent element tripping characteristic shall be set to not infringe upon the resource
capability (including the Mvar output of the resource and any static or dynamic reactive power
devices). Figure A of PRC-025-2 illustrates that the overcurrent element does not infringe upon
the asynchronous resource capability. The upper hashed area of Figure A represents Exclusion 7.
Asynchronous Generator Phase Time Overcurrent Relays – Voltage Controlled (e.g.,
51V-C) (Option 6)

Table 1, Option 6, is provided for assessing loadability for asynchronous generators applying
phase time overcurrent relays which are enabled as a function of voltage (“voltage-controlled”).
These margins are based on guidance found in Chapter 2 of the Considerations for Power Plant
and Transmission System Protection Coordination technical reference document.
Option 6 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation that
approximates the stressed system conditions.
For Option 6, the voltage control setting shall be set less than 75 percent of the calculated
generator bus voltage. The voltage setting must be set such that the function (e.g., 51V-C) will
not trip under extreme emergency conditions as the time overcurrent function will be set less
than generator full load current. Relays enabled as a function of voltage are indifferent as to the
current setting, and this option simply requires that the relays not respond for the depressed
voltage.
Generator Step-up Transformer (Synchronous Generators) Phase Distance Relays –
Directional Toward Transmission System (e.g., 21) (Options 7a, 7b, and 7c)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. These margins
are based on guidance found in Chapter 2 of the Considerations for Power Plant and Transmission
System Protection Coordination technical reference document.

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Table 1, Options 7a, 7b, and 7c, are provided for assessing loadability of phase distance relays
that are directional toward the Transmission system and connected to the generator-side of the
GSU transformer of a synchronous generator. For applications where the relay is connected on
the high-side of the GSU transformer, use Option 14.
Option 7a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Option 7b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on the 0.85 per unit nominal voltage, at the high-side terminals of the GSU
transformer, as well as the turns ratio and impedance. The actual generator bus voltage may be
higher depending on the GSU transformer impedance and the actual Reactive Power achieved.
This calculation is a more in-depth and precise method for setting the impedance element than
Option 7a.
Option 7c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more indepth and precise method for setting the impedance element than Options 7a or 7b.
For Options 7a and 7b, the impedance element shall be set less than the calculated impedance
derived from 115 percent of both: the Real Power output of 100 percent of the aggregate
generation MW capability reported to the Transmission Planner, and the Reactive Power output
that equates to 150 percent of the aggregate generation MW value (derived from the generator
nameplate MVA rating at rated power factor).
For Option 7c, the impedance element shall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation.
Generator Step-up Transformer (Synchronous Generators) Phase Overcurrent Relay
(e.g., 50 or 51) (Options 8a, 8b and 8c)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the
setting criteria established within the Table 1 options differ from Chapter 2 of the Considerations
for Power Plant and Transmission System Protection Coordination technical reference document.
Rather than establishing a uniform loadability threshold of 200 percent of the generator

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nameplate MVA rating at rated power factor for all applications, the setting criteria are based on
the maximum expected generator output.
Table 1, Options 8a, 8b, and 8c, are provided for assessing loadability of phase overcurrent relays
that are connected to the generator-side of the GSU transformer of a synchronous generator.
For applications where the relay is connected on the high-side of the GSU transformer, use
Option 15.
Option 8a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Option 8b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on the 0.85 per unit nominal voltage, at the high-side terminals of the GSU
transformer, as well as the turns ratio and impedance. The actual generator bus voltage may be
higher depending on the GSU transformer impedance and the actual Reactive Power achieved.
This calculation is a more in-depth and precise method for setting the overcurrent element than
Option 8a.
Option 8c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more indepth and precise method for setting the overcurrent element than Options 8a or 8b.
For Options 8a and 8b, the overcurrent element shall be set greater than 115 percent of the
calculated current derived from both: the Real Power output of 100 percent of the aggregate
generation MW capability reported to the Transmission Planner, and the Reactive Power output
that equates to 150 percent of the aggregate generation MW value (derived from the generator
nameplate MVA rating at rated power factor).
For Option 8c, the overcurrent element shall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation.
Generator Step-up Transformer (Synchronous Generators) Phase Directional
Overcurrent Relay – Directional Toward Transmission System (e.g., 67) (Options 9a,
9b and 9c)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the

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setting criteria established within the Table 1 options differ from Chapter 2 of the Considerations
for Power Plant and Transmission System Protection Coordination technical reference document.
Rather than establishing a uniform loadability threshold of 200 percent of the generator
nameplate MVA rating at rated power factor for all applications, the setting criteria are based on
the maximum expected generator output.
Table 1, Options 9a, 9b, and 9c, are provided for assessing loadability of phase directional
overcurrent relays directional toward the Transmission System that are connected to the
generator-side of the GSU transformer of a synchronous generator. For applications where the
relay is connected on the high-side of the GSU transformer, use Option 16.
Option 9a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Option 9b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on the 0.85 per unit nominal voltage, at the high-side terminals of the GSU
transformer, as well as the turns ratio and impedance. The actual generator bus voltage may be
higher depending on the GSU transformer impedance and the actual Reactive Power achieved.
This calculation is a more in-depth and precise method for setting the overcurrent element than
Option 9a.
Option 9c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more indepth and precise method for setting the overcurrent element than Options 9a or 9b.
For Options 9a and 9b, the overcurrent element shall be set greater than 115 percent of the
calculated current derived from both: the Real Power output of 100 percent of the aggregate
generation MW capability reported to the Transmission Planner, and the Reactive Power output
that equates to 150 percent of the aggregate generation MW value (derived from the generator
nameplate MVA rating at rated power factor).
For Option 9c, the overcurrent element shall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation.

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Generator Step-up Transformer (Asynchronous Generators) Phase Distance Relay –
Directional Toward Transmission System (e.g., 21) (Option 10)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Table 1, Option
10 is provided for assessing loadability for GSU transformers applying phase distance relays that
are directional toward the Transmission System that are connected to the generator-side of the
GSU transformer of an asynchronous generator. These margins are based on guidance found in
Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document. For applications where the relay is connected on the
high-side of the GSU transformer, use Option 17.
Option 10 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Since the relay voltage is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; hence the voltage drop due to Reactive Power flow through
the GSU transformer is not as significant. Therefore, the generator bus voltage can be
conservatively estimated by reflecting the high-side nominal voltage to the generator-side based
on the GSU transformer’s turns ratio.
For Option 10, the impedance element shall be set less than the calculated impedance, derived
from 130 percent of the maximum aggregate nameplate MVA output at rated power factor,
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Generator Step-up Transformer (Asynchronous Generators) Phase Overcurrent Relay
(e.g., 50 or 51) (Option 11)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the
setting criteria established within the Table 1 options differ from Chapter 2 of the Considerations
for Power Plant and Transmission System Protection Coordination technical reference document.
Rather than establishing a uniform loadability threshold of 200 percent of the generator
nameplate MVA rating at rated power factor for all applications, the setting criteria are based on
the maximum expected generator output.
Table 1, Option 11 is provided for assessing loadability of phase overcurrent relays that are
connected to the generator-side of the GSU transformer of an asynchronous generator. For

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applications where the relay is connected on the high-side of the GSU transformer, use Option
18.
Option 11 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Since the relay current is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; hence the voltage drop due to Reactive Power flow through
the GSU transformer is not as significant. Therefore, the generator bus voltage can be
conservatively estimated by reflecting the high-side nominal voltage to the generator-side based
on the GSU transformer’s turns ratio.
For Option 11, the overcurrent element shall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor,
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Generator Step-up Transformer (Asynchronous Generators) Phase Directional
Overcurrent Relay – Directional Toward Transmission System (e.g., 67) (Option 12)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the
setting criteria established within the Table 1 options differ from Chapter 2 of the Considerations
for Power Plant and Transmission System Protection Coordination technical reference document.
Rather than establishing a uniform loadability threshold of 200 percent of the generator
nameplate MVA rating at rated power factor for all applications, the setting criteria are based on
the maximum expected generator output.
Table 1, Option 12 is provided for assessing loadability of phase directional overcurrent relays
directional toward the Transmission System that are connected to the generator-side of the GSU
transformer of an asynchronous generator. For applications where the relay is connected on the
high-side of the GSU transformer, use Option 19.
Option 12 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.

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Since the relay current is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; hence the voltage drop due to Reactive Power flow through
the GSU transformer is not as significant. Therefore, the generator bus voltage can be
conservatively estimated by reflecting the high-side nominal voltage to the generator-side based
on the GSU transformer’s turns ratio.
For Option 12, the overcurrent element shall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor,
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Unit Auxiliary Transformers Phase Overcurrent Relay (e.g., 50 or 51) (Options 13a
and 13b)

In FERC Order No. 733, paragraph 104, directs NERC to include in this standard a loadability
requirement for relays used for overload protection of the UAT that supply normal station service
for a generating unit. For the purposes of this standard, UATs provide the overall station power
to support the unit at its maximum gross operation.
Table 1, Options 13a and 13b provide two options for addressing phase overcurrent relaying
applied at the high-side of UATs. The transformer high-side winding may be directly connected
to the transmission grid or at the generator isolated phase bus (IPB) or iso-phase bus. Phase
overcurrent relays applied at the high-side of the UAT that remove the transformer from service
resulting in an immediate (e.g., via lockout or auxiliary tripping relay operation) or consequential
trip of the associated generator are to be compliant with the relay setting criteria in this standard.
Due to the complexity of the application of low-side overload relays for single or multi-winding
transformers, phase overcurrent relaying applied at the low-side of the UAT are not addressed in
this standard. The NERC System Protection and Control Subcommittee addressed low-side UAT
protection in the document called “Unit Auxiliary Transformer Overcurrent Relay Loadability
During a Transmission Depressed Voltage Condition, March 2016.” These relays include, but are
not limited to, a relay used for arc flash protection, feeder protection relays, breaker failure, and
relays whose operation may result in a generator runback.

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Refer to the Figures 7 and 8 below for example configurations:

Transformers
Covered by this
standard
Transfer
Switch

Unit Auxiliary
Transformers

System

Station
Loads

System

G
GSU
Figure 7: Auxiliary Power System (independent from generator)

Unit Auxiliary
Transformer

Transformer
Covered by this
standard

GSU
Station
Loads

G

System

Figure 8: Typical auxiliary power system for generation units or plants

The UATs supplying power to the unit or plant electrical auxiliaries are sized to accommodate the
maximum expected overall UAT load demand at the highest generator output. Although the
transformer nameplate MVA size normally includes capacity for future loads as well as capacity

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for starting of large induction motors on the original unit or plant design, the nameplate MVA
capacity of the transformer may be near full load.
Because of the various design and loading characteristics of UATs, two options (i.e., 13a and 13b)
are provided to accommodate an entity’s protection philosophy while preventing the UAT
transformer phase overcurrent relays from operating during the dynamic conditions anticipated
by this standard.
Options 13a and 13b are based on the transformer bus voltage corresponding to 1.0 per unit
nominal voltage on the high-side winding of the UAT.
For Option 13a, the overcurrent element shall be set greater than 150 percent of the calculated
current derived from the UAT maximum nameplate MVA rating. This is a simple calculation that
approximates the stressed system conditions.
For Option 13b, the overcurrent element shall be set greater than 150 percent of the UAT
measured current at the generator maximum gross MW capability reported to the Transmission
Planner. This allows for a reduced setting compared to Option 13a and the relay setting
philosophy of the applicable entity. This is a more involved calculation that approximates the
stressed system conditions by allowing the entity to consider the actual load placed on the UAT
based on the generator’s maximum gross MW capability reported to the Transmission Planner.
The performance of the UAT loads during stressed system conditions (i.e., depressed voltages) is
very difficult to determine. Rather than requiring responsible entities to determine the response
of UAT loads to depressed voltage, the technical experts writing the standard elected to increase
the margin to 150 percent from that used elsewhere in this standard (e.g., 115 percent) and use
a generator bus voltage of 1.0 per unit. A minimum setting current based on 150 percent of
maximum transformer nameplate MVA rating at 1.0 per unit generator bus voltage will provide
adequate transformer protection based on IEEE C37.91 at full load conditions while providing
sufficient relay loadability to prevent a trip of the UAT, and subsequent unit trip, due to increased
UAT load current during stressed system voltage conditions. Even if the UAT is equipped with an
automatic tap changer, the tap changer may not respond quickly enough for the conditions
anticipated within this standard, and thus shall not be used to reduce this margin.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Synchronous Generators) Phase Distance Relays – Directional Toward Transmission
System (e.g., 21) (Options 14a and 14b)

Relays applied on Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
These margins are based on guidance found in Chapter 2 of the Considerations for Power Plant
and Transmission System Protection Coordination technical reference document. Relays applied
on the high-side of the GSU transformer respond to the same quantities as the relays applied at

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the remote end of the line for Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or
generating plant, thus Option 14 is used for these relays as well.
Table 1, Options 14a and 14b, establish criteria for phase distance relays directional toward the
Transmission system to prevent Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or
generating plant from tripping during the dynamic conditions anticipated by this standard. The
stressed system conditions, anticipated by Option 14a reflects a 0.85 per unit of the line nominal
voltage; therefore, establishing that the impedance value used for applying the Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant phase distance relays that are directional
toward the Transmission system be calculated from the apparent power addressed within the
criteria, with application of a 0.85 per unit of the line nominal voltage at the relay location.
Consideration of the voltage drop across the GSU transformer is not necessary. Option 14b
simulates the line voltage coincident with the highest Reactive Power output achieved during
field-forcing in response to a 0.85 per unit line nominal voltage at the remote end of the line prior
to field-forcing. Using a 0.85 per unit line nominal voltage at the remote end of the line is
representative of the lowest voltage expected during a depressed voltage condition on Elements
that are used exclusively to export energy directly from a BES generating unit or generating plant
to the Transmission system. Using simulation is a more involved, more precise setting of the
overcurrent element overall.
For Option 14a, the impedance element shall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 120 percent of the aggregate generation MW value, derived from the generator
nameplate MVA rating at rated power factor. This Reactive Power value differs from the 150
percent multiplier used in other applications to account for the Reactive Power losses in the GSU
transformer. This is a simple calculation that approximates the stressed system conditions.
For Option 14b, the impedance element shall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation. Option 14b uses the simulated line voltage at the relay location coincident with the
highest Reactive Power output achieved during field-forcing in response to a 0.85 per unit of the
line nominal voltage at the remote end of the line prior to field-forcing. Using simulation is a
more involved, more precise setting of the impedance element overall.

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Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Synchronous Generators) Phase Time Overcurrent Relay (e.g., 50 or 51) (Options
15a and 15b)

Relays applied on Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
Note that the setting criteria established within the Table 1 options differ from Chapter 2 of the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document. Rather than establishing a uniform setting threshold of 200 percent of the
generator nameplate MVA rating at rated power factor for all applications, the setting criteria
are based on the maximum expected generator output. Relays applied on the high-side of the
GSU transformer respond to the same quantities as the relays applied at the remote end of the
line for Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant, thus Option
15 is used for these relays as well.

Table 1, Options 15a and 15b, establish criteria for phase instantaneous and/or time overcurrent
relays to prevent Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant from
tripping during the dynamic conditions anticipated by this standard. The stressed system
conditions, anticipated by Option 15a reflects a 0.85 per unit of the line nominal voltage at the
relay location; therefore, establishing that the current value used for applying the Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant phase instantaneous and/or time
overcurrent relays be calculated from the apparent power addressed within the criteria, with
application of a 0.85 per unit of the line nominal voltage at the relay location. Consideration of
the voltage drop across the GSU transformer is not necessary. Option 15b simulates the line
voltage coincident with the highest Reactive Power output achieved during field-forcing in
response to a 0.85 per unit line nominal voltage at the remote end of the line prior to fieldforcing. Using a 0.85 per unit line nominal voltage at the remote end of the line is representative
of the lowest voltage expected during a depressed voltage condition on Elements that are used
exclusively to export energy directly from a BES generating unit or generating plant to the
Transmission system. Using simulation is a more involved, more precise setting of the
overcurrent element overall.
For Option 15a, the overcurrent element shall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 120 percent of the aggregate generation MW value, derived from the generator
nameplate MVA rating at rated power factor. This Reactive Power value differs from the 150
percent multiplier used in other applications to account for the Reactive Power losses in the GSU
transformer. This is a simple calculation that approximates the stressed system conditions.

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For Option 15b, the overcurrent element shall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation. Option 15b uses the simulated line voltage at the relay location coincident with the
highest Reactive Power output achieved during field-forcing in response to a 0.85 per unit of the
line nominal voltage at the remote end of the line prior to field-forcing. Using simulation is a
more involved, more precise setting of the overcurrent element overall.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Synchronous Generators) Phase Directional Overcurrent Relay – Directional Toward
Transmission System (e.g., 67) (Options 16a and 16b)

Relays applied on Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
Note that the setting criteria established within the Table 1 options differ from Chapter 2 of the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document. Rather than establishing a uniform setting threshold of 200 percent of the
generator nameplate MVA rating at rated power factor for all applications, the setting criteria
are based on the maximum expected generator output. Relays applied on the high-side of the
GSU transformer respond to the same quantities as the relays applied at the remote end of the
line for Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant, thus Option
16 is used for these relays as well.

Table 1, Options 16a and 16b, establish criteria for phase directional overcurrent relays that are
directional toward the Transmission system to prevent Elements that connect a GSU transformer
to the Transmission system that are used exclusively to export energy directly from a BES
generating unit or generating plant from tripping during the dynamic conditions anticipated by
this standard. The stressed system conditions, anticipated by Option 16a reflects a 0.85 per unit
of the line nominal voltage at the relay location; therefore, establishing that the current value
used for applying the interconnection Facilities phase directional overcurrent relays be calculated
from the apparent power addressed within the criteria, with application of a 0.85 per unit of the
line nominal voltage at the relay location. Consideration of the voltage drop across the GSU
transformer is not necessary. Option 16b simulates the line voltage coincident with the highest
Reactive Power output achieved during field-forcing in response to a 0.85 per unit line nominal
voltage at the remote end of the line prior to field-forcing. Using a 0.85 per unit line nominal
voltage at the remote end of the line is representative of the lowest voltage expected during a
depressed voltage condition on Elements that are used exclusively to export energy directly from
a BES generating unit or generating plant to the Transmission system. Using simulation is a more
involved, more precise setting of the overcurrent element overall.

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For Option 16a, the overcurrent element shall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 120 percent of the aggregate generation MW value, derived from the generator
nameplate MVA rating at rated power factor. This Reactive Power value differs from the 150
percent multiplier used in other applications to account for the Reactive Power losses in the GSU
transformer. This is a simple calculation that approximates the stressed system conditions.
For Option 16b, the overcurrent element shall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation. Option 16b uses the simulated line voltage at the relay location coincident with the
highest Reactive Power output achieved during field-forcing in response to a 0.85 per unit of the
line nominal voltage at the remote end of the line prior to field-forcing. Using simulation is a
more involved, more precise setting of the overcurrent element overall.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Asynchronous Generators) Phase Distance Relay – Directional Toward Transmission
System (e.g., 21) (Option 17)

Relays installed on the high-side of the GSU transformer, including relays installed on the remote
end of the line, for Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
These margins are based on guidance found in Chapter 2 of the Considerations for Power Plant
and Transmission System Protection Coordination technical reference document.
Table 1, Option 17 establishes criteria for phase distance relays that are directional toward the
Transmission system to prevent Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or
generating plant from tripping during the dynamic conditions anticipated by this standard.
Option 17 applies a 1.0 per unit line nominal voltage at the relay location to calculate the
impedance from the maximum aggregate nameplate MVA.
For Option 17, the impedance element shall be set less than the calculated impedance derived
from 130 percent of the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay. This is a simple calculation that approximates the stressed system conditions.

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Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Asynchronous Generators) Phase Overcurrent Relay (e.g., 50 and 51) (Option 18)

Relays installed on the high-side of the GSU transformer, including relays installed on the remote
end of the line, for Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
Note that the setting criteria established within the Table 1 options differ from Chapter 2 of the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document. Rather than establishing a uniform setting threshold of 200 percent of the
generator nameplate MVA rating at rated power factor for all applications, the setting criteria
are based on the maximum expected generator output.
Table 1, Option 18 establishes criteria for phase overcurrent relays to prevent Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant from tripping during the dynamic
conditions anticipated by this standard. Option 18 applies a 1.0 per unit line nominal voltage at
the location of the relay to calculate the current from the maximum aggregate nameplate MVA.
For Option 18, the overcurrent element shall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay. This is a simple calculation that approximates the stressed system conditions.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Asynchronous Generators) Phase Directional Overcurrent Relay – Directional
Toward Transmission System (e.g., 67) (Option 19)

Relays installed on the high-side of the GSU transformer, including relays installed on the remote
end of the line, for Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
Note that the setting criteria established within the Table 1 options differ from Chapter 2 of the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document. Rather than establishing a uniform setting threshold of 200 percent of the
generator nameplate MVA rating at rated power factor for all applications, the setting criteria
are based on the maximum expected generator output.
Table 1, Option 19 establishes criteria for phase directional overcurrent relays that are directional
toward the Transmission system to prevent Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant from tripping during the dynamic conditions anticipated by this standard.

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Option 19 applies a 1.0 per unit line nominal voltage at the relay location to calculate the current
from the maximum aggregate nameplate MVA.
For Option 19, the overcurrent element shall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay. This is a simple calculation that approximates the stressed system conditions.

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Example Calculations
Introduction
Example Calculations

Input Descriptions

Input Values

Synchronous Generator nameplate (MVA @ rated pf):

𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 903 𝑀𝑀𝑀𝑀𝑀𝑀

Generator rated voltage (Line-to-Line):
Real Power output in MW as reported to the TP:
Generator step-up (GSU) transformer rating:
GSU transformer reactance (903 MVA base):
GSU transformer MVA base:
GSU transformer turns ratio:
High-side nominal system voltage (Line-to-Line):
Current transformer (CT) ratio:
Potential transformer (PT) ratio low-side:
PT ratio high-side:
Unit auxiliary transformer (UAT) nameplate:
UAT high-side voltage:
UAT CT ratio:
CT high voltage ratio:
Reactive Power output of static reactive device:

𝑝𝑝𝑝𝑝 = 0.85

𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔_𝑛𝑛𝑛𝑛𝑛𝑛 = 22 𝑘𝑘𝑘𝑘

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺 = 903 𝑀𝑀𝑀𝑀𝑀𝑀
𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺 = 12.14%

𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 767.6 𝑀𝑀𝑀𝑀𝑀𝑀
𝐺𝐺𝐺𝐺𝑈𝑈𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

22 𝑘𝑘𝑘𝑘
346.5 𝑘𝑘𝑘𝑘

𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 345 𝑘𝑘𝑘𝑘
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

25000
5
200
1

𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣 =

2000
1

𝑈𝑈𝑈𝑈𝑈𝑈𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 60 𝑀𝑀𝑀𝑀𝑀𝑀
𝑉𝑉𝑈𝑈𝑈𝑈𝑈𝑈 = 13.8 𝑘𝑘𝑘𝑘
𝐶𝐶𝐶𝐶𝑈𝑈𝑈𝑈𝑈𝑈 =

5000
5

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣 =

2000
5

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
58 of 115

PRC-025-2 — Application Guidelines

Example Calculations

Reactive Power output of static reactive device
generation:
Asynchronous generator nameplate (MVA @ rated pf):

Asynchronous CT ratio:
Asynchronous high voltage CT ratio:
CT remote substation bus

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 40 𝑀𝑀𝑀𝑀𝑀𝑀
𝑝𝑝𝑝𝑝 = 0.85

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

5000
5

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣 =

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑏𝑏𝑏𝑏𝑏𝑏 =

300
5

2000
5

59 of 115

PRC-025-2 — Application Guidelines

Example Calculations: Option 1a

Option 1a represents the simplest calculation for synchronous generators applying a phase
distance relay (e.g., 21) directional toward the Transmission system.
Real Power output (P):
Eq. (1) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (2) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 1a, Table 1 – Bus Voltage, calls for a 0.95 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (3) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (4) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (5) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(20.81 𝑘𝑘𝑘𝑘)2
1347.4∠ − 58.7° 𝑀𝑀𝑀𝑀𝑀𝑀
60 of 115

PRC-025-2 — Application Guidelines

Example Calculations: Option 1a

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.321∠58.7° Ω

Secondary impedance (Zsec):
Eq. (6) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.321∠58.7° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.321∠58.7° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 8.035∠58.7° Ω

To satisfy the 115% margin in Option 1a:
Eq. (7) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

8.035∠58.7° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 6.9873∠58.7° Ω
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 58.7°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (8) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
6.9873 Ω
cos(85.0° − 58.7°)
6.9873 Ω
0.896

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 7.793∠85.0° Ω

61 of 115

PRC-025-2 — Application Guidelines

Example Calculations: Options 1b and 7b

Option 1b represents a more complex, more precise calculation for synchronous generators
applying a phase distance relay (e.g., 21) directional toward the Transmission system. This
option requires calculating low-side voltage taking into account voltage drop across the GSU
transformer. Similarly these calculations may be applied to Option 7b for GSU transformers
applying a phase distance relay (e.g., 21) directional toward the Transmission system.
Real Power output (P):
Eq. (9) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (10) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Convert Real Power, Reactive Power, and transformer reactance to per unit values on a 767.6
MVA base (MVAbase):
Real Power output (P):
Eq. (11) 𝑃𝑃𝑝𝑝𝑝𝑝 =
𝑃𝑃𝑝𝑝𝑝𝑝 =

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
700.0 𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑃𝑃𝑝𝑝𝑝𝑝 = 0.91 𝑝𝑝. 𝑢𝑢.

Reactive Power output (Q):
Eq. (12) 𝑄𝑄𝑝𝑝𝑝𝑝 =
𝑄𝑄𝑝𝑝𝑝𝑝 =

𝑄𝑄
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑄𝑄𝑝𝑝𝑝𝑝 = 1.5 𝑝𝑝. 𝑢𝑢.

62 of 115

PRC-025-2 — Application Guidelines

Example Calculations: Options 1b and 7b

Transformer impedance (Xpu):
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
�
Eq. (13) 𝑋𝑋𝑝𝑝𝑝𝑝 = 𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺(𝑜𝑜𝑜𝑜𝑜𝑜) × �
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺
𝑋𝑋𝑝𝑝𝑝𝑝 = 12.14% × �
𝑋𝑋𝑝𝑝𝑝𝑝 = 0.1032 𝑝𝑝. 𝑢𝑢.

767.6 𝑀𝑀𝑀𝑀𝑀𝑀
�
903 𝑀𝑀𝑀𝑀𝑀𝑀

Using the formula below; calculate the low-side GSU transformer voltage (Vlow-side) using 0.85
p.u. high-side voltage (Vhigh-side). Assume initial low-side voltage to be 0.95 p.u. and repeat the
calculation as necessary until Vlow-side converges. A convergence of less than one percent
(<1%) between iterations is considered sufficient:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (14) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.95 × 0.85)

Eq. (15)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.7°

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.7°) ± �|0.85|2 × cos 2 (6.7°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9931 ± √0.7225 × 0.9864 + 0.6192
2
0.8441 ± 1.1541
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9991 𝑝𝑝. 𝑢𝑢.

63 of 115

PRC-025-2 — Application Guidelines

Example Calculations: Options 1b and 7b

Use the new estimated Vlow-side value of 0.9991 per unit for the second iteration:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (16) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.9991 × 0.85)

Eq. (17)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.3°

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝
2

|0.85| × cos(6.3°) ± �|0.85|2 × cos 2 (6.3°) + 4 × 1.5 × 0.1032
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
2
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

|0.85| × 0.9940 ± √0.7225 × 0.9880 + 0.6192
2
0.8449 ± 1.1546
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9998 𝑝𝑝. 𝑢𝑢.

To account for system high-side nominal voltage and the transformer tap ratio:
Eq. (18) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = |𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.9998 𝑝𝑝. 𝑢𝑢.× 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 21.90 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (19) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° MVA

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PRC-025-2 — Application Guidelines

Example Calculations: Options 1b and 7b

Primary impedance (Zpri):
Eq. (20) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝑆𝑆 ∗

(21.90 𝑘𝑘𝑘𝑘)2
1347.4∠ − 58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.356∠58.7° Ω

Secondary impedance (Zsec):
Eq. (21) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.356∠58.7° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.356∠58.7° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 8.900∠58.7° Ω

To satisfy the 115% margin in Options 1b and 7b:
Eq. (22) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

8.900∠58.7° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 7.74∠58.7° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 58.7°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (23) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
7.74 Ω
cos(85.0° − 58.7°)

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PRC-025-2 — Application Guidelines

Example Calculations: Options 1b and 7b

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

7.74 Ω
0.8965

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 8.633∠85.0° Ω
Example Calculations: Options 1c and 7c

Option 1c represents a more involved, more precise setting of the impedance element. This
option requires determining maximum generator Reactive Power output during field-forcing
and the corresponding generator bus voltage. Once these values are determined, the
remainder of the calculation is the same as Options 1a and 1b.
The generator Reactive Power and generator bus voltage are determined by simulation. The
maximum Reactive Power output on the low-side of the GSU transformer during field-forcing
is used as this value will correspond to the lowest apparent impedance. The corresponding
generator bus voltage is also used in the calculation. Note that although the excitation limiter
reduces the field, the duration of the Reactive Power output achieved for this condition is
sufficient to operate a phase distance relay.
1.25

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

200

0

4

8

12

16

20

0

Time (s)

In this simulation the following values are derived:
𝑄𝑄 = 827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.989 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔_𝑛𝑛𝑛𝑛𝑛𝑛 = 21.76 𝑘𝑘V
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PRC-025-2 — Application Guidelines

Example Calculations: Options 1c and 7c

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

Apparent power (S):

Eq. (24) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1083.8∠49.8° MVA

Primary impedance (Zpri):
Eq. (25) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑆𝑆 ∗

(21.76 𝑘𝑘𝑘𝑘)2
1083.8∠ − 49.8° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.437∠49.8° Ω

Secondary impedance (Zsec):
Eq. (26) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.437∠49.8° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.437∠49.8° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 10.92∠49.8° Ω

To satisfy the 115% margin in the requirement in Options 1c and 7c:
Eq. (27) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

10.92∠49.8° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 9.50∠49.8° Ω

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PRC-025-2 — Application Guidelines

Example Calculations: Options 1c and 7c

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 49.8°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (28) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
9.50 Ω
cos(85.0° − 49.8°)
9.50 Ω
0.8171

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 11.63∠85.0° Ω
Example Calculations: Option 2a

Option 2a represents the simplest calculation for synchronous generators applying a phase
overcurrent (e.g., 50, 51, or 51V-R) relay:
Real Power output (P):
Eq. (29) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (30) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 2a, Table 1 – Bus Voltage, calls for a 0.95 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (31) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
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PRC-025-2 — Application Guidelines

Example Calculations: Option 2a

𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (32) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (33) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 20.81 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 37383 𝐴𝐴

Secondary current (Isec):
Eq. (34) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

37383 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.477 𝐴𝐴

To satisfy the 115% margin in Option 2a:
Eq. (35) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.477 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.598 𝐴𝐴

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PRC-025-2 — Application Guidelines

Example Calculations: Option 2b

Option 2b represents a more complex calculation for synchronous generators applying a
phase overcurrent (e.g., 50, 51, or 51V-R) relay:
Real Power output (P):
Eq. (36) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (37) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Convert Real Power, Reactive Power, and transformer reactance to per unit values on 767.6
MVA base (MVAbase).
Real Power output (P):
Eq. (38) 𝑃𝑃𝑝𝑝𝑝𝑝 =
𝑃𝑃𝑝𝑝𝑝𝑝 =

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
700.0 𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑃𝑃𝑝𝑝𝑝𝑝 = 0.91 𝑝𝑝. 𝑢𝑢.

Reactive Power output (Q):
Eq. (39) 𝑄𝑄𝑝𝑝𝑝𝑝 =
𝑄𝑄𝑝𝑝𝑝𝑝 =

𝑄𝑄
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑄𝑄𝑝𝑝𝑝𝑝 = 1.5 𝑝𝑝. 𝑢𝑢.

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PRC-025-2 — Application Guidelines

Example Calculations: Option 2b

Transformer impedance:
Eq. (40) 𝑋𝑋𝑝𝑝𝑝𝑝 = 𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺(𝑜𝑜𝑜𝑜𝑜𝑜) ×

𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺

𝑋𝑋𝑝𝑝𝑝𝑝 = 12.14% × �
𝑋𝑋𝑝𝑝𝑝𝑝 = 0.1032 𝑝𝑝. 𝑢𝑢.

767.6 𝑀𝑀𝑀𝑀𝑀𝑀
�
903 𝑀𝑀𝑀𝑀𝑀𝑀

Using the formula below; calculate the low-side GSU transformer voltage (Vlow-side) using 0.85
p.u. high-side voltage (Vhigh-side). Assume initial low-side voltage to be 0.95 p.u. and repeat the
calculation as necessary until Vlow-side converges. A convergence of less than one percent
(<1%) between iterations is considered sufficient:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (41) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.95 × 0.85)

Eq. (42)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.7°

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.7°) ± �|0.85|2 × cos 2 (6.7°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9931 ± √0.7225 × 0.9864 + 0.6192
2
0.8441 ± 1.1541
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9991 𝑝𝑝. 𝑢𝑢.

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Example Calculations: Option 2b

Use the new estimated Vlow-side value of 0.9991 per unit for the second iteration:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (43) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.9991 × 0.85)

Eq. (44)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.3°

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝
2

|0.85| × cos(6.3°) ± �|0.85|2 × cos 2 (6.3°) + 4 × 1.5 × 0.1032
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
2
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

|0.85| × 0.9940 ± √0.7225 × 0.9880 + 0.6192
2
0.8449 ± 1.1546
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9998 𝑝𝑝. 𝑢𝑢.

To account for system high-side nominal voltage and the transformer tap ratio:
Eq. (45) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = |𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.9998 𝑝𝑝. 𝑢𝑢.× 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 21.90 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (46) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

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Example Calculations: Option 2b

Primary current (Ipri):
Eq. (47) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.90 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 35553 𝐴𝐴

Secondary current (Isec):
Eq. (48) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

35553 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.111 𝐴𝐴

To satisfy the 115% margin in Option 2b:
Eq. (49) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.111 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.178 𝐴𝐴

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Example Calculations: Option 2c

Option 2c represents a more involved, more precise setting of the overcurrent element for
the phase overcurrent (e.g., 50, 51, or 51V-R) relay. This option requires determining
maximum generator Reactive Power output during field-forcing and the corresponding
generator bus voltage. Once these values are determined, the remainder of the calculation is
the same as Options 2a and 2b.
The generator Reactive Power and generator bus voltage are determined by simulation. The
maximum Reactive Power output on the low-side of the GSU transformer during field-forcing
is used as this value will correspond to the highest current. The corresponding generator bus
voltage is also used in the calculation. Note that although the excitation limiter reduces the
field, the duration of the Reactive Power output achieved for this condition is sufficient to
operate a voltage-restrained phase overcurrent relay.
1.25

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
400

0.95

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

200

0

4

8

12

16

20

0

Time (s)

In this simulation the following values are derived:
𝑄𝑄 = 827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.989 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔_𝑛𝑛𝑛𝑛𝑛𝑛 = 21.76 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

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Example Calculations: Option 2c

Apparent power (S):
Eq. (50) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1083.8∠49.8° MVA

Primary current (Ipri):
Eq. (51) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
1083.8 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.76 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 28790 𝐴𝐴

Secondary current (Isec):
Eq. (52) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

28790 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.758 𝐴𝐴

To satisfy the 115% margin in Option 2c:
Eq. (53) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.758 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.622 𝐴𝐴

Example Calculations: Options 3 and 6

Option 3 represents the only calculation for synchronous generators applying a phase time
overcurrent (e.g., 51V-C) relay (Enabled to operate as a function of voltage). Similarly, Option
6 uses the same calculation for asynchronous generators.

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Example Calculations: Options 3 and 6

Options 3 and 6, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal
voltage for the generator bus voltage (Vgen):
Eq. (54) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

The voltage setting shall be set less than 75% of the generator bus voltage:
Eq. (55) 𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 < 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 × 75%

𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 < 21.9 𝑘𝑘𝑘𝑘 × 0.75
𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 < 16.429 𝑘𝑘𝑘𝑘

Example Calculations: Option 4

This represents the calculation for an asynchronous generator (including inverter-based
installations) applying a phase distance relay (e.g., 21) directional toward the Transmission
system.
Real Power output (P):
Eq. (56) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 34.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (57) 𝑄𝑄 = 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos−1(𝑝𝑝𝑝𝑝))
𝑄𝑄 = 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1(0.85))
𝑄𝑄 = 21.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

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PRC-025-2 — Application Guidelines

Example Calculations: Option 4

Option 4, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (58) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (59) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 34.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗21.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 40.0∠31.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (60) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(21.9 𝑘𝑘𝑘𝑘)2
40.0∠ − 31.8° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 11.99 ∠31.8° Ω

Secondary impedance (Zsec):
Eq. (61) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 11.99 ∠31.8° Ω ×

5000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 11.99 ∠31.8° Ω × 5
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 59.95 ∠31.8° Ω

To satisfy the 130% margin in Option 4:
Eq. (62) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
130%
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PRC-025-2 — Application Guidelines

Example Calculations: Option 4

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

59.95∠31.8° Ω
1.30

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 46.12∠31.8° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 31.8°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (63) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
46.12 Ω
cos(85.0° − 31.8°)
46.12 Ω
0.599

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 77.0∠85.0° Ω
Example Calculations: Option 5a

This represents the calculation for three asynchronous generators applying a phase
overcurrent (e.g., 50, 51, or 51V-R) relay. In this application it was assumed that 20 Mvar of
total static compensation was added.
Real Power output (P):
Eq. (64) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (65) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

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Example Calculations: Option 5a

Option 5a, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (66) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (67) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (68) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 3473∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (69) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

3473∠ − 39.2° 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.473∠ − 39.2° 𝐴𝐴

To satisfy the 130% margin in Option 5a:
Eq. (70) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 130%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.473∠ − 39.2° 𝐴𝐴 × 1.30
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PRC-025-2 — Application Guidelines

Example Calculations: Option 5a

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.52∠ − 39.2° 𝐴𝐴
Example Calculations: Option 5b

Similarly to Option 5a, this example represents the calculation for three asynchronous
generators applying a phase overcurrent (e.g., 50, 51, or 51V-R) relay. In this application it
was assumed that 20 Mvar of total static compensation was added.
Real Power output (P):
Eq. (71) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (72) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 5b, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (73) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (74) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

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PRC-025-2 — Application Guidelines

Example Calculations: Option 5b

Primary current (Ipri):
Eq. (75) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 3473∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (76) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

3473∠ − 39.2° 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.473∠ − 39.2° 𝐴𝐴

To satisfy Option 5b, the lower tolerance of the overcurrent element tripping characteristic
shall not infringe upon the resource capability (including the Mvar output of the resource and
any static or dynamic reactive power devices) See Figure A for more details.

Example Calculations: Options 7a and 10

These examples represent the calculation for a mixture of asynchronous (i.e., Option 10) and
synchronous (i.e., Option 7a) generation (including inverter-based installations) applying a
phase distance relay (e.g., 21) directional toward the Transmission system. In this application
it was assumed 20 Mvar of total static compensation was added.
Synchronous Generation (Option 7a)

Real Power output (𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ):

Eq. (77) 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 767.6 𝑀𝑀𝑀𝑀

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Example Calculations: Options 7a and 10

Reactive Power output (𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ ):

Eq. (78) 𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 150% × 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ

𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1151.3 𝑀𝑀𝑀𝑀

Apparent power (SSynch):

Eq. (79) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Asynchronous Generation (Option 10)

Real Power output (PAsynch):
Eq. (80) 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (QAsynch):

Eq. (81) 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos−1(0.85)))
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Apparent power (SAsynch):

Eq. (82) 𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ + 𝑗𝑗𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ

𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

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PRC-025-2 — Application Guidelines

Example Calculations: Options 7a and 10

Options 7a and 10, Table 1 – Bus Voltage, Option 7a specifies 0.95 per unit of the high-side
nominal voltage for the generator bus voltage and Option 10 specifies 1.0 per unit of the
high-side nominal voltage for generator bus voltage. Due to the presence of the synchronous
generator, the 0.95 per unit bus voltage will be used as (Vgen) as it results in the most
conservative voltage:
Eq. (83) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S) accounted for 115% margin requirement for a synchronous generator
and 130% margin requirement for an asynchronous generator:
Eq. (84) 𝑆𝑆 = 115% × �𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ � + 130% × (𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ + 𝑗𝑗𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ )
𝑆𝑆 = 1.15 × (700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀) + 1.30 × (102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀)

𝑆𝑆 = 1711.8 ∠56.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (85) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑉𝑉𝑔𝑔2𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(20.81 𝑘𝑘𝑘𝑘)2
1711.8∠ − 56.8° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.2527∠56.8° Ω

Secondary impedance (Zsec):
Eq. (86) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.2527∠56.8° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.2527∠56.8° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 6.32∠56.8° Ω

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PRC-025-2 — Application Guidelines

Example Calculations: Options 7a and 10

No additional margin is needed because the synchronous apparent power has been
multiplied by 1.15 (115%) and the asynchronous apparent power has been multiplied by 1.30
(130%) in Equation 84 to satisfy the margin requirements in Options 7a and 10.
Eq. (87) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
100%

6.32 ∠56.8° Ω
1.00

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 6.32 ∠56.8° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 56.8°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (88) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
6.32 Ω
cos(85.0° − 56.8°)
6.32 Ω
0.881

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 7.17∠85.0° Ω
Example Calculations: Options 8a and 9a

Options 8a and 9a represent the simplest calculation for synchronous generators applying a
phase overcurrent (e.g., 50, 51, or 67) relay. The following uses the GENSynch_nameplate value to
represent an “aggregate” value to illustrate the option:
Real Power output (P):
Eq. (89) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

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PRC-025-2 — Application Guidelines

Example Calculations: Options 8a and 9a

Reactive Power output (Q):
Eq. (90) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Options 8a and 9a, Table 1 – Bus Voltage, calls for a generator bus voltage corresponding to
0.95 per unit of the high-side nominal voltage times the turns ratio of the generator step-up
transformer generator bus voltage (Vgen):
Eq. (91) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (92) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (93) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 20.81 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 37383 𝐴𝐴

Secondary current (Isec):
Eq. (94) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

37383 𝐴𝐴
25000
5
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PRC-025-2 — Application Guidelines

Example Calculations: Options 8a and 9a

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.477 𝐴𝐴

To satisfy the 115% margin in Options 8a and 9a:
Eq. (95) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.477 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.598 𝐴𝐴

Example Calculations: Options 8b and 9b

Options 8b and 9b represent a more precise calculation for synchronous generators applying
a phase overcurrent (e.g., 50, 51, or 67) relay. The following uses the GENSynch_nameplate value
to represent an “aggregate” value to illustrate the option:
Real Power output (P):
Eq. (96) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (97) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Convert Real Power, Reactive Power, and transformer reactance to per unit values on 767.6
MVA base (GSU transformer MVAbase).
Real Power output (P):
Eq. (98) 𝑃𝑃𝑝𝑝𝑝𝑝 =
𝑃𝑃𝑝𝑝𝑝𝑝 =

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
700.0 𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

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PRC-025-2 — Application Guidelines

Example Calculations: Options 8b and 9b

𝑃𝑃𝑝𝑝𝑝𝑝 = 0.91 𝑝𝑝. 𝑢𝑢.

Reactive Power output (Q):
Eq. (99) 𝑄𝑄𝑝𝑝𝑝𝑝 =
𝑄𝑄𝑝𝑝𝑝𝑝 =

𝑄𝑄
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑄𝑄𝑝𝑝𝑝𝑝 = 1.5 𝑝𝑝. 𝑢𝑢.

Transformer impedance:

Eq. (100) 𝑋𝑋𝑝𝑝𝑝𝑝 = 𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺(𝑜𝑜𝑜𝑜𝑜𝑜) ×

𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺

𝑋𝑋𝑝𝑝𝑝𝑝 = 12.14% × �
𝑋𝑋𝑝𝑝𝑝𝑝 = 0.1032 𝑝𝑝. 𝑢𝑢.

767.6 𝑀𝑀𝑀𝑀𝑀𝑀
�
903 𝑀𝑀𝑀𝑀𝑀𝑀

Using the formula below; calculate the low-side GSU transformer voltage (Vlow-side) using 0.85
p.u. high-side voltage (Vhigh-side). Assume initial low-side voltage to be 0.95 p.u. and repeat the
calculation as necessary until Vlow-side converges. A convergence of less than one percent
(<1%) between iterations is considered sufficient:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (101) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��

Eq. (102)

(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.95 × 0.85)

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.7°) ± �|0.85|2 × cos 2 (6.7°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9931 ± √0.7225 × 0.9864 + 0.6192
2

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PRC-025-2 — Application Guidelines

Example Calculations: Options 8b and 9b

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

0.8441 ± 1.1541
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9991 𝑝𝑝. 𝑢𝑢.

Use the new estimated Vlow-side value of 0.9991 per unit for the second iteration:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (103) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.9991 × 0.85)

Eq. (104)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.3°

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.3°) ± �|0.85|2 × cos 2 (6.3°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9940 ± √0.7225 × 0.9880 + 0.6192
2
0.8449 ± 1.1546
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9998 𝑝𝑝. 𝑢𝑢.

To account for system high-side nominal voltage and the transformer tap ratio:
Eq. (105) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = |𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.9998 𝑝𝑝. 𝑢𝑢.× 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 21.90 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (106) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗
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PRC-025-2 — Application Guidelines

Example Calculations: Options 8b and 9b

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (107) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.90 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 35553 𝐴𝐴

Secondary current (Isec):
Eq. (108) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

35553 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.111 𝐴𝐴

To satisfy the 115% margin in Options 8b and 9b:
Eq. (109) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.111 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.178 𝐴𝐴

Example Calculations: Options 8a, 9a, 11, and 12

This example represents the calculation for a mixture of asynchronous and synchronous
generators applying a phase overcurrent (e.g., 50, 51, or 67) relays. In this application it was
assumed 20 Mvar of total static compensation was added. The current transformers (CT) are
located on the low-side of the GSU transformer.

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Example Calculations: Options 8a, 9a, 11, and 12
Synchronous Generation (Options 8a and 9a)

Real Power output (PSynch):
Eq. (110) 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × .85
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (QSynch):

Eq. (111) 𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 150% × 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ

𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Apparent power (SSynch):

Eq. (112) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1347.4 ∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Option 8a, Table 1 – Bus Voltage calls for a 0.95 per unit of the high-side nominal voltage as a
basis for generator bus voltage (Vgen):
Eq. (113) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Primary current (Ipri-sync):
Eq. (114) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =

∗
115% × 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

1.15 × (1347.4 ∠ − 58.7° 𝑀𝑀𝑀𝑀𝑀𝑀)
1.73 × 20.81 𝑘𝑘𝑘𝑘
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Example Calculations: Options 8a, 9a, 11, and 12

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 43061 ∠ − 58.7° 𝐴𝐴

Asynchronous Generation (Options 11 and 12)

Real Power output (PAsynch):
Eq. (115) 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (QAsynch):

Eq. (116) 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos−1(𝑝𝑝𝑝𝑝))
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos−1(0.85)))
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 11, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen), however due to the presence of synchronous generator 0.95
per unit bus voltage will be used:
Eq. (117) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (SAsynch):

Eq. (118) 𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 130% × (𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ + 𝑗𝑗𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ )

𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 1.30 × (102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀)
𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 171.1 ∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri-async):
Eq. (119) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 =

𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
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Example Calculations: Options 8a, 9a, 11, and 12

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 =

171.1 ∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 20.81 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 4755 ∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (120) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
+
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

43061 ∠ − 58.7° 𝐴𝐴
4755∠ − 39.2° 𝐴𝐴
+
25000
25000
5
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 9.514∠ − 56.8° 𝐴𝐴

No additional margin is needed because the synchronous apparent power has been
multiplied by 1.15 (115%) in Equation 114 and the asynchronous apparent power has been
multiplied by 1.30 (130%) in Equation 118.
Eq. (121) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 100%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 9.514∠ − 56.8° 𝐴𝐴 × 1.00
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 9.514∠ − 56.8° 𝐴𝐴

Example Calculations: Options 8c and 9c

This example uses Option 15b as a simulation example for a synchronous generator applying
a phase overcurrent relay (e.g., 50, 51, or 67). In this application the same synchronous
generator is modeled as for Options 1c, 2c, and 7c. The CTs are located on the low-side of the
GSU transformer.
The generator Reactive Power and generator bus voltage are determined by simulation. The
maximum Reactive Power output on the low-side of the GSU transformer, during fieldforcing, is used since this value will correspond to the highest current. The corresponding
generator bus voltage is also used in the calculation. Note that although the excitation limiter
reduces the field, the duration of the Reactive Power output achieved for this condition is
sufficient to operate a phase overcurrent relay.

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Example Calculations: Options 8c and 9c
1.25

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

200

0

4

8

12

16

20

0

Time (s)

In this simulation the following values are derived:
𝑄𝑄 = 827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.989 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.76 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

Apparent power (S):

Eq. (122) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1083.8∠49.8°

Primary current (Ipri):

Eq. (123) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
1083.8 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.76 𝑘𝑘𝑘𝑘

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Example Calculations: Options 8c and 9c

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 28790 𝐴𝐴

Secondary current (Isec):
Eq. (124) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

28790 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.758 𝐴𝐴

To satisfy the 115% margin in Options 8c and 9c:
Eq. (125) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.758 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.622 𝐴𝐴

Example Calculations: Option 10

This example represents the calculation for three asynchronous generators (including
inverter-based installations) applying a phase distance relay (e.g., 21) directional toward the
Transmission system. In this application it was assumed 20 Mvar of total static compensation
was added.
Real Power output (P):
Eq. (126) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (127) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos−1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

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Example Calculations: Option 10

Option 10, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (128) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (129) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (130) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(21.9 𝑘𝑘𝑘𝑘)2
131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 3.644 ∠39.2° Ω

Secondary impedance (Zsec):
Eq. (131) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 3.644 ∠39.2° Ω ×

5000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 3.644 ∠39.2° Ω × 5
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 18.22 ∠39.2° Ω

To satisfy the 130% margin in Option 10:
Eq. (132) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
130%
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Example Calculations: Option 10

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

18.22∠39.2° Ω
1.30

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 14.02∠39.2° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 39.2°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (133) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
14.02 Ω
cos(85.0° − 39.2°)
14.02 Ω
0.6972

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 20.11∠85.0° Ω
Example Calculations: Options 11 and 12

Option 11 represents the calculation for a GSU transformer applying a phase overcurrent
(e.g., 50 or 51) relay connected to three asynchronous generators. Similarly, these
calculations can be applied to Option 12 for a phase directional overcurrent relay (e.g., 67)
directional toward the Transmission system. In this application it was assumed 20 Mvar of
total static compensation was added.
Real Power output (P):
Eq. (134) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (135) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))

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Example Calculations: Options 11 and 12

𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Options 11 and 12, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal
voltage for the generator bus voltage (Vgen):
Eq. (136) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (137) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6 ∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (138) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

131.6 ∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 3473∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (139) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

3473∠ − 39.2° 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.473∠ − 39.2° 𝐴𝐴

To satisfy the 130% margin in Options 11 and12:
Eq. (140) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 130%
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Example Calculations: Options 11 and 12

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.473∠ − 39.2° 𝐴𝐴 × 1.30
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.515∠ − 39.2° 𝐴𝐴

Example Calculations: Options 13a and 13b

Option 13a for the UAT assumes the maximum nameplate rating of the winding is utilized for
the purposes of the calculations and the appropriate voltage. Similarly, Option 13b uses the
measured current while operating at the maximum gross MW capability reported to the
Transmission Planner.
Primary current (Ipri):
Eq. (141) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑈𝑈𝑈𝑈𝑈𝑈𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛
√3 × 𝑉𝑉𝑈𝑈𝑈𝑈𝑈𝑈

60 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 13.8 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2510.2 𝐴𝐴

Secondary current (Isec):
Eq. (142) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑈𝑈𝑈𝑈𝑈𝑈

2510.2 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 2.51 A

To satisfy the 150% margin in Options 13a:
Eq. (143) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 150%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 2.51 𝐴𝐴 × 1.50
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.77 𝐴𝐴

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Example Calculations: Option 14a

Option 14a represents the calculation for relays installed on the high-side of the GSU
transformer, including relays installed on the remote end of line, for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant that connected to synchronous
generation. In this example, the Element is protected by a phase distance (e.g., 21) relay
directional toward the Transmission system. The CTs are located on the high-side of the GSU
transformer.
Real Power output (P):
Eq. (144) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (145) 𝑄𝑄 = 120% × 𝑃𝑃

𝑄𝑄 = 1.20 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 921.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 14a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the line nominal voltage for the
GSU transformer voltage (Vnom):
Eq. (146) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.85 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 293.25 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (147) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157.0∠52.77° 𝑀𝑀𝑀𝑀𝑀𝑀

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 52.77°

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Example Calculations: Option 14a

Primary impedance (Zpri):
Eq. (148) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝑆𝑆 ∗

(293.25 𝑘𝑘𝑘𝑘)2
1157.0∠ − 52.77° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 74.335∠52.77° Ω

Secondary impedance (Zsec):
Eq. (149) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 74.335∠52.77° Ω ×

2000
5
2000
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 74.335∠52.77° Ω × 0.2
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 14.867∠52.77° Ω

To satisfy the 115% margin in Option 14a:
Eq. (150) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

14.867∠52.77° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 12.928∠52.77° Ω
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 52.77°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (151) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
12.928 Ω
cos(85.0° − 52.77°)

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Example Calculations: Option 14a

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

12.928 Ω
0.846

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 15.283∠85.0° Ω
Example Calculations: Option 14b

Option 14b represents the simulation for relays installed on the high-side of the GSU
transformer, including relays installed on the remote end of line, for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant connected to synchronous generation.
In this example, the Element is protected by a phase distance (e.g., 21) relay directional
toward the Transmission system. The CTs are located on the high-side of the GSU
transformer.
Relays installed on the high-side of the GSU transformer, including relays installed on the
remote end of line, simulation is used to determine the simulated line voltage at the relay
location coincident with the highest Reactive Power output achieved during field-forcing in
response to a 0.85 per unit of the line nominal voltage at the remote end of the line prior to
field-forcing. This is achieved by modeling a shunt at the remote end (i.e., at the Transmission
system) of the line during simulation.
The maximum Reactive Power flow and coincident voltage for both the high-side of the GSU
transformer and remote end of the line are determined by simulation. The maximum
Reactive Power output on the high-side of the GSU transformer and remote end of the line
during field-forcing is used as these values will correspond to the lowest apparent impedance
at the relay location. The corresponding simulated voltage is also used in the calculation.
Note that although the excitation limiter reduces the field, the duration of the Reactive
Power output achieved for this condition is sufficient to operate a phase distance relay.

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Example Calculations: Option 14b

1.02 p.u.

GSU High-side Voltage

Generator Reactive Power

Generator Bus Voltage
440.7 Mvar

In this simulation the following values are derived:
𝑄𝑄 = 440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 1.02 × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 351.9 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

Apparent power (S):

Eq. (152) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗
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Example Calculations: Option 14b

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 827.2∠32.2° 𝑀𝑀𝑀𝑀𝑀𝑀

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 32.2°

Primary impedance (Zpri):
Eq. (153) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑆𝑆 ∗

(351.9 𝑘𝑘𝑘𝑘)2
=
827.2∠ − 32.2° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 149.7∠32.2° Ω

Secondary impedance (Zsec):

Eq. (154) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 149.7∠32.2° Ω ×

2000
5
2000
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 149.7∠32.2° Ω × 0.2
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 29.9∠32.2° Ω

To satisfy the 115% margin in Option 14b:
Eq. (155) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

29.9∠32.2° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 26.0∠32.2° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 32.2°

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Example Calculations: Option 14b

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (156) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
26.0 Ω
cos(85.0° − 32.2°)
26.0 Ω
0.61

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 43.0∠85.0° Ω

Example Calculations: Options 15a and 16a

Options 15a and 16a represent the calculation for relay installed on the high-side of the GSU
transformer, including relays installed at the remote end of the line, for Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant connected to synchronous
generation.
Option 15a represents applying a phase time overcurrent relay (e.g., 51) and/or phase
instantaneous overcurrent supervisory elements (e.g., 50) associated with current-based,
communication-assisted schemes where the scheme is capable of tripping for loss of
communications installed on the high-side of the GSU transformer, including relays installed
at the remote end of the line.
Option 16a represents applying a phase directional instantaneous overcurrent supervisory
element (e.g., 67) associated with current-based, communication-assisted schemes where
the scheme is capable of tripping for loss of communications directional toward the
Transmission system installed on the high-side of the GSU and at the remote end of the line
and/or a phase time directional overcurrent relay (e.g., 67) directional toward the
Transmission system installed on the high-side of the GSU transformer, including relays
installed at the remote end of the line.
Example calculations are provided for the case, where potential transformers (PT) and
current transformers (CT) are located at the high-side of the GSU transformer and the 0.85
per unit of the line nominal voltage at the high-side of the GSU transformer. Example
calculations are also provided for the case where PTs and CTs are located at the remote end

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Example Calculations: Options 15a and 16a

of the line and the 0.85 per unit of the line nominal voltage will be at the remote bus
location.
Calculations at the high-side of the GSU transformer.

Real Power output (P):
Eq. (157) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (158) 𝑄𝑄 = 120% × 𝑃𝑃

𝑄𝑄 = 1.20 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 15a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the line nominal voltage:
Eq. (159) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 293.25 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (160) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157∠52.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (161) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

1157∠ − 52.8° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 293.25 𝑘𝑘𝑘𝑘
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Example Calculations: Options 15a and 16a

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2280.6∠ − 52.8° 𝐴𝐴

Secondary current (Isec):
Eq. (162) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

2280.6∠ − 52.8° 𝐴𝐴
2000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.701 ∠ − 52.8° 𝐴𝐴

To satisfy the 115% margin in Options 15a and 16a:
Eq. (163) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.701 ∠ − 52.8° 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.56 ∠ − 52.8° 𝐴𝐴

Calculations at the remote end of the line from the plant.

Real Power output (P):
Eq. (164) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (165) 𝑄𝑄 = 120% × 𝑃𝑃

𝑄𝑄 = 1.20 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 15a and 16a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the line nominal voltage
at the relay location, in this example the relay location is at the remote substation bus.
Eq. (166) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.85 × 345 𝑘𝑘𝑘𝑘

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Example Calculations: Options 15a and 16a

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 293.25 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (167) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157∠52.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (168) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
1157∠ − 52.8° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 293.25 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2280.6∠ − 52.8° 𝐴𝐴

Secondary current (Isec):
Eq. (169) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑏𝑏𝑏𝑏𝑏𝑏

2280.6∠ − 52.8° 𝐴𝐴
2000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.701 ∠ − 52.8° 𝐴𝐴

To satisfy the 115% margin in Options 15a and 16a:
Eq. (170) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.701 ∠ − 52.8° 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.56 ∠ − 52.8° 𝐴𝐴

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Example Calculations: Options 15b and 16b

Options 15b and 16b represent the calculation for relays installed on the high-side of the GSU
transformer, including relays installed at the remote end of the line, for Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant connected to synchronous
generation.
Option 15b represents applying a phase time overcurrent relay (e.g., 51) and/or phase
instantaneous overcurrent supervisory elements (e.g., 50) associated with current-based,
communication-assisted schemes where the scheme is capable of tripping for loss of
communications installed on the high-side of the GSU transformer, including relays at the
remote end of the line.
Option 16b represents applying a phase directional instantaneous overcurrent supervisory
element (e.g., 67) associated with current-based, communication-assisted schemes where
the scheme is capable of tripping for loss of communications directional toward the
Transmission system and/or a phase directional time overcurrent relay (e.g., 67) directional
toward the Transmission system installed on the high-side of the GSU, including relays at the
remote end of the line.
Example calculations are provided for the case where relays are installed on the high-side of
the GSU transformer, including relays installed on the remote end of line. Simulation is used
to determine the line voltage at the relay location coincident with the highest Reactive Power
output achieved during field-forcing in response to a 0.85 per unit of the line nominal voltage
at the remote end of the line prior to field-forcing. This is achieved by modeling a shunt at the
remote end (i.e., at the Transmission system) of the line during simulation.
The maximum Reactive Power flow and coincident voltage for both the high-side of the GSU
transformer and remote end of the line are determined by simulation. The maximum
Reactive Power output on the high-side of the GSU transformer and remote end of the line
during field-forcing is used as these values will correspond to the lowest apparent impedance
at the relay location. The corresponding simulated voltage is also used in the calculation.
Note that although the excitation limiter reduces the field, the duration of the Reactive
Power output achieved for this condition is sufficient to operate a phase overcurrent relay.

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Example Calculations: Options 15b and 16b

1.02 p.u.

GSU High-side Voltage

Generator Reactive Power

Generator Bus Voltage
440.7 Mvar

In this simulation the following values are derived:
𝑄𝑄 = 440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 1.02 × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 351.9 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

Apparent power (S):

Eq. (171) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗
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Example Calculations: Options 15b and 16b

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 827.2∠32.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (172) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

827.2∠ − 32.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 351.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 1357.1∠ − 32.2° 𝐴𝐴

Secondary current (Isec):
Eq. (173) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

1357.1∠ − 32.2° 𝐴𝐴
2000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.39 ∠ − 32.2° 𝐴𝐴

To satisfy the 115% margin in Options 15b and 16b:
Eq. (174) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.39 ∠ − 32.2° 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.90 ∠ − 32.2° 𝐴𝐴

Example Calculations: Option 17

Option 17 represents the calculation for relays installed on the high-side of the GSU
transformer, including relays installed on the remote end of line, for Elements that connect a
GSU transformer for three asynchronous generators to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant that
is applying a phase distance relay (e.g., 21) directional toward the Transmission system. In
this application it was assumed 20 Mvar of total static compensation was added.

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Example Calculations: Option 17

Real Power output (P):
Eq. (175) 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (176)

𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
+ �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1(𝑝𝑝𝑝𝑝))�

𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos−1(0.85)))
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 17, Table 1 – Bus Voltage, calls for a 1.0 per unit of the line nominal voltage for the
bus voltage (Vbus):
Eq. (177) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 345.0 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (178) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (179) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝑆𝑆 ∗

(345.0 𝑘𝑘𝑘𝑘)2
131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 904.4∠39.2° Ω

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Example Calculations: Option 17

Secondary impedance (Zsec):
Eq. (180) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
300
5

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 904.4∠39.2° Ω × 2000
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 904.4∠39.2° Ω × 0.03
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 27.13∠39.2° Ω

To satisfy the 130% margin in Option 17:
Eq. (181) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
130%

27.13∠39.2° Ω
1.30

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 20.869∠39.2° Ω
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 39.2°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°, and
then the maximum allowable impedance reach is:
Eq. (182) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
20.869 Ω
cos(85.0° − 39.2°)
20.869 Ω
0.697

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 29.941∠85.0° Ω
Example Calculations: Options 18 and 19

Option 18 represents the calculation for relays on relays installed on the high-side of the GSU
transformer, including relays installed on the remote end of line, for Elements that connect a

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Example Calculations: Options 18 and 19

GSU transformer for three asynchronous generators to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant.
Option 18 represents applying a phase time overcurrent (e.g., 51) and/or phase
instantaneous overcurrent supervisory elements (e.g., 50) associated with current-based,
communication-assisted schemes where the scheme is capable of tripping for loss of
communications installed on the high-side of the GSU transformer, including relays at the
remote end of the line.
Similarly, Option 19 may also be applied here for the phase directional overcurrent relays
(e.g., 67) directional toward the Transmission system for Elements that connect a GSU
transformer, including relays at the remote end of the line to the Transmission system that
are used exclusively to export energy directly from a BES generating unit or generating plant.
In this application it was assumed 20 Mvar of total static compensation was added.
Real Power output (P):
Eq. (183) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (184)

𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
+ �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1(𝑝𝑝𝑝𝑝))�

𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Options 18 and 19, Table 1 – Bus Voltage, calls for a 1.0 per unit of the line nominal voltage
(Vbus):
Eq. (185) 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 1.0 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 345 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (186) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗
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Example Calculations: Options 18 and 19

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (187) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 345 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 220.5 ∠ − 39.2°𝐴𝐴

Secondary current (Isec):
Eq. (188) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

220.5∠ − 39.2° 𝐴𝐴
300
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.675∠ − 39.2° 𝐴𝐴

To satisfy the 130% margin in Options 18 and 19:
Eq. (189) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 130%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.675∠ − 39.2° 𝐴𝐴 × 1.30
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.778∠ − 39.2° 𝐴𝐴

End of calculations

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PRC-025-2 — Application Guidelines

Rationale

During development of this standard, text boxes were embedded within the standard to explain
the rationale for various parts of the standard. Upon BOT approval, the text from the rationale
text boxes was moved to this section.
Rationale for R1

Requirement R1 is a risk-based requirement that requires the responsible entity to be aware of
each protective relay subject to the standard and applies an appropriate setting based on its
calculations or simulation for the conditions established in Attachment 1.
The criteria established in Attachment 1 represent short-duration conditions during which
generation Facilities are capable of providing system reactive resources, and for which
generation Facilities have been historically recorded to disconnect, causing events to become
more severe.
The term, “while maintaining reliable fault protection” in Requirement R1 describes that the
responsible entity is to comply with this standard while achieving their desired protection goals.
Refer to the Guidelines and Technical Basis, Introduction, for more information.

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PRC-025-2 - Redline Version

PRC-025-12— Generator Relay Loadability

A. Introduction
1.

Title:

Generator Relay Loadability

2.

Number:

PRC-025-12

3.

Purpose: To set load-responsive protective relays associated with generation
Facilities at a level to prevent unnecessary tripping of generators during a system
disturbance for conditions that do not pose a risk of damage to the associated
equipment.

4.

Applicability:
4.1.

4.2.

5.

1

Functional Entities:
4.1.1.

Generator Owner that applies load-responsive protective relays 1 at
the terminals of the Elements listed in 34.2, Facilities.

4.1.2.

Transmission Owner that applies load-responsive protective
relaysrelays1 at the terminals of the Elements listed in 34.2, Facilities.

4.1.3.

Distribution Provider that applies load-responsive protective
relaysrelays1 at the terminals of the Elements listed in 34.2, Facilities.

Facilities: The following Elements associated with Bulk Electric System (BES)
generating units and generating plants, including those generating units and
generating plants identified as Blackstart Resources in the Transmission
Operator’s system restoration plan:
4.2.1.

Generating unit(s).

4.2.2.

Generator step-up (i.e., GSU) transformer(s).

4.2.3.

Unit auxiliary transformer(s) (UAT) that supply overall auxiliary power
necessary to keep generating unit(s) online.2

4.2.4.

Elements that connect the GSU transformer(s) to the Transmission
system that are used exclusively to export energy directly from a BES
generating unit or generating plant., except that Elements may also
supply generating plant loads.

4.2.5.

Elements utilized in the aggregation of dispersed power producing
resources.

Effective Date: See Implementation Plan

Relays include low voltage protection devices that have adjustable settings.

These transformers are variably referred to as station power, unit auxiliary transformer(s) (UAT), or station service
transformer(s) used to provide overall auxiliary power to the generator station when the generator is running. Loss of these
transformers will result in removing the generator from service. Refer to the PRC-025-12 Guidelines and Technical Basis for
more detailed information concerning unit auxiliary transformers.
2

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PRC-025-12— Generator Relay Loadability

5.6. Background: After analysis of many of the major disturbances in the last 25 years on
the North American interconnected power system, generators have been found to have
tripped for conditions that did not apparently pose a direct risk to those generators and
associated equipment within the time period where the tripping occurred. This tripping
has often been determined to have expanded the scope and/or extended the duration
of that disturbance. This was noted to be a serious issue in the August 2003 “blackout”
in the northeastern North American continent. 3
During the recoverable phase of a disturbance, the disturbance may exhibit a “voltage
disturbance” behavior pattern, where system voltage may be widely depressed and
may fluctuate. In order to support the system during this transient phase of a
disturbance, this standard establishes criteria for setting load-responsive protective
relays such that individual generators may provide Reactive Power within their dynamic
capability during transient time periods to help the system recover from the voltage
disturbance. The premature or unnecessary tripping of generators resulting in the
removal of dynamic Reactive Power exacerbates the severity of the voltage disturbance,
and as a result changes the character of the system disturbance. In addition, the loss of
Real Power could initiate or exacerbate a frequency disturbance.
7.

Standard Only Definition: None.

6.1. Effective Date: See Implementation Plan

B. Requirements and Measures
R1.

Each Generator Owner, Transmission Owner, and Distribution Provider shall apply
settings that are in accordance with PRC-025-12 – Attachment 1: Relay Settings, on each
load-responsive protective relay while maintaining reliable fault protection. [Violation
Risk Factor: High] [Time Horizon: Long-Term Planning]

M1. For each load-responsive protective relay, each Generator Owner, Transmission Owner,
and Distribution Provider shall have evidence (e.g., summaries of calculations,
spreadsheets, simulation reports, or setting sheets) that settings were applied in
accordance with PRC-025-12 – Attachment 1: Relay Settings.

C. Compliance
1.

Compliance Monitoring Process
6.1. Compliance Enforcement Authority
1.1.

As defined in the NERC Rules of Procedure,: “Compliance Enforcement
Authority” means NERC or the Regional Entity, or any entity as otherwise

Interim Report: Interim Report: Causes of the August 14th Blackout in the United States and Canada, U.S.-Canada Power
System Outage Task Force, November 2003 (http://www.nerc.com/docs/docs/blackout/814BlackoutReport.pdf)).
3

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PRC-025-12— Generator Relay Loadability

designated by an Applicable Governmental Authority, in their respective roles
of monitoring and/or enforcing compliance with the NERCmandatory and
enforceable Reliability Standards in their respective jurisdictions.
1.2.

Evidence Retention: The following evidence retention periodsperiod(s)
identify the period of time an entity is required to retain specific evidence to
demonstrate compliance. For instances where the evidence retention period
specified below is shorter than the time since the last audit, the Compliance
Enforcement Authority (CEA) may ask an entity to provide other evidence to
show that it was compliant for the full time period since the last audit.
The Generator Owner, Transmission Owner, and Distribution
Providerapplicable entity shall keep data or evidence to show compliance as
identified below unless directed by its CEACompliance Enforcement
Authority to retain specific evidence for a longer period of time as part of an
investigation:
•
•

The Generator Owner, Transmission Owner, and Distribution Provider
shall retain evidence of Requirement R1 and Measure M1 for the most
recent three calendar years.
If a Generator Owner, Transmission Owner, or Distribution Provider is
found non-compliant, it shall keep information related to the noncompliance until mitigation is complete and approved or for the time
specified above, whichever is longer.

The CEA shall keep the last audit records and all requested and submitted
subsequent audit records.
6.2. Compliance Monitoring and Assessment Processes
Compliance Audit
Self-Certification
Spot Checking
Compliance Investigation
Self-Reporting
Complaint
6.3. Additional Compliance Information
None

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PRC-025-12— Generator Relay Loadability

Table of Compliance Elements

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PRC-025-12— Generator Relay Loadability

Violation Severity Levels
R#

Time
Horizon

Lower VSL
LongTerm
Planning

R1

Violation Severity Levels

VRF

Moderate VSL

High VSL

High

N/A

N/A

N/A

Severe VSL
The Generator Owner,
Transmission Owner,
and Distribution
Provider did not apply
settings in accordance
with PRC-025-12 –
Attachment 1: Relay
Settings, on an applied
load-responsive
protective relay.

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PRC-025-12— Generator Relay Loadability

D. Regional Variances
None.

E. Interpretations
None.

F.E.

Associated Documents
NERC System Protection and Control Subcommittee, July 2010, ““Considerations for Power Plant and Transmission System
Protection Coordination.”,” technical reference document, Revision 2. (Date of Publication: July 2015)
NERC System Protection and Control Subcommittee, “Unit Auxiliary Transformer Overcurrent Relay Loadability During a
Transmission Depressed Voltage Condition.” (Date of Publication: March 2016)
IEEE C37.102-2006, “IEEE Guide for AC Generator Protection.” (Date of Publication: 2006)
IEEE C37.17-2012, “IEEE Standard for Trip Systems for Low-Voltage (1000 V and below) AC and General Purpose (1500 V
and below) DC Power Circuit Breakers.” (Date of Publication: September 18, 2012)
IEEE C37.2-2008, “IEEE Standard for Electrical Power System Device Function Numbers, Acronyms, and Contact
Designations.” (Date of Publication: October 3, 2008)

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PRC-025-12— Generator Relay Loadability

Version History
Version

Date

Action

1

August 15,
2013

Adopted by NERC Board of Trustees

1

July 17, 2014

FERC order issued approving PRC-025-1

2

April 19, 2017

SAR accepted by Standards Committee

2

February 8,
2018

Adopted by NERC Board of Trustees

Change
Tracking

New

Project 2016-04
Revision

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PRC-025-12— Generator Relay Loadability

PRC-025-12 – Attachment 1: Relay Settings
Introduction

This standard does not require the Generator Owner, Transmission Owner, or Distribution
Provider to use any of the protective functions listed in Table 1. Each Generator Owner,
Transmission Owner, and Distribution Provider that applies load-responsive protective relays on
their respective Elements listed in 34.2, Facilities, shall use one of the following Options in Table
1, Relay Loadability Evaluation Criteria (“Table 1”), to set each load-responsive protective relay
element according to its application and relay type. The bus voltage is based on the criteria for
the various applications listed in Table 1.
Generators

Synchronous generator relay pickup setting criteria values are derived from the unit’s maximum
gross Real Power capability, in megawatts (MW), as reported to the Transmission Planner, and
the unit’s Reactive Power capability, in megavoltampere-reactive (Mvar), is determined by
calculating the MW value based on the unit’s nameplate megavoltampere (MVA) rating at rated
power factor. If different seasonal capabilities are reported, the maximum capability shall be
used for the purposes of this standard as a minimum requirement. The Generator Owner may
base settings on a capability that is higher than what is reported to the Transmission Planner.
Asynchronous generator relay pickup setting criteria values (including inverter-based
installations) are derived from the site’s aggregate maximum complex power capability, in MVA,
as reported to the Transmission Planner, including the Mvar output of any static or dynamic
reactive power devices. If different seasonal capabilities are reported, the maximum capability
shall be used for the purposes of this standard as a minimum requirement. The Generator Owner
may base settings on a capability that is higher than what is reported to the Transmission Planner.
For the application caseapplications where synchronous and asynchronous generator types are
combined on a generator step-up transformer or on Elements that connect the generator stepup (GSU) transformer(s) to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant (except that Elements may also supply
generating plant loads.),), the pickup setting criteria shall be determined by vector summing the
pickup setting criteria of each generator type, and using the bus voltage for the given
synchronous generator application and relay type.
Transformers

Calculations using the GSU transformer turns ratio shall use the actual tap that is applied (i.e., in
service) for GSU transformers with deenergizedde-energized tap changers (DETC). If load tap
changers (LTC) are used, the calculations shall reflect the tap that results in the lowest generator
bus voltage. When the criterion specifies the use of the GSU transformer’s impedance, the
nameplate impedance at the nominal GSU transformer turns ratio shall be used.
Applications that use more complex topology, such as generators connected to a multiple
winding transformer, are not directly addressed by the criteria in Table 1. These topologies can

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PRC-025-12— Generator Relay Loadability

result in complex power flows, and may require simulation to avoid overly conservative
assumptions to simplify the calculations. Entities with these topologies should set their relays in
such a way that they do not operate for the conditions being addressed in this standard.
Multiple Lines

Applications that use more complex topology, such as multiple lines that connect the generator
step-up (GSU) transformer(s) to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant (except that Elements may also
supply generating plant loads) are not directly addressed by the criteria in Table 1. These
topologies can result in complex power flows, and it may require simulation to avoid overly
conservative assumptions to simplify the calculations. Entities with these topologies should set
their relays in such a way that they do not operate for the conditions being addressed in this
standard.
Exclusions

The following protection systems are excluded from the requirements of this standard:
1. Any relay elements that are in service only during start up.
2. Load-responsive protective relay elements that are armed only when the generator is
disconnected from the system, (e.g., non-directional overcurrent elements used in
conjunction with inadvertent energization schemes, and open breaker flashover
schemes).
3. Phase fault detector relay elements employed to supervise other load-responsive phase
distance elements (e.g., in order to prevent false operation in the event of a loss of
potential) provided the distance element is set in accordance with the criteria outlined in
the standard.
4. Protective relay elements that are only enabled when other protection elements fail (e.g.,
overcurrent elements that are only enabled during loss of potential conditions).
5. Protective relay elements used only for Special Protection SystemsRemedial Action
Schemes that are subject to one or more requirements in a NERC or Regional Reliability
Standard.
6. Protection systems that detect generator overloads that are designed to coordinate with
the generator short time capability by utilizing an extremely inverse characteristic set to
operate no faster than 7 seconds at 218% of fullloadfull load current (e.g., rated armature
current), and prevent operation below 115% of full-load current. 4
7. Protection systems that detect transformer overloads and are designed only to respond
in time periods which allow an operator 15 minutes or greater to respond to overload
conditions.
8. Low voltage protection devices that do not have adjustable settings.
Table 1

Table 1 beginning on the next pagebelow is structured and formatted to aid the reader with
identifying an option for a given load-responsive protective relay.
4

IEEE C37.102-2006, “Guide for AC Generator Protection,” Section 4.1.1.2.

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PRC-025-12— Generator Relay Loadability

The first column identifies the application (e.g., synchronous or asynchronous generators,
generator step-up transformers, unit auxiliary transformers, Elements that connect the GSU
transformer(s) to the Transmission system that are used exclusively to export energy directly
from a BES generating unit or generating plant. Elements may also supply generating plant
loads).). Dark blue horizontal bars, excluding the header which repeats at the top of each page,
demarcate the various applications.
The second column identifies the load-responsive distance or overcurrent protective relay by
IEEE device numbers (e.g., 21, 50, 51, 51V-C, 51V-R, or 67) according to the applied application in
the first column. This also includes manufacture protective device trip unit designations for longtime delay, short-time delay, and instantaneous (e.g., L, S, and I). A light blue horizontal bar
between the relay types is the demarcation between relay types for a given application. These
light blue bars will contain no text., except when the same application continues on the next page
of the table with a different relay type.
The third column uses numeric and alphabetic options (i.e., index numbering) to identify the
available options for setting load-responsive protective relays according to the application and
applied relay type. Another, shorter, light blue bar contains the word “OR,” and reveals to the
reader that the relay for that application has one or more options (i.e., “ways”) to determine the
bus voltage and pickup setting criteria in the fourth and fifth column, respectively. The bus
voltage column and pickup setting criteria columns provide the criteria for determining an
appropriate setting.
The table is further formatted by shading groups of relays associated with asynchronous
generator applications. Synchronous generator applications and the unit auxiliary transformer
applications are not shaded. Also, intentional buffers were added to the table such that similar
options, as possible, would be paired together on a per page basis. Note that some applications
may have an additional pairing that might occur on adjacent pages.

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PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Pickup Setting Criteria

1a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output –100% of the maximum gross Mvar
output during field-forcing as determined by simulation

OR
Synchronous
generating unit(s),
orincluding Elements
utilized in the
aggregation of
dispersed power
producing resources

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system

1b

OR

1c

The same application continues on the next page with a different relay type

Calculations using the generator step-up (GSU) transformer turns ratio shall use the actual tap that is applied (i.e., in service) for GSU transformers with deenergizeddeenergized tap changers (DETC). If load tap changers (LTC) are used, the calculations shall reflect the tap that results in the lowest generator bus voltage. When the criterion
specifies the use of the GSU transformer’s impedance, the nameplate impedance at the nominal GSU turns ratio shall be used.
5

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PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Pickup Setting Criteria

2a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

2b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the gross MW capability
reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the MW value, derived
from the generator nameplate MVA rating at rated power factor

OR

Synchronous
generating unit(s),
orincluding Elements
utilized in the
aggregation of
dispersed power
producing resources

Phase time
overcurrent relay
(e.g., 50, 51), or
(51V-R) – voltagerestrained)

OR

2c

Phase time
overcurrent relay
(e.g., 51V-C) –
voltage controlled
(Enabled to
operate as a
function of
voltage)

3

Simulated generator bus voltage
coincident with the highest
The overcurrent element shall be set greater than 115% of the
Reactive Power output achieved
calculated current derived from:
during field-forcing in response to a (1) Real Power output – 100% of the gross MW capability
0.85 per unit nominal voltage on
reported to the Transmission Planner or, and
the high-side terminals of the
(2) Reactive Power output –100% of the maximum gross Mvar
generator step-up transformer
output during field-forcing as determined by simulation
prior to field-forcing
The same application continues with a different relay type below
Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

Voltage control setting shall be set less than 75% of the
calculated generator bus voltage

A different application starts on the next page

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PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

4

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The impedance element shall be set less than the calculated
impedance derived from 130% of the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

55a

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

5b

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The lower tolerance of the overcurrent element tripping
characteristic shall not infringe upon the resource capability
(including the Mvar output of the resource and any static or
dynamic reactive power devices) See Figure A.

6

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

Voltage control setting shall be set less than 75% of the
calculated generator bus voltage

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system

Asynchronous
generating unit(s)
(including inverterbased installations),
orincluding Elements
utilized in the
aggregation of
dispersed power
producing resources

Phase time
overcurrent relay
(e.g., 50, 51), or
(51V-R) – voltagerestrained)

Phase time
overcurrent relay
(e.g., 51V-C) –
voltage controlled
(Enabled to
operate as a
function of
voltage)

OR

Pickup Setting Criteria

A different application starts on the next page

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PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on
generator-side 6 of the
Generator step-up
transformer(s)
connected to
synchronous
generators

Relay Type

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system – installed
on generator-side
of the GSU
transformer
If the relay is
installed on the
high-side of the
GSU transformer
use Option 14

Option

Bus Voltage 5

Pickup Setting Criteria

7a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

7b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

7c

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR

OR

The same application continues on the next page with a different relay type

6

If the relay is installed on the high-side of the GSU transformer, use Option 14.

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PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on
generator-side 7 of the
Generator step-up
transformer(s)
connected to
synchronous
generators

Relay Type

Phase time
overcurrent relay
(e.g., 50 or 51) –
installed on
generator-side of
the GSU
transformer
If the relay is
installed on the
high-side of the
GSU transformer
use Option 15

Option

Bus Voltage 5

Pickup Setting Criteria

8a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

8b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

8c

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR

OR

The same application continues on the next page with a different relay type

7

If the relay is installed on the high-side of the GSU transformer use, Option 15.

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PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on
generator-side 8 of the
Generator step-up
transformer(s)
connected to
synchronous
generators

Relay Type

Phase directional
time overcurrent
relay (e.g., 67) –
directional toward
the Transmission
system – installed
on generator-side
of the GSU
transformer
If the relay is
installed on the
high-side of the
GSU transformer
use Option 16

Option

Bus Voltage 5

Pickup Setting Criteria

9a

Generator bus voltage
corresponding to 0.95 per unit of
the high-side nominal voltage times
the turns ratio of the generator
step-up transformer

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

9b

Calculated generator bus voltage
corresponding to 0.85 per unit
nominal voltage on the high-side
terminals of the generator step-up
transformer (including the
transformer turns ratio and
impedance)

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 150% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

9c

Simulated generator bus voltage
coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit nominal voltage on
the high-side terminals of the
generator step-up transformer
prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR

OR

A different application starts on the next page

8

If the relay is installed on the high-side of the GSU transformer use, Option 16.

16 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on
generator-side of the
Generator step-up
transformer(s)
connected to
asynchronous
generators only
(including inverterbased installations)

Relay Type
Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system – installed
on generator-side
of the GSU
transformer
If the relay is
installed on the
high-side of the
GSU transformer
use Option 17 9
Phase time
overcurrent relay
(e.g., 50 or 51) –
installed on
generator-side of
the GSU
transformer
If the relay is
installed on the
high-side of the
GSU transformer
use Option 18 10

Option

Bus Voltage 5

10

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

The impedance element shall be set less than the calculated
impedance derived from 130% of the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

11

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer for overcurrent relays
installed on the low-side

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

Pickup Setting Criteria

The same application continues on the next page with a different relay type

9

If the relay is installed on the high-side of the GSU transformer, use Option 17.
If the relay is installed on the high-side of the GSU transformer, use Option 18.

10

17 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Generator step-up
transformer(s)
connected to
asynchronous
generators only
(including inverterbased installations)

Relay Type

Option

Bus Voltage 5

12

Generator bus voltage
corresponding to 1.0 per unit of the
high-side nominal voltage times the
turns ratio of the generator step-up
transformer

Phase directional
time overcurrent
relay (e.g., 67) –
directional toward
the Transmission
system – installed
on generator-side
of the GSU
transformer

Pickup Setting Criteria

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

If the relay is
installed on the
high-side of the
GSU transformer
use Option 19 11

A different application starts belowon the next page

Unit auxiliary
transformer(s) (UAT)

11

Phase time
overcurrent relay
(e.g., 50 or 51)
applied at the high-

13a
OR

1.0 per unit of the winding nominal
voltage of the unit auxiliary
transformer

The overcurrent element shall be set greater than 150% of the
calculated current derived from the unit auxiliary transformer
maximum nameplate MVA rating

If the relay is installed on the high-side of the GSU transformer, use Option 19.

18 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type
side terminals of
the UAT, for which
operation of the
relay will cause the
associated
generator to trip.

Relays installed on the
high-side of the GSU
transformer, 12 including
relays installed on the
remote end of line, for
Elements that connect
the GSU transformer(s)
to the Transmission
system that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant.
(except that Elements
may also supply
generating plant loads.
–) – connected to
synchronous
generators

12

Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system – installed
on the high-side of
the GSU
transformer
If the relay is
installed on the
generator-side of
the GSU
transformer use
Option 7

Option

13b

14a

OR

14b

Bus Voltage 5
Unit auxiliary transformer bus
voltage corresponding to the
measured current

Pickup Setting Criteria
The overcurrent element shall be set greater than 150% of the
unit auxiliary transformer measured current at the generator
maximum gross MW capability reported to the Transmission
Planner

A different application starts on the next page
The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
0.85 per unit of the line nominal
MW reported to the Transmission Planner, and
voltage at the relay location
(2) Reactive Power output – 120% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor
Simulated line voltage at the relay
location coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit of the line nominal
voltage onat the high-side
terminalsremote end of the
generator step-up transformerline
prior to field-forcing

The impedance element shall be set less than the calculated
impedance derived from 115% of:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

The same application continues on the next page with a different relay type

If the relay is installed on the generator-side of the GSU transformer, use Option 7.

19 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on the
high-side of the GSU
transformer, 13 including
relays installed at the
remote end of the line,
for Elements that
connect the GSU
transformer(s) to the
Transmission system
that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant.
(except that Elements
may also supply
generating plant loads.
–) – connected to
synchronous
generators

13

Relay Type
Phase
instantaneous
overcurrent
supervisory
element (e.g., 50) –
associated with
current-based,
communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
installed on the
high-side of the
GSU transformer
and/or phase time
overcurrent relay
(e.g., 51) –
installed on the
high-side of the
GSU transformer

Option

15a

Bus Voltage 5

Pickup Setting Criteria

0.85 per unit of the line nominal
voltage at the relay location

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 120% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

Simulated line voltage at the relay
location coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit of the line nominal
voltage onat the high-side
terminalsremote end of the
generator step-up transformerline
prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

OR

15b

If the relay is
installed on the
generator-side of
the GSU
transformer use
Option 8

If the relay is installed on the generator-side of the GSU transformer, use Option 8.

20 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Option

Bus Voltage 5

Pickup Setting Criteria

The same application continues on the next page with a different relay type

Relays installed on the
high-side of the GSU
transformer, 14 including
relays installed at the
remote end of the line,
for Elements that
connect the GSU
transformer(s) to the

14

Phase directional
instantaneous
overcurrent
supervisory
element (e.g., 67) –
associated with
current-based,

16a

0.85 per unit of the line nominal
voltage at the relay location

OR

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output – 120% of the aggregate generation
MW value, derived from the generator nameplate MVA rating
at rated power factor

If the relay is installed on the generator-side of the GSU transformer, use Option 9.

21 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relay Type

Transmission system
that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant.
(except that Elements
may also supply
generating plant load..)
–connected to
synchronous
generators

communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
directional toward
the Transmission
system installed on
the high-side of the
GSU transformer
and/or phase
directional time
overcurrent relay
(e.g., 67) –
directional toward
the Transmission
system installed on
the high-side of the
GSU transformer

Option

Bus Voltage 5

Pickup Setting Criteria

16b

Simulated line voltage at the relay
location coincident with the highest
Reactive Power output achieved
during field-forcing in response to a
0.85 per unit of the line nominal
voltage onat the high-side
terminalsremote end of the
generator step-up transformerline
prior to field-forcing

The overcurrent element shall be set greater than 115% of the
calculated current derived from:
(1) Real Power output – 100% of the aggregate generation gross
MW reported to the Transmission Planner, and
(2) Reactive Power output –100% of the aggregate generation
maximum gross Mvar output during field-forcing as determined
by simulation

If the relay is
installed on the
generator-side of
the GSU
transformer use
Option 9

A different application starts on the next page

22 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on the
high-side of the GSU
transformer, 15 including
relays installed on the
remote end of line, for
Elements that connect
the GSU transformer(s)
to the Transmission
system that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant.
(except that Elements
may also supply
generating plant loads.)
–connected to
asynchronous
generators only
(including inverterbased installations)

15

Relay Type
Phase distance
relay (e.g., 21) –
directional toward
the Transmission
system– installed
on the high-side of
the GSU
transformer

Option

17

Bus Voltage 5

1.0 per unit of the line nominal
voltage at the relay location

Pickup Setting Criteria

The impedance element shall be set less than the calculated
impedance derived from 130% of the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

If the relay is
installed on the
generator-side of
the GSU
transformer use
Option 10

The same application continues on the next page with a different relay type

If the relay is installed on the generator-side of the GSU transformer, use Option 10.

23 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on the
high-side of the GSU
transformer, 16
including, relays
installed on the remote
end of the line, for
Elements that connect
the GSU transformer(s)
to the Transmission
system that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant.
(except that Elements
may also supply
generating plant loads.)
– connected to
asynchronous
generators only
(including inverterbased installations)

Relay Type
Phase
instantaneous
overcurrent
supervisory
element (e.g., 50) –
associated with
current-based,
communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
installed on the
high-side of the
GSU transformer
and/or Phase time
overcurrent relay
(e.g., 51) –
installed on the
high-side of the
GSU transformer

Option

18

Bus Voltage 5

1.0 per unit of the line nominal
voltage at the relay location

Pickup Setting Criteria

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

If the relay is
installed on the
generator-side of
the GSU
transformer use
Option 11

The same application continues on the next page with a different relay type

16

If the relay is installed on the generator-side of the GSU transformer, use Option 11.

24 of 141

PRC-025-12— Generator Relay Loadability

Table 1. Relay Loadability Evaluation Criteria

Application

Relays installed on the
high-side of the GSU
transformer, 17 including
relays installed on the
remote end of the line,
for Elements that
connect the GSU
transformer(s) to the
Transmission system
that are used
exclusively to export
energy directly from a
BES generating unit or
generating plant.
(except that Elements
may also supply
generating plant loads.)
–connected to
asynchronous
generators only
(including inverterbased installations)

Relay Type
Phase directional
instantaneous
overcurrent
supervisory
element (e.g., 67) –
associated with
current-based,
communicationassisted schemes
where the scheme
is capable of
tripping for loss of
communications
directional toward
the Transmission
system installed on
the high-side of the
GSU transformer
and/or Phase
directional time
overcurrent relay
(e.g., 67) –
installed on the
high-side of the
GSU transformer

Option

19

Bus Voltage 5

1.0 per unit of the line nominal
voltage at the relay location

Pickup Setting Criteria

The overcurrent element shall be set greater than 130% of the
calculated current derived from the maximum aggregate
nameplate MVA output at rated power factor (including the
Mvar output of any static or dynamic reactive power devices)

If the relay is
installed on the
generator-side of
the GSU
transformer use
Option 12

End of Table 1

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PRC-025-12— Generator Relay Loadability

Overload Area
Exclusion 7

1000
900

100

Protective Element
Time Tolerance

Protective Element
Operate Area

0.1

Asynchronous
Resource
Capability

Time (s)

10

1

Option 5b – The lower
tolerance of the
overcurrent element
tripping characteristic shall
not infringe on the resource
capability

Protective Element
Pick Tolerance

Protective
Element Non
Operate Area

.01

Current
Figure A

This figure is for demonstration of Option 5b and does not mandate a specific type of
protective curve or device manufacturer.

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PRC-025-12 – Application Guidelines

PRC-025-12 Guidelines and Technical Basis
Introduction

The document, “Power Plant and Transmission System Protection Coordination,”The document,
“Considerations for Power Plant and Transmission System Protection Coordination,” published
by the NERC System Protection and Control Subcommittee (SPCS) provides extensive general
discussion about the protective functions and generator performance addressed within this
standard. This document was last revised in July 20102015.18
The basis for the standard’s loadability criteria for relays applied at the generator terminals or
low-side of the generator step-up (GSU) transformer is the dynamic generating unit loading
values observed during the August 14, 2003 blackout, other subsequent system events, and
simulations of generating unit response to similar system conditions. The Reactive Power output
observed during field-forcing in these events and simulations approaches a value equal to 150
percent of the Real Power (MW) capability of the generating unit when the generator is operating
at its Real Power capability. In the SPCS technical reference document, two operating conditions
were examined based on these events and simulations: (1) when the unit is operating at rated
Real Power in MW with a level of Reactive Power output in Mvar which is equivalent to 150
percent times the rated MW value (representing some level of field-forcing) and (2) when the
unit is operating at its declared low active Real Power operating limit (e.g., 40 percent of rated
Real Power) with a level of Reactive Power output in Mvar which is equivalent to 175 percent
times the rated MW value (representing some additional level of field-forcing).
Both conditions noted above are evaluated with the GSU transformer high-side voltage at 0.85
per unit. These load operating points are believed to be conservatively high levels of Reactive
Power out of the generator with a 0.85 per unit high-side voltage which was based on these
observations. However, for the purposes of this standard it was determined that the second load
point (40 percent) offered no additional benefit and only increased the complexity for an entity
to determine how to comply with the standard. Given the conservative nature of the criteria,
which may not be achievable by all generating units, an alternate method is provided to
determine the Reactive Power output by simulation. Also, to account for Reactive Power losses
in the GSU transformer, a reduced level of output of 120 percent times the rated MW value is
provided for relays applied at the high-side of the GSU transformer and on Elements that connect
a GSU transformer to the Transmission system and are used exclusively to export energy directly
from a BES generating unit or generating plant.
The phrase, “while maintaining reliable fault protection” in Requirement R1, describes that the
Generator Owner, Transmission Owner, and Distribution Provider is to comply with this standard
while achieving its desired protection goals. Load-responsive protective relays, as addressed
18

http://www.nerc.com/docs/pc/spctf/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20SPCS%2020/S
PCS%20
Gen%20Prot%20Coord%20Rev1%20Final%2007-30-201020Coordination%20Technical%20Reference%20Document.pdf.

27 of 141

PRC-025-12 – Application Guidelines

within this standard, may be intended to provide a variety of backup protection functions, both
within the generating unit or generating plant and on the Transmission system, and this standard
is not intended to result in the loss of these protection functions. Instead, it is suggested that the
Generator Owner, Transmission Owner, and Distribution Provider consider both the requirement
within this standard and its desired protection goals, and perform modifications to its protective
relays or protection philosophies as necessary to achieve both.
For example, if the intended protection purpose is to provide backup protection for a failed
Transmission breaker, it may not be possible to achieve this purpose while complying with this
standard if a simple mho relay is being used. In this case, it may be possible to meet this purpose
by replacing the legacy relay with a modern advanced-technology relay that can be set using
functions such as load encroachment. It may otherwise be necessary to reconsider whether this
is an appropriate method of achieving protection for the failed Transmission breaker, and
whether this protection can be better provided by, for example, applying a breaker failure relay
with a transfer trip system.
Requirement R1 establishes that the Generator Owner, Transmission Owner, and Distribution
Provider must understand the applications of Attachment 1: Relay Settings, Table 1: Relay
Loadability Evaluation Criteria (“Table 1”) in determining the settings that it must apply to each
of its load-responsive protective relays to prevent an unnecessary trip of its generator during the
system conditions anticipated by this standard.
Applicability

To achieve the reliability objective of this standard it is necessary to include all load-responsive
protective relays that are affected by increased generator output in response to system
disturbances. This standard is therefore applicable to relays applied by the Generator Owner,
Transmission Owner, and Distribution Provider at the terminals of the generator, GSU
transformer, unit auxiliary transformer (UAT), Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant, and Elements utilized in the aggregation of dispersed power producing
resources.
The Generator Owner’s interconnection facility (in some cases labeled a “transmission Facility”
or “generator leads”) consists of Elements between the GSU transformer and the interface with
the portion of the Bulk Electric System (BES) where Transmission Owners take over the
ownership. This standard does not use the industry recognized term “generator interconnection
Facility” consistent with the work of Project 2010-07 (Generator Requirements at the
Transmission Interface), because the term generator interconnection Facility implies ownership
by the Generator Owner. Instead, this standard refers to these Facilities as “Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant” to include these Facilities when they are
also owned by the Transmission Owner or Distribution Provider. The load-responsive protective
relays in this standard for which an entity shall be in compliance isare dependent on the location
and the application of the protective functions. Figures 1, 2, and 3 illustrate various generator
28 of 141

PRC-025-12 – Application Guidelines

interface connections with the Transmission system, and Figure 4 illustrates examples of
Elements utilized in the aggregation of dispersed power resources that are in scope of the
standard.
Figure 1

Figure 1 is a single (or set) of generators connected to the Transmission system through a radial
line that is used exclusively to export energy directly from a BES generating unit or generating
plant to the network. The protective relay R1 located on the high-side of the GSU transformer
breaker CB100 is generally applied to provide backup protection to the relaying located at Bus A
and in some cases Bus B. Under this application, relay R1 would apply the loadability requirement
in PRC-025-12 using an appropriate option for the application from Table 1 (e.g., Options 14
through 19) for Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant.
The protective relay R2 located on the incoming source breaker CB102 to the generating plant
applies relaying that primarily protects the line by using line differential relaying from Bus A to B
and also provides backup protection to the transmission relaying at Bus B. In this case, the relay
function that provides line protection would apply the loadability requirement in PRC-025-12 and
an appropriate option for the application from Table 1 (e.g., 15a, 15b, 16a, 16b, 18, and 19) for
phase overcurrent supervisory elements (i.e., phase fault detectors) associated with currentbased, communication-assisted schemes (i.e., pilot wire, phase comparison, and line current
differential) where the scheme is capable of tripping for loss of communications. The backup
protective function would apply the requirement in the PRC-025-12 standard using an
appropriate option for the application from Table 1 (e.g., Options 14 through 19) for Elements
that connect a GSU transformer to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant.
In this particular case,
Since Elements that connect the GSU transformer(s) to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant are applicable
responsible entity’s to the standard, the loadability for relays applied on these Elements as shown
in the shaded area of Figure 1 (i.e., CB102 and CB103) must be considered. If relay R2 or R3 is set
with an element directional relay R3 located on breaker CB103 at Bus B looking toward Bus A
(i.e., generation plant) is not included in either loadability standard (i.e., PRC-023 or PRC-025)
since it is notthe transmission system (e.g., Buses B, C and D) or are non-directional, the relay
would be affected by increased generator output in response to system disturbances and must
meet the loadability setting criteria described in thisthe standard or . If relay R2 or R3 is set with
an element directional toward the generator (e.g., Bus A), the relay would not be affected by
increased transmission system loadinggenerator output in response to system disturbances;
therefore, the entity would not be required to apply the loadability setting criteria described in
PRC-023. Any protective element set to protect in the direction from Bus A to B is included within
the PRC-025-1 this standard. PRC-025-1 is applicable to Relay R3, for example, if the relay is
applied and set to trip for a reverse element directional toward the Transmission system.

29 of 141

PRC-025-12 – Application Guidelines

30 of 141

Transmission System

PRC-025-12 – Application Guidelines

Bus C

Bus A

UAT
CB101

CB102

CB103
Bus B

CB100

R3

R1

Relays subject
to PRC-025

Transmission System

GSU

R2

Bus D

Figure 1.: Generation exported through a single radial line.
Figure 2

Figure 2 is an example of a single (or set) of generators connected to the Transmission system
through multiple lines that are used exclusively to export energy directly from a BES generating
unit or generating plant to the network. The protective relay R1 on the high-side of the GSU
transformer breaker CB100 is generally applied to provide backup protection to the Transmission
relaying located at Bus A and in some cases Bus B. Under this application, relay R1 would apply
the loadability requirement in PRC-025-12 using an appropriate option for the application from
Table 1 (e.g., Options 14 through 19) for Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant.
The protective relays R2 and R3 located on the incoming source breakers CB102 and CB103 to
the generating plant applies relaying that primarily protects the line from Bus A to B and also
provides backup protection to the transmission relaying at Bus B. In this case, the relay function
that provides line protection would apply the loadability requirement in PRC-025-12 and an
appropriate option for the application from Table 1 (e.g., Options 15a, 15b, 16a, 16b, 18, and 19)
for phase overcurrent supervisory elements (i.e., phase fault detectors) associated with currentbased, communication-assisted schemes (i.e., pilot wire, phase comparison, and line current
31 of 141

PRC-025-12 – Application Guidelines

differential) where the scheme is capable of tripping for loss of communications. The backup
protective function would apply the requirement in the PRC-025-12 standard using an
appropriate option for the application from Table 1 (e.g., Options 14 through 19) for Elements
that connect a GSU transformer to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant.
In this particular case, the applicable responsible entity’s directional relay R4 and R5 located on
the breakers CB104 and CB105, respectively at Bus B looking into the generation plant are not
included in either loadability standard (i.e., PRC-023 or PRC-025) since they are not subject to
the stressed loading requirements described in the standard or by increased transmission system
loading described in PRC-023. Any protective element set to protect in the direction from Bus A
to B is included within the PRC-025-1 standard. PRC-025-1 is applicable to Relay R4 and R5,
for example, if the relays are applied and set to trip for a reverse element directional toward the
Transmission system.
Since Elements that connect the GSU transformer(s) to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant are applicable
to the standard, the loadability for relays applied on these Elements as shown in the shaded area
of Figure 2 (i.e., CB102, CB103, CB104, and CB105) must be considered. If relay R2, R3, R4, or R5
is set with an element directional toward the transmission system (e.g., Buses B, C and D) or are
non-directional, the relay would be affected by increased generator output in response to system
disturbances and must meet the loadability setting criteria described in the standard. If relay R2,
R3, R4, or R5 is set with an element directional toward the generator (e.g., Bus A), the relay would
not be affected by increased generator output in response to system disturbances; therefore,
the entity would not be required to apply the loadability setting criteria described in this
standard.

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Bus C

Bus A
UAT

CB102
CB101

R1

CB104

R2

CB100
GSU

Bus B

R4

CB103
R3

CB105
R5

Relays subject
to PRC-025

Bus D

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PRC-025-12 – Application Guidelines

Bus C

Bus A
UAT

CB102
CB101

R2

CB104
R4

Bus B

GSU

R1

CB103
R3

Relays subject
to PRC-025

CB105
R5

Transmission System

CB100

Bus D

Figure 2.: Generation exported through multiple radial lines.
Figure 3

Figure 3 is example a single (or set) of generators exporting power dispersed through multiple
lines to the Transmission system through a network. The protective relay R1 on the high-side of
the GSU transformer breaker CB100 is generally applied to provide backup protection to the
Transmission relaying located at Bus A and in some cases Bus C or Bus D. Under this application,
relay R1 would apply the applicable loadability requirement in PRC-025-12 using an appropriate
option for the application from Table 1 (e.g., Options 14 through 19) for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy directly
from a BES generating unit or generating plant.
Since the lines from Bus A to Bus C and from Bus A to Bus D are part of the transmission network,
these lines would not be considered as Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant. Therefore, the applicable responsible entity would be responsible for
the load-responsive protective relays R2 and R3 under the PRC-023 standard. The applicable
responsible entity’s loadability relays R4 and R5 located on the breakers CB104 and CB105 at Bus
C and D are also subject to the requirements of the PRC-023 standard.

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Bus C
R4

CB104

Bus A
UAT

CB102
CB101

R2

CB103

CB100
GSU

R1

Relays subject
to PRC-025

R3

CB105
R5

Bus D

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Bus C
R4

CB104

Bus A
UAT

CB102
R2

CB101

CB102

CB100
R3

R1

Relays subject
to PRC-025

Transmission System

GSU

CB105
R5

Bus D

Figure 3.: Generation exported through a network.

Elements utilized in the aggregation of dispersed power producing resources (in some cases
referred to as a “collector system”) consist of the Elements between individual generating units
and the common point of interconnection to the Transmission system.
This standard is also applicable to the UATs that supply station service power to support the online operation of generating units or generating plants. These transformers are variably referred
to as station power, unit auxiliary transformer(s), or station service transformer(s) used to
provide overall auxiliary power to the generator station when the generator is running. Inclusion
of these transformers satisfies a directive in FERC Order No. 733, paragraph 104, which directs
NERC to include in this standard a loadability requirement for relays used for overload protection
of the UAT(s) that supply normal station service for a generating unit. The NERC System
Protection and Control Subcommittee addressed low-side UAT protection in the document called
Unit Auxiliary Transformer Overcurrent Relay Loadability During a Transmission Depressed
Voltage Condition, 19 March 2016.
http://www.nerc.com/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20SPCS%2020
/NERC%20-%20SPCS%20UAT%20-%20FEB_2016_final.pdf.
19

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PRC-025-12 – Application Guidelines

Figure 4

Elements utilized in the aggregation of dispersed power producing resources (in some cases
referred to as a “collector system” or “feeders”) consist of the Elements between individual
generating units and the common point of interconnection to the Transmission system.

To GSU

Included in PRC-25-2
as collector system or
feeders
Low Voltage
Molded Case
Circuit Breaker
Circuit Breaker,
other than
To other DR
Molded Case
Circuit Breaker

To other DR

DR

DR

DR

DR

DR

DR

DR

Figure-4: Elements utilized in the aggregation of dispersed power producing
resources (DR)
Synchronous Generator Performance

When a synchronous generator experiences a depressed voltage, the generator will respond by
increasing its Reactive Power output to support the generator terminal voltage. This operating
condition, known as “field-forcing,” results in the Reactive Power output exceeding the steadystate capability of the generator and may result in operation of generation system loadresponsive protective relays if they are not set to consider this operating condition. The ability of
the generating unit to withstand the increased Reactive Power output during field-forcing is
limited by the field winding thermal withstand capability. The excitation limiter will respond to
begin reducing the level of field-forcing in as little as one second, but may take much longer,
depending on the level of field-forcing given the characteristics and application of the excitation
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system. Since this time may be longer than the time-delay of the generator load-responsive
protective relay, it is important to evaluate the loadability to prevent its operation for this
condition.
The generator bus voltage during field-forcing will be higher than the high-side voltage due to
the voltage drop across the GSU transformer. When the relay voltage is supplied from the
generator bus, it is necessary to assess loadability using the generator bus voltage. The criteria
established within Table 1 are based on 0.85 per unit of Transmission systemthe line nominal
voltage. This voltage was widely observed during the events of August 14, 2003, and was
determined during the analysis of the events to represent a condition from which the System
may have recovered, had not other undesired behavior not occurred.
The dynamic load levels specified in Table 1 under column “Pickup Setting Criteria” are
representative of the maximum expected apparent power during field-forcing with the
Transmission system voltage at 0.85 per unit, for example, at the high-side of the GSU
transformer. These values are based on records from the events leading to the August 14, 2003
blackout, other subsequent System events, and simulations of generating unit responses to
similar conditions. Based on these observations, the specified criteria represent conservative but
achievable levels of Reactive Power output of the generator with a 0.85 per unit high-side voltage
at the point of interconnection.
The dynamic load levels were validated by simulating the response of synchronous generating
units to depressed Transmission system voltages for 67 different generating units. The generating
units selected for the simulations represented a broad range of generating unit and excitation
system characteristics as well as a range of Transmission system interconnection characteristics.
The simulations confirmed, for units operating at or near the maximum Real Power output, that
it is possible to achieve a Reactive Power output of 1.5 times the rated Real Power output when
the Transmission system voltage is depressed to 0.85 per unit. While the simulations
demonstrated that all generating units may not be capable of this level of Reactive Power output,
the simulations confirmed that approximately 20 percent of the units modeled in the simulations
could achieve these levels. On the basis of these levels, Table 1, Options 1a (i.e., 0.95 per unit)
and 1b (i.e., 0.85 per unit), for example, are based on relatively simple, but conservative
calculations of the high-side nominal voltage. In recognition that not all units are capable of
achieving this level of output Option 1c (i.e., simulation) was developed to allow the Generator
Owner, Transmission Owner, or Distribution Provider to simulate the output of a generating unit
when the simple calculation is not adequate to achieve the desired protective relay setting.
Dispersed Generation

This standard is applicable to dispersed generation such as wind farms and solar arrays. The
intent of this standard is to ensure the aggregate facility as defined above will remain on-line
during a system disturbance; therefore, all output load-responsive protective elementsrelays
associated with the facility are included in PRC-025.

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Dispersed power producing resources with aggregate capacity greater than 75 MVA (gross
aggregate nameplate rating) utilizing a system designed primarily for aggregating capacity,
connected at a common point at a voltage of 100 kV or above are included in PRC-025-12. Loadresponsive protective relays that are applied on Elements that connect these individual
generating units through the point of interconnection with the Transmission system are within
the scope of PRC-025-12. For example, feeder overcurrent relays and feeder step-up transformer
overcurrent relays (see Figure 56) are included because these relays are challenged by generator
loadability.
In the case of solar arrays where there are multiple voltages utilized in converting the solar panel
DC output to a 60Hz AC waveform, the “terminal” is defined at the 60Hz AC output of the
inverter-solar panel combination.
Asynchronous Generator Performance

Asynchronous generators, however, do not have excitation systems and will not respond to a
disturbance with the same magnitude of apparent power that a synchronous generator will
respond. Asynchronous generators, though, will support the system during a disturbance.
Inverter-based generators will provide Real Power and Reactive Power (depending on the
installed capability and regional grid code requirements) and may even provide a faster Reactive
Power response than a synchronous generator. The magnitude of this response may slightly
exceed the steady-state capability of the inverter but only for a short duration before a crowbar
functionlimiter functions will activate. Although induction generators will not inherently supply
Reactive Power, induction generator installations may include static and/or dynamic reactive
devices, depending on regional grid code requirements. These devices also may provide Real
Power during a voltage disturbance. Thus, tripping asynchronous generators may exacerbate a
disturbance.
Inverters, including wind turbines (i.e., Types 3 and 4) and photovoltaic solar, are commonly
available with 0.90 power factor capability. This calculates to an apparent power magnitude of
1.11 per unit of rated MW.
Similarly, induction generator installations, including Type 1 and Type 2 wind turbines, often
include static and/or dynamic reactive devices to meet grid code requirements and may have
apparent power output similar to inverter-based installations; therefore, it is appropriate to use
the criteria established in the Table 1 (i.e., Options 4, 5, 6, 10, 11, 12, 17, 18, and 19) for
asynchronous generator installations.
Synchronous Generator Simulation Criteria

The Generator Owner, Transmission Owner, or Distribution Provider who elects a simulation
option to determine the synchronous generator performance on which to base relay settings
may simulate the response of a generator by lowering the Transmission system voltage onat the
remote end of the line or at the high-side of the GSU transformer. (as prescribed by the Table 1
criteria). This can be simulated by means such as modeling the connection of a shunt reactor onat
the Transmission system to lowerremote end of the line or at the GSU transformer high-side to

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lower the voltage to 0.85 per unit prior to field-forcing. The resulting step change in voltage is
similar to the sudden voltage depression observed in parts of the Transmission system on August
14, 2003. The initial condition for the simulation should represent the generator at 100 percent
of the maximum gross Real Power capability in MW as reported to the Transmission Planner. The
simulation is used to determine the Reactive Power and voltage to be usedat the relay location
to calculate relay pickup setting limits. The Reactive Power value obtained by simulation is the
highest simulated level of Reactive Power achieved during field-forcing. The voltage value
obtained by simulation is the simulated voltage coincident with the highest Reactive Power
achieved during field-forcing. These values of Reactive Power and voltage correspond to the
minimum apparent impedance and maximum current observed during field-forcing.
Phase Distance Relay – Directional Toward Transmission System (e.g., 21)

Generator phase distance relays that are directional toward the Transmission system, whether
applied for the purpose of primary or backup GSU transformer protection, external system
backup protection, or both, were noted during analysis of the August 14, 2003 disturbance event
to have unnecessarily or prematurely tripped a number of generating units or generating plants,
contributingwhich contributed to the scope of that disturbance. Specifically, eight generators are
known to have been tripped by this protection function. These options establish criteria for phase
distance relays that are directional toward the Transmission system to help assure that
generators, to the degree possible, will provide System support during disturbances in an effort
to minimize the scope of those disturbances.
The phase distance relay that is directional toward the Transmission system measures impedance
derived from the quotient of generator terminal voltage divided by generator stator current.
Section 4.6.1.1 of IEEE C37.102-2006, “Guide for AC Generator Protection,” describes the
purpose of this protection as follows (emphasis added):
“The distance relay applied for this function is intended to isolate
the generator from the power system for a fault that is not cleared
by the transmission line breakers. In some cases this relay is set
with a very long reach. A condition that causes the generator
voltage regulator to boost generator excitation for a sustained
period may result in the system apparent impedance, as monitored
at the generator terminals, to fall within the operating
characteristics of the distance relay. Generally, a distance relay
setting of 150% to 200% of the generator MVA rating at its rated
power factor has been shown to provide good coordination for
stable swings, system faults involving in-feed, and normal loading
conditions. However, this setting may also result in failure of the
relay to operate for some line faults where the line relays fail to
clear. It is recommended that the setting of these relays be
evaluated between the generator protection engineers and the
system protection engineers to optimize coordination while still
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protecting the turbine generator. Stability studies may be needed
to help determine a set point to optimize protection and
coordination. Modern excitation control systems include
overexcitation limiting and protection devices to protect the
generator field, but the time delay before they reduce excitation is
several seconds. In distance relay applications for which the voltage
regulator action could cause an incorrect trip, consideration should
be given to reducing the reach of the relay and/or coordinating the
tripping time delay with the time delays of the protective devices in
the voltage regulator. Digital multifunction relays equipped with
load encroachment binders [sic] can prevent misoperation for these
conditions. Within its operating zone, the tripping time for this
relay must coordinate with the longest time delay for the phase
distance relays on the transmission lines connected to the
generating substation bus. With the advent of multifunction
generator protection relays, it is becoming more common to use
two-phase distance zones. In this case, the second zone would be
set as previously described. When two zones are applied for backup
protection, the first zone is typically set to see the substation bus
(120% of the GSU transformer). This setting should be checked for
coordination with the zone-1 element on the shortest line off of the
bus. The normal zone-2 time-delay criteria would be used to set the
delay for this element. Alternatively, zone-1 can be used to provide
high-speed protection for phase faults, in addition to the normal
differential protection, in the generator and iso-phase bus with
partial coverage of the GSU transformer. For this application, the
element would typically be set to 50% of the transformer
impedance with little or no intentional time delay. It should be
noted that it is possible that this element can operate on an out-ofstep power swing condition and provide misleading targeting.”
If a mho phase distance relay that is directional toward the Transmission system cannot be set
to maintain reliable fault protection and also meet the criteria in accordance with Table 1, there
may be other methods available to do both, such as application of blinders to the existing relays,
implementation of lenticular characteristic relays, application of offset mho relays, or
implementation of load encroachment characteristics. Some methods are better suited to
improving loadability around a specific operating point, while others improve loadability for a
wider area of potential operating points in the R-X plane. The operating point for a stressed
System condition can vary due to the pre-event system conditions, severity of the initiating event,
and generator characteristics such as Reactive Power capability.
For this reason, it is important to consider the potential implications of revising the shape of the
relay characteristic to obtain a longer relay reach, as this practice may result in a relay
characteristic that overlaps the capability of the generating unit when operating at a Real Power
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PRC-025-12 – Application Guidelines

output level other than 100 percent of the maximum Real Power capability. Overlap of the relay
characteristic and generator capability could result in tripping the generating unit for a loading
condition within the generating unit capability. The examples in Appendix E of the Considerations
for Power Plant and Transmission System Protection Coordination technical reference document
illustrate the potential for, and need to avoid, encroaching on the generating unit capability.
Phase Instantaneous Overcurrent Relay (e.g., 50)

The 50 element is a non-directional overcurrent element that typically has no intentional time
delay. The primary application is for close-in high current faults where high speed operation is
required or preferred. The instantaneous overcurrent elements are subject to the same
loadability issues as the time overcurrent elements referenced in this standard.
Phase Time Overcurrent Relay (e.g., 51)

See section 3.9.Chapter 2 of the Considerations for Power Plant and Transmission System
Protection Coordination technical reference document for a detailed discussion of this protection
function. Note that the Table 1 setting criteria established within the Table 1 options differ from
section 3.9.2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document. Rather than establishing a uniform setting threshold
of 200 percent of the generator MVA rating at rated power factor for all applications, the Table
1 setting criteria are based on the maximum expected generator Real Power output based on
whether the generator operatesis a synchronous or asynchronous unit.
Phase Time Overcurrent Relay – Voltage-Restrained (e.g., 51V-R)

Phase time overcurrent voltage-restrained relays (e.g., 51V-R), which change their sensitivity as
a function of voltage, whether applied for the purpose of primary or backup GSU transformer
protection, for external system phase backup protection, or both, were noted, during analysis of
the August 14, 2003 disturbance event to have unnecessarily or prematurely tripped a number
of generating units or generating plants, contributing to the scope of that disturbance.
Specifically, 20 generators are known to have been tripped by voltage-restrained and voltagecontrolled protection functions together. These protective functions are variably referred to by
IEEE function numbers 51V, 51R, 51VR, 51V/R, 51V-R, or other terms. See section 3.10Chapter 2
of the Considerations for Power Plant and Transmission System Protection Coordination
technical reference document for a detailed discussion of this protection function.
Phase Time Overcurrent Relay – Voltage Controlled (e.g., 51V-C)

Phase time overcurrent voltage-controlled relays (e.g., 51V-C), enabled as a function of voltage,
are variably referred to by IEEE function numbers 51V, 51C, 51VC, 51V/C, 51V-C, or other terms.
See section 3.10Chapter 2 of the Considerations for Power Plant and Transmission System
Protection Coordination technical reference document for a detailed discussion of this protection
function.

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Phase Directional Time Overcurrent Relay – Directional Toward Transmission
System (e.g., 67)

See section 3.9.Chapter 2 of the Considerations for Power Plant and Transmission System
Protection Coordination technical reference document for a detailed discussion of the phase time
overcurrent protection function. The basis for setting directional and non-directional time
overcurrent relays is similar. Note that the Table 1setting setting criteria established within the
Table 1 options differ from section 3.9.2 of the Considerations for Power Plant and Transmission
System Protection Coordination technical reference document. Rather than establishing a
uniform setting threshold of 200 percent of the generator MVA rating at rated power factor for
all applications, the Table 1 setting criteria are based on the maximum expected generator Real
Power output based on whether the generator operatesis a synchronous or asynchronous unit.

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Table 1, Options
Introduction

The margins in the Table 1 options are based on guidance found in the Considerations for Power
Plant and Transmission System Protection Coordination technical reference document. The
generator bus voltage during field-forcing will be higher than the high-side voltage due to the
voltage drop across the GSU transformer. When the relay voltage is supplied from the generator
bus, it is necessary to assess loadability using the generator bus voltage.
Relay Connections

Figures 45 and 56 below illustrate the connections for each of the Table 1 options provided in
PRC-025-12, Attachment 1: Relay Settings, Table 1: Relay Loadability Evaluation Criteria.

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PRC-025-12 – Application Guidelines

2000/1

To 345 kV system
GSU Data
903 MVA
345 kV / 22 kV
X = 12.14%

2000/5
Options 14a and 14b
2000/5

21
21T

GSU

Options 16a and 16b
67

Options 7a, 7b, and 7c

51
67

Options 15a and 15b
25000/5

21
5000/5

51

Options 9a, 9b, and 9c

Options 8a, 8b, and 8c

UAT

200/1
51

To auxiliary
loads

Options 13a and 13b

Options 1a, 1b, and 1c
25000/5

21
51 V-R 51 V-C

Option 3

Generator Nameplate
903 MVA @ 0.85 pf
22 kV

Options 2a, 2b, and 2c

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2000/1

To 345 kV system
GSU Data
903 MVA
345 kV / 22 kV
X = 12.14%

2000/5
Options 14a and 14b
2000/5

21
21T

GSU

Options 16a and 16b
67

Options 7a, 7b, and 7c

50/51

67
Options 15a and 15b
25000/5

21

50/51

5000/5

UAT

Options 9a, 9b, and 9c

Options 8a, 8b, and 8c

200/1
50/51

To auxiliary
loads

Options 13a and 13b

Options 1a, 1b, and 1c
25000/5

21
50/51

51 V-R 51 V-C

Option 3

Generator Nameplate
903 MVA @ 0.85 pf
22 kV

Options 2a, 2b, and 2c

Figure 4.5: Relay Connection for corresponding synchronous options.

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PRC-025-12 – Application Guidelines

To 345 kV system

2000/1

GSU Data
150 MVA
346.5 kV / 22 kV
X = 12.14%

300/5
Option 17
300/5

21
21T

Option 19

67

GSU

Option 10

51

Option 12
67

Option 18

5000/5

Option 11
21
5000/5

200/1
Aggregated
Mvar
15 Mvar

51
UAT

To auxiliary
loads

51
Options 13a and 13b
22 kV / 12 kV

Aggregated MVA
3-40 MVA @ 0.85 pf
1-5 Mvar

51
51

Options
4, 5, & 6
21
51 V-C 51 V-R

21

51

5000/5

5000/5
Option 5

Option 5

21

5000/5

Options
4, 5, & 6 51 V-R

51 V-C 51 V-R

51 V-C

5 Mvar

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To 345 kV system

2000/1

GSU Data
150 MVA
346.5 kV / 22 kV
X = 12.14%

300/5
Option 17
300/5

21
21T

Option 19

67

GSU

Option 10

50/51

Option 12
67

Option 18

5000/5

Option 11

200/1

21

50/51

5000/5

UAT

Aggregated
Mvar
15 Mvar

To auxiliary
loads

50/51

Options 13a and 13b
22 kV / 12 kV
Aggregated MVA
3-40 MVA @ 0.85 pf
1-5 Mvar

50/51

50/51

Options
4, 5, & 6
21
51 V-C 51 V-R

21

50/51

5000/5

5000/5
Option 5

Option 5

21

5000/5

Options
4, 5, & 6 51 V-R

51 V-C 51 V-R

51 V-C

5 Mvar

Figure 5.6: Relay Connection for corresponding asynchronous options including
inverter-based installations.
Synchronous Generators Phase Distance Relay – Directional Toward Transmission
System (e.g., 21) (Options 1a, 1b, and 1c)

Table 1, Options 1a, 1b, and 1c, are provided for assessing loadability for synchronous generators
applying phase distance relays that are directional toward the Transmission system. These
margins are based on guidance found in section 3.1Chapter 2 of the Considerations for Power
Plant and Transmission System Protection Coordination technical reference document.
Option 1a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is the simplest

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calculation that approximatesis a straightforward way to approximate the stressed system
conditions.
Option 1b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on a 0.85 per unit nominal voltage at the high-side terminals of the GSU
transformer and accounts foras well as the turns ratio and impedance. The actual generator bus
voltage may be higher depending on the GSU transformer impedance and the actual Reactive
Power achieved. This calculation is a more involved, morein-depth and precise method for setting
of the impedance element than Option 1a.
Option 1c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more
involved, more precise setting of the impedance element overall.
For Options 1a and 1b, the impedance element isshall be set less than the calculated impedance
derived from 115percent115 percent of both: the Real Power output of 100 percent of the
maximum gross MW capability reported to the Transmission Planner, and the Reactive Power
output that equates to 150 percent of the MW value, derived from the generator nameplate
MVA rating at rated power factor.
For Option 1c, the impedance element isshall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the maximum gross MW
capability reported to the Transmission Planner, and the Reactive Power output that equates to
100 percent of the maximum gross Mvar output during field-forcing as determined by simulation.
Synchronous Generators Phase Time Overcurrent Relay – (e.g., 50, 51, or 51V-R –
Voltage -Restrained (51V-R) (Options 2a, 2b, and 2c)

Table 1, Options 2a, 2b, and 2c, are provided for assessing loadability for synchronous generators
applying phase time overcurrent relays which change their sensitivity as a function of(e.g., 50, 51,
or 51V-R – voltage (“voltage-restrained”).). These margins are based on guidance found in section
3.10Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document.
Option 2a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is the simplest
calculation that approximatesis a straightforward way to approximate the stressed system
conditions.
Option 2b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
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PRC-025-12 – Application Guidelines

is calculated based on a 0.85 per unit nominal voltage at the high-side terminals of the GSU
transformer and accountsas well as for the turns ratio and impedance. The actual generator bus
voltage may be higher depending on the GSU transformer impedance and the actual Reactive
Power achieved. This calculation is a more involved, morein-depth and precise method for setting
of the overcurrent element than Option 2a.
Option 2c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more
involved, more precise setting of the overcurrent element overall.
For Options 2a and 2b, the overcurrent element isshall be set greater than 115 percent of the
calculated current derived from both: the Real Power output of 100 percent of the maximum
gross MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 150 percent of the MW value, derived from the generator nameplate MVA rating at
rated power factor.
For Option 2c, the overcurrent element isshall be set greater than the calculated current derived
from 115 percent of both: the Real Power output of 100 percent of the maximum gross MW
capability reported to the Transmission Planner, and the Reactive Power output that equates to
100 percent of the maximum gross Mvar output during field-forcing as determined by simulation.
Synchronous Generators Phase Time Overcurrent Relay – Voltage Controlled (e.g.,
51V-C) (Option 3)

Table 1, Option 3, is provided for assessing loadability for synchronous generators applying phase
time overcurrent relays which are enabled as a function of voltage (“voltage-controlled”). These
margins are based on guidance found in section 3.10Chapter 2 of the Considerations for Power
Plant and Transmission System Protection Coordination technical reference document.
Option 3 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation
that approximates the stressed system conditions.
For Option 3, the voltage control setting isshall be set less than 75 percent of the calculated
generator bus voltage. The voltage setting must be set such that the function (e.g., 51V-C) will
not trip under extreme emergency conditions as the time overcurrent function will be set less
than generator full load current. Relays enabled as a function of voltage are indifferent as to the
current setting, and this option simply requires that the relays not respond for the depressed
voltage.

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Asynchronous Generators Phase Distance Relay – Directional Toward Transmission
System (e.g., 21) (Option 4)

Table 1, Option 4 is provided for assessing loadability for asynchronous generators applying
phase distance relays that are directional toward the Transmission system. These margins are
based on guidance found in section 3.1Chapter 2 of the Considerations for Power Plant and
Transmission System Protection Coordination technical reference document.

Option 4 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation
that approximates the stressed system conditions.
Since the relay voltage is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant. Therefore, the generator bus voltage can be conservatively
estimated by reflecting the high-side nominal voltage to the generator-side based on the GSU
transformer’s turns ratio.
For Option 4, the impedance element shall be set less than the calculated impedance derived
from 130 percent of the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Asynchronous Generators Phase Overcurrent Relay – (e.g., 50, 51, or 51V-R – Voltage
Restrained) (Options 5a and 5b)

Table 1, Option 5a is provided for assessing loadability for asynchronous generators applying
phase overcurrent relays (e.g., 50, 51, or 51V-R – voltage-restrained). These margins are based
on guidance found in Chapter 2 of the Considerations for Power Plant and Transmission System
Protection Coordination technical reference document.
Option 5a calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation that
approximates the stressed system conditions.
Since the relay voltage is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant. Therefore, the generator bus voltage can be conservatively

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estimated by reflecting the high-side nominal voltage to the generator-side based on the GSU
transformer’s turns ratio.
For Option 4, the impedance element is
For Option 5a, the overcurrent element shall be set less than the calculated impedance derived
from 130 percent of the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Asynchronous Generators Phase Time Overcurrent Relay – Voltage-Restrained
(51V-R) (Option 5)
Table 1, Option 5 is provided for assessing loadability for asynchronous generators applying
phase time overcurrent relays which change their sensitivity as a function of voltage (“voltagerestrained”). These margins are based on guidance found in section 3.10 of the Power Plant and
Transmission System Protection Coordination technical reference document.
Option 5 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on the
high-side terminals of the GSU transformer. The generator bus voltage is calculated by multiplying
a 1.0 per unit nominal voltage at the high-side terminals of the GSU transformer times the GSU
transformer turns ratio (excluding the impedance). This is a simple calculation that approximates
the stressed system conditions.
Since the relay voltage is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant. Therefore, the generator bus voltage can be conservatively
estimated by reflecting the high-side nominal voltage to the generator-side based on the GSU
transformer’s turns ratio.
For Option 5, the overcurrent element is set greater than 130 percent of the calculated current
derived from the maximum aggregate nameplate MVA output at rated power factor including
the Mvar output of any static or dynamic Reactive Power devices. This is determined by summing
the total MW and Mvar capability of the generation equipment behind the relay and any static
or dynamic Reactive Power devices that contribute to the power flow through the relay.
For Option 5b, the overcurrent element shall be set to exceed the maximum capability of the
asynchronous resource and applicable equipment (e.g., windings, power electronics, cables, or
bus). This is determined by summing the total current capability of the generation equipment
behind the overcurrent element and any static or dynamic Reactive Power devices that
contribute to the power flow through the overcurrent element. The lower tolerance of the
overcurrent element tripping characteristic shall be set to not infringe upon the resource
capability (including the Mvar output of the resource and any static or dynamic reactive power
devices). Figure A of PRC-025-2 illustrates that the overcurrent element does not infringe upon
the asynchronous resource capability. The upper hashed area of Figure A represents Exclusion 7.

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Asynchronous Generator Phase Time Overcurrent Relays – Voltage Controlled (e.g.,
51V-C) (Option 6)

Table 1, Option 6, is provided for assessing loadability for asynchronous generators applying
phase time overcurrent relays which are enabled as a function of voltage (“voltage-controlled”).
These margins are based on guidance found in section 3.10Chapter 2 of the Considerations for
Power Plant and Transmission System Protection Coordination technical reference document.
Option 6 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation
that approximates the stressed system conditions.
For Option 6, the voltage control setting isshall be set less than 75 percent of the calculated
generator bus voltage. The voltage setting must be set such that the function (e.g., 51V-C) will
not trip under extreme emergency conditions as the time overcurrent function will be set less
than generator full load current. Relays enabled as a function of voltage are indifferent as to the
current setting, and this option simply requires that the relays not respond for the depressed
voltage.
Generator Step-up Transformer (Synchronous Generators) Phase Distance Relays –
Directional Toward Transmission System (e.g., 21) (Options 7a, 7b, and 7c)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. These margins
are based on guidance found in Chapter 2 of the Considerations for Power Plant and Transmission
System Protection Coordination technical reference document.
Table 1, Options 7a, 7b, and 7c, are provided for assessing loadability of phase distance relays
that are directional toward the Transmission system and connected to the generator-side of the
GSU transformer of a synchronous generator. For applications where the relay is connected on
the high-side of the GSU transformer, use Option 14.
Option 7a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Option 7b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on the 0.85 per unit nominal voltage, at the high-side terminals of the GSU
transformer, as well as the turns ratio and impedance. The actual generator bus voltage may be
higher depending on the GSU transformer impedance and the actual Reactive Power achieved.

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This calculation is a more in-depth and precise method for setting the impedance element than
Option 7a.
Option 7c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more indepth and precise method for setting the impedance element than Options 7a or 7b.
For Options 7a and 7b, the impedance element shall be set less than the calculated impedance
derived from 115 percent of both: the Real Power output of 100 percent of the aggregate
generation MW capability reported to the Transmission Planner, and the Reactive Power output
that equates to 150 percent of the aggregate generation MW value (derived from the generator
nameplate MVA rating at rated power factor).
For Option 7c, the impedance element shall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation.
Generator Step-up Transformer (Synchronous Generators) Phase Overcurrent Relay
(e.g., 50 or 51) (Options 8a, 8b and 8c)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. These margins
are based on guidance found in section 3.Note that the setting criteria established within the Table
1 of theoptions differ from Chapter 2 of the Considerations for Power Plant and Transmission
System Protection Coordination technical reference document. Rather than establishing a
uniform loadability threshold of 200 percent of the generator nameplate MVA rating at rated
power factor for all applications, the setting criteria are based on the maximum expected
generator output.
Table 1, Options 7a, 7b8a, 8b, and 7c8c, are provided for assessing loadability for GSU
transformers applyingof phase distanceovercurrent relays that are directional toward the
Transmission system on synchronous generators that are connected to the generator-side of the
GSU transformer of a synchronous generator. For applications where the relay is connected on
the high-side of the GSU transformer, use Option 15.

Option 8a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. 14.
Option 7a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is the simplest

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calculation that approximatesis a straightforward way to approximate the stressed system
conditions.
Option 8b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer.
Option 7b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on athe 0.85 per unit nominal voltage, at the high-side terminals of the GSU
transformer and accounts for , as well as the turns ratio and impedance. The actual generator bus
voltage may be higher depending on the GSU transformer impedance and the actual Reactive
Power achieved. The actual generator bus voltage may be higher depending on the GSU
transformer impedance and the actual Reactive Power achieved. This calculation is a more
involved, morein-depth and precise method for setting of the impedanceovercurrent element
than Option 7a8a.
Option 7c8c simulates the generator bus voltage coincident with the highest Reactive Power
output achieved during field-forcing. This output is in response to a 0.85 per unit nominal
voltage on the high-side terminals of the GSU transformer prior to field-forcing. Using
simulation is a more involved, more in-depth and precise method for setting of the overcurrent
element overall.
Forthan Options 7a8a or 8b.
For Options 8a and 7b8b, the impedanceovercurrent element isshall be set lessgreater than 115
percent of the calculated impedancecurrent derived from 115 percent of: the Real Power output
of 100 percent of the aggregate generation MW capability reported to the Transmission Planner,
and Reactive Power output that equates to 150 percent of the aggregate generation MW value,
derived from the generator nameplate MVA rating at rated power factor.both
For Option 7c, the impedance element is set less than the calculated impedance derived from 115
percent of: the Real Power output of 100 percent of the aggregate generation MW capability
reported to the Transmission Planner, and the Reactive Power output that equates to 150
percent of the aggregate generation MW value (derived from the generator nameplate MVA
rating at rated power factor).
For Option 8c, the overcurrent element shall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation.

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Generator Step-up Transformer (Synchronous Generators) Phase TimeDirectional
Overcurrent Relay (51– Directional Toward Transmission System (e.g., 67) (Options
8a, 8b9a, 9b and 8c9c)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the
setting criteria established within thesethe Table 1 options differ from section 3.9.Chapter 2 of
the Considerations for Power Plant and Transmission System Protection Coordination technical
reference document. Rather than establishing a uniform settingloadability threshold of 200
percent of the generator nameplate MVA rating at rated power factor for all applications, the
setting criteria are based on the maximum expected generator output.
Table 1, Options 8a, 8b9a, 9b, and 8c9c, are provided for assessing loadability for GSU
transformers applying phase time overcurrent relays on synchronous generators that are connected
to the generator-side of the GSU transformer of a synchronous generator. Where the relay is
connected on the high-side of the GSU transformer, use Option 15.
Option 8a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying a 0.95 per unit nominal voltage at the high-side terminals of the GSU transformer
times the GSU transformer turns ratio (excluding the impedance). This is the simplest calculation
that approximates the stressed system conditions.
Option 8b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU
transformer is calculated based on a 0.85 per unit nominal voltage at the high-side terminals of
the GSU transformer and accounts for the turns ratio and impedance. The actual generator bus
voltage may be higher depending on the GSU transformer impedance and the actual Reactive
Power achieved. This calculation is a more involved, more precise setting of the impedance
element than Option 8a.
Option 8c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing in response to a 0.85 per unit nominal voltage on the high-side
terminals of the GSU transformer prior to field-forcing. Using simulation is a more involved, more
precise setting of the overcurrent element overall.of
For Options 8a and 8b, the overcurrent element is set greater than 115 percent of the calculated
current derived from: the Real Power output of 100 percent of the aggregate generation MW
capability reported to the Transmission Planner, and Reactive Power output that equates to 150
percent of the aggregate generation MW value, derived from the generator nameplate MVA rating
at rated power factor.
For Option 8c, the overcurrent element is set greater than 115 percent of the calculated current
derived from: the Real Power output of 100 percent of the aggregate generation MW capability
reported to the Transmission Planner, and Reactive Power output that equates to 100 percent of
the maximum gross Mvar output during field-forcing as determined by simulation.

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Generator Step-up Transformer (Synchronous Generators) Phase Directional
Time Overcurrent Relay – Directional Toward Transmission System (67) (Options
9a, 9b and 9c)
The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the
setting criteria established within these options differ from section 3.9.2 of the Power Plant and
Transmission System Protection Coordination technical reference document. Rather than
establishing a uniform setting threshold of 200 percent of the generator nameplate MVA rating at
rated power factor for all applications, the setting criteria are based on the maximum expected
generator output.
Table 1, Options 9a, 9b, and 9c, are provided for assessing loadability for GSU transformers
applying phase directional time overcurrent relays directional toward the Transmission System
that are connected to the generator-side of the GSU transformer of a synchronous generator.
For applications where the relay is connected on the high-side of the GSU transformer, use
Option 16.
Option 9a calculates a generator bus voltage corresponding to 0.95 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 0.95 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is the simplest
calculation that approximatesis a straightforward way to approximate the stressed system
conditions.
Option 9b calculates the generator bus voltage corresponding to 0.85 per unit nominal voltage
on the high-side terminals of the GSU transformer. The voltage drop across the GSU transformer
is calculated based on athe 0.85 per unit nominal voltage, at the high-side terminals of the GSU
transformer and accounts for, as well as the turns ratio and impedance. The actual generator bus
voltage may be higher depending on the GSU transformer impedance and the actual Reactive
Power achieved. This calculation is a more involved, morein-depth and precise method for setting
of the impedanceovercurrent element than Option 9a.
Option 9c simulates the generator bus voltage coincident with the highest Reactive Power output
achieved during field-forcing. This output is in response to a 0.85 per unit nominal voltage on the
high-side terminals of the GSU transformer prior to field-forcing. Using simulation is a more
involved, morein-depth and precise method for setting of the overcurrent element overallthan
Options 9a or 9b.
For Options 9a and 9b, the overcurrent element isshall be set greater than 115 percent of the
calculated current derived from both: the Real Power output of 100 percent of the aggregate
generation MW capability reported to the Transmission Planner, and the Reactive Power output
that equates to 150 percent of the aggregate generation MW value, (derived from the generator
nameplate MVA rating at rated power factor.).

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For Option 9c, the overcurrent element isshall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation.
Generator Step-up Transformer (Asynchronous Generators) Phase Distance Relay –
Directional Toward Transmission System (e.g., 21) (Option 10)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Table 1, Option
10 is provided for assessing loadability for GSU transformers applying phase distance relays that
are directional toward the Transmission System that are connected to the generator-side of the
GSU transformer of an asynchronous generator. These margins are based on guidance found in
section 3.1Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document. For applications where the relay is connected on the
high-side of the GSU transformer, use Option 17.
Option 10 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation
that approximatesis a straightforward way to approximate the stressed system conditions.
Since the relay voltage is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Since the relay voltage is supplied from the generator bus, it is
necessary to assess loadability using the generator-side voltage. Asynchronous generators do not
produce as much Reactive Power as synchronous generators; hence the voltage drop due to
Reactive Power flow through the GSU transformer is not as significant. Therefore, the generator
bus voltage can be conservatively estimated by reflecting the high-side nominal voltage to the
generator-side based on the GSU transformer’s turns ratio.
For Option 10, the impedance element isshall be set less than the calculated impedance, derived
from 130 percent of the maximum aggregate nameplate MVA output at rated power factor,
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Generator Step-up Transformer (Asynchronous Generators) Phase Time Overcurrent
Relay (e.g., 50 or 51) (Option 11)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the
setting criteria established within these options differ from section 3.9.2 of the Power Plant and
Transmission System Protection Coordination technical reference document. Rather than
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establishing a uniform setting threshold of 200 percent of the generator nameplate MVA rating at
rated power factor for all applications, the setting criteria are based on the maximum expected
generator output.
Table 1, Option 11 is provided for assessing loadability for GSU transformers applying phase
time overcurrent relays on asynchronous generators that are connected to the generator-side of
the GSU transformer. Where the relay is connected on the high-side of the GSU transformer, use
Option 18.
the Table 1 options differ from Chapter 2 of the Considerations forOption 11 calculates the
generator bus voltage corresponding to 1.0 per unit nominal voltage on the high-side terminals
of the GSU transformer. The generator bus voltage is calculated by multiplying a 1.0 per unit
nominal voltage at the high-side terminals of the GSU transformer times the GSU transformer
turns ratio (excluding the impedance). This is a simple calculation that approximates the stressed
system conditions.
Since the relay current is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant. Therefore, the generator bus voltage can be conservatively
estimated by reflecting the high-side nominal voltage to the generator-side based on the GSU
transformer’s turns ratio.
For Option 11, the overcurrent element is set greater than 130 percent of the calculated current
derived from the maximum aggregate nameplate MVA output at rated power factor including the
Mvar output of any static or dynamic Reactive Power devices. This is determined by summing the
total MW and Mvar capability of the generation equipment behind the relay and any static or
dynamic Reactive Power devices that contribute to the power flow through the relay.
Generator Step-up Transformer (Asynchronous Generators) Phase Directional
Time Overcurrent Relay – Directional Toward Transmission System (67) (Option
12)
The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers. Note that the
setting criteria established within these options differ from section 3.9.2 of the Power Plant and
Transmission System Protection Coordination technical reference document. Rather than
establishing a uniform settingloadability threshold of 200 percent of the generator nameplate
MVA rating at rated power factor for all applications, the setting criteria are based on the
maximum expected generator output.
Table 1, Option 1211 is provided for assessing loadability of phase overcurrent relays that are
connected to the generator-side of the GSU transformer of an asynchronous generator. For
applications where the relay is connected on the high-side of the GSU transformer, use Option
18.

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Option 11 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying the 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer,
by the GSU transformer turns ratio (excluding the impedance). This calculation is a
straightforward way to approximate the stressed system conditions.
Since the relay current is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; hence the voltage drop due to Reactive Power flow through
the GSU transformer is not as significant. Therefore, the generator bus voltage can be
conservatively estimated by reflecting the high-side nominal voltage to the generator-side based
on the GSU transformer’s turns ratio.
For Option 11, the overcurrent element shall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor,
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
Generator Step-up Transformer (Asynchronous Generators) Phase Directional
Overcurrent Relay – Directional Toward Transmission System (e.g., 67) (Option 12)

The Federal Energy Regulatory Commission, in FERC Order No. 733, paragraph 104, directs that
NERC address relay loadability for protective relays applied on GSU transformers applying. Note
that the setting criteria established within the Table 1 options differ from Chapter 2 of the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document. Rather than establishing a uniform loadability threshold of 200 percent of
the generator nameplate MVA rating at rated power factor for all applications, the setting criteria
are based on the maximum expected generator output.
Table 1, Option 12 is provided for assessing loadability of phase directional time overcurrent
relays directional toward the Transmission System on asynchronous generators that are
connected to the generator-side of the GSU transformer of an asynchronous generator. For
applications where the relay is connected on the high-side of the GSU transformer, use Option
19.
Option 12 calculates the generator bus voltage corresponding to 1.0 per unit nominal voltage on
the high-side terminals of the GSU transformer. The generator bus voltage is calculated by
multiplying athe 1.0 per unit nominal voltage, at the high-side terminals of the GSU transformer
times, by the GSU transformer turns ratio (excluding the impedance). This is a simple calculation
that approximatesis a straightforward way to approximate the stressed system conditions.
Since the relay current is supplied from the generator bus, it is necessary to assess loadability
using the generator-side voltage. Asynchronous generators do not produce as much Reactive

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Power as synchronous generators; hence the voltage drop due to Reactive Power flow through
the GSU transformer is not as significant. Therefore, the generator bus voltage can be
conservatively estimated by reflecting the high-side nominal voltage to the generator-side based
on the GSU transformer’s turns ratio.
For Option 12, the overcurrent element isshall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor,
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay.
This is determined by summing the total MW and Mvar capability of the generation equipment
behind the relay and any static or dynamic Reactive Power devices that contribute to the power
flow through the relay.
Unit Auxiliary Transformers Phase Time Overcurrent Relay (e.g., 50 or 51) (Options
13a and 13b)

In FERC Order No. 733, paragraph 104, directs NERC to include in this standard a loadability
requirement for relays used for overload protection of the UAT that supply normal station service
for a generating unit. For the purposes of this standard, UATs provide the overall station power
to support the unit at its maximum gross operation.

Table 1, Options 13a and 13b provide two options for addressing phase time overcurrent relaying
applied at the high-side of UATs. The transformer high-side winding may be directly connected
to the transmission grid or at the generator isolated phase bus (IPB) or iso-phase bus. Phase time
overcurrent relays applied at the high-side of the UAT that remove the transformer from service
resulting in an immediate (e.g., via lockout or auxiliary tripping relay operation) or consequential
trip of the associated generator are to be compliant with the relay setting criteria in this standard.
Due to the complexity of the application of low-side overload relays for single or multi-winding
transformers, phase time overcurrent relaying applied toat the low-side of the UAT are not
addressed in this standard. The NERC System Protection and Control Subcommittee addressed
low-side UAT protection in the document called “Unit Auxiliary Transformer Overcurrent Relay
Loadability During a Transmission Depressed Voltage Condition, March 2016.” These relays
include, but are not limited to, a relay used for arc flash protection, feeder protection relays,
breaker failure, and relays whose operation may result in a generator runback. Although the UAT
is not directly in the output path from the generator to the Transmission system, it is an essential
component for operation of the generating unit or plant.

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Refer to the Figures 67 and 78 below for example configurations:

Transformers
Covered by this
standard
Transfer
Switch

Unit Auxiliary
Transformers

System

Station
Loads

System

G
GSU

Figure-6 – 7: Auxiliary Power System (independent from generator).)

Unit Auxiliary
Transformer

Transformer
Covered by this
standard

GSU
Station
Loads

G

System

Figure-7 – 8: Typical auxiliary power system for generation units or plants.

The UATs supplying power to the unit or plant electrical auxiliaries are sized to accommodate the
maximum expected overall UAT load demand at the highest generator output. Although the
transformer nameplate MVA size normally includes capacity for future loads as well as capacity

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for starting of large induction motors on the original unit or plant design, the nameplate MVA
capacity of the transformer may be near full load.
Because of the various design and loading characteristics of UATs, two options (i.e., 13a and 13b)
are provided to accommodate an entity’s protection philosophy while preventing the UAT
transformer phase time overcurrent relays from operating during the dynamic conditions
anticipated by this standard.
Options 13a and 13b are based on the transformer bus voltage corresponding to 1.0 per unit
nominal voltage on the high-side winding of the UAT.
For Option 13a, the overcurrent element shall be set greater than 150 percent of the calculated
current derived from the UAT maximum nameplate MVA rating. This is a simple calculation that
approximates the stressed system conditions.
For Option 13b, the overcurrent element shall be set greater than 150 percent of the UAT
measured current at the generator maximum gross MW capability reported to the Transmission
Planner. This allows for a reduced setting pickup compared to Option 13a and the entity’s relay
setting philosophy of the applicable entity. This is a more involved calculation that approximates
the stressed system conditions by allowing the entity to consider the actual load placed on the
UAT based on the generator’s maximum gross MW capability reported to the Transmission
Planner.
The performance of the UAT loads during stressed system conditions (i.e., depressed voltages) is
very difficult to determine. Rather than requiring responsible entities to determine the response
of UAT loads to depressed voltage, the technical experts writing the standard elected to increase
the margin to 150 percent from that used elsewhere in this standard (e.g., 115 percent) and use
a generator bus voltage of 1.0 per unit. A minimum pickupsetting current based on 150 percent
of maximum transformer nameplate MVA rating at 1.0 per unit generator bus voltage will provide
adequate transformer protection based on IEEE C37.91 at full load conditions while providing
sufficient relay loadability to prevent a trip of the UAT, and subsequent unit trip, due to increased
UAT load current during stressed system voltage conditions. Even if the UAT is equipped with an
automatic tap changer, the tap changer may not respond quickly enough for the conditions
anticipated within this standard, and thus shall not be used to reduce this margin.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Synchronous Generators) Phase Distance Relays – Directional Toward Transmission
System (e.g., 21) (Options 14a and 14b)

Relays applied on Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
These margins are based on guidance found in section 3.1Chapter 2 of the Considerations for
Power Plant and Transmission System Protection Coordination technical reference document.

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Relays applied on the high-side of the GSU transformer respond to the same quantities as the
relays connected on theapplied at the remote end of the line for Elements that connect a GSU
transformer to the Transmission system that are used exclusively to export energy directly from
a BES generating unit or generating plant, thus Option 14 is used for these relays as well.
Table 1, Options 14a and 14b, establish criteria for phase distance relays directional toward the
Transmission system to prevent Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or
generating plant from operatingtripping during the dynamic conditions anticipated by this
standard. The stressed system conditions, anticipated by Option 14a reflects a 0.85 per unit
Transmission systemof the line nominal voltage; therefore, establishing that the impedance value
used for applying the Elements that connect a GSU transformer to the Transmission system that
are used exclusively to export energy directly from a BES generating unit or generating plant
phase distance relays that are directional toward the Transmission system be calculated from the
apparent power addressed within the criteria, with application of a 0.85 per unit Transmission
systemof the line nominal voltage at the relay location. Consideration of the voltage drop across
the GSU transformer is not necessary. Option 14b simulates the line voltage coincident with the
highest Reactive Power output achieved during field-forcing in response to a 0.85 per unit
nominal voltage on the high-side terminals of the GSU transformer prior to field-forcing.line
nominal voltage at the remote end of the line prior to field-forcing. Using a 0.85 per unit line
nominal voltage at the remote end of the line is representative of the lowest voltage expected
during a depressed voltage condition on Elements that are used exclusively to export energy
directly from a BES generating unit or generating plant to the Transmission system. Using
simulation is a more involved, more precise setting of the overcurrent element overall.
For Option 14a, the impedance element isshall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 120 percent of the aggregate generation MW value, derived from the generator
nameplate MVA rating at rated power factor. This Reactive Power value differs from the 150
percent multiplier used in other applicationapplications to account for the Reactive Power losses
in the GSU transformer. This is a simple calculation that approximates the stressed system
conditions.
For Option 14b, the impedance element isshall be set less than the calculated impedance derived
from 115 percent of both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation. Option 14b uses the simulated line voltage at the relay location coincident with the
highest Reactive Power output achieved during field-forcing in response to a 0.85 per unit of the
line nominal voltage at the remote end of the line prior to field-forcing. Using simulation is a
more involved, more precise setting of the impedance element overall.

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Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Synchronous Generators) Phase Time Overcurrent Relay (e.g., 50 or 51) (Options
15a and 15b)

Relays applied on Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
Note that the setting criteria established within thesethe Table 1 options differ from section
3.9.Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document. Rather than establishing a uniform setting threshold
of 200 percent of the generator nameplate MVA rating at rated power factor for all applications,
the setting criteria are based on the maximum expected generator output. Relays applied on the
high-side of the GSU transformer respond to the same quantities as the relays connected on
theapplied at the remote end of the line for Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant, thus Option 15 is used for these relays as well.
Table 1, Options 15a and 15b, establish criteria for phase instantaneous and/or time overcurrent
relays to prevent Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant from
operatingtripping during the dynamic conditions anticipated by this standard. The stressed
system conditions, anticipated by Option 15a reflects a 0.85 per unit Transmission systemof the
line nominal voltage at the relay location; therefore, establishing that the current value used for
applying the Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant phase
instantaneous and/or time overcurrent relays be calculated from the apparent power addressed
within the criteria, with application of a 0.85 per unit Transmission systemof the line nominal
voltage at the relay location. Consideration of the voltage drop across the GSU transformer is not
necessary. Option 15b simulates the line voltage coincident with the highest Reactive Power
output achieved during field-forcing in response to a 0.85 per unit nominal voltage on the highside terminals of the GSU transformer prior to field-forcing.line nominal voltage at the remote
end of the line prior to field-forcing. Using a 0.85 per unit line nominal voltage at the remote end
of the line is representative of the lowest voltage expected during a depressed voltage condition
on Elements that are used exclusively to export energy directly from a BES generating unit or
generating plant to the Transmission system. Using simulation is a more involved, more precise
setting of the overcurrent element overall.
For Option 15a, the overcurrent element isshall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 120 percent of the aggregate generation MW value, derived from the generator
nameplate MVA rating at rated power factor. This Reactive Power value differs from the 150
percent multiplier used in other applicationapplications to account for the Reactive Power losses

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in the GSU transformer. This is a simple calculation that approximates the stressed system
conditions.
For Option 15b, the overcurrent element isshall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation. Option 15b uses the simulated line voltage at the relay location coincident with the
highest Reactive Power output achieved during field-forcing in response to a 0.85 per unit of the
line nominal voltage at the remote end of the line prior to field-forcing. Using simulation is a
more involved, more precise setting of the overcurrent element overall.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Synchronous Generators) Phase Directional Time Overcurrent Relay – Directional
Toward Transmission System (e.g., 67) (Options 16a and 16b)

Relays applied on Elements that connect a GSU transformer to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant are
challenged by loading conditions similar to relays applied on generators and GSU transformers.
Note that the setting criteria established within thesethe Table 1 options differ from section
3.9.Chapter 2 of the Considerations for Power Plant and Transmission System Protection
Coordination technical reference document. Rather than establishing a uniform setting threshold
of 200 percent of the generator nameplate MVA rating at rated power factor for all applications,
the setting criteria are based on the maximum expected generator output. Relays applied on the
high-side of the GSU transformer respond to the same quantities as the relays connected on
theapplied at the remote end of the line for Elements that connect a GSU transformer to the
Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant, thus Option 16 is used for these relays as well.
Table 1, Options 16a and 16b, establish criteria for phase directional time overcurrent relays that
are directional toward the Transmission system to prevent Elements that connect a GSU
transformer to the Transmission system that are used exclusively to export energy directly from
a BES generating unit or generating plant from operatingtripping during the dynamic conditions
anticipated by this standard. The stressed system conditions, anticipated by Option 16a reflects
a 0.85 per unit Transmission systemof the line nominal voltage at the relay location; therefore,
establishing that the current value used for applying the interconnection Facilities phase
directional time overcurrent relays be calculated from the apparent power addressed within the
criteria, with application of a 0.85 per unit Transmission systemof the line nominal voltage at the
relay location. Consideration of the voltage drop across the GSU transformer is not necessary.
Option 16b simulates the line voltage coincident with the highest Reactive Power output
achieved during field-forcing in response to a 0.85 per unit nominal voltage on the high-side
terminals of the GSU transformer prior to field-forcing.line nominal voltage at the remote end of
the line prior to field-forcing. Using a 0.85 per unit line nominal voltage at the remote end of the
line is representative of the lowest voltage expected during a depressed voltage condition on

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Elements that are used exclusively to export energy directly from a BES generating unit or
generating plant to the Transmission system. Using simulation is a more involved, more precise
setting of the overcurrent element overall.
For Option 16a, the overcurrent element isshall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 120 percent of the aggregate generation MW value, derived from the generator
nameplate MVA rating at rated power factor. This Reactive Power value differs from the 150
percent multiplier used in other applicationapplications to account for the Reactive Power losses
in the GSU transformer. This is a simple calculation that approximates the stressed system
conditions.
For Option 16b, the overcurrent element isshall be set greater than 115 percent of the calculated
current derived from both: the Real Power output of 100 percent of the aggregate generation
MW capability reported to the Transmission Planner, and the Reactive Power output that
equates to 100 percent of the maximum gross Mvar output during field-forcing as determined by
simulation. Option 16b uses the simulated line voltage at the relay location coincident with the
highest Reactive Power output achieved during field-forcing in response to a 0.85 per unit of the
line nominal voltage at the remote end of the line prior to field-forcing. Using simulation is a
more involved, more precise setting of the overcurrent element overall.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Asynchronous Generators) Phase Distance Relay – Directional Toward Transmission
System (e.g., 21) (Option 17)

Relays applied oninstalled on the high-side of the GSU transformer, including relays installed on
the remote end of the line, for Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or
generating plant are challenged by loading conditions similar to relays applied on generators and
GSU transformers. These margins are based on guidance found in section 3.1Chapter 2 of the
Considerations for Power Plant and Transmission System Protection Coordination technical
reference document.

Table 1, Option 17 establishes criteria for phase distance relays that are directional toward the
Transmission system to prevent Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or
generating plant from operatingtripping during the dynamic conditions anticipated by this
standard. Option 17 applies a 1.0 per unit line nominal voltage onat the high-side terminals of the
GSU transformerrelay location to calculate the impedance from the maximum aggregate
nameplate MVA. Asynchronous generators do not produce as much Reactive Power as
synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant.

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For Option 17, the impedance element isshall be set less than the calculated impedance derived
from 130 percent of the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay. This is a simple calculation that approximates the stressed system conditions.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Asynchronous Generators) Phase Time Overcurrent Relay (e.g., 50 and 51) (Option
18)

Relays applied oninstalled on the high-side of the GSU transformer, including relays installed on
the remote end of the line, for Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or
generating plant are challenged by loading conditions similar to relays applied on generators and
GSU transformers. Note that the setting criteria established within thesethe Table 1 options differ
from section 3.9.Chapter 2 of the Considerations for Power Plant and Transmission System
Protection Coordination technical reference document. Rather than establishing a uniform
setting threshold of 200 percent of the generator nameplate MVA rating at rated power factor
for all applications, the setting criteria are based on the maximum expected generator output.

Table 1, Option 18 establishes criteria for phase time overcurrent relays to prevent Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant from operatingtripping during the dynamic
conditions anticipated by this standard. Option 18 applies a 1.0 per unit line nominal voltage onat
the high-side terminalslocation of the GSU transformerrelay to calculate the current from the
maximum aggregate nameplate MVA. Asynchronous generators do not produce as much Reactive
Power as synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant.
For Option 18, the overcurrent element isshall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay. This is a simple calculation that approximates the stressed system conditions.
Elements that connect a GSU transformer to the Transmission system that are used
exclusively to export energy directly from a BES generating unit or generating plant
(Asynchronous Generators) Phase Directional Time Overcurrent Relay – Directional
Toward Transmission System (e.g., 67) (Option 19)

Relays applied oninstalled on the high-side of the GSU transformer, including relays installed on
the remote end of the line, for Elements that connect a GSU transformer to the Transmission
system that are used exclusively to export energy directly from a BES generating unit or

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generating plant are challenged by loading conditions similar to relays applied on generators and
GSU transformers. Note that the setting criteria established within thesethe Table 1 options differ
from section 3.9.Chapter 2 of the Considerations for Power Plant and Transmission System
Protection Coordination technical reference document. Rather than establishing a uniform
setting threshold of 200 percent of the generator nameplate MVA rating at rated power factor
for all applications, the setting criteria are based on the maximum expected generator output.
Table 1, Option 19 establishes criteria for phase directional time overcurrent relays that are
directional toward the Transmission system to prevent Elements that connect a GSU transformer
to the Transmission system that are used exclusively to export energy directly from a BES
generating unit or generating plant from operatingtripping during the dynamic conditions
anticipated by this standard. Option 19 applies a 1.0 per unit line nominal voltage onat the highside terminals of the GSU transformerrelay location to calculate the current from the maximum
aggregate nameplate MVA. Asynchronous generators do not produce as much Reactive Power as
synchronous generators; the voltage drop due to Reactive Power flow through the GSU
transformer is not as significant.
For Option 19, the overcurrent element isshall be set greater than 130 percent of the calculated
current derived from the maximum aggregate nameplate MVA output at rated power factor
including the Mvar output of any static or dynamic Reactive Power devices. This is determined
by summing the total MW and Mvar capability of the generation equipment behind the relay and
any static or dynamic Reactive Power devices that contribute to the power flow through the
relay. This is a simple calculation that approximates the stressed system conditions.

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Example Calculations
Introduction
Example Calculations.

Input Descriptions

Input Values

Synchronous Generator nameplate (MVA @ rated pf):

𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 903 𝑀𝑀𝑀𝑀𝑀𝑀

Generator rated voltage (Line-to-Line):
Real Power output in MW as reported to the TP:
Generator step-up (GSU) transformer rating:
GSU transformer reactance (903 MVA base):
GSU transformer MVA base:
GSU transformer turns ratio:
High-side nominal system voltage (Line-to-Line):
Current transformer (CT) ratio:
Potential transformer (PT) ratio low-side:
PT ratio high-side:
Unit auxiliary transformer (UAT) nameplate:
UAT highlow-side voltage:
UAT CT ratio:
CT high voltage ratio:
Reactive Power output of static reactive device:

𝑝𝑝𝑝𝑝 = 0.85

𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔_𝑛𝑛𝑛𝑛𝑛𝑛 = 22 𝑘𝑘𝑘𝑘

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺 = 903 𝑀𝑀𝑀𝑀𝑀𝑀
𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺 = 12.14%

𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 767.6 𝑀𝑀𝑀𝑀𝑀𝑀
𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

22 𝑘𝑘𝑘𝑘
346.5 𝑘𝑘𝑘𝑘

𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 345 𝑘𝑘𝑘𝑘
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

25000
5
200
1

𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣 =

2000
1

𝑈𝑈𝑈𝑈𝑈𝑈𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 60 𝑀𝑀𝑀𝑀𝑀𝑀
𝑉𝑉𝑈𝑈𝑈𝑈𝑈𝑈 = 13.8 𝑘𝑘𝑘𝑘
𝐶𝐶𝐶𝐶𝑈𝑈𝑈𝑈𝑈𝑈 =

5000
5

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣 =

2000
5

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
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Example Calculations.

Reactive Power output of static reactive device
generation:
Asynchronous generator nameplate (MVA @ rated pf):

Asynchronous CT ratio:
Asynchronous high voltage CT ratio:
CT remote substation bus

𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 = 40 𝑀𝑀𝑀𝑀𝑀𝑀
𝑝𝑝𝑝𝑝 = 0.85

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 =

5000
5

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣 =

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑏𝑏𝑏𝑏𝑏𝑏 =

300
5

2000
5

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Example Calculations: Option 1a

Option 1a represents the simplest calculation for synchronous generators applying a phase
distance relay (e.g., 21) directional toward the Transmission system.
Real Power output (P):
Eq. (1) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (2) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 1a, Table 1 – Bus Voltage, calls for a 0.95 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (3) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (4) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (5) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(20.81 𝑘𝑘𝑘𝑘)2
1347.4∠ − 58.7° 𝑀𝑀𝑀𝑀𝑀𝑀
72 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Option 1a

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.321∠58.7° Ω

Secondary impedance (Zsec):
Eq. (6) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.321∠58.7° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.321∠58.7° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 8.035∠58.7° Ω

To satisfy the 115% margin in Option 1a:
Eq. (7) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

8.035∠58.7° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 6.9873∠58.7° Ω
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 58.7°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚,85°,
then the maximum allowable impedance reach is:
Eq. (8) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
6.9873 Ω
cos(85.0° − 58.7°)
6.9873 Ω
0.896

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 7.793∠85.0° Ω

73 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 1b and 7b

Option 1b represents a more complex, more precise calculation for synchronous generators applying a
phase distance relay (e.g., 21) directional toward the Transmission system. This option requires
calculating low-side voltage taking into account voltage drop across the GSU transformer. Similarly these
calculations may be applied to Option 7b for GSU transformers applying a phase distance relay (e.g., 21)
directional toward the Transmission system.
Real Power output (P):
Eq. (9) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (10) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Convert Real Power, Reactive Power, and transformer reactance to per unit values on a 767.6 MVA base
(MVAbase):
Real Power output (P):
Eq. (11) 𝑃𝑃𝑝𝑝𝑝𝑝 =
𝑃𝑃𝑝𝑝𝑝𝑝 =

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
700.0 𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑃𝑃𝑝𝑝𝑝𝑝 = 0.91 𝑝𝑝. 𝑢𝑢.

Reactive Power output (Q):
Eq. (12) 𝑄𝑄𝑝𝑝𝑝𝑝 =
𝑄𝑄𝑝𝑝𝑝𝑝 =

𝑄𝑄
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑄𝑄𝑝𝑝𝑝𝑝 = 1.5 𝑝𝑝. 𝑢𝑢.

74 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 1b and 7b

Transformer impedance (Xpu):
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
�
Eq. (13) 𝑋𝑋𝑝𝑝𝑝𝑝 = 𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺(𝑜𝑜𝑜𝑜𝑜𝑜) × �
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺
𝑋𝑋𝑝𝑝𝑝𝑝 = 12.14% × �
𝑋𝑋𝑝𝑝𝑝𝑝 = 0.1032 𝑝𝑝. 𝑢𝑢.

767.6 𝑀𝑀𝑀𝑀𝑀𝑀
�
903 𝑀𝑀𝑀𝑀𝑀𝑀

Using the formula below; calculate the low-side GSU transformer voltage (Vlow-side) using 0.85 p.u. highside voltage (Vhigh-side). EstimateAssume initial low-side voltage to be 0.95 p.u. and repeat the calculation as
necessary until Vlow-side converges. A convergence of less than one percent (<1%) between iterations is
considered sufficient:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (14) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.95 × 0.85)

Eq. (15)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.7°

Eq. (15)

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.7°) ± �|0.85|2 × cos 2 (6.7°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9931 ± √0.7225 × 0.9864 + 0.6192
2
0.8441 ± 1.1541
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9991 𝑝𝑝. 𝑢𝑢.

75 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 1b and 7b

Use the new estimated Vlow-side value of 0.9991 per unit for the second iteration:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (16) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.9991 × 0.85)

Eq. (17)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.3°

Eq. (17)

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝
2

|0.85| × cos(6.3°) ± �|0.85|2 × cos 2 (6.3°) + 4 × 1.5 × 0.1032
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
2
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

|0.85| × 0.9940 ± √0.7225 × 0.9880 + 0.6192
2
0.8449 ± 1.1546
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9998 𝑝𝑝. 𝑢𝑢.

To account for system high-side nominal voltage and the transformer tap ratio:
Eq. (18) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = |𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.9998 𝑝𝑝. 𝑢𝑢.× 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 21.90 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (19) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° MVA

76 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 1b and 7b

Primary impedance (Zpri):
Eq. (20) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝑆𝑆 ∗

(21.90 𝑘𝑘𝑘𝑘)2
1347.4∠ − 58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.356∠58.7° Ω

Secondary impedance (Zsec):
Eq. (21) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.356∠58.7° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.356∠58.7° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 8.900∠58.7° Ω

To satisfy the 115% margin in Options 1b and 7b:
Eq. (22) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

8.900∠58.7° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 7.74∠58.7° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 58.7°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚,85°, then the
maximum allowable impedance reach is:
Eq. (23) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �

7.74 Ω
cos(85.0˚ − 58.7°) cos(85.0° − 58.7°)
7.74 Ω

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PRC-025-12 – Application Guidelines

Example Calculations: Options 1b and 7b

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

7.74 Ω
0.8965

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 8.633∠85.0° Ω
Example Calculations: Options 1c and 7c
Option 1c represents a more involved, more precise setting of the impedance element. This option requires
determining maximum generator Reactive Power output during field-forcing and the corresponding generator bus
voltage. Once these values are determined, the remainder of the calculation is the same as Options 1a and 1b.

Option 1c represents a more involved, more precise setting of the impedance element. This
option requires determining maximum generator Reactive Power output during field-forcing
and the corresponding generator bus voltage. Once these values are determined, the
remainder of the calculation is the same as Options 1a and 1b.
The generator Reactive Power and generator bus voltage are determined by simulation. The
maximum Reactive Power output on the low-side of the GSU transformer during field-forcing
is used as this value will correspond to the lowest apparent impedance. The corresponding
generator bus voltage is also used in the calculation. Note that although the excitation limiter
reduces the field, the duration of the Reactive Power output achieved for this condition is
sufficient to operate a phase distance relay.
In this simulation the following values are derived:
1.25

1000

Generator Reactive Power
1.15

Generator Real Power
1.05

Voltage (p.u.)

600

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

800

200

0

4

8

12

16

20

0

Time (s)

78 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 1c and 7c

In this simulation the following values are derived:
𝑄𝑄 = 827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

= 0.989 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔_𝑛𝑛𝑛𝑛𝑛𝑛 = 21.76 𝑘𝑘V

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀
1.25

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

200

0

4

8

12

16

20

0

Time (s)

Apparent power (S):
Eq. (24) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1083.8∠49.8° MVA

Primary impedance (Zpri):
Eq. (25) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉2𝑏𝑏𝑏𝑏𝑏𝑏 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑆𝑆∗

𝑆𝑆 ∗

(21.76 𝑘𝑘𝑘𝑘)2
1083.8∠ − 49.8° 𝑀𝑀𝑀𝑀𝑀𝑀
79 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 1c and 7c

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.437∠49.8° Ω

Secondary impedance (Zsec):
Eq. (26) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.437∠49.8° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.437∠49.8° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 10.92∠49.8° Ω

To satisfy the 115% margin in the requirement in Options 1c and 7c:
Eq. (27) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

10.92∠49.8° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 9.50∠49.8° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 49.8°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚,85°,
then the maximum allowable impedance reach is:
Eq. (28) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �

9.50 Ω
cos(85.0˚ − 49.8°) cos(85.0° − 49.8°)
9.50 Ω

9.50 Ω
0.8171

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 11.63∠85.0° Ω

80 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Option 2a

Option 2a represents the simplest calculation for synchronous generators applying a phase
time overcurrent (e.g., 50, 51, or 51V-R) voltage restrained relay:
Real Power output (P):
Eq. (29) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (30) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 2a, Table 1 – Bus Voltage, calls for a 0.95 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (31) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (32) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (33) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 20.81 𝑘𝑘𝑘𝑘
81 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Option 2a

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 37383 𝐴𝐴

Secondary current (Isec):
Eq. (34) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

37383 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.477 𝐴𝐴

To satisfy the 115% margin in Option 2a:
Eq. (35) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.477 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.598 𝐴𝐴

Example Calculations: Option 2b

Option 2b represents a more complex calculation for synchronous generators applying a phase time
overcurrent (e.g., 50, 51, or 51V-R) voltage restrained relay:
Real Power output (P):
Eq. (36) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (37) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

82 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Option 2b

Convert Real Power, Reactive Power, and transformer reactance to per unit values on 767.6 MVA base
(MVAbase).
Real Power output (P):
Eq. (38) 𝑃𝑃𝑝𝑝𝑝𝑝 =
𝑃𝑃𝑝𝑝𝑝𝑝 =

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
700.0 𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑃𝑃𝑝𝑝𝑝𝑝 = 0.91 𝑝𝑝. 𝑢𝑢.

Reactive Power output (Q):
Eq. (39) 𝑄𝑄𝑝𝑝𝑝𝑝 =
𝑄𝑄𝑝𝑝𝑝𝑝 =

𝑄𝑄
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑄𝑄𝑝𝑝𝑝𝑝 = 1.5 𝑝𝑝. 𝑢𝑢.

Transformer impedance:

Eq. (40) 𝑋𝑋𝑝𝑝𝑝𝑝 = 𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺(𝑜𝑜𝑜𝑜𝑜𝑜) ×

𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺

𝑋𝑋𝑝𝑝𝑝𝑝 = 12.14% × �
𝑋𝑋𝑝𝑝𝑝𝑝 = 0.1032 𝑝𝑝. 𝑢𝑢.

767.6 𝑀𝑀𝑀𝑀𝑀𝑀
�
903 𝑀𝑀𝑀𝑀𝑀𝑀

Using the formula below; calculate the low-side GSU transformer voltage (Vlow-side) using 0.85 p.u. highside voltage (Vhigh-side). EstimateAssume initial low-side voltage to be 0.95 p.u. and repeat the calculation as
necessary until Vlow-side converges. A convergence of less than one percent (<1%) between iterations is
considered sufficient:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (41) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.95 × 0.85)

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PRC-025-12 – Application Guidelines

Example Calculations: Option 2b

Eq. (42)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.7°

Eq. (42)

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.7°) ± �|0.85|2 × cos2 (6.7°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9931 ± √0.7225 × 0.9864 + 0.6192
2
0.8441 ± 1.1541
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9991 𝑝𝑝. 𝑢𝑢.

Use the new estimated Vlow-side value of 0.9991 per unit for the second iteration:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq. (43) 𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.9991 × 0.85)

Eq. (44)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.3°

Eq. (44)

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.3°) ± �|0.85|2 × cos2 (6.3°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9940 ± √0.7225 × 0.9880 + 0.6192
2
0.8449 ± 1.1546
2

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Example Calculations: Option 2b

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9998 𝑝𝑝. 𝑢𝑢.

To account for system high-side nominal voltage and the transformer tap ratio:
Eq. (45) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = |𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.9998 𝑝𝑝. 𝑢𝑢.× 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 21.90 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (46) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (47) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.90 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 35553 𝐴𝐴

Secondary current (Isec):
Eq. (48) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

35553 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.111 𝐴𝐴

To satisfy the 115% margin in Option 2b:
Eq. (49) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.111 𝐴𝐴 × 1.15
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Example Calculations: Option 2b

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.178 𝐴𝐴
Example Calculations: Option 2c

Option 2c represents a more involved, more precise setting of the overcurrent element for
the phase time overcurrent (e.g., 50, 51, or 51V-R) voltage restrained relay. This option requires
determining maximum generator Reactive Power output during field-forcing and the
corresponding generator bus voltage. Once these values are determined, the remainder of
the calculation is the same as Options 2a and 2b.
The generator Reactive Power and generator bus voltage are determined by simulation. The
maximum Reactive Power output on the low-side of the GSU transformer during field-forcing
is used as this value will correspond to the highest current. The corresponding generator bus
voltage is also used in the calculation. Note that although the excitation limiter reduces the
field, the duration of the Reactive Power output achieved for this condition is sufficient to
operate a voltage-restrained phase overcurrent relay.
1.25

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

200

0

4

12

8

16

20

0

The generator Reactive Power and
generator bus voltage are determined by simulation. The maximum Reactive Power output
on the low-side of the GSU transformer during field-forcing is used as this value will
correspond to the highest current. The corresponding generator bus voltage is also used in
the calculation. Note that although the excitation limiter reduces the field, the duration of
the Reactive Power output achieved for this condition is sufficient to operate a voltagerestrained phase overcurrent relay.In this simulation the following values are derived:
Time (s)

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PRC-025-12 – Application Guidelines

Example Calculations: Option 2c

In this simulation the following values are derived:

𝑄𝑄 = 827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.989 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔_𝑛𝑛𝑛𝑛𝑛𝑛 = 𝑄𝑄

= 827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀21.76 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.989 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔_𝑛𝑛𝑛𝑛𝑛𝑛
is modeled in the simulation at 100% of the gross MW
= 21.76 𝑘𝑘𝑘𝑘
capability reported to the Transmission Planner. In this
case:
The other value required is the Real Power output
which is modeled in the simulation at 100% of the gross
MW capability reported to the Transmission Planner. In
this case:
1.25

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

200

0

4

8

12

16

20

0

Time (s)

Apparent power (S):
Eq. (50) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1083.8∠49.8° MVA

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PRC-025-12 – Application Guidelines

Example Calculations: Option 2c

Primary current (Ipri):
Eq. (51)

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
=

1083.8 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.76 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 28790 𝐴𝐴
Eq. (52) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

To satisfy the 115% margin in Option 2c:

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 √3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
Secondary current (Isec):

𝑆𝑆

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

28790 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.758 𝐴𝐴

Eq. (53) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.758 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.622 𝐴𝐴

Example Calculations: Options 3 and 6

Option 3 represents the only calculation for synchronous generators applying a phase time
overcurrent (e.g., 51V-C) – voltage controlled relay (Enabled to operate as a function of voltage).
Similarly, Option 6 uses the same calculation for asynchronous generators.
Options 3 and 6, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal
voltage for the generator bus voltage (Vgen):
Eq. (54) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

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PRC-025-12 – Application Guidelines

Example Calculations: Options 3 and 6

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

The voltage setting shall be set less than 75% of the generator bus voltage:
Eq. (55) 𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 < 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 × 75%

𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 < 21.9 𝑘𝑘𝑘𝑘 × 0.75
𝑉𝑉𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 < 16.429 𝑘𝑘𝑘𝑘

Example Calculations: Option 4

This represents the calculation for an asynchronous generator (including inverter-based
installations) applying a phase distance relay (e.g., 21) – directional toward the Transmission
system.
Real Power output (P):
Eq. (56) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 34.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (57) 𝑄𝑄 = 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos−1(𝑝𝑝𝑝𝑝))
𝑄𝑄 = 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1(0.85))
𝑄𝑄 = 21.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 4, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (58) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
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PRC-025-12 – Application Guidelines

Example Calculations: Option 4

𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (59) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 34.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗21.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 40.0∠31.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (60) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑉𝑉𝑔𝑔2𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(21.9 𝑘𝑘𝑘𝑘)2
40.0∠ − 31.8° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 11.99 ∠31.8° Ω

Secondary impedance (Zsec):
Eq. (61) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 11.99 ∠31.8° Ω ×

5000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 11.99 ∠31.8° Ω × 5
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 59.95 ∠31.8° Ω

To satisfy the 130% margin in Option 4:
Eq. (62) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
130%

59.95∠31.8° Ω
1.30

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 46.12∠31.8° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 31.8°

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PRC-025-12 – Application Guidelines

Example Calculations: Option 4

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚,85°,
then the maximum allowable impedance reach is:
Eq. (63) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
46.12 Ω
cos(85.0° − 31.8°)
46.12 Ω
0.599

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 77.0∠85.0° Ω
Example Calculations: Option 55a

This represents the calculation for three asynchronous generators applying a phase time
overcurrent (e.g., 50, 51, or 51V-R) – voltage-restrained relay. In this application it was assumed
that 20 Mvar of total static compensation was added.
Real Power output (P):
Eq. (64) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (65) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 55a, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (66) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

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Example Calculations: Option 55a

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (67) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (68) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 3473∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (69) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

3473∠ − 39.2° 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.473∠ − 39.2° 𝐴𝐴

To satisfy the 130% margin in Option 55a:
Eq. (70) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 130%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.473∠ − 39.2° 𝐴𝐴 × 1.30
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.52∠ − 39.2° 𝐴𝐴

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PRC-025-12 – Application Guidelines

Example Calculations: Options 7a and 10Option 5b
ThisSimilarly to Option 5a, this example represents the calculation for a mixture ofthree
asynchronous (i.e., Option 10) and synchronous (i.e., Option 7a) generation (including inverter-based
installations)generators applying a phase distanceovercurrent (e.g., 50, 51, or 51V-R) relay (21) –
directional toward the Transmission system.. In this application it was assumed that 20 Mvar of total

static compensation was added.

Synchronous Generation (Option 7a)

Real Power output (𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ):P):

Eq. (71) 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (72) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 5b, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (73) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (74) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

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PRC-025-12 – Application Guidelines

Example Calculations: Options 7a and 10Option 5b

Primary current (Ipri):
Eq. (75) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 3473∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (76) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

3473∠ − 39.2° 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.473∠ − 39.2° 𝐴𝐴

To satisfy Option 5b, the lower tolerance of the overcurrent element tripping characteristic
shall not infringe upon the resource capability (including the Mvar output of the resource and
any static or dynamic reactive power devices) See Figure A for more details.

Example Calculations: Options 7a and 10

These examples represent the calculation for a mixture of asynchronous (i.e., Option 10) and
synchronous (i.e., Option 7a) generation (including inverter-based installations) applying a
phase distance relay (e.g., 21) directional toward the Transmission system. In this application
it was assumed 20 Mvar of total static compensation was added.
Synchronous Generation (Option 7a)

Real Power output (𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ):

Eq. (77) 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 767.6 𝑀𝑀𝑀𝑀

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Example Calculations: Options 7a and 10

Reactive Power output (𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠ℎ ):

Eq. (7278) 𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 150% × 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ

𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1151.3 𝑀𝑀𝑀𝑀

Apparent power (SSynch):

Eq. (7379) 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Asynchronous Generation (Option 10)
Real Power output (PAsynch):

Real Power output (PAsynch):
Eq. (7480) 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (QAsynch):

Eq. (7581) 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1(0.85)))
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Apparent power (SAsynch):

Eq. (7682) 𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ + 𝑗𝑗𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ

𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

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Example Calculations: Options 7a and 10

Options 7a and 10, Table 1 – Bus Voltage, Option 7a specifies 0.95 per unit of the high-side
nominal voltage for the generator bus voltage and Option 10 specifies 1.0 per unit of the
high-side nominal voltage for generator bus voltage. Due to the presence of the synchronous
generator, the 0.95 per unit bus voltage will be used as (Vgen) as it results in the most
conservative voltage:
Eq. (7783) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S) accounted for 115% margin requirement for a synchronous generator
and 130% margin requirement for an asynchronous generator:
Eq. (7884) 𝑆𝑆 = 115% × �𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ � + 130% × (𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ + 𝑗𝑗𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ )
𝑆𝑆 = 1.15 × (700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀) + 1.30 × (102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀)

𝑆𝑆 = 1711.8 ∠56.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (7985) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑉𝑉𝑔𝑔2𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(20.81 𝑘𝑘𝑘𝑘)2
1711.8∠ − 56.8° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 0.2527∠56.8° Ω

Secondary impedance (Zsec):
Eq. (8086) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.2527∠56.8° Ω ×

25000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 0.2527∠56.8° Ω × 25
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 6.32∠56.8° Ω

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PRC-025-12 – Application Guidelines

Example Calculations: Options 7a and 10

No additional margin is needed; therefore, the margin is 100% because the synchronous apparent
power has been multiplied by 1.15 (115%) and the asynchronous apparent power has been
multiplied by 1.30 (130%) in Equation 8584 to satisfy the margin requirements in Options 7a
and 10:.
Eq. (8187) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
100%

6.32 ∠56.8° Ω
1.00

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 6.32 ∠56.8° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 56.8°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚,85°,
then the maximum allowable impedance reach is:
Eq. (8288) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
6.32 Ω
cos(85.0° − 56.8°)
6.32 Ω
0.881

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 7.17∠85.0° Ω
Example Calculations: Options 8a and 9a

Options 8a and 9a representsrepresent the simplest calculation for synchronous generators
applying a phase time overcurrent (e.g., 50, 51, or 67) relay. The following uses the
GENSynch_nameplate value to represent an “aggregate” value to illustrate the option:
Real Power output (P):
Eq. (8389) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

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PRC-025-12 – Application Guidelines

Example Calculations: Options 8a and 9a

Reactive Power output (Q):
Eq. (8490) 𝑄𝑄 = 150% × 𝑃𝑃

𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Options 8a and 9a, Table 1 – Bus Voltage, calls for a generator bus voltage corresponding to
0.95 per unit of the high-side nominal voltage times the turns ratio of the generator step-up
transformer generator bus voltage (Vgen):
Eq. (8591) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (8692) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (8793) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 20.81 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 37383 𝐴𝐴

Secondary current (Isec):
Eq. (8894) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

37383 𝐴𝐴
25000
5
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PRC-025-12 – Application Guidelines

Example Calculations: Options 8a and 9a

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.477 𝐴𝐴

To satisfy the 115% margin in Options 8a and 9a:
Eq. (8995) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.477 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.598 𝐴𝐴

Example Calculations: Options 8b and 9b

Options 8b and 9b representsrepresent a more complexprecise calculation for synchronous
generators applying a phase time overcurrent (e.g., 50, 51, or 67) relay. The following uses the
GENSynch_nameplate value to represent an “aggregate” value to illustrate the option:
Real Power output (P):
Eq. 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
(9096)
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. 𝑄𝑄 = 150% × 𝑃𝑃
(9197)
𝑄𝑄 = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Convert Real Power, Reactive Power, and transformer reactance to per unit values on 767.6
MVA base (GSU transformer MVAbase).
Real Power output (P):
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
Eq.
𝑃𝑃𝑝𝑝𝑝𝑝 =
(9298)
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

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PRC-025-12 – Application Guidelines

Example Calculations: Options 8b and 9b

𝑃𝑃𝑝𝑝𝑝𝑝 =

700.0 𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑃𝑃𝑝𝑝𝑝𝑝 = 0.91 𝑝𝑝. 𝑢𝑢.

Reactive Power output (Q):
𝑄𝑄
Eq.
𝑄𝑄𝑝𝑝𝑝𝑝 =
(9399)
𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
𝑄𝑄𝑝𝑝𝑝𝑝 =

1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
767.6 𝑀𝑀𝑀𝑀𝑀𝑀

𝑄𝑄𝑝𝑝𝑝𝑝 = 1.5 𝑝𝑝. 𝑢𝑢.

Transformer impedance:

𝑀𝑀𝑀𝑀𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
Eq.
𝑋𝑋𝑝𝑝𝑝𝑝 = 𝑋𝑋𝐺𝐺𝐺𝐺𝐺𝐺(𝑜𝑜𝑜𝑜𝑜𝑜) ×
(94100)
𝑀𝑀𝑀𝑀𝑀𝑀𝐺𝐺𝐺𝐺𝐺𝐺
𝑋𝑋𝑝𝑝𝑝𝑝 = 12.14% × �
𝑋𝑋𝑝𝑝𝑝𝑝 = 0.1032 𝑝𝑝. 𝑢𝑢.

767.6 𝑀𝑀𝑀𝑀𝑀𝑀
�
903 𝑀𝑀𝑀𝑀𝑀𝑀

Using the formula below; calculate the low-side GSU transformer voltage (Vlow-side) using 0.85
p.u. high-side voltage (Vhigh-side). EstimateAssume initial low-side voltage to be 0.95 p.u. and
repeat the calculation as necessary until Vlow-side converges. A convergence of less than one
percent (<1%) between iterations is considered sufficient:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq.
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(95101)
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��

Eq.
(102)
Eq. (96)

(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.95 × 0.85)
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 |
=

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2 (𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝
2

100 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 8b and 9b

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

|0.85| × cos(6.7°) ± �|0.85|2 × cos 2 (6.7°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9931 ± √0.7225 × 0.9864 + 0.6192
2
0.8441 ± 1.1541
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9991 𝑝𝑝. 𝑢𝑢.

Use the new estimated Vlow-side value of 0.9991 per unit for the second iteration:
�𝑃𝑃𝑝𝑝𝑝𝑝 × �𝑋𝑋𝑝𝑝𝑝𝑝 ��
Eq.
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(97103)
�|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × �𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ��
(0.91 × 0.1032)
𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = sin−1 �
�
(0.9991 × 0.85)

Eq.
(104)
Eq. (98)

𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 6.3°
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 |
=

2

�𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos(𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) ± ��𝑉𝑉ℎ𝑖𝑖𝑖𝑖ℎ−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 � × cos2 (𝜃𝜃𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) + 4 × 𝑄𝑄𝑝𝑝𝑝𝑝 × 𝑋𝑋𝑝𝑝𝑝𝑝

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =
|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | =

2

|0.85| × cos(6.3°) ± �|0.85|2 × cos 2 (6.3°) + 4 × 1.5 × 0.1032
2
|0.85| × 0.9940 ± √0.7225 × 0.9880 + 0.6192
2
0.8449 ± 1.1546
2

|𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | = 0.9998 𝑝𝑝. 𝑢𝑢.

To account for system high-side nominal voltage and the transformer tap ratio:
Eq. 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = |𝑉𝑉𝑙𝑙𝑙𝑙𝑙𝑙−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 | × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
(99105)
101 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 8b and 9b

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.9998 𝑝𝑝. 𝑢𝑢.× 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 21.90 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗
(100106)
𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1347.4∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):

𝑆𝑆
Eq.
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
(101107)
√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

1347.4 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.90 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 35553 𝐴𝐴

Secondary current (Isec):

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
Eq.
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
(102108)
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

35553 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 7.111 𝐴𝐴

To satisfy the 115% margin in Options 8b and 9b:
Eq. 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%
(103109)
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 7.111 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 8.178 𝐴𝐴

102 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 8a, 9a, 11, and 12

This example represents the calculation for a mixture of asynchronous and synchronous
generators applying a phase time overcurrent (e.g., 50, 51, or 67) relays. In this application it
was assumed 20 Mvar of total static compensation was added. The current transformers (CT)
are located on the low-side of the GSU transformer.
Synchronous Generation (Options 8a and 9a)
Real Power output (PSynch):

Real Power output (PSynch):
Eq. 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
(104110)
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × .85
𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (QSynch):

Eq. 𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 150% × 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ
(105111)
𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1.50 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Apparent power (SSynch):

Eq. 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ
(106112)
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗1151.3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ = 1347.4 ∠58.7° 𝑀𝑀𝑀𝑀𝑀𝑀

Option 8a, Table 1 – Bus Voltage calls for a 0.95 per unit of the high-side nominal voltage as a
basis for generator bus voltage (Vgen):
Eq. 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
(107113)
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘
103 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 8a, 9a, 11, and 12

𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

Primary current (Ipri-sync):

∗

115% × 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ
Eq.
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =
(108114)
√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =

1.15 × (1347.4 ∠ − 58.7° 𝑀𝑀𝑀𝑀𝑀𝑀)
1.73 × 20.81 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 43061 ∠ − 58.7° 𝐴𝐴

Asynchronous Generation (Options 11 and 12)
Real Power output (PAsynch):

Real Power output (PAsynch):
Eq. 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
(109115)
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (QAsynch):

Eq. 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos−1(𝑝𝑝𝑝𝑝))
(110116)
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos−1(0.85)))
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 11, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen), however due to the presence of synchronous generator 0.95
per unit bus voltage will be used:
Eq. 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
(111117)
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.95 × 345 𝑘𝑘𝑘𝑘 × �
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 20.81 𝑘𝑘𝑘𝑘

22 𝑘𝑘𝑘𝑘
�
346.5 𝑘𝑘𝑘𝑘

104 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 8a, 9a, 11, and 12

Apparent power (SAsynch):
Eq. 𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 130% × (𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ + 𝑗𝑗𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ )
(112118)
𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 1.30 × (102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀)
𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 171.1 ∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri-async):

𝑆𝑆𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ
Eq. 𝐼𝐼
𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 =
(113119)
√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 =

171.1 ∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 20.81 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 4755 ∠ − 39.2° 𝐴𝐴

Secondary current (Isec):

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝−𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
Eq.
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
+
(114120)
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

43061 ∠ − 58.7° 𝐴𝐴
4755∠ − 39.2° 𝐴𝐴
+
25000
25000
5
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 9.514∠ − 56.8° 𝐴𝐴

No additional margin is needed; therefore, the margin is 100% because the synchronous apparent
power has been multiplied by 1.15 (115%) in Equation 94114 and the asynchronous apparent
power has been multiplied by 1.30 (130%) in Equation 98:118.
Eq. 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 100%
(115121)

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 9.514∠ − 56.8° 𝐴𝐴 × 1.00
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 9.514∠ − 56.8° 𝐴𝐴

105 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 8c and 9c
This example uses Option 15b as a simulation example for a synchronous generator applying a phase time
overcurrent relay. In this application the same synchronous generator is modeled as for Options 1c, 2c, and 7c.
The CTs are located on the low-side of the GSU transformer.

This example uses Option 15b as a simulation example for a synchronous generator applying
a phase overcurrent relay (e.g., 50, 51, or 67). In this application the same synchronous
generator is modeled as for Options 1c, 2c, and 7c. The CTs are located on the low-side of the
GSU transformer.
The generator Reactive Power and generator bus voltage are determined by simulation. The
maximum Reactive Power output on the low-side of the GSU transformer, during fieldforcing, is used assince this value will correspond to the highest current. The corresponding
generator bus voltage is also used in the calculation. Note that although the excitation limiter
reduces the field, the duration of the Reactive Power output achieved for this condition is
sufficient to operate a phase overcurrent relay.
1.25

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

200

0

4

8

12

16

20

0

Time (s)

In this simulation the following values are derived:
𝑄𝑄 = 827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

= 0.989 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.76 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀
106 of 141

PRC-025-12 – Application Guidelines

Example Calculations: Options 8c and 9c

Apparent power (S):
Eq. (122) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗827.4 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1083.8∠49.8°

Primary current (Ipri):

Eq. (123) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
1083.8 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.76 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 28790 𝐴𝐴

Secondary current (Isec):
Eq. (124) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

28790 𝐴𝐴
25000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.758 𝐴𝐴

To satisfy the 115% margin in Options 8c and 9c:
Eq. (125) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.758 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.622 𝐴𝐴

Example Calculations: Option 10

This example represents the calculation for three asynchronous generators (including
inverter-based installations) applying a phase distance relay (e.g., 21) directional toward the
Transmission system. In this application it was assumed 20 Mvar of total static compensation
was added.

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Example Calculations: Option 10

Real Power output (P):
Eq. (126) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (127) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos−1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 10, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for
the generator bus voltage (Vgen):
Eq. (128) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (129) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (130) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝

𝑉𝑉𝑔𝑔2𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

(21.9 𝑘𝑘𝑘𝑘)2
=
131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 3.644 ∠39.2° Ω

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Example Calculations: Option 10

Secondary impedance (Zsec):
Eq. (131) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 3.644 ∠39.2° Ω ×

5000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 3.644 ∠39.2° Ω × 5
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 18.22 ∠39.2° Ω

To satisfy the 130% margin in Option 10:
Eq. (132) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
130%

18.22∠39.2° Ω
1.30

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 14.02∠39.2° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 39.2°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (133) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
14.02 Ω
cos(85.0° − 39.2°)
14.02 Ω
0.6972

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 20.11∠85.0° Ω

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Example Calculations: Options 11 and 12

Option 11 represents the calculation for a GSU transformer applying a phase overcurrent
(e.g., 50 or 51) relay connected to three asynchronous generators. Similarly, these
calculations can be applied to Option 12 for a phase directional overcurrent relay (e.g., 67)
directional toward the Transmission system. In this application it was assumed 20 Mvar of
total static compensation was added.
Real Power output (P):
Eq. (134) 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (135) 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Options 11 and 12, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal
voltage for the generator bus voltage (Vgen):
Eq. (136) 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (137) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6 ∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (138) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
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Example Calculations: Options 11 and 12

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

131.6 ∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 3473∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (139) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

3473∠ − 39.2° 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.473∠ − 39.2° 𝐴𝐴

To satisfy the 130% margin in Options 11 and12:
Eq. (140) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 130%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.473∠ − 39.2° 𝐴𝐴 × 1.30
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.515∠ − 39.2° 𝐴𝐴

Example Calculations: Options 13a and 13b

Option 13a for the UAT assumes the maximum nameplate rating of the winding is utilized for
the purposes of the calculations and the appropriate voltage. Similarly, Option 13b uses the
measured current while operating at the maximum gross MW capability reported to the
Transmission Planner.
Primary current (Ipri):
Eq. (141) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑈𝑈𝑈𝑈𝑈𝑈𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛
√3 × 𝑉𝑉𝑈𝑈𝑈𝑈𝑈𝑈

60 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 13.8 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2510.2 𝐴𝐴

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Example Calculations: Options 13a and 13b

Secondary current (Isec):
Eq. (142) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑈𝑈𝑈𝑈𝑈𝑈

2510.2 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 2.51 A

To satisfy the 150% margin in Options 13a:
Eq. (143) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 150%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 2.51 𝐴𝐴 × 1.50
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.77 𝐴𝐴

Example Calculations: Option 14a

Option 14a represents the calculation for relays installed on the high-side of the GSU
transformer, including relays installed on the remote end of line, for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant that connected to synchronous
generation. In this example, the Element is protected by a phase distance (e.g., 21) relay
directional toward the Transmission system. The CTs are located on the high-side of the GSU
transformer.
Real Power output (P):
Eq. (144) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. (145) 𝑄𝑄 = 120% × 𝑃𝑃

𝑄𝑄 = 1.20 × 767.6 𝑀𝑀𝑀𝑀
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Example Calculations: Option 14a

𝑄𝑄 = 921.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 14a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the line nominal voltage for the
GSU transformer voltage (Vnom):
Eq. (146) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.85 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 293.25 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (147) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157.0∠52.77° 𝑀𝑀𝑀𝑀𝑀𝑀

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 52.77°

Primary impedance (Zpri):
Eq. (148) 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝑆𝑆 ∗

(293.25 𝑘𝑘𝑘𝑘)2
=
1157.0∠ − 52.77° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 74.335∠52.77° Ω

Secondary impedance (Zsec):
Eq. (149) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 74.335∠52.77° Ω ×

2000
5
2000
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 74.335∠52.77° Ω × 0.2
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 14.867∠52.77° Ω

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Example Calculations: Option 14a

To satisfy the 115% margin in Option 14a:
Eq. (150) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

14.867∠52.77° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 12.928∠52.77° Ω
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 52.77°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (151) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
12.928 Ω
cos(85.0° − 52.77°)
12.928 Ω
0.846

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 15.283∠85.0° Ω

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Example Calculations: Option 14b

Option 14b represents the simulation for relays installed on the high-side of the GSU
transformer, including relays installed on the remote end of line, for Elements that connect a
GSU transformer to the Transmission system that are used exclusively to export energy
directly from a BES generating unit or generating plant connected to synchronous generation.
In this example, the Element is protected by a phase distance (e.g., 21) relay directional
toward the Transmission system. The CTs are located on the high-side of the GSU
transformer.
Relays installed on the high-side of the GSU transformer, including relays installed on the
remote end of line, simulation is used to determine the simulated line voltage at the relay
location coincident with the highest Reactive Power output achieved during field-forcing in
response to a 0.85 per unit of the line nominal voltage at the remote end of the line prior to
field-forcing. This is achieved by modeling a shunt at the remote end (i.e., at the Transmission
system) of the line during simulation.
The maximum Reactive Power flow and coincident voltage for both the high-side of the GSU
transformer and remote end of the line are determined by simulation. The maximum
Reactive Power output on the high-side of the GSU transformer and remote end of the line
during field-forcing is used as these values will correspond to the lowest apparent impedance
at the relay location. The corresponding simulated voltage is also used in the calculation.
Note that although the excitation limiter reduces the field, the duration of the Reactive
Power output achieved for this condition is sufficient to operate a phase distance relay.

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Example Calculations: Option 14b

1.02 p.u.

GSU High-side Voltage

Generator Reactive Power

Generator Bus Voltage
440.7 Mvar

In this simulation the following values are derived:
𝑄𝑄 = 440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 1.02 × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 351.9 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

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Example Calculations: Option 14b
1.25

1000

Generator Reactive Power
800

Generator Real Power
600

Voltage (p.u.)

1.05

Generator Bus Voltage
0.95

400

GSU High-Side Voltage
0.85

0.75

Real and Reactive Power (MW/Mvar)

1.15

200

0

4

8

12

16

20

0

Time (s)

Apparent power (S):
Eq. (116152) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗827.4𝑗𝑗440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1083.8∠49.8°827.2∠32.2° 𝑀𝑀𝑀𝑀𝑀𝑀
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 32.2°

Primary current (Ipriimpedance (Zpri):
Eq. (117153) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑉𝑉2𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑆𝑆∗

1083.8 𝑀𝑀𝑀𝑀𝑀𝑀
𝑍𝑍
1.73 × 21.76 𝑘𝑘𝑘𝑘 𝑝𝑝𝑝𝑝𝑝𝑝

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 28790 𝐴𝐴𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝

=

2

(351.9 𝑘𝑘𝑘𝑘)
827.2∠ − 32.2° 𝑀𝑀𝑀𝑀𝑀𝑀

= 149.7∠32.2° Ω

Secondary current (Isecimpedance (Zsec):
Eq. (118154) 𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

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PRC-025-12 – Application Guidelines

Example Calculations: Option 14b
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

28790 𝐴𝐴
𝑍𝑍
25000 𝑠𝑠𝑠𝑠𝑠𝑠
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.758 𝐴𝐴𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠

= 149.7∠32.2° Ω ×

2000
5
2000
1

= 149.7∠32.2° Ω × 0.2

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 29.9∠32.2° Ω

To satisfy the 115% margin in Options 8c and 9cOption 14b:
Eq. (119155) 𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
𝐼𝐼
> 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%
115% sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙
29.9∠32.2° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 26.0∠32.2° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 32.2°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85°,
then the maximum allowable impedance reach is:
Eq. (156) 𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
26.0 Ω
cos(85.0° − 32.2°)
26.0 Ω
0.61

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 43.0∠85.0° Ω

Example Calculations: Options 15a and 16a

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.758 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.622 𝐴𝐴

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Example Calculations: Option10
This represents the calculation for three asynchronous generators (including inverter-based installations) applying
a phase distance relay (21) – directional toward the Transmission system. In this application it was assumed 20
Mvar of total static compensation was added.

Options 15a and 16a represent the calculation for relay installed on the high-side of the GSU
transformer, including relays installed at the remote end of the line, for Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant connected to synchronous
generation.
Option 15a represents applying a phase time overcurrent relay (e.g., 51) and/or phase
instantaneous overcurrent supervisory elements (e.g., 50) associated with current-based,
communication-assisted schemes where the scheme is capable of tripping for loss of
communications installed on the high-side of the GSU transformer, including relays installed
at the remote end of the line.
Option 16a represents applying a phase directional instantaneous overcurrent supervisory
element (e.g., 67) associated with current-based, communication-assisted schemes where
the scheme is capable of tripping for loss of communications directional toward the
Transmission system installed on the high-side of the GSU and at the remote end of the line
and/or a phase time directional overcurrent relay (e.g., 67) directional toward the
Transmission system installed on the high-side of the GSU transformer, including relays
installed at the remote end of the line.
Example calculations are provided for the case, where potential transformers (PT) and
current transformers (CT) are located at the high-side of the GSU transformer and the 0.85
per unit of the line nominal voltage at the high-side of the GSU transformer. Example
calculations are also provided for the case where PTs and CTs are located at the remote end
of the line and the 0.85 per unit of the line nominal voltage will be at the remote bus
location.
Calculations at the high-side of the GSU transformer.

Real Power output (P):
Eq. (120)

𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Eq. (157) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

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Example Calculations: Option10

Reactive Power output (Q):
Eq. (158) 𝑄𝑄 = 120% × 𝑃𝑃

𝑄𝑄 = 1.20 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 15a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the line nominal voltage:
Eq. (159) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 × 345 𝑘𝑘𝑘𝑘

Eq. (121)

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 293.25 𝑘𝑘𝑘𝑘

𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 10, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for the generator bus
voltage (Vgen):
Eq. (122)

𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):
Eq. (123)

𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary impedance (Zpri):
Eq. (124)

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔
𝑆𝑆 ∗

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

(21.9 𝑘𝑘𝑘𝑘)2
131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
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PRC-025-12 – Application Guidelines

Example Calculations: Option10

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 3.644 ∠39.2° Ω

Secondary impedance (Zsec):
Eq. (125)

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 3.644 ∠39.2° Ω ×

5000
5
200
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 3.644 ∠39.2° Ω × 5
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 18.22 ∠39.2° Ω

To satisfy the 130% margin in Option 10:
Eq. (126)

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
130%

18.22∠39.2° Ω
1.30

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 14.02∠39.2° Ω

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 39.2°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚, then the maximum
allowable impedance reach is:
Eq. (127)

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

14.02 Ω
cos(85.0° − 39.2°)
14.02 Ω
0.6972

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 20.11∠85.0° Ω
Eq. (160) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157∠52.8° 𝑀𝑀𝑀𝑀𝑀𝑀

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Example Calculations: Options 11 and 12
Option 11 represents the calculation for a GSU transformer applying a phase time overcurrent (51) relay
connected to three asynchronous generators. Similarly, these calculations can be applied to Option 12 for a phase
directional time overcurrent relay (67) directional toward the Transmission system. In this application it was
assumed 20 Mvar of total static compensation was added.
Real Power output (P):
Eq. (128)

𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝

𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (129)

𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�
𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Options 11 and 12, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for the
generator bus voltage (Vgen):
Eq. (130)

𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 × 𝐺𝐺𝐺𝐺𝐺𝐺𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

22 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘 × �
�
346.5 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 21.9 𝑘𝑘𝑘𝑘

Apparent power (S):
Eq. (131)

𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6 ∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (161) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

1157∠ − 52.8° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 293.25 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2280.6∠ − 52.8° 𝐴𝐴

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Eq. (132)

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔

131.6 ∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 21.9 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 3473∠ − 39.2° 𝐴𝐴

Secondary current (Isec):
Eq. (133)

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

3473∠ − 39.2° 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.473∠ − 39.2° 𝐴𝐴

To satisfy the 130% margin in Options 11 and12:
Eq. (134)

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 130%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.473∠ − 39.2° 𝐴𝐴 × 1.30
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.515∠ − 39.2° 𝐴𝐴

Example Calculations: Options 13a and 13b
Option 13a for the UAT assumes that the maximum nameplate rating of the winding utilized for the purposes of
the calculations and the appropriate voltage. Similarly, Option 13b uses the measured current while operating at
the maximum gross MW capability reported to the Transmission Planner.
Primary current (Ipri):
Eq. (135)

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑈𝑈𝑈𝑈𝑈𝑈𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛
√3 × 𝑉𝑉𝑈𝑈𝑈𝑈𝑈𝑈

60 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 13.8 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2510.2 𝐴𝐴

Secondary current (Isec):
Eq. (136)

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑈𝑈𝑈𝑈𝑈𝑈

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Example Calculations: Options 13a and 13b
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

2510.2 𝐴𝐴
5000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 2.51 A

To satisfy the 150% margin in Options 13a:
Eq. (137)

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 150%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 2.51 𝐴𝐴 × 1.50
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.77 𝐴𝐴
Eq. (162) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

2280.6∠ − 52.8° 𝐴𝐴
2000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.701 ∠ − 52.8° 𝐴𝐴

To satisfy the 115% margin in Options 15a and 16a:
Eq. (163) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.701 ∠ − 52.8° 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.56 ∠ − 52.8° 𝐴𝐴

Example Calculations: Option 14a

Option 14a represents the calculation for a synchronous generation Elements that connect a GSU transformer to
the Transmission system that are used exclusively to export energy directly from a BES generating unit or
generating plant that is applying a phase distance (21) relay directional toward the Transmission system. The CTs
are located on the high-side of the GSU transformer.

Calculations at the remote end of the line from the plant.

Real Power output (P):
Eq. (138)

𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝

Eq. (164) 𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝

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𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (139)

𝑄𝑄 = 120% × 𝑃𝑃

Eq. (165) 𝑄𝑄 = 120% × 𝑃𝑃

𝑄𝑄 = 1.20 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 921.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 14a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the high-side nominal voltage for the GSU
transformer voltage (Vnom):
Eq. (140)

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛

𝑄𝑄 = 921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 15a and 16a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the line nominal voltage
at the relay location, in this example the relay location is at the remote substation bus.
Eq. (166) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.85 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 293.25 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 0.85 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 293.25 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. (167) 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157∠52.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (168) 𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

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𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

1157∠ − 52.8° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 293.25 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2280.6∠ − 52.8° 𝐴𝐴

Secondary current (Isec):
Eq. (169) 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_𝑏𝑏𝑏𝑏𝑏𝑏

2280.6∠ − 52.8° 𝐴𝐴
2000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.701 ∠ − 52.8° 𝐴𝐴

To satisfy the 115% margin in Options 15a and 16a:
Eq. (170) 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.701 ∠ − 52.8° 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.56 ∠ − 52.8° 𝐴𝐴

Example Calculations: Options 15b and 16b
Eq. (141)

𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

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Example Calculations: Options 15b and 16b

Options 15b and 16b represent the calculation for relays installed on the high-side of the GSU
transformer, including relays installed at the remote end of the line, for Elements that
connect a GSU transformer to the Transmission system that are used exclusively to export
energy directly from a BES generating unit or generating plant connected to synchronous
generation.
Option 15b represents applying a phase time overcurrent relay (e.g., 51) and/or phase
instantaneous overcurrent supervisory elements (e.g., 50) associated with current-based,
communication-assisted schemes where the scheme is capable of tripping for loss of
communications installed on the high-side of the GSU transformer, including relays at the
remote end of the line.
Option 16b represents applying a phase directional instantaneous overcurrent supervisory
element (e.g., 67) associated with current-based, communication-assisted schemes where
the scheme is capable of tripping for loss of communications directional toward the
Transmission system and/or a phase directional time overcurrent relay (e.g., 67) directional
toward the Transmission system installed on the high-side of the GSU, including relays at the
remote end of the line.
Example calculations are provided for the case where relays are installed on the high-side of
the GSU transformer, including relays installed on the remote end of line. Simulation is used
to determine the line voltage at the relay location coincident with the highest Reactive Power
output achieved during field-forcing in response to a 0.85 per unit of the line nominal voltage
at the remote end of the line prior to field-forcing. This is achieved by modeling a shunt at the
remote end (i.e., at the Transmission system) of the line during simulation.
The maximum Reactive Power flow and coincident voltage for both the high-side of the GSU
transformer and remote end of the line are determined by simulation. The maximum
Reactive Power output on the high-side of the GSU transformer and remote end of the line
during field-forcing is used as these values will correspond to the lowest apparent impedance
at the relay location. The corresponding simulated voltage is also used in the calculation.
Note that although the excitation limiter reduces the field, the duration of the Reactive
Power output achieved for this condition is sufficient to operate a phase overcurrent relay.

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Example Calculations: Options 15b and 16b

1.02 p.u.

GSU High-side Voltage

Generator Reactive Power

Generator Bus Voltage
440.7 Mvar

In this simulation the following values are derived:
𝑄𝑄 = 440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 1.02 × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 351.9 𝑘𝑘𝑘𝑘

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157.0∠52.77° 𝑀𝑀𝑀𝑀𝑀𝑀

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 52.77°

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Example Calculations: Options 15b and 16b

Primary impedance (Zpri):
Eq. (142)

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =
𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

2
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝑆𝑆 ∗

(293.25 𝑘𝑘𝑘𝑘)2
1157.0∠ − 52.77° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 74.335∠52.77° Ω

Secondary impedance (Zsec):
Eq. (143)

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×

𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 74.335∠52.77° Ω ×

2000
5
2000
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 74.335∠52.77° Ω × 0.2
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 14.867∠52.77° Ω

To satisfy the 115% margin in Option 14a:
Eq. (144)

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
115%

14.867∠52.77° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 12.928∠52.77° Ω
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 52.77°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚, then the maximum
allowable impedance reach is:
Eq. (145)

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
12.928 Ω
cos(85.0° − 52.77°)
12.928 Ω
0.846

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 15.283∠85.0° Ω

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Example Calculations: Option 14b
Option 14b represents the simulation for a synchronous generation Elements that connect a GSU transformer to
the Transmission system that are used exclusively to export energy directly from a BES generating unit or
generating plant that is applying a phase distance (21) relay directional toward the Transmission system. The CTs
are located on the high-side of the GSU transformer.
The Reactive Power flow and high-side bus voltage are determined by simulation. The maximum Reactive Power
output on the high-side of the GSU transformer during field-forcing is used as this value will correspond to the
lowest apparent impedance. The corresponding high-side bus voltage is also used in the calculation. Note that
although the excitation limiter reduces the field, the duration of the Reactive Power output achieved for this
condition is sufficient to operate a phase distance relay.
In this simulation the following values are derived:
𝑄𝑄 = 703.6 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.908 × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 313.3 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at
100% of the gross MW capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

1000

1.25

800

1.15

600

Voltage (p.u.)

1.05

Generator Reactive Power
400

0.95

Real and Reactive Power (MW/Mvar)

Generator Real Power

GSU High-Side Voltage
200

0.85

0

0.75
0

4

8

12

16

20

Time (s)

Apparent power (S):
Eq. 𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗
(146171)
𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗703.6𝑗𝑗440.7 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
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Example Calculations: Option 14b

𝑆𝑆 = 992.5∠45.1827.2∠32.2° 𝑀𝑀𝑀𝑀𝑀𝑀
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 45.1°

Primary impedance (Zpricurrent (Ipri):

2
𝑆𝑆∗
Eq. 𝑍𝑍 = 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝐼𝐼
=
𝑝𝑝𝑝𝑝𝑝𝑝
𝑆𝑆 ∗ 𝑝𝑝𝑝𝑝𝑝𝑝 �3 × 𝑉𝑉
(147172)
𝑏𝑏𝑏𝑏𝑏𝑏_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

(313.3 𝑘𝑘𝑘𝑘)2
𝐼𝐼
992.5∠ − 45.1° 𝑀𝑀𝑀𝑀𝑀𝑀 𝑝𝑝𝑝𝑝𝑝𝑝

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 98.90∠45.1° Ω𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝

827.2∠ − 32.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 351.9 𝑘𝑘𝑘𝑘

=

= 1357.1∠ − 32.2° 𝐴𝐴

Secondary impedance (Zseccurrent (Isec):

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
Eq.
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×
(148173)
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 98.90∠45.1° Ω ×

2000
5
2000
1

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 98.90∠45.1° Ω × 0.2𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 19.78∠45.1° Ω

1357.1∠ − 32.2° 𝐴𝐴
2000
5

= 3.39 ∠ − 32.2° 𝐴𝐴

To satisfy the 115% margin in Option 14bOptions 15b and 16b:
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
Eq.
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
(149174)
115%
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

19.78∠45.1° Ω
1.15

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 17.20∠45.1° Ω𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 45.1°𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙

> 3.39 ∠ − 32.2° 𝐴𝐴 × 1.15
> 3.90 ∠ − 32.2° 𝐴𝐴

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚, then the maximum
allowable impedance reach is:
Eq. (150)

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |

cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
17.20 Ω
cos(85.0° − 45.1°)

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Example Calculations: Option 14b
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

17.20 Ω
0.767

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 22.42∠85.0° Ω

Example Calculations: Options 15a and 16a
Options 15a and 16a represent the calculation for a synchronous generation Elements that connect a GSU
transformer to the Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant. Option 15a represents applying a phase time overcurrent relay (51) or Phase overcurrent
supervisory elements (50) associated with current-based, communication-assisted schemes where the scheme is
capable of tripping for loss of communications – installed on the high-side of the GSU transformer. Option 16a
represents applying a phase directional time overcurrent relay or Phase directional overcurrent supervisory
elements (67) associated with current-based, communication-assisted schemes where the scheme is capable of
tripping for loss of communications – directional toward the Transmission system– installed on the high-side of
the GSU.
This example uses Option 15a as an example, where PTs and CTs are located in the high-side of the GSU
transformer.

Real Power output (P):
Eq. (151)

𝑃𝑃 = 𝐺𝐺𝐺𝐺𝐺𝐺𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝

𝑃𝑃 = 903 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 767.6 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (152)

𝑄𝑄 = 120% × 𝑃𝑃

𝑄𝑄 = 1.20 × 767.6 𝑀𝑀𝑀𝑀
𝑄𝑄 = 921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 15a, Table 1 – Bus Voltage, calls for a 0.85 per unit of the high-side nominal voltage:
Eq. (153)

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.85 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 293.25 𝑘𝑘𝑘𝑘

Apparent power (S):
Eq. (154)

𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗
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PRC-025-12 – Application Guidelines

Example Calculations: Options 15a and 16a

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗921.12 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 1157∠52.8° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (155)

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

1157∠ − 52.8° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 293.25 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 2280.6∠ − 52.8° 𝐴𝐴

Secondary current (Isec):
Eq. (156)

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

2280.6∠ − 52.8° 𝐴𝐴
2000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 5.701 ∠ − 52.8° 𝐴𝐴

To satisfy the 115% margin in Options 15a and 15b:
Eq. (157)

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.701 ∠ − 52.8° 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 6.56 ∠ − 52.8° 𝐴𝐴

Example Calculations: Options 15b and 16b

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PRC-025-12 – Application Guidelines

Options 15b and 16b represent the calculation for a synchronous generation Elements that connect a GSU
transformer to the Transmission system that are used exclusively to export energy directly from a BES generating
unit or generating plant. Option 15b represents applying a phase time overcurrent relay (51) or Phase overcurrent
supervisory elements (50) associated with current-based, communication-assisted schemes where the scheme is
capable of tripping for loss of communications – installed on the high-side of the GSU transformer. Option 16b
represents applying a phase directional time overcurrent relay or Phase directional overcurrent supervisory elements
(67) associated with current-based, communication-assisted schemes where the scheme is capable of tripping for
loss of communications – directional toward the Transmission system– installed on the high-side of the GSU.
This example uses Option 15b as a simulation example, where PTs and CTs are located in the high-side of the GSU
transformer.
The Reactive Power flow and high-side bus voltage are determined by simulation. The maximum Reactive Power
output on the high-side of the GSU transformer during field-forcing is used as this value will correspond to the
lowest apparent impedance. The corresponding high-side bus voltage is also used in the calculation. Note that
although the excitation limiter reduces the field, the duration of the Reactive Power output achieved for this
condition is sufficient to operate a phase overcurrent relay.
In this simulation the following values are derived:
𝑄𝑄 = 703.6 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 0.908 × 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 313.3 𝑘𝑘𝑘𝑘

The other value required is the Real Power output which is modeled in the simulation at 100% of the gross MW
capability reported to the Transmission Planner. In this case:
𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 700.0 𝑀𝑀𝑀𝑀

1000

1.25

800

1.15

600

Voltage (p.u.)

1.05

Generator Reactive Power
400

0.95

Real and Reactive Power (MW/Mvar)

Generator Real Power

GSU High-Side Voltage
200

0.85

0

0.75
0

4

8

12

16

20

Time (s)

Apparent power (S):
Eq. (158)

𝑆𝑆 = 𝑃𝑃𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 + 𝑗𝑗𝑗𝑗

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PRC-025-12 – Application Guidelines

𝑆𝑆 = 700.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗703.6 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 992.5∠45.1° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):
Eq. (159)

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

𝑆𝑆 ∗

√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏

992.5∠ − 45.1° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 313.3 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 1831.2∠ − 45.1° 𝐴𝐴

Secondary current (Isec):
Eq. (160)

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
𝐶𝐶𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣

1831.2∠ − 45.1° 𝐴𝐴
2000
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 4.578 ∠ − 45.1° 𝐴𝐴

To satisfy the 115% margin in Options 15b and 16b:
Eq. (161)

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 115%

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.578 ∠ − 45.1° 𝐴𝐴 × 1.15
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 5.265 ∠ − 45.1° 𝐴𝐴

Example Calculations: Option 17
Option 17 represents the calculation for three asynchronous generation Elements that connect a GSU transformer
to the Transmission system that are used exclusively to export energy directly from a BES generating unit or
generating plant that is applying a phase distance relay (21) - directional toward the Transmission system. In this
application it was assumed 20 Mvar of total static compensation was added.

Option 17 represents the calculation for relays installed on the high-side of the GSU
transformer, including relays installed on the remote end of line, for Elements that connect a
GSU transformer for three asynchronous generators to the Transmission system that are
used exclusively to export energy directly from a BES generating unit or generating plant that
is applying a phase distance relay (e.g., 21) directional toward the Transmission system. In
this application it was assumed 20 Mvar of total static compensation was added.

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Example Calculations: Option 17

Real Power output (P):
Eq. (162)

𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝

Eq. (175) 𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):
Eq. (163)

Eq. (176)

𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos −1 (𝑝𝑝𝑝𝑝))�

𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
+ �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos−1(𝑝𝑝𝑝𝑝))�

𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos−1(0.85)))
𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

Option 17, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-side nominal voltage for the bus voltage
(Vbus):
Eq. (164)

𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛

Option 17, Table 1 – Bus Voltage, calls for a 1.0 per unit of the line nominal voltage for the
bus voltage (Vbus):
Eq. (177) 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 1.0 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑔𝑔𝑔𝑔𝑔𝑔 = 345.0 𝑘𝑘𝑘𝑘

Apparent power (S):
Eq. (165)

𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

Eq. (178) 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗

𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

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Example Calculations: Option 17

Primary impedance (Zpri):
2
Eq.
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝑍𝑍
=
𝑝𝑝𝑝𝑝𝑝𝑝
(166179)
𝑆𝑆 ∗

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 =

(345.0 𝑘𝑘𝑘𝑘)2
131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 = 904.4∠39.2° Ω

Secondary impedance (Zsec):

𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
Eq.
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝 ×
(167180)
𝑃𝑃𝑃𝑃𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
300
5

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 904.4∠39.2° Ω × 2000
1

𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 904.4∠39.2° Ω × 0.03
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠 = 27.13∠39.2° Ω

To satisfy the 130% margin in Option 17:
𝑍𝑍𝑠𝑠𝑠𝑠𝑠𝑠
Eq.
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =
(168181)
130%
𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

27.13∠39.2° Ω
1.30

𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 20.869∠39.2° Ω
𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 39.2°

Assume a Mho distance impedance relay with a maximum torque angle (MTA) set at 85˚,85°,
and then the maximum allowable impedance reach is:
|𝑍𝑍sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 |
Eq.
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <
(169182)
cos�𝜃𝜃𝑀𝑀𝑀𝑀𝑀𝑀 − 𝜃𝜃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 �
𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

20.869 Ω
cos(85.0° − 39.2°)

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Example Calculations: Option 17

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 <

20.869 Ω
0.697

𝑍𝑍𝑚𝑚𝑚𝑚𝑚𝑚 < 29.941∠85.0° Ω
Example Calculations: Options 18 and 19

Option 18 represents the calculation for three generation Elements that connect a relays on relays
installed on the high-side of the GSU transformer, including relays installed on the remote
end of line, for Elements that connect a GSU transformer for three asynchronous generators
to the Transmission system that are used exclusively to export energy directly from a BES
generating unit or generating plant that is .
Option 18 represents applying a phase time overcurrent (e.g., 51) relay connected to three
asynchronous generators. and/or phase instantaneous overcurrent supervisory elements (e.g., 50)
associated with current-based, communication-assisted schemes where the scheme is
capable of tripping for loss of communications installed on the high-side of the GSU
transformer, including relays at the remote end of the line.
Similarly, Option 19 may also be applied here for the phase directional time overcurrent relays
(e.g., 67) directional toward the Transmission system for Elements that connect a GSU
transformer, including relays at the remote end of the line to the Transmission system that
are used exclusively to export energy directly from a BES generating unit or generating plant.
In this application it was assumed 20 Mvar of total static compensation was added.
Real Power output (P):
Eq. 𝑃𝑃 = 3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × 𝑝𝑝𝑝𝑝
(170183)
𝑃𝑃 = 3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × 0.85
𝑃𝑃 = 102.0 𝑀𝑀𝑀𝑀

Reactive Power output (Q):

Eq. 𝑄𝑄 = 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑔𝑔𝑔𝑔𝑔𝑔_𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
(171184)
+ �3 × 𝐺𝐺𝐺𝐺𝐺𝐺𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 × sin(cos−1(𝑝𝑝𝑝𝑝))�

𝑄𝑄 = 15 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + 5 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 + (3 × 40 𝑀𝑀𝑀𝑀𝑀𝑀 × sin(cos −1 (0.85)))
𝑄𝑄 = 83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

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PRC-025-12 – Application Guidelines

Example Calculations: Options 18 and 19

Options 18 and 19, Table 1 – Bus Voltage, calls for a 1.0 per unit of the high-sideline nominal
voltage (Vbus):
Eq. 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛 = 1.0 𝑝𝑝. 𝑢𝑢.× 𝑉𝑉𝑛𝑛𝑛𝑛𝑛𝑛
(172185)
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 1.0 × 345 𝑘𝑘𝑘𝑘
𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏 = 345 𝑘𝑘𝑘𝑘

Apparent power (S):

Eq. 𝑆𝑆 = 𝑃𝑃 + 𝑗𝑗𝑗𝑗
(173186)
𝑆𝑆 = 102.0 𝑀𝑀𝑀𝑀 + 𝑗𝑗83.2 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀
𝑆𝑆 = 131.6∠39.2° 𝑀𝑀𝑀𝑀𝑀𝑀

Primary current (Ipri):

𝑆𝑆 ∗
Eq.
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =
(174187)
√3 × 𝑉𝑉𝑏𝑏𝑏𝑏𝑏𝑏
𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 =

131.6∠ − 39.2° 𝑀𝑀𝑀𝑀𝑀𝑀
1.73 × 345 𝑘𝑘𝑘𝑘

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝 = 220.5 ∠ − 39.2°𝐴𝐴

Secondary current (Isec):

𝐼𝐼𝑝𝑝𝑝𝑝𝑝𝑝
Eq.
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =
(175188)
𝐶𝐶𝐶𝐶𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴ℎ_𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟_ℎ𝑣𝑣
𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 =

220.5∠ − 39.2° 𝐴𝐴
300
5

𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 = 3.675∠ − 39.2° 𝐴𝐴

To satisfy the 130% margin in Options 18 and 19:
Eq. 𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠 × 130%
(176189)

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PRC-025-12 – Application Guidelines

Example Calculations: Options 18 and 19

𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 3.675∠ − 39.2° 𝐴𝐴 × 1.30
𝐼𝐼sec 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 > 4.778∠ − 39.2° 𝐴𝐴

End of calculations

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PRC-025-12 – Application Guidelines

Rationale:

During development of this standard, text boxes were embedded within the standard to explain
the rationale for various parts of the standard. Upon BOT approval, the text from the rationale
text boxes was moved to this section.
Rationale for R1:

Requirement R1 is a risk-based requirement that requires the responsible entity to be aware of
each protective relay subject to the standard and applies an appropriate setting based on its
calculations or simulation for the conditions established in Attachment 1.
The criteria established in Attachment 1 represent short-duration conditions during which
generation Facilities are capable of providing system reactive resources, and for which
generation Facilities have been historically recorded to disconnect, causing events to become
more severe.
The term, “while maintaining reliable fault protection” in Requirement R1 describes that the
responsible entity is to comply with this standard while achieving their desired protection goals.
Refer to the Guidelines and Technical Basis, Introduction, for more information.

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