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3 Mathematic Model of Five-Phase PMSM
With the transformation matrix (6), the voltage space vector in the
α
1-
β
1 sub-
space and
α
3-
β
3 subspace is defined.
V
α
1
β
1
=
v
α
1
+
jv
β
1
=
2
5
(
V
AN
+
e
jα
V
BN
+
e
j
2
α
V
CN
+
e
j
3
α
V
DN
+
e
j
4
α
V
EN
) (16)
V
α
3
β
3
=
v
α
3
+
jv
β
3
=
2
5
(
V
AN
+
e
3
jα
V
BN
+
e
jα
V
CN
+
e
j
4
α
V
DN
+
e
j
2
α
V
EN
) (17)
There are total 32(2
5
) voltage space vectors with different combination of five-
phase VSI. These vectors are divided into four groups according to vector am-
plitude.
The vector mapping is different in
α
1-
β
1 subspace and
α
3-
β
3 subspace. The
vector distribution in
α
1-
β
1 subspace is shown in Fig.3. The vector distribution
in
α
3-
β
3 subspace is shown in Fig.4.
Fig. 3.
Voltage vectors in
α
1-
β
1 subspace
Fig. 4.
Voltage vectors in
α
3-
β
3 subspace
In the SVPWM algorithm of three-phase VSI, the voltage vector is imple-
mented by the near two vectors, according to the volt-second balance principle.
In the five-phase VSI, the voltage vector can be implemented by the near two
largest vectors and two zero vectors.
In a modulation section, the period is defined as
T
s
. The two largest vectors
are
V
k
and
V
k
+1
. The equations are established.
T
s
V
ref
=
T
k
V
k
+
T
k
+1
V
k
+1
T
s
=
T
k
+
T
k
+1
+
T
0
(18)
Where
T
k
is the action time of
V
k
in one modulation period.
T
k
+1
is the action
time of
V
k
+1
in one modulation period. The
T
k
and
T
k
+1
are calculated from
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