Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

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