29-11-2012, 05:30 PM
Definition and Classification of Power System Stability
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Abstract
The problem of defining and classifying power
system stability has been addressed by several previous CIGRE
and IEEE Task Force reports. These earlier efforts, however,
do not completely reflect current industry needs, experiences
and understanding. In particular, the definitions are not precise
and the classifications do not encompass all practical instability
scenarios.
This report developed by a Task Force, set up jointly by the
CIGRE Study Committee 38 and the IEEE Power System Dynamic
Performance Committee, addresses the issue of stability definition
and classification in power systems from a fundamental viewpoint
and closely examines the practical ramifications. The report aims
to define power system stability more precisely, provide a systematic
basis for its classification, and discuss linkages to related issues
such as power system reliability and security.
Index Terms—Frequency stability, Lyapunov stability, oscillatory
stability, power system stability, small-signal stability, terms
and definitions, transient stability, voltage stability.
INTRODUCTION
POWERsystem stability has been recognized as an important
problem for secure system operation since the 1920s [1], [2].
Many major blackouts caused by power system instability have
illustrated the importance of this phenomenon [3]. Historically,
transient instability has been the dominant stability problem on
most systems, and has been the focus of much of the industry’s
attention concerning system stability. As power systems have
evolved through continuing growth in interconnections, use of
new technologies and controls, and the increased operation in
highly stressed conditions, different forms of system instability
have emerged. For example, voltage stability, frequency stability
and interarea oscillations have become greater concerns than
in the past. This has created a need to review the definition and
classification of power system stability. A clear understanding
of different types of instability and how they are interrelated
is essential for the satisfactory design and operation of power
systems. As well, consistent use of terminology is required
for developing system design and operating criteria, standard
analytical tools, and study procedures.
Discussion and Elaboration
The definition applies to an interconnected power system as a
whole. Often, however, the stability of a particular generator or
group of generators is also of interest. A remote generator may
lose stability (synchronism) without cascading instability of the
main system. Similarly, stability of particular loads or load areas
may be of interest; motors may lose stability (run down and stall)
without cascading instability of the main system.
The power system is a highly nonlinear system that operates
in a constantly changing environment; loads, generator outputs
and key operating parameters change continually. When
subjected to a disturbance, the stability of the system depends
on the initial operating condition as well as the nature of the
disturbance.
Stability of an electric power system is thus a property of the
system motion around an equilibrium set, i.e., the initial operating
condition. In an equilibrium set, the various opposing
forces that exist in the system are equal instantaneously (as in
the case of equilibrium points) or over a cycle (as in the case of
slow cyclical variations due to continuous small fluctuations in
loads or aperiodic attractors).
Power systems are subjected to a wide range of disturbances,
small and large. Small disturbances in the form of load changes
occur continually; the system must be able to adjust to the
changing conditions and operate satisfactorily. It must also
be able to survive numerous disturbances of a severe nature,
such as a short circuit on a transmission line or loss of a large
generator. A large disturbance may lead to structural changes
due to the isolation of the faulted elements.
Need for Classification
Power system stability is essentially a single problem;
however, the various forms of instabilities that a power system
may undergo cannot be properly understood and effectively
dealt with by treating it as such. Because of high dimensionality
and complexity of stability problems, it helps to make
simplifying assumptions to analyze specific types of problems
using an appropriate degree of detail of system representation
and appropriate analytical techniques. Analysis of stability,
including identifying key factors that contribute to instability
and devising methods of improving stable operation, is greatly
facilitated by classification of stability into appropriate categories
[8]. Classification, therefore, is essential for meaningful
practical analysis and resolution of power system stability
problems. As discussed in Section V-C-I, such classification is
entirely justified theoretically by the concept of partial stability
[9]–[11].
Analysis of Power System Security
The analysis of security relates to the determination of the robustness
of the power system relative to imminent disturbances.
There are two important components of security analysis. For a
power system subjected to changes (small or large), it is important
that when the changes are completed, the system settles to
new operating conditions such that no physical constraints are
violated. This implies that, in addition to the next operating conditions
being acceptable, the system must survive the transition
to these conditions.
Stability of Linear Systems:
The direct ways to establish stability in terms of the preceding
definitions are constructive; the long experience with Lyapunov
stability offers guidelines for generating candidate Lyapunov
functions for various classes of systems, but no general systematic
procedures. For the case of power systems, Lyapunov
functions are known to exist for simplified models with special
features [56], [57], but again not for many realistic models.
Similarly, there are no general constructive methods to establish
input-to-output stability using (9) for nonlinear systems.
One approach of utmost importance in power engineering
practice is then to try to relate stability of a nonlinear system
to the properties of a linearized model at a certain operating
point. While such results are necessarily local, they are still of
great practical interest, especially if the operating point is judiciously
selected. This is the method of choice for analytical
(as contrasted with simulation-based) software packages used
in the power industry today. The precise technical conditions required
from the linearization procedure are given, for example,
in [62, p. 209-211]. The essence of the approach is that if the linearized
system is uniformly asymptotically stable (in the nonautonomous
case, where it is equivalent to exponential stability),
or if all eigenvalues have negative real parts (in the autonomous
case), then the original nonlinear system is also locally stable
in the suitable sense. The autonomous system case when some
eigenvalues have zero real parts, and others have negative real
parts, is covered by the center manifold theory; see [54] for an
introduction.
SUMMARY
This report has addressed the issue of stability definition and
classification in power systems from a fundamental viewpoint
and has examined the practical ramifications of stability
phenomena in significant detail. A precise definition of power
system stability that is inclusive of all forms is provided.
A salient feature of the report is a systematic classification
of power system stability, and the identification of different
categories of stability behavior. Linkages between power
system reliability, security, and stability are also established
and discussed. The report also includes a rigorous treatment
of definitions and concepts of stability from mathematics
and control theory. This material is provided as background
information and to establish theoretical connections.