SYNCHRONOUS MACHINE STABILITY BASICS
3-6
If the per unit regulation is to be expressed in the system base, which may be different from the
machine base,
m
s
m
sms
s
P
P
R
P
PPRPR
R
pu
2
o
2
o
pu
===
ωω
(3.27)
The droop characteristic shown in Figure 3.2 is obtained in the speed control system with the
help of feedback. Equation (3.25) describes the steady state regulation characteristics. Transient
characteristics depend on the dynamic response characteristics of the turbine control system
involving various time lags in the feedback elements of the speed control system and in the
steam paths.
Small Disturbance Performance of Unregulated Synchronous Machine System
In this section we investigate the general behavior of an electric power system when subjected to
small disturbances. Such disturbances are always present during normal operation of power
systems. The response of a power system following a disturbance is oscillatory. For stable and
satisfactory operation, oscillations must damp out and the system must return to a steady state in
a reasonably short period of time. Note that if the system survives a large disturbance such as a
system fault followed by opening of one or more transmission lines, the system response, after
the initial impact of the disturbance is over, is essentially determined by the small disturbance
performance of the system.
A good qualitative picture of the basic system dynamic behavior can be obtained by employing
the simplest dynamic model of the power system. In this model the power system is reduced,
retaining only the major synchronous machines in the area under investigation. The number of
synchronous machines retained would depend on the relative impact of these machines on the
particular study. In a simplified analysis intended to reveal the essential dynamic characteristics
of the system, the synchronous machines may be represented by constant voltage magnitude
behind transient reactance (the so-called classical model).
A drawback of the simplified representation is that it excludes machine damping and, therefore,
system simulations using this model fail to reveal the system damping behavior. Damping is
inherently small in electric power systems. The small amount of damping originates mainly in
the synchronous machines due to the electromagnetic interaction, and to some extent in specific
load types. When damping is definitely known to exist, an approximate damping term may be
included in the swing equation. Synchronous machine damping can be significantly affected,
sometimes to the detriment of satisfactory system performance, due to the action of automatic
voltage regulators and governors. Analyses of synchronous machine damping and the effect of
excitation control will be discussed in detail in Chapter 6.
For small disturbance analysis the system equations may be linearized around an operating point
and the stability and dynamic response characteristics of the resulting linear system may be
investigated using the techniques discussed in Chapter 2.
Single machine connected to infinite bus
Consider a synchronous machine connected to an infinite bus through an impedance as depicted
in Figure 3.3. The equation of motion of the synchronous machine is given by