Handbook of Electrical Engineering

494 HANDBOOK OF ELECTRICAL ENGINEERING

Equations (20.12) to (20.16) become:-









vd

vq

0

0







=









Ra+LapωLdq Mp ωM

−ωLdq Ra+Lap −ωM Mp

Mp 0 Rk+Lkp 0

0 Mp 0 Rk+Lkp

















id

iq

ikd

ikq







 (^20.^23 )

whereωis the rotor speed,

Ldq=M+Lla

and Lk=M+Lkd=M+Lkq

The operational impedances become:-

Xd(p)=Xq(p)=

( 1 +Td′′p)

1 +Tdo′′p

Xd

where Tq′′=Td′′

and Tqo′′=Tdo′′

AndG(p)does not exist.

Tdo′′=Tqo′′=

1

ωRk

(Xk+Xm)

Td′′=Tq′′=

1

ωRk

[

Xk+

XmXa

Xm+Xa

]

Tk=

Xk

ωRk

Tdo′ andTd′do not exist.

The flux linkage equations can be rewritten using the symmetrical parameters and the rotor
speed asωr:-

vd=Raid+pψd−ωrψq

vq=Raiq+pψq+ωrψd

0 =Rkikd+pψkd

0 =Rkikq+pψkq

Application of a three-phase short circuit to the terminals of an unloaded induction motor is
not a practical factory test, especially for a large high-voltage motor, because the motor can only be
excited at its stator windings from the power supply. A three-phase short circuit at or near the stator
terminals can occur in practice e.g. damaged supply cable, damage in the cable terminal box. The
parameters of the stator and rotor windings can be obtained from other factory tests. However, the
derived reactance can be defined in the same manner as those for the synchronous machine, but with