Handbook of Electrical Engineering

SYNCHRONOUS GENERATORS AND MOTORS 69

To distinguish between the sending-end and the receiving-end the subscripts ‘s’and‘r’are
introduced for theδangles betweenEandEq,andV andVqrespectively. Hence their compo-
nents are:-

Vd=Vsinδr

Vq=Vcosδr

Ed=Esinδs

Eq=Ecosδs

Id=−Isin(Ø+δr)

Iq=Icos(Ø+δr)

Equations (3.9) and (3.10) can be transposed to findIdandIq,

Id=

(Eq−Vq)Xq+(Ed−Vd)Rq

XdXq+RdRq

And

Iq=

(Eq−Vq)Rd−(Ed−Vd)Xd

XdXq+RdRq

Active and reactive power leaving the terminals of the ‘receiving-end’ and received by the
load are,

Pr=

Pr 1 +Pr 2

DEN

Qr=

Qr 1 +Qr 2

DEN

Where,

Pr 1 =Vsinδr(EqXq+EdRq)+

V^2

2

sin 2δr(Xd−Xq)

Pr 2 =Vcosδr(EqRd−EdXd)−V^2 (Rqsinδr+Rdcos^2 δr)

Qr 1 =Vcosδr(EqXq+EdRq)+

V^2

2

sin 2δr(Rd−Rq)

Qr 2 =Vsinδr(EdXd−EqRd)−V^2 (Xdsin^2 δr+Xqcos^2 δr)

DEN=XdXq+RdRq

Also the active and reactive power leaving the shaft and the exciter are,

Ps=Real part of(EI∗)

=I

(

Eqcos(δr+Ø)+Edsin(δr+Ø)

)

Where I∗denotes the conjugate of the phasor I.