Electrical Power Systems

\ i asy max =
from which
Synchronous Machine: Steady State and Transient Operations 93
HG
I
Eo
Xd¢¢
KJ +
HG
max E
iasy = o
3
Xd
¢¢
HG
Eo
2 ...(4.40)
X ¢¢
d
I
KJ
2 2
I
KJ
...(4.41)
The momentary duty of a circuit breaker is given in terms of the asymmetrical short-circuit
current.
4.9 EECT O LOAD CURRENT
If the fault occurs when the synchronous generator is delivering a perfault load current, two
methods might be used in the solution of three-phase symmetrical fault currents.
4.9.1 Use of Internal Voltages Behind Reactances
When there is a prefault load current, three internal voltages E², E¢ and E may be considered
to be during subtransient, transient and the steady state periods, respectively and these
voltages are known as the voltage behind subtransient reactance, voltage behind transient
reactance and voltage behind synchronous reactance. Consider the single line diagram of a
loaded generator as given in ig. 4.12.
ig. 4.12: (a) Single line diageram of a loaded generator (b) Phasor diagram.
rom ig. 4.11(b), we can write
E² = V + jX ² d IL E¢ = V + jX ¢ d IL E = V + jX d IL ...(4.42)
4.9.2 Use of Thévenin’s Theorem and Superposition with Load Current
An alternate method of computing short-circuit current is through use of Thévenin’s theorem
and superposition of prefault load current. Here it is illustrated through an example.
Consider a synchronous generator feeding a synchronous motor load, over a transmission
line. igure 4.13 (a) shows the circuit model under steady load conditions. ault computations