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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Sensorless Speed <strong>Direct</strong> <strong>Torque</strong> <strong>Control</strong> <strong>with</strong> <strong>Space</strong> <strong>Vector</strong> <strong>Modulation</strong> (<strong>DTC</strong>-<strong>SVM</strong>)<br />
The stator current trajectory can be divided in to eight sectors (see Fig. 6.5a).<br />
7π<br />
8<br />
o<br />
157 .5<br />
Sector 4<br />
− +<br />
5π<br />
8<br />
o<br />
112 .5<br />
Sector 3<br />
− −<br />
3π<br />
8<br />
+ −<br />
o<br />
67 .5<br />
Sector 2<br />
I s<br />
o<br />
22.5<br />
π<br />
8<br />
+ +<br />
Sector 5<br />
o<br />
202 .5<br />
9π<br />
8<br />
Sector 6<br />
+ −<br />
o<br />
247 .5<br />
11π<br />
8<br />
− −<br />
Sector 7<br />
− +<br />
o<br />
292 .5<br />
13π<br />
8<br />
+ +<br />
Sector 8<br />
Sector 1<br />
15π<br />
8 π<br />
−<br />
8<br />
o<br />
337 .5<br />
Figure 6.5. Stator current trajectory.<br />
Based on the measured response <strong>of</strong> phase currents in α,<br />
β coordinates, the<br />
( ) sign I s<br />
+ and sign( I s<br />
)<br />
− is calculated from following formulas:<br />
sign( I )<br />
+ = I + I − I<br />
(6.1)<br />
s sα<br />
sβ<br />
s<br />
sign( I )<br />
− = I −I − I<br />
(6.2)<br />
s sα<br />
sβ<br />
s<br />
The possible combinations <strong>of</strong> sign( I s<br />
)<br />
+ and sign( I s<br />
)<br />
− are shown in Fig. 6.6:<br />
Figure 6.6. Possible combination <strong>of</strong> sign( I s<br />
)<br />
+<br />
sign( I s<br />
) + + − −<br />
−<br />
sign( I s<br />
) + − − +<br />
+ and sign( I s<br />
)<br />
− under short pulse supply.<br />
Let us assuming, for example, the case where the sign( I s<br />
)<br />
+ and sign( I s<br />
)<br />
− have positive<br />
π π<br />
sign. The position γ m<br />
exist in the domain <strong>of</strong> − ~ or 7 π 9 π<br />
~ and two estimated<br />
8 8 8 8<br />
position can be obtained.<br />
The mathematical analysis <strong>of</strong> I , I<br />
sα<br />
sβ waveforms leads to following equations:<br />
I = I +∆ I cos 2γ<br />
(6.3)<br />
sα<br />
s s m<br />
125