Environmental Engineering Reference

In-Depth Information

in each phase at standstill is
V
r
. Since the induced voltage is proportional to the rate

of change of flux (2.10), the rotor voltage at a particular slip
s
will be

rotor voltage
¼
s
V
r

The torque developed by the induction machine will depend on the current

flowing in each rotor phase (2.7). The rotor phase current for a given slip will be

determined by the rotor phase voltage
s
V
r
applied across the rotor impedance. This

consists of resistance
R
r
and inductive reactance
L
r
. The reactance depends on the

rotor current frequency. If the standstill rotor reactance is
X
r
¼w
s
L
r
, then its value

at slip
s
will be
sX
r
. The rotor current is therefore given by

s
V
r

R
r
þ
j
sX
r

I
r
¼

Note that the slip-dependent rotor voltage may be replaced by the standstill rotor

voltage as follows:

V
r

R
r
=
s
þ
j
X
r

I
r
¼

The standstill rotor voltage can be referred to the stator circuit, given the effective

rotor/stator turns ratio
N
:

V
r

N

The rotor current referred to the stator is

V
0
r
¼

I
0
r
¼
N
I
r

It is instructive to develop an equivalent circuit representing each phase of the

induction machine. This is analogous to the equivalent circuit for a transformer

shown in Figure 2.3, with machine rotor in place of transformer secondary and

machine stator in place of transformer primary. It is convenient to refer all quan-

tities to the stator. The current in a rotor phase will be 1/
N
times the current in a

stator phase, to achieve the m.m.f. balance required for transformer action (see

Section 2.2.5). Rotor impedance referred to the stator must therefore be scaled by

1/
N
2
to give the same relative voltage drop and power loss in the stator. Thus

R
r

N
2

R
r
¼

X
r

N
2

X
r
¼

The rotor circuit referred to the stator is shown to the right of aa
0
in Figure 3.12.

The stator resistance
R
s
and stator leakage reactance
X
s
are also shown in

Figure 3.12. The equivalent circuit is completed by the magnetising reactance
X
m
.

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