Page 91 - Handbook of Electrical Engineering

SYNCHRONOUS GENERATORS AND MOTORS 71

Where,

V 2
P r1 = V sin δ(E q X q ) + sin 2δ(X d − X q )
2
2
P r2 = V cos δ(E q R a ) − V R a
Q r1 = V cos δ(E q X q )
2
2
2
Q r2 = V sin δ(−E q R a ) − V (X d sin δ + X q cos δ)
2
DEN = X d X q + R a
The sending-end variables become,

P S = IE q cos(δ + φ)
Q S = IE q sin(δ + φ)

3.5.3 A Simpler Case of a Salient Pole Generator

Most practical generators have an armature resistance R a that is much less in value than the syn-
chronous reactances X d and X q . Consequently the equations in sub-section 3.5.2 can be further
simplified without incurring a noticeable error. They become,

V d = V sin δ
V q = V cos δ
E q = E

I d =−I sin(φ + δ)
I q = I cos(φ + δ)

E q − V q
I d =
X d
V d
I q =
X q
P r1 + P r2
P r =
DEN
Q r1 + Q r2
Q r =
DEN
Where,

V 2 2
P r1 = V sin δ(E q X q ) + sin δ(X d − X q )
2
P r2 = 0

Q r1 = V cos δ(E q X q )