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

Modeling and control modes of PM synchronous motor drives
Solving for the torque angle δ
I
:
2 2
PM PM
4 Is
( Ld Lq)
Lq
Ψ − Ψ − −
−1
δ
I
= cos [ ]
2( L − L ) I
d q s
(2.76)
only positive sign should be take into consideration.
After obtaining δ I
the amplitude of stator voltage vector can be calculated from
equation (2.70) and amplitude of stator flux vector from (2.71). The active and reactive
power and also the power factor can be obtained from equations (2.41),(2.46), (2.47).
Constant stator flux (CSF) control
As it can be see from the torque expression (2.58) for a given stator flux amplitude
the electromagnetic torque
amplitude
M
e
is a function of torque angle δ Ψ
. The stator flux linkage
Ψ
s
is kept constant of the permanent magnet flux amplitude Ψ
PM
.
I s
q − axis
Ψs
Ψ
s
δ I
δ Ψ
d − axis
Figure 2.14. Flux vector and permanent magnet flux vector under constant stator flux operation
(CSFC).
The amplitude of the stator flux linkage vector is
Ψ PM
2 2 2 2
Ψ
s
= Ψ
sd
+Ψ
sq
= ( LI
q sq
) + ( LI
d sd
+Ψ
PM
)
(2.77)
Equating
Ψ =Ψ (2.78)
s
PM
can be obtain the relationship for rotor frame currents as:
2 2
q sq d sd d PM sd
( LI ) + ( LI ) + 2LΨ I = 0
(2.79)
This condition is true if I
sd
< 0 , because expression
always positive values.
2 2
q sq
LI
d sd
( LI ) + ( ) and L , Ψ are
d
PM
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