Basic Concepts
Power system
stability is the ability of the system, for a given initial operating
condition, to regain a normal state of equilibrium after being subjected
to a disturbance.
Stability is a condition of equilibrium between
opposing forces; instability results when a disturbance leads to a
sustained imbalance between the opposing forces.
The power system is a highly nonlinear system that operates in a constantly changing environment; loads, generator outputs, topology, and key operating parameters change continually.
When
subjected to a transient disturbance, the stability of the system
depends on the nature of the disturbance as well as the initial
operating condition. The disturbance may be small or large. Small
disturbances in the form of load changes occur continually, and the
system adjusts to the changing conditions. The system must be able to
operate satisfactorily under these conditions and successfully meet the
load demand. 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.
Following a transient disturbance,
if the power system is stable, it will reach a new equilibrium state
with practically the entire system intact; the actions of automatic
controls and possibly human operators will eventually restore the 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.
The
response of the power system to a disturbance may involve much of the
equipment. For instance, a fault on a critical element followed by its
isolation by protective relays will cause variations in power flows,
network bus voltages, and machine rotor speeds; the voltage variations
will actuate both generator and transmission network voltage regulators;
the generator speed variations will actuate prime mover governors; and
the voltage and frequency variations will affect the system loads to
varying degrees depending on their individual characteristics.
Further,
devices used to protect individual equipment may respond to variations
in system variables and thereby affect the power system performance. A
typical modern power system is thus a very high-order multi-variable
process whose dynamic performance is influenced by a wide array of
devices with different response rates and characteristics. Hence,
instability in a power system may occur in many different ways depending
on the system topology, operating mode, and the form of the
disturbance.
Traditionally, the stability problem has been one of
maintaining synchronous operation. Since power systems rely on
synchronous machines for generation of electrical power, a necessary
condition for satisfactory system operation is that all synchronous
machines remain in synchronism or, colloquially, “in step.”
This
aspect of stability is influenced by the dynamics of generator rotor
angles and power-angle relationships. Instability may also be
encountered without the loss of synchronism. For example, a system
consisting of a generator feeding an induction motor can become unstable
due to collapse of load voltage. In this instance, it is the stability
and control of voltage that is the issue, rather than the maintenance of
synchronism. This type of instability can also occur in the case of
loads covering an extensive area in a
large system.
large system.
In the
event of a significant load/generation mismatch, generator and prime
mover controls become important, as well as system controls and special
protections. If not properly coordinated, it is possible for the system
frequency to become unstable, and generating units and/or loads may
ultimately be tripped possibly leading to a system blackout. This is
another case where units may remain in synchronism (until tripped by
such protections as under-frequency), but the system becomes unstable.
Because
of the high dimensionality and complexity of stability problems, it is
essential to make simplifying assumptions and to analyze specific types
of problems using the right degree of detail of system representation.
The following subsection describes the classification of power system
stability into different categories.
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