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

Direct Torque Control with Space Vector Modulation
5.3.2 Digital torque control loop
The PMSM equations (2.27a,b-2.28a,b) in stator flux coordinates under the assumption
L
d
= L can be written as:
q
U = R I +ΩΨ
Ψ (5.59)
sy s sy s s
0 LI sin
= −Ψ (5.60)
s sy PM
δ Ψ
3
M
e
= pb Ψ I
s sy
(5.61)
2
dΩ m 1 = ( M
e − M
l )
(5.62)
dt J
The load angle can be expressed (Fig. 5.1):
δ = θ − p γ , (5.63)
Ψ
Ψs b m
Where: δ Ψ
is torque angle, θ Ψ s
is stator flux vector position, and γ
m
is rotor position in stator
α,
β coordinates,
p
b
is number of pole pars.
After differentiation equation (5.63) can be written as:
dδ
dθ
dγ
dt dt dt
Ψ Ψs
m
= − pb
(5.64)
δ Ψ
d
dt
δ Ψ
d
=ΩΨ
−p
s bΩm
⇒Ω Ψ s
= + pbΩ m
(5.65)
dt
Putting equations (5.64) and (5.65) into voltage equation (5.59) one obtains:
dδ Usy = RsIsy +Ω ( )
s s
RsI Ψ
Ψ
Ψ =
sy
+ Ψ
s
+ pbΩ m
(5.66)
dt
From equation 0= LI −Ψ sin with assumption that for small angle δ = sinδ
, the
s sy PM
torque angle can be expressed as:
δ Ψ
Ψ
Ψ
L I
s sy
δ Ψ
= (5.67)
Ψ
PM
So, the voltage equation (5.59) becomes:
L dI
s sy
Usy = Rs Isy +ΩΨ
Ψ ( )
s s
= Rs Isy + Ψ
s
+ pbΩm
Ψ dt
PM
(5.68)
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