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

Modeling and control modes of PM synchronous motor drives
2 2 2 2 2 2
d q s
δI d PM s
δI q s
( L − L ) I cos + 2L Ψ I cos + L I = 0 (2.80)
Solving for the torque angle δ
I
2 2 2 2 2 2
d PM d PM s
(
d q
)
q
−L Ψ ± L Ψ − I L −L L
−1
δ
I
= cos [ ]
( L L ) I
2 2
d
−
q s
(2.81)
For givenδ I
, the amplitude of stator voltage vector we 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),
respectively for defined speed.
Comparison study
In order to compare the control strategies and to cancel dependence of machine power,
per unit values defined as shown in Table 2.1 below have been introduced [3,9].
The value of current vector:
I
sN
= Is
Is
I
= 2I
(2.82)
b
srms( rated )
The value of voltage vector: U
s
U
s
U
sN
= = (2.83)
Ub ΩΨ
b PM
where: Ω b
= 2 π f and b
fb
is rated frequency
of the PM motor.
The value of flux vector is: Ψ
s
Ψ
s
Ψ
sN
= =
(2.84)
Ψb
ΨPM
The value of torque is:
Me
Me
M
eN
= =
(2.85)
M 3
b pbΨ
PMIb
2
The value of apparent power vector
S S
S = N
S
= 3
(2.86)
b UI
b b
2
The value of active power
P
PN
= (2.87)
Sb
The value of reactive power
Q
QN
= (2.88)
S
b
Table 2.1. Per unit values definition.
In order to compare the steady state performance characteristic of the above discussed
control strategies, for each of the control strategy some important quantities of the
machine have been plotted as a function of the torque. The PMSM parameters, which
are used for the calculations are given in Appendices.
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