Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

Modeling and control modes of PM synchronous motor drives
From Fig. 2.8, it can be seen that
M is maximum when torque angle is 90 < < 180
e
The relevant torque equation in this mode of operation becomes from (2.55).
δ
I
.
The steady state voltage equations can be written using the current vector amplitude
I
s
and the torque angle δ
I
as:
U = R I cosδ
+ p Ω L I sinδ
(2.73a)
sd s s I b m q s I
U = R I sinδ
− p Ω L I cosδ
+ p Ω Ψ (2.73b)
sq s s I b m d s I b m PM
The amplitude of stator voltage vector can be calculated from equation (2.70) and
amplitude of stator flux vector from (2.71). The active and reactive power and also the
power factor can be obtained from equations (2.41),(2.46), (2.47).
Unity power factor (UPF) control
Under this control strategy there is no phase different between the current vector and the
voltage vector. Hence, power factor angle φ (see Fig. 2.13) becomes zero. Since only
active power is supplied to the machine under unity power factor operation, the VA
rating requirement of the inverter can be reduced.
q − axis
U s
φ = 0
I s
δ I
d − axis
Figure 2.13. Current vector and permanent magnet flux vector under unity power factor
operation (UPFC).
Ψ PM
In this case when φ = 0 we have the relationship:
U
U
sq
sd
Isq
= = tanδ
I
(2.74)
I
sq
Substituting the voltage equations (2.69a-b) into (2.71) and made some simplifying, we
can obtain:
I L −L −Ψ + L I = (2.75)
2
s
(
d q)cos δI PM
cosδI q s
0
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