Page 130 - Handbook of Electrical Engineering

112 HANDBOOK OF ELECTRICAL ENGINEERING

The core loss current per phase I c is:-

V m 225.06 − j11.604
I c = = = 1.9574 − j0.1009 amps
R c 115.0
Therefore the total shunt current I o at the air gap is:-

I o = I m + I c = 2.6400 − j13.342 amps

The input kVA S in is:-

∗
3 × I 1 × V p 3
S in = = (34.2982 + j19.0987)(239.6 + j0.0)
1000 1000
= 24.653 + j13.728 kVA, which has a magnitude of 28.218 kVA.

Hence the input active power P in in kW and input reactive power Q in in kVAr are:-

P in = 24.653 kW and Q in = 13.728 kVAr

The input power factor PF in of the stator current is:-

P in 24.653
PF in = = = 0.8737 pu lagging
S in 28.218
The efficiency η of the motor at full-load is:-

P out 22.004
η = = = 0.8925 pu
P in 24.653

The full-load torque T e is:-

2 2
3sR 2 V m 3 × 0.02208 × (0.1474 × 225.395)
T e = = = 22524.2nm
2 2 2 2 2
R 2 + s X 2 0.1474 + (0.02208 × 0.8122)
b) Solution for starting.
The same sequence of calculations can be followed for the starting condition as was used for the
full-load condition, but with the slip set to unity. The results of each step are summarised below:-

R 2 = R 21 = 0.253 ohms and X 2 = X 21 = 0.333 ohms

The rotor ‘output power’ resistance R out is zero.

The total rotor impedance Z 22 is:-

Z 22 = R 2 + jX 2 + 0.0 = 0.253 + j0.333 ohms