This document provides an introduction to power system stability concepts. It defines power system stability as the ability to maintain equilibrium after a disturbance. Stability is classified into categories like rotor angle stability, voltage stability, and frequency stability based on the nature and time span of the instability. Transient stability refers to the ability to maintain synchronism during large disturbances. Small signal stability considers stability during small disturbances. The document outlines challenges to stable operation in modern power systems and emphasizes the need for comprehensive stability analysis tools.

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INTRODUCTION TO POWER SYSTEM
STABILITY
Copyright © P. Kundur
This material should not be used without the author's consent

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Introduction to Power System Stability
Outline
1. Basic Concepts, Definitions and Classification of
Power System Stability
2. Challenges to Stable and Secure Operation of Power
Systems in the New Industry Environment
3. Comprehensive Study Procedures and Tools for
Stability Analysis
Appendix
Concepts of Active Power and Reactive Power

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Power System Stability: Basic Concepts
and Definition
 Power System Stability denotes the ability of an
electric power system, for a given initial operating
condition, to regain a state of operating equilibrium
after being subjected to a physical disturbance, with
all system variables bounded so that the system
integrity is preserved
 Integrity of the system is preserved when
practically the entire power system remains
intact with no tripping of generators or loads,
except for those disconnected by isolation of
the faulted elements or intentionally tripped to
preserve the continuity of operation of the rest
of the system
 Stability is a condition of equilibrium between
opposing forces:
 instability results when a disturbance leads to
a sustained imbalance between the opposing
forces
 instability is a run-away or run-down situation

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Basic Concepts (cont’d)
 The power system is a highly nonlinear system
which operates in a constantly changing
environment:
 loads, generator outputs, topology and key
operating parameters change continually
 When subjected to a disturbance, the system
stability depends on:
 the nature of the disturbance, as well as
 the initial operating condition
 The disturbances may be small or large:
 small disturbances in the form of load changes
occur continually
 large disturbances of a severe nature, such as
a short-circuit on a transmission line or loss of
a large generator

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Basic Concepts (cont’d)
 Following a transient disturbance, if the power
system is stable it will reach a new equilibrium state
with practically the entire system intact:
 faulted element and any connected load
disconnected
 actions of automatic controls and possibly
operator action will eventually restore system
to normal state
 On the other hand, if the system is unstable, it will
result in a run-away or run-down situation; for
example,
 a progressive increase in angular separation
of generator rotors, or
 a progressive decrease in bus voltages
 An unstable system condition could lead to
cascading outages, and a shut-down of a major
portion of the power system

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Need for Classification of Stability
 Power system dynamic performance is influenced
by a wide array of devices with different response
rates and characteristics
 Instability may be manifested in many different ways
depending on system configuration and operating
conditions
 mode of instability depends on which set of
balancing forces experience a sustained
imbalance
 Due to the high dimensionality and complexity of
the system, it is essential to make simplifying
assumptions and to analyze specific problems using
the right degree of detail
 Not very effective to study power system stability as
a single problem

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Classification of Power System Stability
 Classification of stability into various categories
greatly facilitates:
 analysis of stability problems
 identification of essential factors which
contribute to instability
 devising methods of improving stable
operation
 This is addressed by a Joint IEEE/CIGRE TF set up
in 2001: report published in 2003 as:
 an IEEE Transaction paper (copy attached);
 CIGRE Technical Brochure # 231, June 2003
 Classification based on the following
considerations:
 physical nature of the resulting instability
 size of the disturbance considered
 devices, processes, and the time span
involved

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Classification of Power System Stability
Short
Term
Power System Stability
Angle
Stability
Voltage
Stability
Small
Signal
Stability
Transient
Stability
Large
Disturbance
Voltage
Stability
Small
Disturbance
Voltage
Stability
Long
Term
Short
Term
Long
Term
Consideration
for
Classification
Physical Nature/
Main System
Parameter
Size of
Disturbance
Time Span
Frequency
Stability
– ability to remain in operating equilibrium
– equilibrium between opposing forces
– ability to maintain synchronism
– torque balance of synchronous
machines
Short
Term
– ability to maintain frequency
within nominal range
– generation/load balance
– ability to maintain steady
voltages
– reactive power balance
– equilibrium of voltage control

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Rotor Angle Stability
 Ability of interconnected synchronous machines to
remain in synchronism under normal conditions and
after being subjected to a disturbance
 Depends on the ability to maintain/restore
equilibrium between electromagnetic torque and
mechanical torque of each synchronous machine in
the system
 If the generators become unstable when perturbed,
it is as a result of
 a run-away situation due to torque imbalance
 A fundamental factor is the manner in which power
outputs of synchronous machines vary as their
rotor angles swing
 Instability that may result occurs in the form of
increasing angular swings of some generators
leading to loss of synchronism with other
generators

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Rotor Angle Stability (cont’d)
 Under steady-state conditions, there is equilibrium
between electromagnetic and mechanical torques
 If the system is perturbed, this equilibrium is upset,
causing acceleration or deceleration of the rotor
 synchronism is maintained through
development of restoring forces
 Change in electrical torque can be resolved into two
components:
 TS is the synchronizing torque coefficient
 TD is the damping torque coefficient
 Lack of synchronizing torque results in aperiodic
instability
 Lack of damping torque results in oscillatory
instability
    DSe TTT

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Transient Stability
 Term used traditionally to denote large-disturbance
angle stability
 Ability of a power system to maintain synchronism
when subjected to a severe transient disturbance:
 resulting system response involves large
excursions of generator rotor angles and is
influenced by the nonlinear power-angle
relationship
 stability depends on the initial operating
condition, severity of the disturbance, and
strength of post-fault transmission network
 A wide variety of disturbances can occur on the
system:
 varying degree of severity and probability of
occurrence
 the system is, however, designed and operated
so as to be stable for a selected set of
contingencies
usually, transmission faults: L-G, L-L-G,
three phase

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Small-Signal (Angle) Stability
 Small-Signal (or Small Disturbance) Stability is the
ability of a power system to maintain synchronism
under small disturbances:
 such disturbances occur continually on the
system due to small variations in loads and
generation
 disturbance considered sufficiently small if
linearization of system equations is
permissible for analysis
 instability that may result can be of two forms:
aperiodic increase in rotor angle due to
lack of sufficient synchronizing torque
rotor oscillations of increasing amplitude
due to lack of sufficient damping torque
 Corresponds to Liapunov’s first method of stability
analysis

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Voltage Stability
 Ability of power system to maintain steady voltages
at all buses in the system after being subjected to a
disturbance from a given initial operating condition
 A system experiences voltage instability when a
disturbance, increase in load demand, or change in
system condition causes:
 a progressive and uncontrollable fall or rise in
voltage of some buses
 Main factor causing voltage instability is the
inability of power system to maintain a proper
balance of reactive power and voltage control
actions
 The driving force for voltage instability is usually
the loads. Following a condition of reduced
transmission system voltages,
 power consumed by the loads tend to be
restored by the action if distribution voltage
regulators, tap changing transformers, and
thermostats

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Frequency Stability
 Ability to maintain steady frequency within a
nominal range following a disturbance resulting in a
significant imbalance between system generation
and load:
 instability that may result occurs in the form of
sustained frequency swings leading to tripping
of generating units and/or loads
 determined by the overall response of the
system as evidenced by its mean frequency
rather than relative motions of rotors of
generators
 In a small “island” system, frequency stability could
be of concern for any disturbance causing a
significant loss of load and/or generation
 In a large interconnected system, frequency stability
would be of concern only following a severe system
upset resulting in the system splitting into one or
more islands
 Generally, frequency stability problems are
associated with inadequacies in equipment
responses, poor coordination of control and
protection systems

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Design and Operating Criteria for Power
System Security
 For reliable service, a power system must remain
intact and be capable of withstanding a wide variety of
disturbances
 Impractical to achieve stable operation for all possible
disturbances or contingencies
 The general practice is to design and operate the
power system so that the more probable
contingencies can be sustained without loss of
system integrity
 "Normal Design Contingencies"
 loss of any single element, either spontaneously
or proceeded by a fault
 This is referred to as the "N-1 criterion" because it
examines the behaviour of an N-component grid
following the loss of any one major components
 Events that exceed the severity of normal design
contingencies can in fact occur:
 "Extreme Contingencies"
 measures should be taken to minimize their
occurrence and impact

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Power System Stability: Historical
Perspective
 Recognized as an important problem for secure
system operation since the 1920s
 Major concern since the infamous November 9, 1965
blackout of Northeast U.S.A. and Ontario, Canada
 criteria and analytical tools used worldwide
until now largely based on the developments
that followed this blackout
 Presents many new challenges for today's power
systems

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Traditional Approach to Power System
Stability
 Focus on "transient (rotor angle) stability"
 System designed and operated to withstand
 loss of any single element preceded by single-,
double-, or three-phase fault
 referred to as "N-1" criterion
 Analysis by time-domain simulations of selected
operating conditions
 scenarios based on judgment/experience
 Operating limits based on off-line studies
 system operated conservatively within pre-
established limits

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Challenges to Secure Operation of
Today's Power Systems
 Power systems are more complex
 national/continental/regional grids
 many processes whose operations need to be
coordinated; thousands of devices requiring a
harmonious interplay
 complex modes of instability
 "Deregulated" market environment
 many entities with diverse business interests
 system expansion and operation driven by
economic drivers
 lack of coordinated planning!
 power systems pushed "harder"; more
frequent changes in power flow patterns

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Examples of Major System Disturbances
We had several wake up calls in recent years:
 July 1996 WSCC System Disturbance
 August 1996 WSCC System Disturbance
 March 1999 Brazil blackout
 July 1999 Taiwan blackout
 August 2003 NE U.S.A. and Ontario blackout
 September 2003 Italy blackout
 September 2003 South Sweden and Eastern
Denmark blackout
 Other blackouts in 2003/04: England, S.W. Australia,
Croatia, Greece, Brazil
 November 2006 European Power Grid Disturbance:
UCTE network split into 3 islands

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Comprehensive Study Procedures
and Tools
 All categories of system stability should be
considered
 We should always keep in mind the overall stability
 solutions to problems of one category should
not be at the expense of another
 Stability depends on the harmonious interplay of all
elements of the power system:
 knowledge of the characteristics of individual
elements is essential for the understanding
and study of power system stability
 proper selection and coordination of controls
and protective equipment are of paramount
importance
 Analytical tools and system models should be
validated against measured response
 Analytical tools should:
 not only determine if system stable or unstable
 but also provide insight into factors
influencing stability

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Concepts of Active Power
and Reactive Power

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Power in an A.C. Circuit
 Let us first look at simple dc circuits:
Energy is stored in inductance L and capacitance C
 With A.C., energy is stored and discharged twice every
cycle
 Instantaneous power, p = ei

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Concepts of Active and Reactive Powers
Consider the single phase circuit shown in Fig. A.1 with
e = Em Sin ωt
i = Im Sin (ωt - Φ)
Instantaneous power:
i
e
Fig. A.1

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Figure A.2 shows plots of e, i, p, pp and pq.
 Active Power (pp) represents the component of p
utilized for permanent irreversible consumption. It has
an average value of P.
 Reactive Power (pq) is utilized in establishing either a
magnetic or electrostatic field; it is stored in
inductance or capacitance and then returned to the
source. It has a zero average value.
 result of the associated component of current
being in quadrature with the voltage

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1 ACTIVE POWER pp = P (1 - cos 2 a t)
2 REACTIVE POWER pq = -Q sin a t
Fig. A.2 Plots of e, i, p, pp and pq

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Reactive Power - Sign Conventions
 By convention, the Q associated with:
 inductive load is positive
 capacitive load is negative
An inductive load absorbs Q
A capacitive load supplies Q
 A synchronous machine:
 when overexcited, supplies reactive power
 when underexcited, absorbs reactive

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Special Comments on Reactive Power
 Although the Reactive Power associated with an element
has a zero average value, it represents real power required
to store and discharge magnetic energy in an inductance or
electrostatic energy in a capacitance, twice every cycle.
 In a network the interchange of energy takes place between
the source, inductive elements and capacitive elements.
The net energy associated with reactive power is the sum
of various inductive and capacitive stored energies.
 The oscillatory transfer of reactive power between points in
a power system results in voltage drops and losses in
generation and transmission equipment.
As efficiency and voltage regulation are very important, the
transfer of reactive power over the system is of prime
importance.

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General Observations on Active and
Reactive Power Flow
 In a practical transmission system, normally:
 the active power flow is determined primarily by
angular differences between bus voltages; and
 the reactive power flow by magnitude differences of
bus voltages
 Active Power is supplied only by generators:
 the desired flow of active power from a generator is
achieved by control of prime mover mechanical
torque.
 Increasing the mechanical torque advances the
generator rotor and hence, the "internal voltage"
with respect to other system voltages.
 Sources of Reactive Power:
 synchronous machines (over excited)
 static capacitors
 capacitance of transmission lines
 Consumers of Reactive Power:
 synchronous machines (under excited)
 induction motors
 inductive static loads
 inductance of transmission lines, transformers
 AC/DC and DC/AC converters

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 At any junction:
; P = 0
; Q = 0
They can be added arithmetically
 For a system:
 a balance sheet of active and reactive power can be
drawn;
 the total injected P and Q are equal to the total
extracted P and Q, plus any P and Q losses.
 Under steady-state conditions;
 P and Q flow over a network are fairly independent
of each other and are influenced by different control
actions.

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