Electrical Power Systems

om ig. 4.6,
Synchronous Machine: Steady State and Transient Operations 87
ig. 4.6: Phasor diagram of a salient pole
synchronous generator.
|E| = |V| cos d + xdId The three-phase real power at the generator terminal is
rom ig. 4.6,
rom eqn. (4.26) and (4.27), we get
Again from ig. 4.6,
...(4.25)
P = 3|V| |I a| cos q ...(4.26)
|I a|cos q = I q cos d + I d sin d ...(4.27)
|V| sin d = x qI q
\ I q =
rom eqn. (4.25), we get
P = 3|V| (I q cos d + I d sin d ) ...(4.28)
| |sin V
x
q
d
||| E - V|cos
d
Id =
x
rom eqn. (4.28), (4.29) and (4.30) we get,
P3f = 3 + 3
xd
d
| E|| V|
2 ( xd - xq)
sin d | V|
sin 2d
2 x x
d q
...(4.29)
...(4.30)
...(4.31)
In eqn. (4.31), second term is known as the reluctance power. Note that equations (4.25) and
(4.31) can be utilized for steady state analysis. Under transient conditions, xd takes on different
values depending upon the transient time following the short circuit.
Example 4.3: A 25 MVA, 13.8 kV, 50 Hz synchronous generator has a synchronous reactance of
1.2 pu and a resistance of 0.02 pu calculate (a) the base voltage, base power and base impedance
of the generator. (b) The actual value of the synchronous reactance (c) The actual winding
resistance per phase (d) the total full load copper loss.
Solution.
(a) The base voltage is
E B =
13. 8
= 7.967 kV.
3