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 />
where<br />
U ,<br />
sA, U<br />
sB<br />
U<br />
sC<br />
are the instantaneous stator voltage values, I<br />
sA<br />
I<br />
sB<br />
, I<br />
sC<br />
, are<br />
instantaneous values <strong>of</strong> the current,<br />
R = R = R = R is the resistance <strong>of</strong> the stator<br />
s<br />
sA<br />
sB<br />
sC<br />
windings, and ΨsA,<br />
Ψ<br />
sB<br />
and Ψ<br />
sC<br />
are magnetic flux linkages stator windings A, B and<br />
C , respectively.<br />
Using the space vector theory to voltage equations we can written in vector form<br />
where:<br />
U<br />
d Ψ<br />
dt<br />
sABC<br />
sABC<br />
= Rs<br />
I<br />
sABC<br />
+ (2.4)<br />
2 2<br />
U<br />
sABC<br />
= (1 UsA + aUsB + a UsC<br />
) ,<br />
2 2<br />
2 2<br />
I<br />
sABC<br />
= (1 IsA + aIsB + a IsC<br />
) ,<br />
sABC (1<br />
sA<br />
a<br />
sB<br />
a<br />
sC )<br />
3<br />
3<br />
3<br />
stator voltage, current and flux space vectors, respectively.<br />
Ψ = Ψ + Ψ + Ψ are the<br />
The stator winding flux consist <strong>of</strong> rotor flux and stator flux linkages:<br />
where,<br />
Ψ<br />
sABC<br />
=Ψ<br />
ABC ( s) +Ψ<br />
ABC( r)<br />
(2.5)<br />
⎡ LsA MsAB MsAC⎤⎡IsA⎤<br />
⎢<br />
M L M<br />
⎥⎢<br />
I<br />
⎥<br />
Ψ<br />
ABC( s)<br />
= ⎢ sBA sB sBC ⎥⎢ sB ⎥<br />
⎢⎣ M<br />
sCA<br />
MsCB L ⎥⎢<br />
sC ⎦⎣I<br />
⎥<br />
sC ⎦<br />
(2.6)<br />
⎡<br />
⎤<br />
⎢ cosθ<br />
⎥<br />
r<br />
⎢<br />
⎥<br />
2π<br />
Ψ<br />
ABC ( r)<br />
=Ψ ⎢<br />
PM<br />
cos( θr<br />
− ) ⎥<br />
⎢ 3 ⎥<br />
⎢<br />
2π<br />
⎥<br />
cos( θr<br />
+ )<br />
⎢⎣<br />
3 ⎥⎦<br />
(2.7)<br />
and, θr<br />
is electrical rotor position. Mechanical rotor position is defined as:<br />
θ = p γ<br />
(2.8)<br />
r b m<br />
where: pb<br />
- number <strong>of</strong> pole pairs, γ<br />
m<br />
- mechanical position.<br />
In equation (2.6) LsA<br />
is the self-inductance <strong>of</strong> phase A winding, M<br />
sAB<br />
and M<br />
sAC<br />
are the<br />
mutual inductances between A and B phase, A and C phase, respectively. For self and<br />
mutual inductances <strong>of</strong> B and C phase the same notations used. In (2.7),<br />
Ψ<br />
PM<br />
is the<br />
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