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

Modeling and control modes of PM synchronous motor drives
2π
2π
4π
j 1 3
where:1,
3 2
− j j 1 3
a= e =− + j , a = e
3
= e
3
=− − j - complex vectors, 2/3 –
2 2
2 2
normalization factor (guarantee that for balanced sinusoidal waveforms the magnitude
of the space vector is equal to the amplitude of that phase waveforms).
The elements of this space vector satisfy the condition:
KA + KB + KC
= 0
(2.2)
and it means that we have three-phase system without neutral wire.
2.1.1 Voltage and current equations
For idealized motor (Fig. 2.1), the following equations of the instantaneous stator phase
voltages can be written [3]:
B
b
Z sB
I sB
a
U sB
S
N
N
S
U sA
γ m
Z sA
A
I sA
I sC
Z sC
U sC
N
S
C
c
Figure 2.1. Layout and symbols for three-phase PMSM electric motor windings.
dΨ
dt
sA
sA
=
sA sA
+ (2.3a)
U I R
U I R
dΨ
dt
sB
sB
=
sB sB
+ (2.3b)
U I R
dΨ
dt
sC
sC
=
sC sC
+ (2.3c)
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