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

Modeling and control modes of PM synchronous motor drives
In general, for a drive system,
J = J + J
(2.61)
m
where: J
m
- motor inertia, J
l
load moments of inertia.
l
From equation (2.55) and (2.56) one can write:
and, with (2.50),
dΩ m 1 = ( M
e − M
l )
(2.62)
dt J
dΩ m 1 3
∗
= ( pb
Im( Ψ
s
Is
) − Ml
)
(2.63)
dt J 2
Finally, the full mathematical model of PM synchronous machine which is used in
simulation studies [Appendices] is described in dq , reference frame as:
dΨ
sd
Usd = Rs Isd + − pbΩmΨ sq
(2.64a)
dt
dΨ
sq
Usq = Rs Isq + + pbΩmΨ sd
(2.64b)
dt
Ψ
sd
= LsdIsd +Ψ
PM
(2.65a)
Ψ
sq
= LsqIsq
(2.65b)
dΩ m 1 = ( M
e − M
l )
(2.66)
dt J
3 ∗ 3
M
e
= pbIm( Ψ
s
Is) = pb( ΨsdIsq −Ψ
sqIsd)
(2.67)
2 2
Based on above equations we can create the block scheme of the PMSM machine (Fig.
2.9), where the input signals are the voltage components in dq , reference frame
U , U and the output signal is the mechanical speed of the rotor Ω
m
. As the external
sd
sq
load torque
M
l
is disturbance.
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