Handbook of Electrical Engineering

SYNCHRONOUS GENERATORS AND MOTORS 71

Where,

Pr 1 =Vsinδ(EqXq)+

V^2

2

sin 2δ(Xd−Xq)

Pr 2 =Vcosδ(EqRa)−V^2 Ra

Qr 1 =Vcosδ(EqXq)

Qr 2 =Vsinδ(−EqRa)−V^2 (Xdsin^2 δ+Xqcos^2 δ)

DEN=XdXq+Ra^2

The sending-end variables become,

PS=IEqcos(δ+φ)

QS=IEqsin(δ+φ)

3.5.3 A simpler case of a salient pole generator

Most practical generators have an armature resistanceRathat is much less in value than the syn-
chronous reactancesXdandXq. Consequently the equations in sub-section 3.5.2 can be further
simplified without incurring a noticeable error. They become,

Vd=Vsinδ

Vq=Vcosδ

Eq=E

Id=−Isin(φ+δ)

Iq=Icos(φ+δ)

Id=

Eq−Vq

Xd

Iq=

Vd

Xq

Pr=

Pr 1 +Pr 2

DEN

Qr=

Qr 1 +Qr 2

DEN

Where,

Pr 1 =Vsinδ(EqXq)+

V^2

2

sin^2 δ(Xd−Xq)

Pr 2 = 0

Qr 1 =Vcosδ(EqXq)