Environmental Engineering Reference
In-Depth Information
calculations if the model based approach is followed as stated above, the expres-
sions for stator voltage V , core voltage E s and stator current I s are
t
m 2p f
3 P
(
)
2
1 ð nP = 60 f Þ
R r
J R r
þ 4p 2 f 2
2
j V
R s þ
ð J L r þ L s Þ
1
ð
nP
=
60 f
Þ
ð 7 : 13 Þ
E s ¼ VZ r J Z r þ Z s Þ
J ¼ 1 þð Z s = Z 0 Þ
ð 7 : 14 Þ
Z s
Z r
I s ¼ E s J þ
ð 7 : 15 Þ
where the equivalent IM circuit values for stator and rotor impedances are defined as
Z 0 ¼ R fe jj jX m
Z s ¼ R s þ jX s
R r
s þ jX r
ð 7 : 16 Þ
Z r ¼
nP
60 f
s ¼ 1
The expressions given in 7.13 through 7.16 all must be solved at each frequency
point, substituted into (7.12) to find the optimum efficiency at that point and its
corresponding voltage set point, then repeated for the next frequency. As more
capable and faster motion control processors become available such as the system on
a chip, then this analytical method would be suitable for real time control.
7.5 Direct torque control
Earlier sections of this chapter have shown how torque and flux control are
decoupled through the use of field orientation principles. In the process of FOC, the
machine controller requires current regulators and coordinate transformations along
with either the appropriate current sensors or through sensorless techniques. Direct
torque control (DTC) achieves much the same response as FOC control but without
the need for inner loop current regulation and coordinate transformations. In DTC a
torque and flux error are used to generate voltage vector selection based on one of
several strategies. Voltage vectors in DTC can be selected based on table-look-up,
direct self-control or inverse-model (e.g. deadbeat control). Inverter switching
frequency becomes a function of motor speed and the selected hysteresis band of
the torque and flux comparators in much the same manner as it would for CRPWM
in a stationary frame regulator.
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