Environmental Engineering Reference
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establishes FOC. By controlling the induction machine to the slip value corre-
sponding to rotor flux orientation that is orthogonal to stator torque current, i qs , the
condition of the dc brush motor is achieved. Torque response is as accurate and
rapid as the controller can change this component of stator current.
Under FOC the induction machine becomes completely decoupled in that q -axis
and d -axis interactions are eliminated. Voltage commands in the d -axis establish
rotor flux, and voltage commands in the q -axis establish torque. The simplified
functional diagram for an induction machine under FOC is given in Figure 7.5.
+
+
w
L m / L r
Σ
sL s
u ds
+
+
Σ
Σ
L r /( pL r + r r )
1/( psL s + r s )
L m r r / L r
l dr
+
-
i ds
3 P
2 2
L m / L r
X
T em
w e sL s
i qs
u qs
-
L m / L r
1/( psL s + r s )
Σ
+
Figure 7.5 Induction machine model under FOC
Under the FOC condition the induction machine electromagnetic torque can be
expressed in terms of stator current and rotor flux in an analogous manner to (7.2)
as follows:
3
2
P
2
L m
L r
Im ð i qds l qdr Þ
m em ¼
ð 7 : 6 Þ
where the conjugate of rotor flux linkage is taken as (l qr þ j l dr ) in the above
expression. Then, setting the q -axis rotor flux to zero, the electromagnetic torque
becomes
3
2
P
2
L m
L r l dr i qs
m em ¼
ð 7 : 7 Þ
When the excitation for the d -axis is held fixed in Figure 7.5, the rotor flux is
fixed, as explained in the case of substituting permanent magnets for field windings
in the brushed dc machine. Then, by current feeding the induction machine at the
i qs point, it is observed that the same expression for torque in terms of stator cur-
rents and rotor flux as given by (7.7) is realized. The induction machine under FOC
thereby exhibits the same control response as a shunt wound dc machine. In early
battery electric vehicle (BEV) work, the shunt field dc machine was indeed
the preferred traction motor candidate and many BEVs were designed using it.
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