Page 30 - Power Electronic Control in Electrical Systems

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20 Electrical power systems ± an overview

Studies involving over-voltages due to lightning and switching operations require a
detailed representation of the transmission system and the electrical properties of the
generators, with particular attention paid to the capacitive effects of transmission
lines, cables, generators and transformers. Over very short time scales the mechanical
parameters of the generators and most controls can be ignored because they have
no time to react to these very fast events, which take place in the time scale
10 7 s t 10 2 s.
On the other hand, the long term dynamics associated with load frequency control
and load shedding involve the dynamic response of the boiler and turbine-governor
set and do not require a detailed representation of the transmission system because at
3
the time scales 10 1 s t 10 s, the electrical transient has already died out. How-
ever, a thorough representation of the turbine governor and boiler controls is
essential if meaningful conclusions are to be obtained. The mechanical behaviour
of the generators has to be represented in some detail because mechanical transients
take much longer to die out than electrical transients.

1.4.1 Transient stability

Sub-synchronous resonance and transient stability studies are used to assess power
systems' dynamic phenomena that lie somewhere in the middle, between electromag-
netic transients due to switching operations and long-term dynamics associated with
load frequency control. In power systems transient stability, the boiler controls and
the electrical transients of the transmission network are neglected but a detailed
representation is needed for the AVR and the mechanical and electrical circuits of
the generator. The controls of the turbine governor are represented in some detail. In
sub-synchronous resonance studies, a detailed representation of the train shaft
system is mandatory (Bremner, 1996).
Arguably, transient stability studies are the most popular dynamic studies. Their
main objective is to determine the synchronous generator's ability to remain stable
after the occurrence of a fault or following a major change in the network such as the
loss of an important generator or a large load (Stagg and El-Abiad, 1968).
Faults need to be cleared as soon as practicable. Transient stability studies provide
valuable information about the critical clearance times before one or more synchron-
ous generators in the network become unstable. The internal angles of the generator
give reasonably good information about critical clearance times.
Figure 1.17 shows a five-node power system, containing two generators, seven
transmission lines and four load points.
A three-phase to ground fault occurs at the terminals of Generator two, located
at node two, and the transient stability study shows that both generators are
stable with a fault lasting 0.1 s, whilst Generator two is unstable with a fault lasting
0.2 s. Figure 1.18 shows the internal voltage angles of the two generators and their
ratio of actual to rated speed. Figures 1.18(a) and (b) show the results of the fault
lasting 0.1 s and (c) and (d) the results of the fault lasting 0.2 s (Stagg and El-Abiad,
1968).
Transient stability studies are time-based studies and involve solving the differen-
tial equations of the generators and their controls, together with the algebraic
equations representing the transmission power network. The differential equations