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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<strong>Direct</strong> <strong>Torque</strong> <strong>Control</strong> <strong>with</strong> <strong>Space</strong> <strong>Vector</strong> <strong>Modulation</strong><br />
5.3.2 Digital torque control loop<br />
The PMSM equations (2.27a,b-2.28a,b) in stator flux coordinates under the assumption<br />
L<br />
d<br />
= L can be written as:<br />
q<br />
U = R I +ΩΨ<br />
Ψ (5.59)<br />
sy s sy s s<br />
0 LI sin<br />
= −Ψ (5.60)<br />
s sy PM<br />
δ Ψ<br />
3<br />
M<br />
e<br />
= pb Ψ I<br />
s sy<br />
(5.61)<br />
2<br />
dΩ m 1 = ( M<br />
e − M<br />
l )<br />
(5.62)<br />
dt J<br />
The load angle can be expressed (Fig. 5.1):<br />
δ = θ − p γ , (5.63)<br />
Ψ<br />
Ψs b m<br />
Where: δ Ψ<br />
is torque angle, θ Ψ s<br />
is stator flux vector position, and γ<br />
m<br />
is rotor position in stator<br />
α,<br />
β coordinates,<br />
p<br />
b<br />
is number <strong>of</strong> pole pars.<br />
After differentiation equation (5.63) can be written as:<br />
dδ<br />
dθ<br />
dγ<br />
dt dt dt<br />
Ψ Ψs<br />
m<br />
= − pb<br />
(5.64)<br />
δ Ψ<br />
d<br />
dt<br />
δ Ψ<br />
d<br />
=ΩΨ<br />
−p<br />
s bΩm<br />
⇒Ω Ψ s<br />
= + pbΩ m<br />
(5.65)<br />
dt<br />
Putting equations (5.64) and (5.65) into voltage equation (5.59) one obtains:<br />
dδ Usy = RsIsy +Ω ( )<br />
s s<br />
RsI Ψ<br />
Ψ<br />
Ψ =<br />
sy<br />
+ Ψ<br />
s<br />
+ pbΩ m<br />
(5.66)<br />
dt<br />
From equation 0= LI −Ψ sin <strong>with</strong> assumption that for small angle δ = sinδ<br />
, the<br />
s sy PM<br />
torque angle can be expressed as:<br />
δ Ψ<br />
Ψ<br />
Ψ<br />
L I<br />
s sy<br />
δ Ψ<br />
= (5.67)<br />
Ψ<br />
PM<br />
So, the voltage equation (5.59) becomes:<br />
L dI<br />
s sy<br />
Usy = Rs Isy +ΩΨ<br />
Ψ ( )<br />
s s<br />
= Rs Isy + Ψ<br />
s<br />
+ pbΩm<br />
Ψ dt<br />
PM<br />
(5.68)<br />
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