Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...
Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...
Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...
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Modeling and control modes <strong>of</strong> PM synchronous motor drives<br />
From Fig. 2.8, it can be seen that<br />
M is maximum when torque angle is 90 < < 180<br />
e<br />
The relevant torque equation in this mode <strong>of</strong> operation becomes from (2.55).<br />
<br />
δ <br />
I<br />
.<br />
The steady state voltage equations can be written using the current vector amplitude<br />
I<br />
s<br />
and the torque angle δ<br />
I<br />
as:<br />
U = R I cosδ<br />
+ p Ω L I sinδ<br />
(2.73a)<br />
sd s s I b m q s I<br />
U = R I sinδ<br />
− p Ω L I cosδ<br />
+ p Ω Ψ (2.73b)<br />
sq s s I b m d s I b m PM<br />
The amplitude <strong>of</strong> stator voltage vector can be calculated from equation (2.70) and<br />
amplitude <strong>of</strong> stator flux vector from (2.71). The active and reactive power and also the<br />
power factor can be obtained from equations (2.41),(2.46), (2.47).<br />
Unity power factor (UPF) control<br />
Under this control strategy there is no phase different between the current vector and the<br />
voltage vector. Hence, power factor angle φ (see Fig. 2.13) becomes zero. Since only<br />
active power is supplied to the machine under unity power factor operation, the VA<br />
rating requirement <strong>of</strong> the inverter can be reduced.<br />
q − axis<br />
U s<br />
φ = 0<br />
I s<br />
δ I<br />
d − axis<br />
Figure 2.13. Current vector and permanent magnet flux vector under unity power factor<br />
operation (UPFC).<br />
Ψ PM<br />
In this case when φ = 0 we have the relationship:<br />
U<br />
U<br />
sq<br />
sd<br />
Isq<br />
= = tanδ<br />
I<br />
(2.74)<br />
I<br />
sq<br />
Substituting the voltage equations (2.69a-b) into (2.71) and made some simplifying, we<br />
can obtain:<br />
I L −L −Ψ + L I = (2.75)<br />
2<br />
s<br />
(<br />
d q)cos δI PM<br />
cosδI q s<br />
0<br />
27