Wind power technology - Wind Power Integration: Connection and System Operational Aspects - page 67

P air gap

R s X s X r ′

a

I r ′

I s

R r s

X m

V s

a ′

Figure 3.12 Single-phase equivalent circuit of an induction machine (Kundur,

1994)

P air gap

R s X s X r ′

a

I r ′

R r s

X m

V s

a ′

Figure 3.13 Equivalent circuit suitable for evaluating simple torque-slip

relationships

It is convenient to place the magnetising reactance across the supply voltage
V s , as shown in Figure 3.13. This simplifies analysis with minimal loss of accuracy.
The power transferred across the air gap to the rotor (of one phase) is

R r

2

s ð I r Þ

P air gap ¼ ð 3 : 10 Þ

The torque developed by the machine (three phase) is obtained from (3.8) and
P air gap ¼ 2 p n s T /60:

R r

T ¼ 3 p f
2

2

s w s ð I r Þ

ð 3 : 11 Þ

where w s ¼ 2 p f s . As seen in (3.11), the torque is slip dependent. For simple analysis
of torque-slip relationships, the equivalent circuit of Figure 3.13 may be used.
From Figure 3.13, the rotor current is

V s
ð R s þ R r = s Þþ j ð X s þ X r Þ

I 0 r ¼ ð 3 : 12 Þ