Page 509 - Handbook of Electrical Engineering

GENERALISED THEORY OF ELECTRICAL MACHINES 499

Figure 20.3 Equivalent circuit of an induction motor using mutual coupling.

these variables and the magnitude of the phase-to-neutral stator supply variables is simply:-
1
V 1 = V d1 + jV q1 = √ (v d1 − jv q1 )
2
1

2 2 2 2
|V 1 |= V d1 + V q1 = √ v d1 + v q1
2

√
2 2
∴ |V 1 |= V d1 + V d1 = 2V d1
An equivalent Tee circuit can be formed by assuming the inductive shunt impedance carries
the sum of the stator and rotor currents.
ω
In (20.33) delete the suffix ‘d’, subtract j X m I 1 from the first term on the right-hand side
ω n
and add it to the second term:-
ω
V d = [R 1 + jω(X L1 − X m )]I 1 + j X m (I 2 + I 1 )
ω n
ω
In (20.35) subtract j X m I 2 from the second term on the right-hand side and add it to the first term:-
ω n
ω
R 2 ω
0 = j X m (I 1 + I 2 ) + + j (X L2 − X m ) I 2
ω n s ω n