PRC-026-1 Reliability Standard

PRC-026-1 — Relay Performance During Stable Power Swings

A. Introduction
1. Title:

Relay Performance During Stable Power Swings

2. Number:

PRC-026-1

3. Purpose:
To ensure that load-responsive protective relays are expected to not trip in
response to stable power swings during non-Fault conditions.
4. Applicability:
4.1.

4.2.

Functional Entities:
4.1.1

Generator Owner that applies load-responsive protective relays as
described in PRC-026-1 – Attachment A at the terminals of the Elements
listed in Section 4.2, Facilities.

4.1.2

Planning Coordinator.

4.1.3

Transmission Owner that applies load-responsive protective relays as
described in PRC-026-1 – Attachment A at the terminals of the Elements
listed in Section 4.2, Facilities.

Facilities: The following Elements that are part of the Bulk Electric System
(BES):
4.2.1

Generators.

4.2.2

Transformers.

4.2.3

Transmission lines.

5. Background:
This is the third phase of a three-phased standard development project that focused on
developing this new Reliability Standard to address protective relay operations due to
stable power swings. The March 18, 2010, Federal Energy Regulatory Commission
(FERC) Order No. 733 approved Reliability Standard PRC-023-1 – Transmission Relay
Loadability. In that Order, FERC directed NERC to address three areas of relay loadability
that include modifications to the approved PRC-023-1, development of a new Reliability
Standard to address generator protective relay loadability, and a new Reliability Standard
to address the operation of protective relays due to stable power swings. This project’s
SAR addresses these directives with a three-phased approach to standard development.
Phase 1 focused on making the specific modifications from FERC Order No. 733 to PRC023-1. Reliability Standard PRC-023-2, which incorporated these modifications, became
mandatory on July 1, 2012.
Phase 2 focused on developing a new Reliability Standard, PRC-025-1 – Generator Relay
Loadability, to address generator protective relay loadability. PRC-025-1 became
mandatory on October 1, 2014, along with PRC-023-3, which was modified to harmonize
PRC-023-2 with PRC-025-1.
Phase 3 focuses on preventing protective relays from tripping unnecessarily due to stable
power swings by requiring identification of Elements on which a stable or unstable power
swing may affect Protection System operation, assessment of the security of loadPage 1 of 84

PRC-026-1 — Relay Performance During Stable Power Swings

responsive protective relays to tripping in response to only a stable power swing, and
implementation of Corrective Action Plans (CAP), where necessary. Phase 3 improves
security of load-responsive protective relays for stable power swings so they are expected
to not trip in response to stable power swings during non-Fault conditions while
maintaining dependable fault detection and dependable out-of-step tripping.
6. Effective Dates:
Requirement R1
First day of the first full calendar year that is 12 months after the date that the standard is
approved by an applicable governmental authority or as otherwise provided for in a
jurisdiction where approval by an applicable governmental authority is required for a
standard to go into effect. Where approval by an applicable governmental authority is not
required, the standard shall become effective on the first day of the first full calendar year
that is 12 months after the date the standard is adopted by the NERC Board of Trustees or
as otherwise provided for in that jurisdiction.
Requirements R2, R3, and R4
First day of the first full calendar year that is 36 months after the date that the standard is
approved by an applicable governmental authority or as otherwise provided for in a
jurisdiction where approval by an applicable governmental authority is required for a
standard to go into effect. Where approval by an applicable governmental authority is not
required, the standard shall become effective on the first day of the first full calendar year
that is 36 months after the date the standard is adopted by the NERC Board of Trustees or
as otherwise provided for in that jurisdiction.

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PRC-026-1 — Relay Performance During Stable Power Swings

B. Requirements and Measures
R1. Each Planning Coordinator shall, at least once each calendar year, provide notification
of each generator, transformer, and transmission line BES Element in its area that
meets one or more of the following criteria, if any, to the respective Generator Owner
and Transmission Owner: [Violation Risk Factor: Medium] [Time Horizon: Long-term
Planning]
Criteria:
1. Generator(s) where an angular stability constraint exists that is addressed by a
System Operating Limit (SOL) or a Remedial Action Scheme (RAS) and those
Elements terminating at the Transmission station associated with the generator(s).
2. An Element that is monitored as part of an SOL identified by the Planning
Coordinator’s methodology1 based on an angular stability constraint.
3. An Element that forms the boundary of an island in the most recent
underfrequency load shedding (UFLS) design assessment based on application of
the Planning Coordinator’s criteria for identifying islands, only if the island is
formed by tripping the Element due to angular instability.
4. An Element identified in the most recent annual Planning Assessment where relay
tripping occurs due to a stable or unstable2 power swing during a simulated
disturbance.
M1. Each Planning Coordinator shall have dated evidence that demonstrates notification of
the generator, transformer, and transmission line BES Element(s) that meet one or
more of the criteria in Requirement R1, if any, to the respective Generator Owner and
Transmission Owner. Evidence may include, but is not limited to, the following
documentation: emails, facsimiles, records, reports, transmittals, lists, or spreadsheets.

1

NERC Reliability Standard FAC-014-2 – Establish and Communicate System Operating Limits, Requirement R3.

An example of an unstable power swing is provided in the Guidelines and Technical Basis section, “Justification
for Including Unstable Power Swings in the Requirements section of the Guidelines and Technical Basis.”
2

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PRC-026-1 — Relay Performance During Stable Power Swings

R2. Each Generator Owner and Transmission Owner shall: [Violation Risk Factor: High]
[Time Horizon: Operations Planning]
2.1 Within 12 full calendar months of notification of a BES Element pursuant to
Requirement R1, determine whether its load-responsive protective relay(s)
applied to that BES Element meets the criteria in PRC-026-1 – Attachment B
where an evaluation of that Element’s load-responsive protective relay(s) based
on PRC-026-1 – Attachment B criteria has not been performed in the last five
calendar years.
2.2 Within 12 full calendar months of becoming aware3 of a generator, transformer,
or transmission line BES Element that tripped in response to a stable or unstable4
power swing due to the operation of its protective relay(s), determine whether its
load-responsive protective relay(s) applied to that BES Element meets the criteria
in PRC-026-1 – Attachment B.
M2. Each Generator Owner and Transmission Owner shall have dated evidence that
demonstrates the evaluation was performed according to Requirement R2. Evidence
may include, but is not limited to, the following documentation: apparent impedance
characteristic plots, email, design drawings, facsimiles, R-X plots, software output,
records, reports, transmittals, lists, settings sheets, or spreadsheets.
R3. Each Generator Owner and Transmission Owner shall, within six full calendar months
of determining a load-responsive protective relay does not meet the PRC-026-1 –
Attachment B criteria pursuant to Requirement R2, develop a Corrective Action Plan
(CAP) to meet one of the following: [Violation Risk Factor: Medium] [Time Horizon:
Operations Planning]


The Protection System meets the PRC-026-1 – Attachment B criteria, while
maintaining dependable fault detection and dependable out-of-step tripping (if outof-step tripping is applied at the terminal of the BES Element); or



The Protection System is excluded under the PRC-026-1 – Attachment A criteria
(e.g., modifying the Protection System so that relay functions are supervised by
power swing blocking or using relay systems that are immune to power swings),
while maintaining dependable fault detection and dependable out-of-step tripping
(if out-of-step tripping is applied at the terminal of the BES Element).

M3. The Generator Owner and Transmission Owner shall have dated evidence that
demonstrates the development of a CAP in accordance with Requirement R3. Evidence
may include, but is not limited to, the following documentation: corrective action
plans, maintenance records, settings sheets, project or work management program
records, or work orders.
R4. Each Generator Owner and Transmission Owner shall implement each CAP developed
pursuant to Requirement R3 and update each CAP if actions or timetables change until
all actions are complete. [Violation Risk Factor: Medium][Time Horizon: Long-Term
Planning]

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M4. The Generator Owner and Transmission Owner shall have dated evidence that
demonstrates implementation of each CAP according to Requirement R4, including
updates to the CAP when actions or timetables change. Evidence may include, but is
not limited to, the following documentation: corrective action plans, maintenance
records, settings sheets, project or work management program records, or work orders.
C. Compliance
1. Compliance Monitoring Process
1.1.

Compliance Enforcement Authority
As defined in the NERC Rules of Procedure, “Compliance Enforcement Authority”
(CEA) means NERC or the Regional Entity in their respective roles of monitoring
and enforcing compliance with the NERC Reliability Standards.

1.2.

Evidence Retention
The following evidence retention periods 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 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, Planning Coordinator, and Transmission Owner shall keep
data or evidence to show compliance as identified below unless directed by its CEA
to retain specific evidence for a longer period of time as part of an investigation.


The Planning Coordinator shall retain evidence of Requirement R1 for a
minimum of one calendar year following the completion of the
Requirement.



The Generator Owner and Transmission Owner shall retain evidence of
Requirement R2 evaluation for a minimum of 12 calendar months following
completion of each evaluation where a CAP is not developed.



The Generator Owner and Transmission Owner shall retain evidence of
Requirements R2, R3, and R4 for a minimum of 12 calendar months
following completion of each CAP.

If a Generator Owner, Planning Coordinator, or Transmission Owner is found noncompliant, it shall keep information related to the non-compliance until mitigation
is complete and approved, or for the time specified above, whichever is longer.

3

Some examples of the ways an entity may become aware of a power swing are provided in the Guidelines and
Technical Basis section, “Becoming Aware of an Element That Tripped in Response to a Power Swing.”
An example of an unstable power swing is provided in the Guidelines and Technical Basis section, “Justification
for Including Unstable Power Swings in the Requirements section of the Guidelines and Technical Basis.”
4

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The CEA shall keep the last audit records and all requested and submitted
subsequent audit records.
1.3.

Compliance Monitoring and Assessment Processes:
As defined in the NERC Rules of Procedure; “Compliance Monitoring and
Assessment Processes” refers to the identification of the processes that will be used
to evaluate data or information for the purpose of assessing performance or
outcomes with the associated reliability standard.

1.4.

Additional Compliance Information
None.

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PRC-026-1 — Relay Performance During Stable Power Swings

Table of Compliance Elements
R#
R1

Time
Horizon
Long-term
Planning

Violation Severity Levels
VRF
Lower VSL
Medium The Planning
Coordinator provided
notification of the
BES Element(s) in
accordance with
Requirement R1, but
was less than or equal
to 30 calendar days
late.

Moderate VSL

High VSL

Severe VSL

The Planning
Coordinator provided
notification of the
BES Element(s) in
accordance with
Requirement R1, but
was more than 30
calendar days and less
than or equal to 60
calendar days late.

The Planning
Coordinator provided
notification of the
BES Element(s) in
accordance with
Requirement R1, but
was more than 60
calendar days and less
than or equal to 90
calendar days late.

The Planning
Coordinator provided
notification of the
BES Element(s) in
accordance with
Requirement R1, but
was more than 90
calendar days late.
OR
The Planning
Coordinator failed to
provide notification
of the BES
Element(s) in
accordance with
Requirement R1.

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R#
R2

Time
Horizon
Operations
Planning

Violation Severity Levels
VRF
High

Lower VSL

Moderate VSL

High VSL

Severe VSL

The Generator Owner
or Transmission
Owner evaluated its
load-responsive
protective relay(s) in
accordance with
Requirement R2, but
was less than or equal
to 30 calendar days
late.

The Generator Owner
or Transmission
Owner evaluated its
load-responsive
protective relay(s) in
accordance with
Requirement R2, but
was more than 30
calendar days and less
than or equal to 60
calendar days late.

The Generator Owner
or Transmission
Owner evaluated its
load-responsive
protective relay(s) in
accordance with
Requirement R2, but
was more than 60
calendar days and less
than or equal to 90
calendar days late.

The Generator Owner
or Transmission
Owner evaluated its
load-responsive
protective relay(s) in
accordance with
Requirement R2, but
was more than 90
calendar days late.
OR
The Generator Owner
or Transmission
Owner failed to
evaluate its loadresponsive protective
relay(s) in accordance
with Requirement R2.

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R#
R3

R4

Time
Horizon
Long-term
Planning

Long-term
Planning

Violation Severity Levels
VRF
Lower VSL
Medium The Generator Owner
or Transmission
Owner developed a
Corrective Action
Plan (CAP) in
accordance with
Requirement R3, but
in more than six
calendar months and
less than or equal to
seven calendar
months.

Medium The Generator Owner
or Transmission
Owner implemented a
Corrective Action
Plan (CAP), but failed
to update a CAP when
actions or timetables
changed, in
accordance with
Requirement R4.

Moderate VSL

High VSL

Severe VSL

The Generator Owner
or Transmission
Owner developed a
Corrective Action
Plan (CAP) in
accordance with
Requirement R3, but
in more than seven
calendar months and
less than or equal to
eight calendar
months.

The Generator Owner
or Transmission
Owner developed a
Corrective Action
Plan (CAP) in
accordance with
Requirement R3, but
in more than eight
calendar months and
less than or equal to
nine calendar months.

The Generator Owner
or Transmission
Owner developed a
Corrective Action
Plan (CAP) in
accordance with
Requirement R3, but
in more than nine
calendar months.

N/A

OR
The Generator Owner
or Transmission
Owner failed to
develop a CAP in
accordance with
Requirement R3.

N/A

The Generator Owner
or Transmission
Owner failed to
implement a
Corrective Action
Plan (CAP) in
accordance with
Requirement R4.

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D. Regional Variances
None.
E. Interpretations
None.
F. Associated Documents
Applied Protective Relaying, Westinghouse Electric Corporation, 1979.
Burdy, John, Loss-of-excitation Protection for Synchronous Generators GER-3183, General
Electric Company.
IEEE Power System Relaying Committee WG D6, Power Swing and Out-of-Step
Considerations on Transmission Lines, July 2005: http://www.pes-psrc.org/Reports
/Power%20Swing%20and%20OOS%20Considerations%20on%20Transmission%20
Lines%20F..pdf.
Kimbark Edward Wilson, Power System Stability, Volume II: Power Circuit Breakers and
Protective Relays, Published by John Wiley and Sons, 1950.
Kundur, Prabha, Power System Stability and Control, 1994, Palo Alto: EPRI, McGraw Hill,
Inc.
NERC System Protection and Control Subcommittee, Protection System Response to Power
Swings, August 2013: http://www.nerc.com/comm/PC/System%20Protection%20
and%20Control%20Subcommittee%20SPCS%2020/SPCS%20Power%20Swing%20
Report_Final_20131015.pdf.
Reimert, Donald, Protective Relaying for Power Generation Systems, 2006, Boca Raton: CRC
Press.

Version History
Version

Date

1

November 13, 2014

Action
Adopted by NERC Board of
Trustees

Change
Tracking
New

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PRC-026-1 — Relay Performance During Stable Power Swings

PRC-026-1 – Attachment A
This standard applies to any protective functions which could trip instantaneously or with a time
delay of less than 15 cycles on load current (i.e., “load-responsive”) including, but not limited to:





Phase distance
Phase overcurrent
Out-of-step tripping
Loss-of-field

The following protection functions are excluded from Requirements of this standard:















Relay elements supervised by power swing blocking
Relay elements that are only enabled when other relays or associated systems fail. For
example:
o Overcurrent elements that are only enabled during loss of potential conditions.
o Relay elements that are only enabled during a loss of communications
Thermal emulation relays which are used in conjunction with dynamic Facility Ratings
Relay elements associated with direct current (dc) lines
Relay elements associated with dc converter transformers
Phase fault detector relay elements employed to supervise other load-responsive phase
distance elements (i.e., in order to prevent false operation in the event of a loss of potential)
Relay elements associated with switch-onto-fault schemes
Reverse power relay on the generator
Generator 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)
Current differential relay, pilot wire relay, and phase comparison relay
Voltage-restrained or voltage-controlled overcurrent relays

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PRC-026-1 — Relay Performance During Stable Power Swings

PRC-026-1 – Attachment B
Criterion A:
An impedance-based relay used for tripping is expected to not trip for a stable power swing,
when the relay characteristic is completely contained within the unstable power swing region.5
The unstable power swing region is formed by the union of three shapes in the impedance (RX) plane; (1) a lower loss-of-synchronism circle based on a ratio of the sending-end to
receiving-end voltages of 0.7; (2) an upper loss-of-synchronism circle based on a ratio of the
sending-end to receiving-end voltages of 1.43; (3) a lens that connects the endpoints of the
total system impedance (with the parallel transfer impedance removed) bounded by varying
the sending-end and receiving-end voltages from 0.0 to 1.0 per unit, while maintaining a
constant system separation angle across the total system impedance where:
1. The system separation angle is:
 At least 120 degrees, or
 An angle less than 120 degrees where a documented transient stability analysis
demonstrates that the expected maximum stable separation angle is less than 120
degrees.
2. All generation is in service and all transmission BES Elements are in their normal
operating state when calculating the system impedance.
3. Saturated (transient or sub-transient) reactance is used for all machines.

5

Guidelines and Technical Basis, Figures 1 and 2.

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PRC-026-1 – Attachment B
Criterion B:
The pickup of an overcurrent relay element used for tripping, that is above the calculated
current value (with the parallel transfer impedance removed) for the conditions below:
1. The system separation angle is:
 At least 120 degrees, or
 An angle less than 120 degrees where a documented transient stability analysis
demonstrates that the expected maximum stable separation angle is less than 120
degrees.
2. All generation is in service and all transmission BES Elements are in their normal
operating state when calculating the system impedance.
3. Saturated (transient or sub-transient) reactance is used for all machines.
4. Both the sending-end and receiving-end voltages at 1.05 per unit.

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PRC-026-1 – Application Guidelines

Guidelines and Technical Basis
Introduction
The NERC System Protection and Control Subcommittee technical document, Protection System
Response to Power Swings, August 2013,6 (“PSRPS Report” or “report”) was specifically prepared
to support the development of this NERC Reliability Standard. The report provided a historical
perspective on power swings as early as 1965 up through the approval of the report by the NERC
Planning Committee. The report also addresses reliability issues regarding trade-offs between
security and dependability of Protection Systems, considerations for this NERC Reliability
Standard, and a collection of technical information about power swing characteristics and varying
issues with practical applications and approaches to power swings. Of these topics, the report
suggests an approach for this NERC Reliability Standard (“standard” or “PRC-026-1”) which is
consistent with addressing three regulatory directives in the FERC Order No. 733. The first
directive concerns the need for “…protective relay systems that differentiate between faults and
stable power swings and, when necessary, phases out protective relay systems that cannot meet
this requirement.”7 Second, is “…to develop a Reliability Standard addressing undesirable relay
operation due to stable power swings.”8 The third directive “…to consider “islanding” strategies
that achieve the fundamental performance for all islands in developing the new Reliability
Standard addressing stable power swings”9 was considered during development of the standard.
The development of this standard implements the majority of the approaches suggested by the
report. However, it is noted that the Reliability Coordinator and Transmission Planner have not
been included in the standard’s Applicability section (as suggested by the PSRPS Report). This is
so that a single entity, the Planning Coordinator, may be the single source for identifying Elements
according to Requirement R1. A single source will insure that multiple entities will not identify
Elements in duplicate, nor will one entity fail to provide an Element because it believes the
Element is being provided by another entity. The Planning Coordinator has, or has access to, the
wide-area model and can correctly identify the Elements that may be susceptible to a stable or
unstable power swing. Additionally, not including the Reliability Coordinator and Transmission
Planner is consistent with the applicability of other relay loadability NERC Reliability Standards
(e.g., PRC-023 and PRC-025). It is also consistent with the NERC Functional Model.
The phrase, “while maintaining dependable fault detection and dependable out-of-step tripping”
in Requirement R3, describes that the Generator Owner and Transmission Owner are 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

6

NERC System Protection and Control Subcommittee, Protection System Response to Power Swings, August 2013:
http://www.nerc.com/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20SPCS%2020/SPC
S%20Power%20Swing%20Report_Final_20131015.pdf)
7

Transmission Relay Loadability Reliability Standard, Order No. 733, P.150 FERC ¶ 61,221 (2010).

8

Ibid. P.153.

9

Ibid. P.162.

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PRC-026-1 – Application Guidelines
this standard is not intended to result in the loss of these protection functions. Instead, the
Generator Owner and Transmission Owner must consider both the Requirements within this
standard and its desired protection goals and perform modifications to its protective relays or
protection philosophies as necessary to achieve both.

Power Swings
The IEEE Power System Relaying Committee WG D6 developed a technical document called
Power Swing and Out-of-Step Considerations on Transmission Lines (July 2005) that provides
background on power swings. The following are general definitions from that document:10
Power Swing: a variation in three phase power flow which occurs when the generator rotor
angles are advancing or retarding relative to each other in response to changes in load
magnitude and direction, line switching, loss of generation, faults, and other system
disturbances.
Pole Slip: a condition whereby a generator, or group of generators, terminal voltage angles
(or phases) go past 180 degrees with respect to the rest of the connected power system.
Stable Power Swing: a power swing is considered stable if the generators do not slip poles
and the system reaches a new state of equilibrium, i.e. an acceptable operating condition.
Unstable Power Swing: a power swing that will result in a generator or group of generators
experiencing pole slipping for which some corrective action must be taken.
Out-of-Step Condition: Same as an unstable power swing.
Electrical System Center or Voltage Zero: it is the point or points in the system where the
voltage becomes zero during an unstable power swing.

Burden to Entities
The PSRPS Report provides a technical basis and approach for focusing on Protection Systems,
which are susceptible to power swings, while achieving the purpose of the standard. The approach
reduces the number of relays to which the PRC-026-1 Requirements would apply by first
identifying the BES Element(s) on which load-responsive protective relays must be evaluated. The
first step uses criteria to identify the Elements on which a Protection System is expected to be
challenged by power swings. Of those Elements, the second step is to evaluate each loadresponsive protective relay that is applied on each identified Element. Rather than requiring the
Planning Coordinator or Transmission Planner to perform simulations to obtain information for
each identified Element, the Generator Owner and Transmission Owner will reduce the need for
simulation by comparing the load-responsive protective relay characteristic to specific criteria in
PRC-026-1 – Attachment B.

10

http://www.pes-psrc.org/Reports/Power%20Swing%20and%20OOS%20Considerations%20on%20Transmission
%20Lines%20F..pdf.

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PRC-026-1 – Application Guidelines

Applicability
The standard is applicable to the Generator Owner, Planning Coordinator, and Transmission
Owner entities. More specifically, the Generator Owner and Transmission Owner entities are
applicable when applying load-responsive protective relays at the terminals of the applicable BES
Elements. The standard is applicable to the following BES Elements: generators, transformers, and
transmission lines. The Distribution Provider was considered for inclusion in the standard;
however, it is not subject to the standard because this entity, by functional registration, would not
own generators, transmission lines, or transformers other than load serving.
Load-responsive protective relays include any protective functions which could trip with or
without time delay, on load current.

Requirement R1
The Planning Coordinator has a wide-area view and is in the position to identify what, if any,
Elements meet the criteria. The criterion-based approach is consistent with the NERC System
Protection and Control Subcommittee (SPCS) technical document, Protection System Response to
Power Swings (August 2013),11 which recommends a focused approach to determine an at-risk
Element. Identification of Elements comes from the annual Planning Assessments pursuant to the
transmission planning (i.e., “TPL”) and other NERC Reliability Standards (e.g., PRC-006), and
the standard is not requiring any other assessments to be performed by the Planning Coordinator.
The required notification on a calendar year basis to the respective Generator Owner and
Transmission Owner is sufficient because it is expected that the Planning Coordinator will make
its notifications following the completion of its annual Planning Assessments. The Planning
Coordinator will continue to provide notification of Elements on a calendar year basis even if a
study is performed less frequently (e.g., PRC-006 – Automatic Underfrequency Load Shedding,
which is five years) and has not changed. It is possible that a Planning Coordinator could utilize
studies from a prior year in determining the necessary notifications pursuant to Requirement R1.
Criterion 1
The first criterion involves generator(s) where an angular stability constraint exists that is
addressed by a System Operating Limit (SOL) or a Remedial Action Scheme (RAS) and those
Elements terminating at the Transmission station associated with the generator(s). For example, a
scheme to remove generation for specific conditions is implemented for a four-unit generating
plant (1,100 MW). Two of the units are 500 MW each; one is connected to the 345 kV system and
one is connected to the 230 kV system. The Transmission Owner has two 230 kV transmission
lines and one 345 kV transmission line all terminating at the generating facility as well as a 345/230
kV autotransformer. The remaining 100 MW consists of two 50 MW combustion turbine (CT)
units connected to four 66 kV transmission lines. The 66 kV transmission lines are not electrically
joined to the 345 kV and 230 kV transmission lines at the plant site and are not subject to the
operating limit or RAS. A stability constraint limits the output of the portion of the plant affected

11

http://www.nerc.com/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20SPCS%20
20/SPCS%20Power%20Swing%20Report_Final_20131015.pdf)

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by the RAS to 700 MW for an outage of the 345 kV transmission line. The RAS trips one of the
500 MW units to maintain stability for a loss of the 345 kV transmission line when the total output
from both 500 MW units is above 700 MW. For this example, both 500 MW generating units and
the associated generator step-up (GSU) transformers would be identified as Elements meeting this
criterion. The 345/230 kV autotransformer, the 345 kV transmission line, and the two 230 kV
transmission lines would also be identified as Elements meeting this criterion. The 50 MW
combustion turbines and 66 kV transmission lines would not be identified pursuant to Criterion 1
because these Elements are not subject to an operating limit or RAS and do not terminate at the
Transmission station associated with the generators that are subject to the SOL or RAS.
Criterion 2
The second criterion involves Elements that are monitored as a part of an established System
Operating Limit (SOL) based on an angular stability limit regardless of the outage conditions that
result in the enforcement of the SOL. For example, if two long parallel 500 kV transmission lines
have a combined SOL of 1,200 MW, and this limit is based on angular instability resulting from a
fault and subsequent loss of one of the two lines, then both lines would be identified as Elements
meeting the criterion.
Criterion 3
The third criterion involves Elements that form the boundary of an island within an underfrequency
load shedding (UFLS) design assessment. The criterion applies to islands identified based on
application of the Planning Coordinator’s criteria for identifying islands, where the island is
formed by tripping the Elements based on angular instability. The criterion applies if the angular
instability is modeled in the UFLS design assessment, or if the boundary is identified “off-line”
(i.e., the Elements are selected based on angular instability considerations, but the Elements are
tripped in the UFLS design assessment without modeling the initiating angular instability). In cases
where an out-of-step condition is detected and tripping is initiated at an alternate location, the
criterion applies to the Element on which the power swing is detected. The criterion does not apply
to islands identified based on other considerations that do not involve angular instability, such as
excessive loading, Planning Coordinator area boundary tie lines, or Balancing Authority boundary
tie lines.
Criterion 4
The fourth criterion involves Elements identified in the most recent annual Planning Assessment
where relay tripping occurs due to a stable or unstable12 power swing during a simulated
disturbance. The intent is for the Planning Coordinator to include any Element(s) where relay
tripping was observed during simulations performed for the most recent annual Planning
Assessment associated with the transmission planning TPL-001-4 Reliability Standard. Note that
relay tripping must be assessed within those annual Planning Assessments per TPL-001-4, R4,

12

Refer to the “Justification for Including Unstable Power Swings in the Requirements” section.

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PRC-026-1 – Application Guidelines
Part 4.3.1.3, which indicates that analysis shall include the “Tripping of Transmission lines and
transformers where transient swings cause Protection System operation based on generic or actual
relay models.” Identifying such Elements according to Criterion 4 and notifying the respective
Generator Owner and Transmission Owner will require that the owners of any load-responsive
protective relay applied at the terminals of the identified Element evaluate the relay’s susceptibility
to tripping in response to a stable power swing.
Planning Coordinators have the discretion to determine whether the observed tripping for a power
swing in its Planning Assessments occurs for valid contingencies and system conditions. The
Planning Coordinator will address tripping that is observed in transient analyses on an individual
basis; therefore, the Planning Coordinator is responsible for identifying the Elements based only
on simulation results that are determined to be valid.
Due to the nature of how a Planning Assessment is performed, there may be cases where a
previously-identified Element is not identified in the most recent annual Planning Assessment. If
so, this is acceptable because the Generator Owner and Transmission Owner would have taken
action upon the initial notification of the previously identified Element. When an Element is not
identified in later Planning Assessments, the risk of load-responsive protective relays tripping in
response to a stable power swing during non-Fault conditions would have already been assessed
under Requirement R2 and mitigated according to Requirements R3 and R4 where the relays did
not meet the PRC-026-1 – Attachment B criteria. According to Requirement R2, the Generator
Owner and Transmission Owner are only required to re-evaluate each load-responsive protective
relay for an identified Element where the evaluation has not been performed in the last five
calendar years.
Although Requirement R1 requires the Planning Coordinator to notify the respective Generator
Owner and Transmission Owner of any Elements meeting one or more of the four criteria, it does
not preclude the Planning Coordinator from providing additional information, such as apparent
impedance characteristics, in advance or upon request, that may be useful in evaluating protective
relays. Generator Owners and Transmission Owners are able to complete protective relay
evaluations and perform the required actions without additional information. The standard does
not include any requirement for the entities to provide information that is already being shared or
exchanged between entities for operating needs. While a Requirement has not been included for
the exchange of information, entities should recognize that relay performance needs to be
measured against the most current information.

Requirement R2
Requirement R2 requires the Generator Owner and Transmission Owner to evaluate its loadresponsive protective relays to ensure that they are expected to not trip in response to stable power
swings.

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PRC-026-1 – Application Guidelines
The PRC-026-1 – Attachment A lists the applicable load-responsive relays that must be evaluated
which include phase distance, phase overcurrent, out-of-step tripping, and loss-of-field relay
functions. Phase distance relays could include, but are not limited to, the following:



Zone elements with instantaneous tripping or intentional time delays of less than 15 cycles
Phase distance elements used in high-speed communication-aided tripping schemes
including:
 Directional Comparison Blocking (DCB) schemes
 Directional Comparison Un-Blocking (DCUB) schemes
 Permissive Overreach Transfer Trip (POTT) schemes
 Permissive Underreach Transfer Trip (PUTT) schemes

A method is provided within the standard to support consistent evaluation by Generator Owners
and Transmission Owners based on specified conditions. Once a Generator Owner or Transmission
Owner is notified of Elements pursuant to Requirement R1, it has 12 full calendar months to
determine if each Element’s load-responsive protective relays meet the PRC-026-1 – Attachment
B criteria, if the determination has not been performed in the last five calendar years. Additionally,
each Generator Owner and Transmission Owner, that becomes aware of a generator, transformer,
or transmission line BES Element that tripped in response to a stable or unstable power swing due
to the operation of its protective relays pursuant to Requirement R2, Part 2.2, must perform the
same PRC-026-1 – Attachment B criteria determination within 12 full calendar months.
Becoming Aware of an Element That Tripped in Response to a Power Swing
Part 2.2 in Requirement R2 is intended to initiate action by the Generator Owner and Transmission
Owner when there is a known stable or unstable power swing and it resulted in the entity’s Element
tripping. The criterion starts with becoming aware of the event (i.e., power swing) and then any
connection with the entity’s Element tripping. By doing so, the focus is removed from the entity
having to demonstrate that it made a determination whether a power swing was present for every
Element trip. The basis for structuring the criterion in this manner is driven by the available ways
that a Generator Owner and Transmission Owner could become aware of an Element that tripped
in response to a stable or unstable power swing due to the operation of its protective relay(s).
Element trips caused by stable or unstable power swings, though infrequent, would be more
common in a larger event. The identification of power swings will be revealed during an analysis
of the event. Event analysis where an entity may become aware of a stable or unstable power swing
could include internal analysis conducted by the entity, the entity’s Protection System review
following a trip, or a larger scale analysis by other entities. Event analysis could include
involvement by the entity’s Regional Entity, and in some cases NERC.
Information Common to Both Generation and Transmission Elements
The PRC-026-1 – Attachment A lists the load-responsive protective relays that are subject to this
standard. Generator Owners and Transmission Owners may own load-responsive protective relays
(e.g., distance relays) that directly affect generation or transmission BES Elements and will require
analysis as a result of Elements being identified by the Planning Coordinator in Requirement R1

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PRC-026-1 – Application Guidelines
or the Generator Owner or Transmission Owner in Requirement R2. For example, distance relays
owned by the Transmission Owner may be installed at the high-voltage side of the generator stepup (GSU) transformer (directional toward the generator) providing backup to generation
protection. Generator Owners may have distance relays applied to backup transmission protection
or backup protection to the GSU transformer. The Generator Owner may have relays installed at
the generator terminals or the high-voltage side of the GSU transformer.
Exclusion of Time Based Load-Responsive Protective Relays
The purpose of the standard is “[t]o ensure that load-responsive protective relays are expected to
not trip in response to stable power swings during non-Fault conditions.” Load-responsive, highspeed tripping protective relays pose the highest risk of operating during a power swing. Because
of this, high-speed tripping protective relays and relays with a time delay of less than 15 cycles are
included in the standard; whereas other relays (i.e., Zones 2 and 3) with a time delay of 15 cycles
or greater are excluded. The time delay used for exclusion on some load-responsive protective
relays is based on the maximum expected time that load-responsive protective relays would be
exposed to a stable power swing with a slow slip rate frequency.
In order to establish a time delay that distinguishes a high-risk load-responsive protective relay
from one that has a time delay for tripping (lower-risk), a sample of swing rates were calculated
based on a stable power swing entering and leaving the impedance characteristic as shown in Table
1. For a relay impedance characteristic that has a power swing entering and leaving, beginning at
90 degrees with a termination at 120 degrees before exiting the zone, the zone timer must be greater
than the calculated time the stable power swing is inside the relay’s operating zone to not trip in
response to the stable power swing.
Eq. (1)

(120° − 𝐴𝑛𝑔𝑙𝑒 𝑜𝑓 𝑒𝑛𝑡𝑟𝑦 𝑖𝑛𝑡𝑜 𝑡ℎ𝑒 𝑟𝑒𝑙𝑎𝑦 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐) × 60
𝑍𝑜𝑛𝑒 𝑡𝑖𝑚𝑒𝑟 > 2 × (
)
(360 × 𝑆𝑙𝑖𝑝 𝑅𝑎𝑡𝑒)

Table 1: Swing Rates
Zone Timer
(Cycles)

Slip Rate
(Hz)

10

1.00

15

0.67

20

0.50

30

0.33

With a minimum zone timer of 15 cycles, the corresponding slip rate of the system is 0.67 Hz.
This represents an approximation of a slow slip rate during a system Disturbance. Longer time
delays allow for slower slip rates.

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PRC-026-1 – Application Guidelines
Application to Transmission Elements
Criterion A in PRC-026-1 – Attachment B describes an unstable power swing region that is formed
by the union of three shapes in the impedance (R-X) plane. The first shape is a lower loss-ofsynchronism circle based on a ratio of the sending-end to receiving-end voltages of 0.7 (i.e., ES /
ER = 0.7 / 1.0 = 0.7). The second shape is an upper loss-of-synchronism circle based on a ratio of
the sending-end to receiving-end voltages of 1.43 (i.e., ES / ER = 1.0 / 0.7 = 1.43). The third shape
is a lens that connects the endpoints of the total system impedance together by varying the sendingend and receiving-end system voltages from 0.0 to 1.0 per unit, while maintaining a constant
system separation angle across the total system impedance (with the parallel transfer impedance
removed—see Figures 1 through 5). The total system impedance is derived from a two-bus
equivalent network and is determined by summing the sending-end source impedance, the line
impedance (excluding the Thévenin equivalent transfer impedance), and the receiving-end source
impedance as shown in Figures 6 and 7. Establishing the total system impedance provides a
conservative condition that will maximize the security of the relay against various system
conditions. The smallest total system impedance represents a condition where the size of the lens
characteristic in the R-X plane is smallest and is a conservative operating point from the standpoint
of ensuring a load-responsive protective relay is expected to not trip given a predetermined angular
displacement between the sending-end and receiving-end voltages. The smallest total system
impedance results when all generation is in service and all transmission BES Elements are modeled
in their “normal” system configuration (PRC-026-1 – Attachment B, Criterion A). The parallel
transfer impedance is removed to represent a likely condition where parallel Elements may be lost
during the disturbance, and the loss of these Elements magnifies the sensitivity of the loadresponsive relays on the parallel line by removing the “infeed effect” (i.e., the apparent impedance
sensed by the relay is decreased as a result of the loss of the transfer impedance, thus making the
relay more likely to trip for a stable power swing—See Figures 13 and 14).
The sending-end and receiving-end source voltages are varied from 0.7 to 1.0 per unit to form the
lower and upper loss-of-synchronism circles. The ratio of these two voltages is used in the
calculation of the loss-of-synchronism circles, and result in a ratio range from 0.7 to 1.43.
Eq. (2)

𝐸𝑆 0.7
=
= 0.7
𝐸𝑅 1.0

Eq. (3):

𝐸𝑆 1.0
=
= 1.43
𝐸𝑅 0.7

The internal generator voltage during severe power swings or transmission system fault conditions
will be greater than zero due to voltage regulator support. The voltage ratio of 0.7 to 1.43 is chosen
to be more conservative than the PRC-02313 and PRC-02514 NERC Reliability Standards where a
lower bound voltage of 0.85 per unit voltage is used. A ±15% internal generator voltage range was
chosen as a conservative voltage range for calculation of the voltage ratio used to calculate the
loss-of-synchronism circles. For example, the voltage ratio using these voltages would result in a
ratio range from 0.739 to 1.353.

13

Transmission Relay Loadability

14

Generator Relay Loadability

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PRC-026-1 – Application Guidelines

Eq. (4)

𝐸𝑆 0.85
=
= 0.739
𝐸𝑅 1.15

Eq. (5):

𝐸𝑆 1.15
=
= 1.353
𝐸𝑅 0.85

The lower ratio is rounded down to 0.7 to be more conservative, allowing a voltage range of 0.7
to 1.0 per unit to be used for the calculation of the loss-of-synchronism circles.15
When the parallel transfer impedance is included in the model, the division of current through the
parallel transfer impedance path results in actual measured relay impedances that are larger than
those measured when the parallel transfer impedance is removed (i.e., infeed effect), which would
make it more likely for an impedance relay element to be completely contained within the unstable
power swing region as shown in Figure 11. If the transfer impedance is included in the evaluation,
a distance relay element could be deemed as meeting PRC-026-1 – Attachment B criteria and, in
fact would be secure, assuming all Elements were in their normal state. In this case, the distance
relay element could trip in response to a stable power swing during an actual event if the system
was weakened (i.e., a higher transfer impedance) by the loss of a subset of lines that make up the
parallel transfer impedance as shown in Figure 10. This could happen because the subset of lines
that make up the parallel transfer impedance tripped on unstable swings, contained the initiating
fault, and/or were lost due to operation of breaker failure or remote back-up protection schemes.
Table 10 shows the percent size increase of the lens shape as seen by the relay under evaluation
when the parallel transfer impedance is included. The parallel transfer impedance has minimal
effect on the apparent size of the lens shape as long as the parallel transfer impedance is at least
10 multiples of the parallel line impedance (less than 5% lens shape expansion), therefore, its
removal has minimal impact, but results in a slightly more conservative, smaller lens shape.
Parallel transfer impedances of 5 multiples of the parallel line impedance or less result in an
apparent lens shape size of 10% or greater as seen by the relay. If two parallel lines and a parallel
transfer impedance tie the sending-end and receiving-end buses together, the total parallel transfer
impedance will be one or less multiples of the parallel line impedance, resulting in an apparent
lens shape size of 45% or greater. It is a realistic contingency that the parallel line could be outof-service, leaving the parallel transfer impedance making up the rest of the system in parallel with
the line impedance. Since it is not known exactly which lines making up the parallel transfer
impedance will be out of service during a major system disturbance, it is most conservative to
assume that all of them are out, leaving just the line under evaluation in service.
Either the saturated transient or sub-transient direct axis reactance may be used for machines in
the evaluation because they are smaller than the un-saturated reactances. Since saturated subtransient generator reactances are smaller than the transient or synchronous reactances, the use of
sub-transient reactances will result in a smaller source impedance and a smaller unstable power
swing region in the graphical analysis as shown in Figures 8 and 9. Because power swings occur
in a time frame where generator transient reactances will be prevalent, it is acceptable to use
saturated transient reactances instead of saturated sub-transient reactances. Because some short-

15

Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations,
April 2004, Section 6 (The Cascade Stage of the Blackout), p. 94 under “Why the Generators Tripped Off,” states,
“Some generator undervoltage relays were set to trip at or above 90% voltage. However, a motor stalls out at about
70% voltage and a motor starter contactor drops out around 75%, so if there is a compelling need to protect the
turbine from the system the under-voltage trigger point should be no higher than 80%.”

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PRC-026-1 – Application Guidelines
circuit models may not include transient reactances, the use of sub-transient reactances is also
acceptable because it produces more conservative results. For this reason, either value is acceptable
when determining the system source impedances (PRC-026-1 – Attachment B, Criterion A and B,
No. 3).
Saturated reactances are used in short-circuit programs that produce the system impedance
mentioned above. Planning and stability software generally use un-saturated reactances. Generator
models used in transient stability analyses recognize that the extent of the saturation effect depends
upon both rotor (field) and stator currents. Accordingly, they derive the effective saturated
parameters of the machine at each instant by internal calculation from the specified (constant)
unsaturated values of machine reactances and the instantaneous internal flux level. The specific
assumptions regarding which inductances are affected by saturation, and the relative effect of that
saturation, are different for the various generator models used. Thus, unsaturated values of all
machine reactances are used in setting up planning and stability software data, and the appropriate
set of open-circuit magnetization curve data is provided for each machine.
Saturated reactance values are smaller than unsaturated reactance values and are used in shortcircuit programs owned by the Generator and Transmission Owners. Because of this, saturated
reactance values are to be used in the development of the system source impedances.
The source or system equivalent impedances can be obtained by a number of different methods
using commercially available short-circuit calculation tools.16 Most short-circuit tools have a
network reduction feature that allows the user to select the local and remote terminal buses to
retain. The first method reduces the system to one that contains two buses, an equivalent generator
at each bus (representing the source impedances at the sending-end and receiving-end), and two
parallel lines; one being the line impedance of the protected line with relays being analyzed, the
other being the parallel transfer impedance representing all other combinations of lines that
connect the two buses together as shown in Figure 6. Another conservative method is to open both
ends of the line being evaluated, and apply a three-phase bolted fault at each bus to determine the
Thévenin equivalent impedance at each bus. The source impedances are set equal to the Thévenin
equivalent impedances and will be less than or equal to the actual source impedances calculated
by the network reduction method. Either method can be used to develop the system source
impedances at both ends.
The two bullets of PRC-026-1 – Attachment B, Criterion A, No. 1, identify the system separation
angles used to identify the size of the power swing stability boundary for evaluating loadresponsive protective relay impedance elements. The first bullet of PRC-026-1 – Attachment B,
Criterion A, No. 1 evaluates a system separation angle of at least 120 degrees that is held constant
while varying the sending-end and receiving-end source voltages from 0.7 to 1.0 per unit, thus
creating an unstable power swing region about the total system impedance in Figure 1. This
unstable power swing region is compared to the tripping portion of the distance relay
characteristic; that is, the portion that is not supervised by load encroachment, blinders, or some
other form of supervision as shown in Figure 12 that restricts the distance element from tripping

16

Demetrios A. Tziouvaras and Daqing Hou, Appendix in Out-Of-Step Protection Fundamentals and
Advancements, April 17, 2014: https://www.selinc.com.

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PRC-026-1 – Application Guidelines
for heavy, balanced load conditions. If the tripping portion of the impedance characteristics are
completely contained within the unstable power swing region, the relay impedance element meets
Criterion A in PRC-026-1 – Attachment B. A system separation angle of 120 degrees was chosen
for the evaluation because it is generally accepted in the industry that recovery for a swing beyond
this angle is unlikely to occur.17
The second bullet of PRC-026-1 – Attachment B, Criterion A, No. 1 evaluates impedance relay
elements at a system separation angle of less than 120 degrees, similar to the first bullet described
above. An angle less than 120 degrees may be used if a documented stability analysis demonstrates
that the power swing becomes unstable at a system separation angle of less than 120 degrees.
The exclusion of relay elements supervised by Power Swing Blocking (PSB) in PRC-026-1 –
Attachment A allows the Generator Owner or Transmission Owner to exclude protective relay
elements if they are blocked from tripping by PSB relays. A PSB relay applied and set according
to industry accepted practices prevent supervised load-responsive protective relays from tripping
in response to power swings. Further, PSB relays are set to allow dependable tripping of supervised
elements. The criteria in PRC-026-1 – Attachment B specifically applies to unsupervised elements
that could trip for stable power swings. Therefore, load-responsive protective relay elements
supervised by PSB can be excluded from the Requirements of this standard.

“The critical angle for maintaining stability will vary depending on the contingency and the system condition at
the time the contingency occurs; however, the likelihood of recovering from a swing that exceeds 120 degrees is
marginal and 120 degrees is generally accepted as an appropriate basis for setting out‐of‐step protection. Given the
importance of separating unstable systems, defining 120 degrees as the critical angle is appropriate to achieve a
proper balance between dependable tripping for unstable power swings and secure operation for stable power
swings.” NERC System Protection and Control Subcommittee, Protection System Response to Power Swings,
August 2013: http://www.nerc.com/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20
SPCS%2020/SPCS%20Power%20Swing%20Report_Final_20131015.pdf), p. 28.
17

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PRC-026-1 – Application Guidelines

Figure 1: An enlarged graphic illustrating the unstable power swing region formed by the union
of three shapes in the impedance (R-X) plane: Shape 1) Lower loss-of-synchronism circle,
Shape 2) Upper loss-of-synchronism circle, and Shape 3) Lens. The mho element characteristic
is completely contained within the unstable power swing region (i.e., it does not intersect any
portion of the unstable power swing region), therefore it meets PRC-026-1 – Attachment B,
Criterion A, No. 1.

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PRC-026-1 – Application Guidelines

Figure 2: Full graphic of the unstable power swing region formed by the union of the three
shapes in the impedance (R-X) plane: Shape 1) Lower loss-of-synchronism circle, Shape 2)
Upper loss-of-synchronism circle, and Shape 3) Lens. The mho element characteristic is
completely contained within the unstable power swing region, therefore it meets PRC-26-1 –
Attachment B, Criterion A, No.1.

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PRC-026-1 – Application Guidelines

Figure 3: System impedances as seen by Relay R (voltage connections are not shown).

Figure 4: The defining unstable power swing region points where the lens shape intersects the
lower and upper loss-of-synchronism circle shapes and where the lens intersects the equal EMF
(electromotive force) power swing.

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PRC-026-1 – Application Guidelines

Figure 5: Full table of 31 detailed lens shape point calculations. The bold highlighted rows
correspond to the detailed calculations in Tables 2-7.

Table 2: Example Calculation (Lens Point 1)
This example is for calculating the impedance the first point of the lens characteristic. Equal
source voltages are used for the 230 kV (base) line with the sending-end voltage (ES) leading
the receiving-end voltage (ER) by 120 degrees. See Figures 3 and 4.
Eq. (6)

𝐸𝑆 =

𝑉𝐿𝐿 ∠120°
√3

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PRC-026-1 – Application Guidelines
Table 2: Example Calculation (Lens Point 1)
𝐸𝑆 =

230,000∠120° 𝑉
√3

𝐸𝑆 = 132,791∠120° 𝑉
Eq. (7)

𝐸𝑅 =
𝐸𝑅 =

𝑉𝐿𝐿 ∠0°
√3
230,000∠0° 𝑉
√3

𝐸𝑅 = 132,791∠0° 𝑉
Positive sequence impedance data (with transfer impedance ZTR set to a large value).
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

Given:

𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

Total impedance between the generators.
Eq. (8)

𝑍𝑡𝑜𝑡𝑎𝑙 =
𝑍𝑡𝑜𝑡𝑎𝑙

(𝑍𝐿 × 𝑍𝑇𝑅 )
(𝑍𝐿 + 𝑍𝑇𝑅 )

((4 + 𝑗20) Ω × (4 + 𝑗20) × 1010 Ω)
=
((4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω)

𝑍𝑡𝑜𝑡𝑎𝑙 = 4 + 𝑗20 Ω
Total system impedance.
Eq. (9)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
𝑍𝑠𝑦𝑠 = (2 + 𝑗10) Ω + (4 + 𝑗20) Ω + (4 + 𝑗20) Ω
𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω

Total system current from sending-end source.
Eq. (10)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

132,791∠120° 𝑉 − 132,791∠0° 𝑉
(10 + 𝑗50 )Ω

𝐼𝑠𝑦𝑠 = 4,511∠71.3° 𝐴
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
Eq. (11)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

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PRC-026-1 – Application Guidelines
Table 2: Example Calculation (Lens Point 1)
(4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 4,511∠71.3° 𝐴 ×
(4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 4,511∠71.3° 𝐴
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (12)

𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝑠𝑦𝑠 )
𝑉𝑆 = 132,791∠120° 𝑉 − [(2 + 𝑗10) Ω × 4,511∠71.3° 𝐴]
𝑉𝑆 = 95,757∠106.1° 𝑉

The impedance seen by the relay on ZL.
Eq. (13)

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

𝑉𝑆
𝐼𝐿

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

95,757∠106.1° 𝑉
4,511∠71.3° 𝐴

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = 17.434 + 𝑗12.113 Ω

Table 3: Example Calculation (Lens Point 2)
This example is for calculating the impedance second point of the lens characteristic. Unequal
source voltages are used for the 230 kV (base) line with the sending-end voltage (ES) at 70% of
the receiving-end voltage (ER) and leading the receiving-end voltage by 120 degrees. See
Figures 3 and 4.
Eq. (14)

𝐸𝑆 =
𝐸𝑆 =

𝑉𝐿𝐿 ∠120°

× 70%
√3
230,000∠120° 𝑉
√3

× 0.70

𝐸𝑆 = 92,953.7∠120° 𝑉
Eq. (15)

𝐸𝑅 =
𝐸𝑅 =

𝑉𝐿𝐿 ∠0°
√3
230,000∠0° 𝑉
√3

𝐸𝑅 = 132,791∠0° 𝑉
Positive sequence impedance data (with transfer impedance ZTR set to a large value).
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

Given:

𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

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PRC-026-1 – Application Guidelines
Table 3: Example Calculation (Lens Point 2)
Total impedance between the generators.
Eq. (16)

𝑍𝑡𝑜𝑡𝑎𝑙 =
𝑍𝑡𝑜𝑡𝑎𝑙

(𝑍𝐿 × 𝑍𝑇𝑅 )
(𝑍𝐿 + 𝑍𝑇𝑅 )

((4 + 𝑗20) Ω × (4 + 𝑗20) × 1010 Ω)
=
((4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω)

𝑍𝑡𝑜𝑡𝑎𝑙 = 4 + 𝑗20 Ω
Total system impedance.
Eq. (17)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
𝑍𝑠𝑦𝑠 = (2 + 𝑗10) Ω + (4 + 𝑗20) Ω + (4 + 𝑗20) Ω
𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω

Total system current from sending-end source.
Eq. (18)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

92,953.7∠120° 𝑉 − 132,791∠0° 𝑉
(10 + 𝑗50) Ω

𝐼𝑠𝑦𝑠 = 3,854∠77° 𝐴
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
Eq. (19)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

(4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 3,854∠77° 𝐴 ×
(4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 3,854∠77° 𝐴
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (20)

𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝑠𝑦𝑠 )
𝑉𝑆 = 92,953∠120° 𝑉 − [(2 + 𝑗10 )Ω × 3,854∠77° 𝐴]
𝑉𝑆 = 65,271∠99° 𝑉

The impedance seen by the relay on ZL.
Eq. (21)

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

𝑉𝑆
𝐼𝐿

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PRC-026-1 – Application Guidelines
Table 3: Example Calculation (Lens Point 2)
𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

65,271∠99° 𝑉
3,854∠77° 𝐴

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = 15.676 + 𝑗6.41 Ω

Table 4: Example Calculation (Lens Point 3)
This example is for calculating the impedance third point of the lens characteristic. Unequal
source voltages are used for the 230 kV (base) line with the receiving-end voltage (ER) at 70%
of the sending-end voltage (ES) and the sending-end voltage leading the receiving-end voltage
by 120 degrees. See Figures 3 and 4.
Eq. (22)

𝐸𝑆 =
𝐸𝑆 =

𝑉𝐿𝐿 ∠120°
√3
230,000∠120° 𝑉
√3

𝐸𝑆 = 132,791∠120° 𝑉
Eq. (23)

𝐸𝑅 =
𝐸𝑅 =

𝑉𝐿𝐿 ∠0°

× 70%
√3
230,000∠0° 𝑉
√3

× 0.70

𝐸𝑅 = 92,953.7∠0° 𝑉
Positive sequence impedance data (with transfer impedance ZTR set to a large value).
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

Given:

𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

Total impedance between the generators.
Eq. (24)

𝑍𝑡𝑜𝑡𝑎𝑙 =
𝑍𝑡𝑜𝑡𝑎𝑙

(𝑍𝐿 × 𝑍𝑇𝑅 )
(𝑍𝐿 + 𝑍𝑇𝑅 )

((4 + 𝑗20) Ω × (4 + 𝑗20) × 1010 Ω)
=
((4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω)

𝑍𝑡𝑜𝑡𝑎𝑙 = 4 + 𝑗20 Ω
Total system impedance.
Eq. (25)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
𝑍𝑠𝑦𝑠 = (2 + 𝑗10) Ω + (4 + 𝑗20) Ω + (4 + 𝑗20) Ω
𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω

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PRC-026-1 – Application Guidelines
Table 4: Example Calculation (Lens Point 3)
Total system current from sending-end source.
Eq. (26)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

132,791∠120° 𝑉 − 92,953.7∠0° 𝑉
(10 + 𝑗50) Ω

𝐼𝑠𝑦𝑠 = 3,854∠65.5° 𝐴
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
Eq. (27)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

(4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 3,854∠65.5° 𝐴 ×
(4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 3,854∠65.5° 𝐴
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (28)

𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝐿 )
𝑉𝑆 = 132,791∠120° 𝑉 − [(2 + 𝑗10) Ω × 3,854∠65.5° 𝐴]
𝑉𝑆 = 98,265∠110.6° 𝑉

The impedance seen by the relay on ZL.
Eq. (29)

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

𝑉𝑆
𝐼𝐿

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

98,265∠110.6° 𝑉
3,854∠65.5° 𝐴

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = 18.005 + 𝑗18.054 Ω

Table 5: Example Calculation (Lens Point 4)
This example is for calculating the impedance fourth point of the lens characteristic. Equal
source voltages are used for the 230 kV (base) line with the sending-end voltage (ES) leading
the receiving-end voltage (ER) by 240 degrees. See Figures 3 and 4.
Eq. (30)

𝐸𝑆 =
𝐸𝑆 =

𝑉𝐿𝐿 ∠240°
√3
230,000∠240° 𝑉
√3

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PRC-026-1 – Application Guidelines
Table 5: Example Calculation (Lens Point 4)
𝐸𝑆 = 132,791∠240° 𝑉
Eq. (31)

𝐸𝑅 =
𝐸𝑅 =

𝑉𝐿𝐿 ∠0°
√3
230,000∠0° 𝑉
√3

𝐸𝑅 = 132,791∠0° 𝑉
Positive sequence impedance data (with transfer impedance ZTR set to a large value).
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

Given:

𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

Total impedance between the generators.
Eq. (32)

𝑍𝑡𝑜𝑡𝑎𝑙 =

(𝑍𝐿 × 𝑍𝑇𝑅 )
(𝑍𝐿 + 𝑍𝑇𝑅 )

𝑍𝑡𝑜𝑡𝑎𝑙 =

((4 + 𝑗20) Ω × (4 + 𝑗20) × 1010 Ω)
((4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω)

𝑍𝑡𝑜𝑡𝑎𝑙 = 4 + 𝑗20 Ω
Total system impedance.
Eq. (33)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
𝑍𝑠𝑦𝑠 = (2 + 𝑗10) Ω + (4 + 𝑗20) Ω + (4 + 𝑗20) Ω
𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω

Total system current from sending-end source.
Eq. (34)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

132,791∠240° 𝑉 − 132,791∠0° 𝑉
(10 + 𝑗50 )Ω

𝐼𝑠𝑦𝑠 = 4,511∠131.3° 𝐴
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
Eq. (35)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

(4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 4,511∠131.1° 𝐴 ×
(4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 4,511∠131.1° 𝐴

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PRC-026-1 – Application Guidelines
Table 5: Example Calculation (Lens Point 4)
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (36)

𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝐿 )
𝑉𝑆 = 132,791∠240° 𝑉 − [(2 + 𝑗10 ) Ω × 4,511∠131.1° 𝐴]
𝑉𝑆 = 95,756∠ − 106.1° 𝑉

The impedance seen by the relay on ZL.
Eq. (37)

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

𝑉𝑆
𝐼𝐿

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

95,756∠ − 106.1° 𝑉
4,511∠131.1° 𝐴

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = −11.434 + 𝑗17.887 Ω

Table 6: Example Calculation (Lens Point 5)
This example is for calculating the impedance fifth point of the lens characteristic. Unequal
source voltages are used for the 230 kV (base) line with the sending-end voltage (ES) at 70% of
the receiving-end voltage (ER) and leading the receiving-end voltage by 240 degrees. See
Figures 3 and 4.
Eq. (38)

𝐸𝑆 =
𝐸𝑆 =

𝑉𝐿𝐿 ∠240°

× 70%
√3
230,000∠240° 𝑉
√3

× 0.70

𝐸𝑆 = 92,953.7∠240° 𝑉
Eq. (39)

𝐸𝑅 =
𝐸𝑅 =

𝑉𝐿𝐿 ∠0°
√3
230,000∠0° 𝑉
√3

𝐸𝑅 = 132,791∠0° 𝑉
Positive sequence impedance data (with transfer impedance ZTR set to a large value).
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

Given:

𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

Total impedance between the generators.
Eq. (40)

𝑍𝑡𝑜𝑡𝑎𝑙 =

(𝑍𝐿 × 𝑍𝑇𝑅 )
(𝑍𝐿 + 𝑍𝑇𝑅 )

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PRC-026-1 – Application Guidelines
Table 6: Example Calculation (Lens Point 5)
𝑍𝑡𝑜𝑡𝑎𝑙

((4 + 𝑗20) Ω × (4 + 𝑗20) × 1010 Ω)
=
((4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω)

𝑍𝑡𝑜𝑡𝑎𝑙 = 4 + 𝑗20 Ω
Total system impedance.
Eq. (41)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
𝑍𝑠𝑦𝑠 = (2 + 𝑗10 Ω) + (4 + 𝑗20 Ω) + (4 + 𝑗20 Ω)
𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω

Total system current from sending-end source.
Eq. (42)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

92,953.7∠240° 𝑉 − 132,791∠0° 𝑉
10 + 𝑗50 Ω

𝐼𝑠𝑦𝑠 = 3,854∠125.5° 𝐴
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
Eq. (43)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

𝐼𝐿 = 3,854∠125.5° 𝐴 ×

(4 + 𝑗20) × 1010 Ω
(4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω

𝐼𝐿 = 3,854∠125.5° 𝐴
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (44)

𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝐿 )
𝑉𝑆 = 92,953.7∠240° 𝑉 − [(2 + 𝑗10 ) Ω × 3,854∠125.5° 𝐴]
𝑉𝑆 = 65,270.5∠ − 99.4° 𝑉

The impedance seen by the relay on ZL.
Eq. (45)

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

𝑉𝑆
𝐼𝐿

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

65,270.5∠ − 99.4° 𝑉
3,854∠125.5° 𝐴

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = −12.005 + 𝑗11.946 Ω

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PRC-026-1 – Application Guidelines
Table 7: Example Calculation (Lens Point 6)
This example is for calculating the impedance sixth point of the lens characteristic. Unequal
source voltages are used for the 230 kV (base) line with the receiving-end voltage (ER) at 70%
of the sending-end voltage (ES) and the sending-end voltage leading the receiving-end voltage
by 240 degrees. See Figures 3 and 4.
Eq. (46)

𝐸𝑆 =
𝐸𝑆 =

𝑉𝐿𝐿 ∠240°
√3
230,000∠240° 𝑉

√3
𝐸𝑆 = 132,791∠240° 𝑉
𝑉𝐿𝐿 ∠0°
Eq. (47)
𝐸𝑅 =
× 70%
√3
230,000∠0° 𝑉
𝐸𝑅 =
× 0.70
√3
𝐸𝑅 = 92,953.7∠0° 𝑉
Positive sequence impedance data (with transfer impedance ZTR set to a large value).
Given:
𝑍𝑆 = 2 + 𝑗10 Ω
𝑍𝐿 = 4 + 𝑗20 Ω
𝑍𝑅 = 4 + 𝑗20 Ω
Given:
𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω
Total impedance between the generators.
(𝑍𝐿 × 𝑍𝑇𝑅 )
Eq. (48)
𝑍𝑡𝑜𝑡𝑎𝑙 =
(𝑍𝐿 + 𝑍𝑇𝑅 )
((4 + 𝑗20) Ω × (4 + 𝑗20) × 1010 Ω)
𝑍𝑡𝑜𝑡𝑎𝑙 =
((4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω)
𝑍𝑡𝑜𝑡𝑎𝑙 = 4 + 𝑗20 Ω
Total system impedance.
𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
Eq. (49)
𝑍𝑠𝑦𝑠 = (2 + 𝑗10) Ω + (4 + 𝑗20) Ω + (4 + 𝑗20) Ω
𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω
Total system current from sending-end source.
𝐸𝑆 − 𝐸𝑅
𝐼𝑠𝑦𝑠 =
Eq. (50)
𝑍𝑠𝑦𝑠
132,791∠240° 𝑉 − 92,953.7∠0° 𝑉
𝐼𝑠𝑦𝑠 =
10 + 𝑗50 Ω
𝐼𝑠𝑦𝑠 = 3,854∠137.1° 𝐴

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PRC-026-1 – Application Guidelines
Table 7: Example Calculation (Lens Point 6)
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
𝑍𝑇𝑅
Eq. (51)
𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×
𝑍𝐿 + 𝑍𝑇𝑅
(4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 3,854∠137.1° 𝐴 ×
(4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω
𝐼𝐿 = 3,854∠137.1° 𝐴
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (52)
𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝐿 )
𝑉𝑆 = 132,791∠240° 𝑉 − [(2 + 𝑗10 ) Ω × 3,854∠137.1° 𝐴]
𝑉𝑆 = 98,265∠ − 110.6° 𝑉
The impedance seen by the relay on ZL.
𝑉𝑆
Eq. (53)
𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =
𝐼𝐿
98,265∠ − 110.6° 𝑉
𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =
3,854∠137.1° 𝐴
𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = −9.676 + 𝑗23.59 Ω

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PRC-026-1 – Application Guidelines

Figure 6: Reduced two bus system with sending-end source impedance ZS, receiving-end
source impedance ZR, line impedance ZL, and parallel transfer impedance ZTR.

Figure 7: Reduced two bus system with sending-end source impedance ZS, receiving-end
source impedance ZR, and line impedance ZL with the parallel transfer impedance ZTR removed.

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PRC-026-1 – Application Guidelines

Figure 8: A strong-source system with a line impedance of ZL = 20.4 ohms (i.e., the thicker red
line). This mho element characteristic (i.e., the blue circle) does not meet the PRC-026-1 –
Attachment B, Criterion A because it is not completely contained within the unstable power
swing region (i.e., the orange characteristic).

Figure 8 above represents a heavily-loaded system with all generation in service and all
transmission BES Elements in their normal operating state. The mho element characteristic (set at
137% of ZL) extends into the unstable power swing region (i.e., the orange characteristic). Using
the strongest source system is more conservative because it shrinks the unstable power swing
region, bringing it closer to the mho element characteristic. This figure also graphically represents
the effect of a system strengthening over time and this is the reason for re-evaluation if the relay
has not been evaluated in the last five calendar years. Figure 9 below depicts a relay that meets the
PRC-026-1 – Attachment B, Criterion A. Figure 8 depicts the same relay with the same setting
five years later, where each source has strengthened by about 10% and now the same mho element
characteristic does not meet Criterion A.

Page 40 of 84

PRC-026-1 – Application Guidelines

Figure 9: A weak-source system with a line impedance of ZL = 20.4 ohms (i.e., the thicker red
line). This mho element characteristic (i.e., the blue circle) meets the PRC-026-1 – Attachment
B, Criterion A because it is completely contained within the unstable power swing region (i.e.,
the orange characteristic).

Figure 9 above represents a lightly-loaded system, using a minimum generation profile. The mho
element characteristic (set at 137% of ZL) does not extend into the unstable power swing region
(i.e., the orange characteristic). Using a weaker source system expands the unstable power swing
region away from the mho element characteristic.

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PRC-026-1 – Application Guidelines

Figure 10: This is an example of an unstable power swing region (i.e., the orange characteristic)
with the parallel transfer impedance removed. This relay mho element characteristic (i.e., the
blue circle) does not meet PRC-026-1 – Attachment B, Criterion A because it is not completely
contained within the unstable power swing region.

Table 8: Example Calculation (Parallel Transfer Impedance Removed)
Calculations for the point at 120 degrees with equal source impedances. The total system current
equals the line current. See Figure 10.
Eq. (54)

𝐸𝑆 =
𝐸𝑆 =

𝑉𝐿𝐿 ∠120°
√3
230,000∠120° 𝑉
√3

𝐸𝑆 = 132,791∠120° 𝑉

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PRC-026-1 – Application Guidelines
Table 8: Example Calculation (Parallel Transfer Impedance Removed)
Eq. (55)

𝐸𝑅 =
𝐸𝑅 =

𝑉𝐿𝐿 ∠0°
√3
230,000∠0° 𝑉
√3

𝐸𝑅 = 132,791∠0° 𝑉
Given impedance data.
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

Given:

𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

Total impedance between the generators.
Eq. (56)

𝑍𝑡𝑜𝑡𝑎𝑙 =
𝑍𝑡𝑜𝑡𝑎𝑙

(𝑍𝐿 × 𝑍𝑇𝑅 )
(𝑍𝐿 + 𝑍𝑇𝑅 )

((4 + 𝑗20) Ω × (4 + 𝑗20) × 1010 Ω)
=
((4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω)

𝑍𝑡𝑜𝑡𝑎𝑙 = 4 + 𝑗20 Ω
Total system impedance.
Eq. (57)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
𝑍𝑠𝑦𝑠 = (2 + 𝑗10) Ω + (4 + 𝑗20) Ω + (4 + 𝑗20) Ω
𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω

Total system current from sending-end source.
Eq. (58)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

132,791∠120° 𝑉 − 132,791∠0° 𝑉
10 + 𝑗50 Ω

𝐼𝑠𝑦𝑠 = 4,511∠71.3° 𝐴
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
Eq. (59)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

𝐼𝐿 = 4,511∠71.3° 𝐴 ×

(4 + 𝑗20) × 1010 Ω
(4 + 𝑗20) Ω + (4 + 𝑗20) × 1010 Ω

𝐼𝐿 = 4,511∠71.3° 𝐴

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PRC-026-1 – Application Guidelines
Table 8: Example Calculation (Parallel Transfer Impedance Removed)
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (60)

𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝑠𝑦𝑠 )
𝑉𝑆 = 132,791∠120° 𝑉 − [(2 + 𝑗10 Ω) × 4,511∠71.3° 𝐴]
𝑉𝑆 = 95,757∠106.1° 𝑉

The impedance seen by the relay on ZL.
Eq. (61)

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

𝑉𝑆
𝐼𝐿

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

95,757∠106.1° 𝑉
4,511∠71.3° 𝐴

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = 17.434 + 𝑗12.113 Ω

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PRC-026-1 – Application Guidelines

Figure 11: This is an example of an unstable power swing region (i.e., the orange characteristic)
with the parallel transfer impedance included causing the mho element characteristic (i.e., the
blue circle) to appear to meet the PRC-026-1 – Attachment B, Criterion A because it is
completely contained within the unstable power swing region. Including the parallel transfer
impedance in the calculation is not allowed by the PRC-026-1 – Attachment B, Criterion A.

In Figure 11 above, the parallel transfer impedance is 5 times the line impedance. The unstable
power swing region has expanded out beyond the mho element characteristic due to the infeed
effect from the parallel current through the parallel transfer impedance, thus allowing the mho
element characteristic to appear to meet the PRC-026-1 – Attachment B, Criterion A. Including
the parallel transfer impedance in the calculation is not allowed by the PRC-026-1 – Attachment
B, Criterion A.

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PRC-026-1 – Application Guidelines
Table 9: Example Calculation (Parallel Transfer Impedance Included)
Calculations for the point at 120 degrees with equal source impedances. The total system current
does not equal the line current. See Figure 11.
Eq. (62)

𝐸𝑆 =
𝐸𝑆 =

𝑉𝐿𝐿 ∠120°
√3
230,000∠120° 𝑉
√3

𝐸𝑆 = 132,791∠120° 𝑉
Eq. (63)

𝐸𝑅 =
𝐸𝑅 =

𝑉𝐿𝐿 ∠0°
√3
230,000∠0° 𝑉
√3

𝐸𝑅 = 132,791∠0° 𝑉
Given impedance data.
Given:
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

𝑍𝑇𝑅 = 𝑍𝐿 × 5
𝑍𝑇𝑅 = (4 + 𝑗20) Ω × 5
𝑍𝑇𝑅 = 20 + 𝑗100 Ω

Total impedance between the generators.
Eq. (64)

𝑍𝑡𝑜𝑡𝑎𝑙 =

(𝑍𝐿 × 𝑍𝑇𝑅 )
(𝑍𝐿 + 𝑍𝑇𝑅 )

𝑍𝑡𝑜𝑡𝑎𝑙 =

(4 + 𝑗20) Ω × (20 + 𝑗100) Ω
(4 + 𝑗20) Ω + (20 + 𝑗100) Ω

𝑍𝑡𝑜𝑡𝑎𝑙 = 3.333 + 𝑗16.667 Ω
Total system impedance.
Eq. (65)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝑡𝑜𝑡𝑎𝑙 + 𝑍𝑅
𝑍𝑠𝑦𝑠 = (2 + 𝑗10) Ω + (3.333 + 𝑗16.667) Ω + (4 + 𝑗20) Ω
𝑍𝑠𝑦𝑠 = 9.333 + 𝑗46.667 Ω

Total system current from sending-end source.
Eq. (66)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

132,791∠120° 𝑉 − 132,791∠0° 𝑉
9.333 + 𝑗46.667 Ω

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PRC-026-1 – Application Guidelines
Table 9: Example Calculation (Parallel Transfer Impedance Included)
𝐼𝑠𝑦𝑠 = 4,833∠71.3° 𝐴
The current, as measured by the relay on ZL (Figure 3), is only the current flowing through that
line as determined by using the current divider equation.
Eq. (67)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

𝐼𝐿 = 4,833∠71.3° 𝐴 ×

(20 + 𝑗100) Ω
(4 + 𝑗20) Ω + (20 + 𝑗100) Ω

𝐼𝐿 = 4,027.4∠71.3° 𝐴
The voltage, as measured by the relay on ZL (Figure 3), is the voltage drop from the sendingend source through the sending-end source impedance.
Eq. (68)

𝑉𝑆 = 𝐸𝑆 − (𝑍𝑆 × 𝐼𝑠𝑦𝑠 )
𝑉𝑆 = 132,791∠120° 𝑉 − [(2 + 𝑗10 Ω) × 4,833∠71.3° 𝐴]
𝑉𝑆 = 93,417∠104.7° 𝑉

The impedance seen by the relay on ZL.
Eq. (69)

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

𝑉𝑆
𝐼𝐿

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 =

93,417∠104.7° 𝑉
4,027∠71.3° 𝐴

𝑍𝐿−𝑅𝑒𝑙𝑎𝑦 = 19.366 + 𝑗12.767 Ω

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PRC-026-1 – Application Guidelines
Table 10: Percent Increase of a Lens Due To Parallel Transfer Impedance.
The following demonstrates the percent size increase of the lens characteristic for ZTR in
multiples of ZL with the parallel transfer impedance included.
ZTR in multiples of ZL

Percent increase of lens with equal EMF
sources (Infinite source as reference)

Infinite

N/A

1000

0.05%

100

0.46%

10

4.63%

5

9.27%

2

23.26%

1

46.76%

0.5

94.14%

0.25

189.56%

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PRC-026-1 – Application Guidelines

Figure 12: The tripping portion of the mho element characteristic (i.e., the blue circle) not
blocked by load encroachment (i.e., the parallel green lines) is completely contained within the
unstable power swing region (i.e., the orange characteristic). Therefore, the mho element
characteristic meets the PRC-026-1 – Attachment B, Criterion A.

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PRC-026-1 – Application Guidelines

Figure 13: The infeed diagram shows the impedance in front of the relay R with the parallel
transfer impedance included. As the parallel transfer impedance approaches infinity, the
impedances seen by the relay R in the forward direction becomes ZL + ZR.

Table 11: Calculations (System Apparent Impedance in the forward direction)
The following equations are provided for calculating the apparent impedance back to the ER
source voltage as seen by relay R. Infeed equations from VS to source ER where ER = 0. See
Figure 13.
𝑉𝑆 − 𝑉𝑅
𝑍𝐿

Eq. (70)

𝐼𝐿 =

Eq. (71)

𝐼𝑠𝑦𝑠 =

Eq. (72)

𝐼𝑠𝑦𝑠 = 𝐼𝐿 + 𝐼𝑇𝑅

Eq. (73)

𝑉𝑅 − 𝐸𝑅
𝑍𝑅

𝐼𝑠𝑦𝑠 =

𝑉𝑅
𝑍𝑅

Since 𝐸𝑅 = 0

Rearranged:

Eq. (74)

𝐼𝐿 =

𝑉𝑆 − 𝐼𝑠𝑦𝑠 × 𝑍𝑅
𝑍𝐿

Eq. (75)

𝐼𝐿 =

𝑉𝑆 − [(𝐼𝐿 + 𝐼𝑇𝑅 ) × 𝑍𝑅 ]
𝑍𝐿

Eq. (76)

𝑉𝑆 = (𝐼𝐿 × 𝑍𝐿 ) + (𝐼𝐿 × 𝑍𝑅 ) + (𝐼𝑇𝑅 × 𝑍𝑅 )

Eq. (77)

𝑍𝑅𝑒𝑙𝑎𝑦 =

Eq. (78)

𝐼𝑇𝑅 = 𝐼𝑠𝑦𝑠 ×

Eq. (79)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

𝑉𝑅 = 𝐼𝑠𝑦𝑠 × 𝑍𝑅

𝑉𝑆
𝐼𝑇𝑅 × 𝑍𝑅
𝐼𝑇𝑅
= 𝑍𝐿 + 𝑍𝑅 +
= 𝑍𝐿 + 𝑍𝑅 × (1 +
)
𝐼𝐿
𝐼𝐿
𝐼𝐿
𝑍𝐿
𝑍𝐿 + 𝑍𝑇𝑅

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

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PRC-026-1 – Application Guidelines
Table 11: Calculations (System Apparent Impedance in the forward direction)
Eq. (80)

𝐼𝑇𝑅
𝑍𝐿
=
𝐼𝐿
𝑍𝑇𝑅

The infeed equations shows the impedance in front of the relay R (Figure 13) with the parallel
transfer impedance included. As the parallel transfer impedance approaches infinity, the
impedances seen by the relay R in the forward direction becomes ZL + ZR.
Eq. (81)

𝑍𝑅𝑒𝑙𝑎𝑦 = 𝑍𝐿 + 𝑍𝑅 × (1 +

𝑍𝐿
)
𝑍𝑇𝑅

Figure 14: The infeed diagram shows the impedance behind relay R with the parallel transfer
impedance included. As the parallel transfer impedance approaches infinity, the impedances
seen by the relay R in the reverse direction becomes ZS.

Table 12: Calculations (System Apparent Impedance in the Reverse Direction)
The following equations are provided for calculating the apparent impedance back to the ES
source voltage as seen by relay R. Infeed equations from VR back to source ES where ES = 0.
See Figure 14.
𝑉𝑅 − 𝑉𝑆
𝑍𝐿

Eq. (82)

𝐼𝐿 =

Eq. (83)

𝐼𝑠𝑦𝑠 =

Eq. (84)

𝐼𝑠𝑦𝑠 = 𝐼𝐿 + 𝐼𝑇𝑅

Eq. (85)

𝐼𝑠𝑦𝑠 =

Eq. (86)

𝐼𝐿 =

𝑉𝑆 − 𝐸𝑆
𝑍𝑆
𝑉𝑆
𝑍𝑆

Since 𝐸𝑠 = 0

Rearranged:

𝑉𝑆 = 𝐼𝑠𝑦𝑠 × 𝑍𝑆

𝑉𝑅 − 𝐼𝑠𝑦𝑠 × 𝑍𝑆
𝑍𝐿

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PRC-026-1 – Application Guidelines
Table 12: Calculations (System Apparent Impedance in the Reverse Direction)
𝑉𝑅 − [(𝐼𝐿 + 𝐼𝑇𝑅 ) × 𝑍𝑆 ]
𝑍𝐿

Eq. (87)

𝐼𝐿 =

Eq. (88)

𝑉𝑅 = (𝐼𝐿 × 𝑍𝐿 ) + (𝐼𝐿 × 𝑍𝑆 ) + (𝐼𝑇𝑅 × 𝑍𝑅𝑆 )

Eq. (89)

𝑍𝑅𝑒𝑙𝑎𝑦 =

Eq. (90)

𝐼𝑇𝑅 = 𝐼𝑠𝑦𝑠 ×

Eq. (91)

𝐼𝐿 = 𝐼𝑠𝑦𝑠 ×

Eq. (92)

𝐼𝑇𝑅
𝑍𝐿
=
𝐼𝐿
𝑍𝑇𝑅

𝑉𝑅
𝐼𝑇𝑅 × 𝑍𝑆
𝐼𝑇𝑅
= 𝑍𝐿 + 𝑍𝑆 +
= 𝑍𝐿 + 𝑍𝑆 × (1 +
)
𝐼𝐿
𝐼𝐿
𝐼𝐿
𝑍𝐿
𝑍𝐿 + 𝑍𝑇𝑅

𝑍𝑇𝑅
𝑍𝐿 + 𝑍𝑇𝑅

The infeed equations shows the impedance behind relay R (Figure 14) with the parallel transfer
impedance included. As the parallel transfer impedance approaches infinity, the impedances
seen by the relay R in the reverse direction becomes ZS.
Eq. (93)

𝑍𝑅𝑒𝑙𝑎𝑦 = 𝑍𝐿 + 𝑍𝑆 × (1 +

Eq. (94)

𝑍𝑅𝑒𝑙𝑎𝑦 = 𝑍𝑆 × (1 +

𝑍𝐿
)
𝑍𝑇𝑅

𝑍𝐿
)
𝑍𝑇𝑅

As seen by relay R at the receiving-end of
the line.
Subtract ZL for relay R impedance as seen
at sending-end of the line.

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PRC-026-1 – Application Guidelines

Figure 15: Out-of-step trip (OST) inner blinder (i.e., the parallel green lines) meets the PRC026-1 – Attachment B, Criterion A because the inner OST blinder initiates tripping either OnThe-Way-In or On-The-Way-Out. Since the inner blinder is completely contained within the
unstable power swing region (i.e., the orange characteristic), it meets the PRC-026-1 –
Attachment B, Criterion A.

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PRC-026-1 – Application Guidelines
Table 13: Example Calculation (Voltage Ratios)
These calculations are based on the loss-of-synchronism characteristics for the cases of N < 1
and N > 1 as found in the Application of Out-of-Step Blocking and Tripping Relays, GER-3180,
p. 12, Figure 3.18 The GE illustration shows the formulae used to calculate the radius and center
of the circles that make up the ends of the portion of the lens.
Voltage ratio equations, source impedance equation with infeed formulae applied, and circle
equations.
Given:

𝐸𝑆 = 0.7

Eq. (95)

𝑁=

𝐸𝑅 = 1.0

|𝐸𝑆 | 0.7
=
= 0.7
|𝐸𝑅 | 1.0

The total system impedance as seen by the relay with infeed formulae applied.
Given:

𝑍𝑆 = 2 + 𝑗10 Ω

𝑍𝐿 = 4 + 𝑗20 Ω

Given:

𝑍𝑇𝑅 = 𝑍𝐿 × 1010 Ω

𝑍𝑅 = 4 + 𝑗20 Ω

𝑍𝑇𝑅 = (4 + 𝑗20) × 1010 Ω
Eq. (96)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 × (1 +

𝑍𝐿
𝑍𝐿
) + [𝑍𝐿 + 𝑍𝑅 × (1 +
)]
𝑍𝑇𝑅
𝑍𝑇𝑅

𝑍𝑠𝑦𝑠 = 10 + 𝑗50 Ω
The calculated coordinates of the lower loss-of-synchronism circle center.
Eq. (97)

𝑍𝐶1 = − [𝑍𝑆 × (1 +

𝑁 2 × 𝑍𝑠𝑦𝑠
𝑍𝐿
)] − [
]
𝑍𝑇𝑅
1 − 𝑁2

𝑍𝐶1 = − [ (2 + 𝑗10) Ω × (1 +

(4 + 𝑗20) Ω
0.72 × (10 + 𝑗50) Ω
−
[
]
)]
(4 + 𝑗20) × 1010 Ω
1 − 0.72

𝑍𝐶1 = −11.608 − 𝑗58.039 Ω
The calculated radius of the lower loss-of-synchronism circle.
Eq. (98)

𝑁 × 𝑍𝑠𝑦𝑠
|
1 − 𝑁2
0.7 × (10 + 𝑗50) Ω
𝑟𝑎 = |
|
1 − 0.72
𝑟𝑎 = |

𝑟𝑎 = 69.987 Ω
The calculated coordinates of the upper loss-of-synchronism circle center.
Given:

18

𝐸𝑆 = 1.0

𝐸𝑅 = 0.7

http://store.gedigitalenergy.com/faq/Documents/Alps/GER-3180.pdf

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PRC-026-1 – Application Guidelines
Table 13: Example Calculation (Voltage Ratios)
|𝐸𝑆 | 1.0
=
= 1.43
|𝐸𝑅 | 0.7

Eq. (99)

𝑁=

Eq. (100)

𝑍𝐶2 = 𝑍𝐿 + [𝑍𝑅 × (1 +

𝑍𝑠𝑦𝑠
𝑍𝐿
)] + [ 2
]
𝑍𝑇𝑅
𝑁 −1

𝑍𝐶2 = 4 + 𝑗20 Ω + [ (4 + 𝑗20) Ω × (1 +

(4 + 𝑗20) Ω
(10 + 𝑗50) Ω
]
)] + [
10
(4 + 𝑗20) × 10 Ω
1.432 − 1

𝑍𝐶2 = 17.608 + 𝑗88.039 Ω
The calculated radius of the upper loss-of-synchronism circle.
Eq. (101)

𝑁 × 𝑍𝑠𝑦𝑠
|
𝑁2 − 1
1.43 × (10 + 𝑗50) Ω
𝑟𝑏 = |
|
1.432 − 1
𝑟𝑏 = |

𝑟𝑏 = 69.987 Ω

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PRC-026-1 – Application Guidelines

Figure 15a: Lower circle loss-of-synchronism region showing the coordinates of the circle
center and the circle radius.

Page 56 of 84

PRC-026-1 – Application Guidelines

Figure 15b: Lower circle loss-of-synchronism region showing the first three steps to calculate
the coordinates of the points on the circle. 1) Identify the lower circle loss-of-synchronism
points that intersect the lens shape where the sending-end to receiving-end voltage ratio is 0.7
(see lens shape calculations in Tables 2-7). 2) Calculate the distance between the two lower
circle loss-of-synchronism points identified in Step 1. 3) Calculate the angle of arc that
connects the two lower circle loss-of-synchronism points identified in Step 1.

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PRC-026-1 – Application Guidelines

Figure 15c: Lower circle loss-of-synchronism region showing the steps to calculate the start
angle, end angle, and the angle step size for the desired number of calculated points. 1)
Calculate the system angle. 2) Calculate the start angle. 3) Calculate the end angle. 4)
Calculate the angle step size for the desired number of points.

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PRC-026-1 – Application Guidelines

Figure 15d: Lower circle loss-of-synchronism region showing the final steps to calculate the
coordinates of the points on the circle. 1) Start at the intersection with the lens shape and
proceed in a clockwise direction. 2) Advance the step angle for each point. 3) Calculate the
new angle after step advancement. 4) Calculate the R–X coordinates.

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Figure 15e: Upper circle loss-of-synchronism region showing the coordinates of the circle
center and the circle radius.

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Figure 15f: Upper circle loss-of-synchronism region showing the first three steps to calculate
the coordinates of the points on the circle. 1) Identify the upper circle points that intersect the
lens shape where the sending-end to receiving-end voltage ratio is 1.43 (see lens shape
calculations in Tables 2-7). 2) Calculate the distance between the two upper circle points
identified in Step 1. 3) Calculate the angle of arc that connects the two upper circle points
identified in Step 1.

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PRC-026-1 – Application Guidelines

Figure 15g: Upper circle loss-of-synchronism region showing the steps to calculate the start
angle, end angle, and the angle step size for the desired number of calculated points. 1) Calculate
the system angle. 2) Calculate the start angle. 3) Calculate the end angle. 4) Calculate the angle
step size for the desired number of points.

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PRC-026-1 – Application Guidelines

Figure 15h: Upper circle loss-of-synchronism region showing the final steps to calculate the
coordinates of the points on the circle. 1) Start at the intersection with the lens shape and
proceed in a clockwise direction. 2) Advance the step angle for each point. 3) Calculate the
new angle after step advancement. 4) Calculate the R-X coordinates.

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Figure 15i: Full tables of calculated lower and upper loss-of-synchronism circle coordinates.
The highlighted row is the detailed calculated points in Figures 15d and 15h.

Application Specific to Criterion B
The PRC-026-1 – Attachment B, Criterion B evaluates overcurrent elements used for tripping. The
same criteria as PRC-026-1 – Attachment B, Criterion A is used except for an additional criterion
(No. 4) that calculates a current magnitude based upon generator internal voltage of 1.05 per unit.
A value of 1.05 per unit generator voltage is used to establish a minimum pickup current value for
overcurrent relays that have a time delay less than 15 cycles. The sending-end and receiving-end
voltages are established at 1.05 per unit at 120 degree system separation angle. The 1.05 per unit
is the typical upper end of the operating voltage, which is also consistent with the maximum power

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transfer calculation using actual system source impedances in the PRC-023 NERC Reliability
Standard. The formulas used to calculate the current are in Table 14 below.

Table 14: Example Calculation (Overcurrent)
This example is for a 230 kV line terminal with a directional instantaneous phase overcurrent
element set to 50 amps secondary times a CT ratio of 160:1 that equals 8,000 amps, primary.
The following calculation is where VS equals the base line-to-ground sending-end generator
source voltage times 1.05 at an angle of 120 degrees, VR equals the base line-to-ground
receiving-end generator internal voltage times 1.05 at an angle of 0 degrees, and Zsys equals the
sum of the sending-end source, line, and receiving-end source impedances in ohms.
Here, the instantaneous phase setting of 8,000 amps is greater than the calculated system current
of 5,716 amps; therefore, it meets PRC-026-1 – Attachment B, Criterion B.
Eq. (102)

𝑉𝑆 =
𝑉𝑆 =

𝑉𝐿𝐿 ∠120°

× 1.05
√3
230,000∠120° 𝑉
√3

× 1.05

𝑉𝑆 = 139,430∠120° 𝑉
Receiving-end generator terminal voltage.
Eq. (103)

𝑉𝑅 =
𝑉𝑅 =

𝑉𝐿𝐿 ∠0°

× 1.05
√3
230,000∠0° 𝑉
√3

× 1.05

𝑉𝑅 = 139,430∠0° 𝑉
The total impedance of the system (Zsys) equals the sum of the sending-end source impedance
(ZS), the impedance of the line (ZL), and receiving-end impedance (ZR) in ohms.
Given:

𝑍𝑆 = 3 + 𝑗26 Ω

Eq. (104)

𝑍𝑠𝑦𝑠 = 𝑍𝑆 + 𝑍𝐿 + 𝑍𝑅

𝑍𝐿 = 1.3 + 𝑗8.7 Ω

𝑍𝑅 = 0.3 + 𝑗7.3 Ω

𝑍𝑠𝑦𝑠 = (3 + 𝑗26) Ω + (1.3 + 𝑗8.7) Ω + (0.3 + 𝑗7.3) Ω
𝑍𝑠𝑦𝑠 = 4.6 + 𝑗42 Ω
Total system current.
Eq. (105)

𝐼𝑠𝑦𝑠 =

(𝑉𝑆 − 𝑉𝑅 )
𝑍𝑠𝑦𝑠

𝐼𝑠𝑦𝑠 =

(139,430∠120° 𝑉 − 139,430∠0° 𝑉)
(4.6 + 𝑗42) Ω

𝐼𝑠𝑦𝑠 = 5,715.82∠66.25° 𝐴

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Application Specific to Three-Terminal Lines
If a three-terminal line is identified as an Element that is susceptible to a power swing based on
Requirement R1, the load-responsive protective relays at each end of the three-terminal line must
be evaluated.
As shown in Figure 15j, the source impedances at each end of the line can be obtained from the
similar short circuit calculation as for the two-terminal line (assuming the parallel transfer
impedances are ignored).

EA

A

B

ZSA

ZL2

ZL1

R

ZSB

EB

ZL3
C
ZSC
EC

Figure 15j: Three-terminal line. To evaluate the load-responsive protective relays on the threeterminal line at Terminal A, the circuit in Figure 15j is first reduced to the equivalent circuit
shown in Figure 15k. The evaluation process for the load-responsive protective relays on the
line at Terminal A will now be the same as that of the two-terminal line.

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Figure 15k: Three-terminal line reduced to a two-terminal line.

Application to Generation Elements
As with transmission BES Elements, the determination of the apparent impedance seen at an
Element located at, or near, a generation Facility is complex for power swings due to various
interdependent quantities. These variances in quantities are caused by changes in machine internal
voltage, speed governor action, voltage regulator action, the reaction of other local generators, and
the reaction of other interconnected transmission BES Elements as the event progresses through
the time domain. Though transient stability simulations may be used to determine the apparent
impedance for verifying load-responsive relay settings,19,20 Requirement R2, PRC-026-1 –
Attachment B, Criteria A and B provides a simplified method for evaluating the load-responsive
protective relay’s susceptibility to tripping in response to a stable power swing without requiring
stability simulations.
In general, the electrical center will be in the transmission system for cases where the generator is
connected through a weak transmission system (high external impedance). In other cases where
the generator is connected through a strong transmission system, the electrical center could be
inside the unit connected zone.21 In either case, load-responsive protective relays connected at the
generator terminals or at the high-voltage side of the generator step-up (GSU) transformer may be
challenged by power swings. Relays that may be challenged by power swings will be determined
by the Planning Coordinator in Requirement R1 or by the Generator Owner after becoming aware
of a generator, transformer, or transmission line BES Element that tripped22 in response to a stable
or unstable power swing due to the operation of its protective relay(s) in Requirement R2.

19

Donald Reimert, Protective Relaying for Power Generation Systems, Boca Raton, FL, CRC Press, 2006.

20

Prabha Kundur, Power System Stability and Control, EPRI, McGraw Hill, Inc., 1994.

21

Ibid, Kundur.

See Guidelines and Technical Basis section, “Becoming Aware of an Element That Tripped in Response to a
Power Swing,”
22

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Voltage controlled time-overcurrent and voltage-restrained time-overcurrent relays are excluded
from this standard. When these relays are set based on equipment permissible overload capability,
their operating times are much greater than 15 cycles for the current levels observed during a power
swing.
Instantaneous overcurrent, time-overcurrent, and definite-time overcurrent relays with a time delay
of less than 15 cycles for the current levels observed during a power swing are applicable and are
required to be evaluated for identified Elements.
The generator loss-of-field protective function is provided by impedance relay(s) connected at the
generator terminals. The settings are applied to protect the generator from a partial or complete
loss of excitation under all generator loading conditions and, at the same time, be immune to
tripping on stable power swings. It is more likely that the loss-of-field relay would operate during
a power swing when the automatic voltage regulator (AVR) is in manual mode rather than when
in automatic mode.23 Figure 16 illustrates the loss-of-field relay in the R-X plot, which typically
includes up to three zones of protection.

Figure 16: An R-X graph of typical impedance settings for loss-of-field relays.

23

John Burdy, Loss-of-excitation Protection for Synchronous Generators GER-3183, General Electric Company.

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Loss-of-field characteristic 40-1 has a wider impedance characteristic (positive offset) than
characteristic 40-2 or characteristic 40-3 and provides additional generator protection for a partial
loss of field or a loss of field under low load (less than 10% of rated). The tripping logic of this
protection scheme is established by a directional contact, a voltage setpoint, and a time delay. The
voltage and time delay add security to the relay operation for stable power swings. Characteristic
40-3 is less sensitive to power swings than characteristic 40-2 and is set outside the generator
capability curve in the leading direction. Regardless of the relay impedance setting, PRC-01924
requires that the “in-service limiters operate before Protection Systems to avoid unnecessary trip”
and “in-service Protection System devices are set to isolate or de-energize equipment in order to
limit the extent of damage when operating conditions exceed equipment capabilities or stability
limits.” Time delays for tripping associated with loss-of-field relays25,26 have a range from 15
cycles for characteristic 40-2 to 60 cycles for characteristic 40-1 to minimize tripping during stable
power swings. In PRC-026-1, 15 cycles establishes a threshold for applicability; however, it is the
responsibility of the Generator Owner to establish settings that provide security against stable
power swings and, at the same time, dependable protection for the generator.
The simple two-machine system circuit (method also used in the Application to Transmission
Elements section) is used to analyze the effect of a power swing at a generator facility for loadresponsive relays. In this section, the calculation method is used for calculating the impedance
seen by the relay connected at a point in the circuit.27 The electrical quantities used to determine
the apparent impedance plot using this method are generator saturated transient reactance (X’d),
GSU transformer impedance (XGSU), transmission line impedance (ZL), and the system equivalent
(Ze) at the point of interconnection. All impedance values are known to the Generator Owner
except for the system equivalent. The system equivalent is obtainable from the Transmission
Owner. The sending-end and receiving-end source voltages are varied from 0.0 to 1.0 per unit to
form the lens shape portion of the unstable power swing region. The voltage range of 0.7 to 1.0
results in a ratio range from 0.7 to 1.43. This ratio range is used to form the lower and upper lossof-synchronism circle shapes of the unstable power swing region. A system separation angle of
120 degrees is used in accordance with PRC-026-1 – Attachment B criteria for each loadresponsive protective relay evaluation.
Table 15 below is an example calculation of the apparent impedance locus method based on
Figures 17 and 18.28 In this example, the generator is connected to the 345 kV transmission system
through the GSU transformer and has the listed ratings. Note that the load-responsive protective
relays in this example may have ownership with the Generator Owner or the Transmission Owner.

24

Coordination of Generating Unit or Plant Capabilities, Voltage Regulating Controls, and Protection

25

Ibid, Burdy.

26

Applied Protective Relaying, Westinghouse Electric Corporation, 1979.

27

Edward Wilson Kimbark, Power System Stability, Volume II: Power Circuit Breakers and Protective Relays,
Published by John Wiley and Sons, 1950.
28

Ibid, Kimbark.

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Figure 17: Simple one-line diagram of the
system to be evaluated.

Figure 18: Simple system equivalent
impedance diagram to be evaluated.29

Table15: Example Data (Generator)
Input Descriptions

Input Values

Synchronous Generator nameplate (MVA)

940 MVA

Saturated transient reactance (940 MVA base)

𝑋𝑑′ = 0.3845 per unit

Generator rated voltage (Line-to-Line)

20 𝑘𝑉

Generator step-up (GSU) transformer rating

880 𝑀𝑉𝐴

GSU transformer reactance (880 MVA base)

XGSU = 16.05%

System Equivalent (100 MVA base)

𝑍𝑒 = 0.00723∠90° per unit

Generator Owner Load-Responsive Protective Relays
Positive Offset Impedance
40-1

Offset = 0.294 per unit
Diameter = 0.294 per unit
Negative Offset Impedance

40-2

Offset = 0.22 per unit
Diameter = 2.24 per unit
Negative Offset Impedance

40-3

Offset = 0.22 per unit
Diameter = 1.00 per unit

21-1

29

Diameter = 0.643 per unit
MTA = 85°

Ibid, Kimbark.

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Table15: Example Data (Generator)
I (pickup) = 5.0 per unit

50

Transmission Owned Load-Responsive Protective Relays
Diameter = 0.55 per unit

21-2

MTA = 85°

Calculations shown for a 120 degree angle and ES/ER = 1. The equation for calculating ZR is:30
Eq. (106)

𝑍𝑅 = (

(1 − 𝑚)(𝐸𝑆 ∠𝛿) + (𝑚)(𝐸𝑅 )
) × 𝑍𝑠𝑦𝑠
𝐸𝑆 ∠𝛿 − 𝐸𝑅

Where m is the relay location as a function of the total impedance (real number less than 1)
ES and ER is the sending-end and receiving-end voltages
Zsys is the total system impedance
ZR is the complex impedance at the relay location and plotted on an R-X diagram
All of the above are constants (940 MVA base) while the angle δ is varied. Table 16 below contains
calculations for a generator using the data listed in Table 15.

Table16: Example Calculations (Generator)
The following calculations are on a 940 MVA base.
Given:

𝑋𝑑′ = 𝑗0.3845 𝑝𝑢

Eq. (107)

𝑍𝑠𝑦𝑠 = 𝑋𝑑′ + 𝑋𝐺𝑆𝑈 + 𝑍𝑒

𝑋𝐺𝑆𝑈 = 𝑗0.17144 𝑝𝑢

𝑍𝑒 = 𝑗0.06796 𝑝𝑢

𝑍𝑠𝑦𝑠 = 𝑗0.3845 𝑝𝑢 + 𝑗0.17144 𝑝𝑢 + 𝑗0.06796 𝑝𝑢
𝑍𝑠𝑦𝑠 = 0.6239 ∠90° 𝑝𝑢
𝑋𝑑′
0.3845
=
= 0.6163
𝑍𝑠𝑦𝑠 0.6239

Eq. (108)

𝑚=

Eq. (109)

𝑍𝑅 = (
𝑍𝑅 = (

30

(1 − 𝑚)(𝐸𝑆 ∠𝛿) + (𝑚)(𝐸𝑅 )
) × 𝑍𝑠𝑦𝑠
𝐸𝑆 ∠𝛿 − 𝐸𝑅

(1 − 0.6163) × (1∠120°) + (0.6163)(1∠0°)
) × (0.6239∠90°) 𝑝𝑢
1∠120° − 1∠0°

Ibid, Kimbark.

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Table16: Example Calculations (Generator)
0.4244 + 𝑗0.3323
Z𝑅 = (
) × (0.6239∠90°) 𝑝𝑢
−1.5 + 𝑗 0.866
Z𝑅 = (0.3116 ∠ − 111.95°) × (0.6239∠90°) 𝑝𝑢
Z𝑅 = 0.194 ∠ − 21.95° 𝑝𝑢
Z𝑅 = −0.18 − 𝑗0.073 𝑝𝑢

Table 17 lists the swing impedance values at other angles and at ES/ER = 1, 1.43, and 0.7. The
impedance values are plotted on an R-X graph with the center being at the generator terminals for
use in evaluating impedance relay settings.

Table 17: Sample Calculations for a Swing Impedance Chart for Varying Voltages
at the Sending-End and Receiving-End.
ES/ER=1

ES/ER=1.43

ES/ER=0.7

ZR

ZR

ZR

Angle ()
(Degrees)

Magnitude
(pu)

Angle
(Degrees)

Magnitude
(pu)

Angle
Magnitude
Angle
(Degrees)
(pu)
(Degrees)

90

0.320

-13.1

0.296

6.3

0.344

-31.5

120

0.194

-21.9

0.173

-0.4

0.227

-40.1

150

0.111

-41.0

0.082

-10.3

0.154

-58.4

210

0.111

-25.9

0.082

190.3

0.154

238.4

240

0.194

201.9

0.173

180.4

0.225

220.1

270

0.320

193.1

0.296

173.7

0.344

211.5

Requirement R2 Generator Examples
Distance Relay Application
Based on PRC-026-1 – Attachment B, Criterion A, the distance relay (21-1) (i.e., owned by the
Generation Owner) characteristic is in the region where a stable power swing would not occur as
shown in Figure 19. There is no further obligation to the owner in this standard for this loadresponsive protective relay.
The distance relay (21-2) (i.e., owned by the Transmission Owner) is connected at the high-voltage
side of the GSU transformer and its impedance characteristic is in the region where a stable power
swing could occur causing the relay to operate. In this example, if the intentional time delay of this
relay is less than 15 cycles, the PRC-026 – Attachment B, Criterion A cannot be met, thus the
Transmission Owner is required to create a CAP (Requirement R3). Some of the options include,

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but are not limited to, changing the relay setting (i.e., impedance reach, angle, time delay), modify
the scheme (i.e., add PSB), or replace the Protection System. Note that the relay may be excluded
from this standard if it has an intentional time delay equal to or greater than 15 cycles.

Figure 19: Swing impedance graph for impedance relays at a generating facility.

Loss-of-Field Relay Application
In Figure 20, the R-X diagram shows the loss-of-field relay (40-1 and 40-2) characteristics are in
the region where a stable power swing can cause a relay operation. Protective relay 40-1 would
be excluded if it has an intentional time delay equal to or greater than 15 cycles. Similarly, 40-2
would be excluded if its intentional time delay is equal to or greater than 15 cycles. For example,
if 40-1 has a time delay of 1 second and 40-2 has a time delay of 0.25 seconds, they are excluded
and there is no further obligation on the Generator Owner in this standard for these relays. The

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loss-of-field relay characteristic 40-3 is entirely inside the unstable power swing region. In this
case, the owner may select high speed tripping on operation of the 40-3 impedance element.

Figure 20: Typical R-X graph for loss-of-field relays with a portion of the unstable power swing
region defined by PRC-026-1 – Attachment B, Criterion A.

Instantaneous Overcurrent Relay
In similar fashion to the transmission line overcurrent example calculation in Table 14, the
instantaneous overcurrent relay minimum setting is established by PRC-026-1 – Attachment B,
Criterion B. The solution is found by:
Eq. (110)

𝐼𝑠𝑦𝑠 =

𝐸𝑆 − 𝐸𝑅
𝑍sys

As stated in the relay settings in Table 15, the relay is installed on the high-voltage side of the GSU
transformer with a pickup of 5.0 per unit. The maximum allowable current is calculated below.
𝐼𝑠𝑦𝑠 =

(1.05∠120° − 1.05∠0°)
𝑝𝑢
0.6239∠90°

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𝐼𝑠𝑦𝑠 =

1.819∠150°
𝑝𝑢
0.6239∠90°

𝐼𝑠𝑦𝑠 = 2.91 ∠60° 𝑝𝑢
The instantaneous phase setting of 5.0 per unit is greater than the calculated system current of 2.91
per unit; therefore, it meets the PRC-026-1 – Attachment B, Criterion B.
Out-of-Step Tripping for Generation Facilities
Out-of-step protection for the generator generally falls into three different schemes. The first
scheme is a distance relay connected at the high-voltage side of the GSU transformer with the
directional element looking toward the generator. Because this relay setting may be the same
setting used for generator backup protection (see Requirement R2 Generator Examples, Distance
Relay Application), it is susceptible to tripping in response to stable power swings and would
require modification. Because this scheme is susceptible to tripping in response to stable power
swings and any modification to the mho circle will jeopardize the overall protection of the outof-step protection of the generator, available technical literature does not recommend using this
scheme specifically for generator out-of-step protection. The second and third out-of-step
Protection System schemes are commonly referred to as single and double blinder schemes.
These schemes are installed or enabled for out-of-step protection using a combination of
blinders, a mho element, and timers. The combination of these protective relay functions
provides out-of-step protection and discrimination logic for stable and unstable power swings.
Single blinder schemes use logic that discriminate between stable and unstable power swings by
issuing a trip command after the first slip cycle. Double blinder schemes are more complex than
the single blinder scheme and, depending on the settings of the inner blinder, a trip for a stable
power swing may occur. While the logic discriminates between stable and unstable power
swings in either scheme, it is important that the trip initiating blinders be set at an angle greater
than the stability limit of 120 degrees to remove the possibility of a trip for a stable power swing.
Below is a discussion of the double blinder scheme.
Double Blinder Scheme
The double blinder scheme is a method for measuring the rate of change of positive sequence
impedance for out-of-step swing detection. The scheme compares a timer setting to the actual
elapsed time required by the impedance locus to pass between two impedance characteristics. In
this case, the two impedance characteristics are simple blinders, each set to a specific resistive
reach on the R-X plane. Typically, the two blinders on the left half plane are the mirror images of
those on the right half plane. The scheme typically includes a mho characteristic which acts as a
starting element, but is not a tripping element.
The scheme detects the blinder crossings and time delays as represented on the R-X plane as
shown in Figure 21. The system impedance is composed of the generator transient (Xd’), GSU
transformer (XT), and transmission system (Xsystem), impedances.
The scheme logic is initiated when the swing locus crosses the outer Blinder R1 (Figure 21), on
the right at separation angle α. The scheme only commits to take action when a swing crosses the
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PRC-026-1 – Application Guidelines
inner blinder. At this point the scheme logic seals in the out-of-step trip logic at separation angle
β. Tripping actually asserts as the impedance locus leaves the scheme characteristic at separation
angle δ.
The power swing may leave both inner and outer blinders in either direction, and tripping will
assert. Therefore, the inner blinder must be set such that the separation angle β is large enough
that the system cannot recover. This angle should be set at 120 degrees or more. Setting the angle
greater than 120 degrees satisfies the PRC-026-1 – Attachment B, Criterion A (No. 1, 1st bullet)
since the tripping function is asserted by the blinder element. Transient stability studies may
indicate that a smaller stability limit angle is acceptable under PRC-026-1 – Attachment B,
Criterion A (No. 1, 2nd bullet). In this respect, the double blinder scheme is similar to the double
lens and triple lens schemes and many transmission application out-of-step schemes.

Figure 21: Double Blinder Scheme generic out of step characteristics.

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PRC-026-1 – Application Guidelines
Figure 22 illustrates a sample setting of the double blinder scheme for the example 940 MVA
generator. The only setting requirement for this relay scheme is the right inner blinder, which
must be set greater than the separation angle of 120 degrees (or a lesser angle based on a
transient stability study) to ensure that the out-of-step protective function is expected to not trip
in response to a stable power swing during non-Fault conditions. Other settings such as the mho
characteristic, outer blinders, and timers are set according to transient stability studies and are not
a part of this standard.

Figure 22: Double Blinder Out-of-Step Scheme with unit impedance data and load-responsive
protective relay impedance characteristics for the example 940 MVA generator, scaled in relay
secondary ohms.

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Requirement R3
To achieve the stated purpose of this standard, which is to ensure that relays are expected to not
trip in response to stable power swings during non-Fault conditions, this Requirement ensures
that the applicable entity develops a Corrective Action Plan (CAP) that reduces the risk of relays
tripping in response to a stable power swing during non-Fault conditions that may occur on any
applicable BES Element.

Requirement R4
To achieve the stated purpose of this standard, which is to ensure that load-responsive protective
relays are expected to not trip in response to stable power swings during non-Fault conditions, the
applicable entity is required to implement any CAP developed pursuant to Requirement R3 such
that the Protection System will meet PRC-026-1 – Attachment B criteria or can be excluded under
the PRC-026-1 – Attachment A criteria (e.g., modifying the Protection System so that relay
functions are supervised by power swing blocking or using relay systems that are immune to power
swings), while maintaining dependable fault detection and dependable out-of-step tripping (if outof-step tripping is applied at the terminal of the BES Element). Protection System owners are
required in the implementation of a CAP to update it when actions or timetable change, until all
actions are complete. Accomplishing this objective is intended to reduce the occurrence of
Protection System tripping during a stable power swing, thereby improving reliability and
minimizing risk to the BES.
The following are examples of actions taken to complete CAPs for a relay that did not meet PRC026-1 – Attachment B and could be at-risk of tripping in response to a stable power swing during
non-Fault conditions. A Protection System change was determined to be acceptable (without
diminishing the ability of the relay to protect for faults within its zone of protection).
Example R4a: Actions: Settings were issued on 6/02/2015 to reduce the Zone 2 reach of
the impedance relay used in the directional comparison unblocking (DCUB) scheme from
30 ohms to 25 ohms so that the relay characteristic is completely contained within the lens
characteristic identified by the criterion. The settings were applied to the relay on
6/25/2015. CAP was completed on 06/25/2015.
Example R4b: Actions: Settings were issued on 6/02/2015 to enable out-of-step blocking
on the existing microprocessor-based relay to prevent tripping in response to stable power
swings. The setting changes were applied to the relay on 6/25/2015. CAP was completed
on 06/25/2015.

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The following is an example of actions taken to complete a CAP for a relay responding to a stable
power swing that required the addition of an electromechanical power swing blocking relay.
Example R4c: Actions: A project for the addition of an electromechanical power swing
blocking relay to supervise the Zone 2 impedance relay was initiated on 6/5/2015 to prevent
tripping in response to stable power swings. The relay installation was completed on
9/25/2015. CAP was completed on 9/25/2015.
The following is an example of actions taken to complete a CAP with a timetable that required
updating for the replacement of the relay.
Example R4d: Actions: A project for the replacement of the impedance relays at both
terminals of line X with line current differential relays was initiated on 6/5/2015 to prevent
tripping in response to stable power swings. The completion of the project was postponed
due to line outage rescheduling from 11/15/2015 to 3/15/2016. Following the timetable
change, the impedance relay replacement was completed on 3/18/2016. CAP was
completed on 3/18/2016.
The CAP is complete when all the documented actions to remedy the specific problem (i.e.,
unnecessary tripping during stable power swings) are completed.

Justification for Including Unstable Power Swings in the Requirements
Protection Systems that are applicable to the Standard and must be secure for a stable power swing
condition (i.e., meets PRC-026-1 – Attachment B criteria) are identified based on Elements that
are susceptible to both stable and unstable power swings. This section provides an example of why
Elements that trip in response to unstable power swings (in addition to stable power swings) are
identified and that their load-responsive protective relays need to be evaluated under PRC-026-1
– Attachment B criteria.

Figure 23: A simple electrical system where two lines tie a small utility to a much larger
interconnection.

In Figure 23 the relays at circuit breakers 1, 2, 3, and 4 are equipped with a typical overreaching
Zone 2 pilot system, using a Directional Comparison Blocking (DCB) scheme. Internal faults (or
power swings) will result in instantaneous tripping of the Zone 2 relays if the measured fault or
power swing impedance falls within the zone 2 operating characteristic. These lines will trip on

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pilot Zone 2 for out-of-step conditions if the power swing impedance characteristic enters into
Zone 2. All breakers are rated for out-of-phase switching.

Figure 24: In this case, the Zone 2 element on circuit breakers 1, 2, 3, and 4 did not meet the
PRC-026-1 – Attachment B criteria (this figure depicts the power swing as seen by relays on
breakers 3 and 4).

In Figure 24, a large disturbance occurs within the small utility and its system goes out-of-step
with the large interconnect. The small utility is importing power at the time of the disturbance. The
actual power swing, as shown by the solid green line, enters the Zone 2 relay characteristic on the
terminals of Lines 1, 2, 3, and 4 causing both lines to trip as shown in Figure 25.

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PRC-026-1 – Application Guidelines

1

Line 1

3
Large

Small
Utility

2

Line 2

4

Interconnect

Figure 25: Islanding of the small utility due to Lines 1 and 2 tripping in response to an unstable
power swing.

In Figure 25, the relays at circuit breakers 1, 2, 3, and 4 have correctly tripped due to the unstable
power swing (shown by the dashed green line in Figure 24), de-energizing Lines 1 and 2, and
creating an island between the small utility and the big interconnect. The small utility shed 500
MW of load on underfrequency and maintained a load to generation balance.

Figure 26: Line 1 is out-of-service for maintenance, Line 2 is loaded beyond its normal rating
(but within its emergency rating).

Subsequent to the correct tripping of Lines 1 and 2 for the unstable power swing in Figure 25,
another system disturbance occurs while the system is operating with Line 1 out-of-service for
maintenance. The disturbance causes a stable power swing on Line 2, which challenges the relays
at circuit breakers 2 and 4 as shown in Figure 27.

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Figure 27: Relays on circuit breakers 2 and 4 were not addressed to meet the PRC-026-1 –
Attachment B criteria following the previous unstable power swing event.

If the relays on circuit breakers 2 and 4 were not addressed under the Requirements for the previous
unstable power swing condition, the relays would trip in response to the stable power swing, which
would result in unnecessary system separation, load shedding, and possibly cascading or blackout.

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PRC-026-1 – Application Guidelines

1

Line 1

3
Large

Small
Utility

2

Line 2

4

Interconnect

Figure 28: Possible blackout of the small utility.

If the relays that tripped in response to the previous unstable power swing condition in Figure 24
were addressed under the Requirements to meet PRC-026-1 - Attachment B criteria, the
unnecessary tripping of the relays for the stable power swing shown in Figure 28 would have been
averted, and the possible blackout of the small utility would have been avoided.

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
The Planning Coordinator has a wide-area view and is in the position to identify generator,
transformer, and transmission line BES Elements which meet the criteria, if any. The criteria-based
approach is consistent with the NERC System Protection and Control Subcommittee (SPCS)
technical document Protection System Response to Power Swings, August 2013 (“PSRPS
Report”),31 which recommends a focused approach to determine an at-risk BES Element. See the
Guidelines and Technical Basis for a detailed discussion of the criteria.
Rationale for R2
The Generator Owner and Transmission Owner are in a position to determine whether their loadresponsive protective relays meet the PRC-026-1 – Attachment B criteria. Generator, transformer,
and transmission line BES Elements are identified by the Planning Coordinator in Requirement
R1 and by the Generator Owner and Transmission Owner following an actual event where the
Generator Owner and Transmission Owner became aware (i.e., through an event analysis or

31

NERC System Protection and Control Subcommittee, Protection System Response to Power Swings, August
2013:
http://www.nerc.com/comm/PC/System%20Protection%20and%20Control%20Subcommittee%20SPCS%2020/SPC
S%20Power%20Swing%20Report_Final_20131015.pdf)

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PRC-026-1 – Application Guidelines
Protection System review) tripping was due to a stable or unstable power swing. A period of 12
calendar months allows sufficient time for the entity to conduct the evaluation.
Rationale for R3
To meet the reliability purpose of the standard, a CAP is necessary to ensure the entity’s Protection
System meets the PRC-026-1 – Attachment B criteria (1st bullet) so that protective relays are
expected to not trip in response to stable power swings. A CAP may also be developed to modify
the Protection System for exclusion under PRC-026-1 – Attachment A (2nd bullet). Such an
exclusion will allow the Protection System to be exempt from the Requirement for future events.
The phrase, “…while maintaining dependable fault detection and dependable out-of-step
tripping…” in Requirement R3 describes that the entity is to comply with this standard, while
achieving their desired protection goals. Refer to the Guidelines and Technical Basis, Introduction,
for more information.
Rationale for R4
Implementation of the CAP must accomplish all identified actions to be complete to achieve the
desired reliability goal. During the course of implementing a CAP, updates may be necessary for
a variety of reasons such as new information, scheduling conflicts, or resource issues.
Documenting CAP changes and completion of activities provides measurable progress and
confirmation of completion.
Rationale for Attachment B (Criterion A)
The PRC-026-1 – Attachment B, Criterion A provides a basis for determining if the relays are
expected to not trip for a stable power swing having a system separation angle of up to 120 degrees
with the sending-end and receiving-end voltages varying from 0.7 to 1.0 per unit (See Guidelines
and Technical Basis).

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