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 />
amplitude <strong>of</strong> the flux linkages established by the permanent magnet on the rotor. The<br />
inductances are described below.<br />
Due to the rotor saliency in IPMSM the air gap is not uniform and, therefore, the self<br />
and mutual inductances <strong>of</strong> stator windings are a function <strong>of</strong> the rotor position.<br />
The derivation <strong>of</strong> these rotor position dependent inductances is available in details in<br />
[5]. The results are summarized here as follows:<br />
The stator winding self-inductances are<br />
L = L + L − L cos 2θ<br />
(2.9a)<br />
sA ls A B r<br />
2π<br />
4π<br />
LsB = Lls + LA −LB cos2( θr − ) = Lls + LA −LB cos(2 θr<br />
− )<br />
3 3<br />
(2.9b)<br />
2π<br />
4π<br />
LsC = Lls + LA − LB cos 2( θr + ) = Lls + LA − LB cos(2 θr<br />
+ )<br />
3 3<br />
(2.9c)<br />
where, Lls<br />
is stator-winding leakage inductance and LA,<br />
LB<br />
are given by<br />
L<br />
A<br />
⎛ms<br />
⎞<br />
= ⎜<br />
2 ⎟<br />
⎝ ⎠<br />
2<br />
πµ rlε<br />
0 1<br />
(2.10a)<br />
L<br />
B<br />
1 ⎛ms<br />
⎞<br />
=<br />
2 ⎜<br />
2 ⎟<br />
⎝ ⎠<br />
2<br />
πµ rlε<br />
0 2<br />
(2.10b)<br />
where,<br />
m<br />
s<br />
is number <strong>of</strong> turns <strong>of</strong> each phase winding, r is radius, which is from center<br />
<strong>of</strong> machine to the inside circumference <strong>of</strong> the stator, and l is the axial length <strong>of</strong> the air<br />
gap <strong>of</strong> the machine, µ<br />
0<br />
is permeability <strong>of</strong> the air, ε<br />
1<br />
and ε<br />
2<br />
are defined as s:<br />
1 1 1<br />
ε<br />
1<br />
= ( + )<br />
(2.11a)<br />
2 g g<br />
min<br />
max<br />
1 1 1<br />
ε<br />
2<br />
= ( − )<br />
(2.11b)<br />
2 g g<br />
min<br />
max<br />
where,<br />
gmin<br />
is minimum air gap length and<br />
max<br />
g<br />
is maximum air gap length.<br />
The mutual inductances between stator phase are:<br />
1 π 1 2π<br />
MsAB = MsBA =− LA −LB cos 2( θr − ) =− LA −LB cos(2 θr<br />
− ) (2.12a)<br />
2 3 2 3<br />
11