As
electric power systems have evolved over the last century, different
forms of instability have emerged as being important during different
periods. The methods of analysis and resolution of stability problems
were influenced by the prevailing developments in computational tools,
stability theory, and power system control technology. A review of the
history of the subject is useful for a better understanding of the
electric power industry’s practices with regard to system stability.
Power
system stability was first recognized as an important problem in the
1920s (Steinmetz, 1920; Evans and Bergvall, 1924; Wilkins, 1926). The
early stability problems were associated with remote power plants
feeding load centers over long transmission lines.
With
slow exciters and non-continuously acting voltage regulators, power
transfer capability was often limited by steady-state as well as
transient rotor angle instability due to insufficient synchronizing
torque.
To analyze system stability, graphical
techniques such as the equal area criterion and power circle diagrams
were developed. These methods were successfully applied to early systems
which could be effectively represented as two machine systems.
As
the complexity of power systems increased, and interconnections were
found to be economically attractive, the complexity of the stability
problems also increased and systems could no longer be treated as two
machine systems. This led to the development in the 1930s of the network
analyzer, which was capable of power flow analysis of multi-machine
systems. System dynamics, however, still had to be analyzed by solving
the swing equations by hand using step-by-step numerical integration.
Generators were represented by the classical ‘‘fixed voltage behind
transient reactance’’ model. Loads were represented as constant impedance.
Improvements in system stability
came about by way of faster fault clearing and fast acting excitation
systems. Steady-state aperiodic instability was virtually eliminated by
the implementation of continuously acting voltage regulators. With
increased dependence on controls, the emphasis of stability studies
moved from transmission network problems to generator problems, and
simulations with more detailed representations of synchronous machines
and excitation systems were required.
The 1950s saw the
development of the analog computer, with which simulations could be
carried out to study in detail the dynamic characteristics of a
generator and its controls rather than the overall behavior of
multi-machine systems.
Later in the 1950s, the digital computer
emerged as the ideal means to study the stability problems associated
with large interconnected systems. In the 1960s, most of the power
systems in the U.S. and Canada were part of one of two large
interconnected systems, one in the east and the other in the west. In
1967, low capacity HVDC ties were also established between the east and
west systems. At present, the power systems in North America form
virtually one large system. There were similar trends in growth of
interconnections in other countries.
While interconnections result
in operating economy and increased reliability through mutual
assistance, they contribute to increased complexity of stability
problems and increased consequences of instability. The Northeast
Blackout of November 9, 1965, made this abundantly clear; it focused the
attention of the public and of regulatory agencies, as well as of
engineers, on the problem of stability and importance of power system
reliability.
Until recently, most industry
effort and interest has been concentrated on transient (rotor angle)
stability. Powerful transient stability simulation programs have been
developed that are capable of modeling large complex systems using
detailed device models. Significant improvements in transient stability
performance of power systems have been achieved through use of
high-speed fault clearing, high-response exciters, series capacitors,
and special stability controls and protection schemes.
The increased use of high response exciters, coupled with decreasing strengths of transmission systems, has led to an increased focus on small signal (rotor angle) stability.
This
type of angle instability is often seen as local plant modes of
oscillation, or in the case of groups of machines interconnected by weak
links, as inter area modes of oscillation. Small signal stability
problems have led to the development of special study techniques, such
as modal analysis using eigenvalue techniques (Martins, 1986; Kundur et
al., 1990). In addition, supplementary control of generator excitation
systems, static Var compensators, and HVDC converters is increasingly
being used to solve system oscillation problems.
There has also
been a general interest in the application of power electronic based
controllers referred to as FACTS (Flexible AC Transmission Systems)
controllers for damping of power system oscillations (IEEE, 1996).
In
the 1970s and 1980s, frequency stability problems experienced following
major system upsets led to an investigation of the underlying causes of
such problems and to the development of long term dynamic simulation
programs to assist in their analysis (Davidson et al., 1975; Converti et
al., 1976; Stubbe et al., 1989; Inoue et al., 1995; Ontario Hydro,
1989). The focus of many of these investigations was on the performance
of thermal power plants during system upsets (Kundur et al., 1985; Chow
et al., 1989; Kundur, 1981; Younkins and Johnson, 1981). Guidelines were
developed by an IEEE Working Group for enhancing power plant response
during major frequency disturbances (1983).
Analysis and modeling
needs of power systems during major frequency disturbances was also
addressed in a recent CIGRE Task Force report (1999). Since the late
1970s, voltage instability has been the cause of several power system
collapses worldwide (Kundur, 1994; Taylor, 1994; IEEE, 1990). Once
associated primarily with weak radial distribution systems, voltage
stability problems are now a source of concern in highly developed and
mature networks as a result of heavier loadings and power transfers over
long distances. Consequently, voltage stability is increasingly being
addressed in system planning and operating studies.
Powerful
analytical tools are available for its analysis (Van Cutsem et al.,
1995; Gao et al., 1992; Morison et al., 1993), and well-established
criteria and study procedures are evolving (Abed, 1999; Gao et al.,
1996).
Present-day power systems are being operated under
increasingly stressed conditions due to the prevailing trend to make the
most of existing facilities. Increased competition, open transmission
access, and construction and environmental constraints are shaping the
operation of electric power systems in new ways that present greater
challenges for secure system operation. This is abundantly clear from
the increasing number of major power-grid blackouts that have been
experienced in recent years; for example, Brazil blackout of March 11,
1999; Northeast USA-Canada blackout of August 14, 2003; Southern Sweden
and Eastern Denmark blackout of September 23, 2003; and Italian blackout
of September 28, 2003. Planning and operation of today’s power systems
require a careful consideration of all forms of system instability.
Significant
advances have been made in recent years in providing the study
engineers with a number of powerful tools and techniques.
A
coordinated set of complementary programs, such as the one described by
Kundur et al. (1994) makes it convenient to carry out a comprehensive
analysis of power system stability.
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