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

Modeling and control modes of PM synchronous motor drives
q−
axis
I sq
I s
Ω s
δ I
d
− axis
I sd
Ψ PM
Figure 2.5. Stator current vector in rotor reference frame.
For two current components using trigonometrical rules we can write:
I = I cosδ
(2.54a)
sd
s
I
I = I sinδ
(2.54b)
sq
s
I
Substituting I , I into equation (2.52), the torque expression can be obtain as:
sd
sq
M 3 1
2
e = b[ PM sin I ( q d) sin2 I]
2 p Ψ I s δ −
2
L − L I s δ
(2.55)
M
es
For given current amplitude the synchronous and reluctances torque varies according to
the sine of torque angle δ
I
. The variation of
M
er
M
es
and M
er
and resultant torque M
e
with
torque angle are illustrated in Fig. 2.6. The IPMSM parameters used for this calculation
are given in the Appendices.
e [ ] M Nm
M [ ] er
Nm M
es
[ Nm ]
[deg] δ I
Figure 2.6. Variation of synchronous torque M es
, reluctance torque M
er
and resultant
torque M as a function of torque angle (for rated current amplitude).
e
20