Handbook of Electrical Engineering

INDUCTION MOTORS 117

Table 5.7. Per-unit resistances and starting-to-full-load current ratio for HV four-pole motors

Rated power

(kW)

Slip (pu) R 1 R 20 R 21 Rc Is/In

630 0.00828 0.00809 0.00688 0.0285 39.01 5.84

800 0.00932 0.00804 0.00764 0.0288 45.16 5.45

1,100 0.01050 0.00780 0.00844 0.0287 52.88 5.00

1,500 0.01120 0.00742 0.00889 0.0280 59.20 4.66

2,500 0.01120 0.00650 0.00878 0.0256 65.29 4.35

5,000 0.00895 0.00495 0.00713 0.0207 62.59 4.40

6,300 0.00785 0.00441 0.00633 0.0189 59.01 4.53

8,000 0.00667 0.00386 0.00545 0.0169 54.24 4.71

11,000 0.00515 0.00308 0.00450 0.0143 53.06 5.02

Table 5.8. Per-unit reactances and starting-to-full-load torque ratio for HV four-pole

motors

Rated power

(kW)

Slip (pu) X 1 X 20 X 21 XM Ts/Tn

630 0.00828 0.109 0.120 0.0594 3.213 0.934

800 0.00932 0.126 0.112 0.0546 3.403 0.828

1,100 0.01050 0.147 0.104 0.0501 3.635 0.697

1,500 0.01120 0.165 0.0996 0.0474 3.834 0.593

2,500 0.01120 0.182 0.0976 0.0460 4.085 0.473

5,000 0.00895 0.177 0.106 0.0498 4.242 0.391

6,300 0.00785 0.173 0.111 0.0528 4.243 0.377

8,000 0.00667 0.155 0.119 0.0570 4.217 0.365

11,000 0.00515 0.135 0.134 0.0647 4.145 0.350

At standstill the slip is 1, therefore the equivalent impedance is,

Z 231 =R 231 +jX 231 =

(R 22 +jX 22 )(R 33 +jX 33 )

R 22 +jX 22 +R 33 +jX 33

( 5. 7 )

At full-load the slip is s, therefore the equivalent impedance is,

Z 230 =R 230 /s+jX 230 =

(R 22 /s+jX 22 )(R 33 /s+jX 33 )

R 22 /s+jX 22 +R 33 /s+jX 33

( 5. 8 )

Taking the real and imaginary parts of each equation separately yields the four equations
required for the solution. The given values areR 230 ,X 230 ,R 231 ,X 231 and the full-load slips.The
solution is the set of valuesR 22 ,X 22 ,R 33 ,andX 33.

The iterative solution can be carried out by one of various algorithms, for example New-
ton’s approximation to find roots, steepest descent to find a minimum quadratic error, rough search,
successive substitution. Newton’s method in four dimensions works reasonably well, although insta-
bility can set in if the incremental changes are allowed to be too large. Hence some ‘deceleration’ is
required to stabilise the algorithm. The method of successive substitution is more efficient, but also