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

Modeling and control modes of PM synchronous motor drives
The steady state voltage components based on the equations (2.34a) and (2.34b) are:
Usd =−pbΩ mLq Iqs =−pbΩ mLq Is
(2.69a)
U = R I + p Ω Ψ = R I + p Ω Ψ (2.69b)
sq s qs b m PM s s b m PM
The amplitude of stator voltage vector can be calculated as:
s
2 2
sd sq
U = U + U
(2.70)
The stator flux vector amplitude can be calculated from equations (2.65a-b) as:
s
2 2
sd sq
Ψ = Ψ +Ψ (2.71)
The active and reactive power and also the power factor can be obtained from equations
(2.41),(2.46), (2.47).
Maximum torque per ampere (MTPA) control
The main idea of this control is develop the torque using minimum value of stator
current amplitude. In this case the I sd
components is not equal zero, and may cancel the
reluctance torque produced by high saliency ratio. Therefore, this control strategy is
recommended for IPMSM.
q−
axis
I s
I sq
δ >= 90
I
d
− axis
I sd
Figure 2.12. Current vector I s and permanent magnet flux vector Ψ
PM
for maximum torque
per ampere operation (MTPAC).
In order to obtain the maximum torque per ampere we should solve the derivative of
torque equations (2.55) in respect to torque angle. Solving for torque angle α and taking
into account that only negative sign should be considered for the solution, we can
calculate torque angle as:
Ψ PM
−1 −1 1 1 2
δ
I
= cos [ − + ( ) ]
4( L −L ) I 2 4( L −L ) I
d q s
d q
s
(2.72)
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