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

Modeling and control modes of PM synchronous motor drives
Figure 2.2 shows axes of reference for the three-stator phase ABC. , , It also shows a
rotating set of x,
y axes, where the angleθ K
is position of x -axis in respect to the stator
A phase axis. Variables along the AB , and C axes can be referred to the x − and
y − axes by the expression:
⎡K
A ⎤
⎡K
x ⎤ 2 ⎡ cosθK cos( θK − 2 π / 3) cos( θK
+ 2 π / 3) ⎤⎢
K
⎥
⎢ B
K
⎥ =
y 3
⎢
sinθK sin( θK 2 π / 3) sin( θK
2 π / 3)
⎥⎢ ⎥
⎣ ⎦ ⎣− − − − + ⎦
⎢⎣K
⎥
C ⎦
(2.16)
y
K B
K ABC
K y
K x
Ω K
x
θ K
K A
K C
Figure 2.2. Stator fixed three phase axes (A,B,C) and general rotating reference frame ( x,
y ).
Finally, the space vector in general rotating frame can be written as:
j K
K = K (cosΘ + jsin Θ ) = K e θ
(2.17)
ABCs K K
K K
In this case the voltage equation (2.4) using (2.17) can written as:
jθK jθ d
K jθK
U
sKe Rs IsKe (
sKe
)
dt
= + Ψ (2.18)
Using chain rule, equation. (2.17) and divided by term
j K
e θ
can be written as:
d Ψ
U
sK
R I j
dt
= + + Ω Ψ (2.19)
sK
s sK K sK
where
U
sK
rotating frame.
, I sK , Ψ sK is the stator voltage, current and flux space vector in general
Making similar arrangement like for the voltage equation the flux linkage vector in
general reference frame can be expressed as:
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