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

Direct Torque Control with Space Vector Modulation
5.2.2 Digital torque control loop
The considered torque control loop is shown in Fig. 5.15.
Ψ s _ ref
M e _ ref
−
Torque
controller
PI
∆δ Ψ
Reference
flux generator
In stator frame
Ψ
s α _ ref
Ψ
s β _ ref
−
∆Ψ sα
−
∆Ψ sβ
Flux
controllers
In stator frame
U
s α _ ref
U
s β _ ref
M e
θ Ψs
Ψ sα
Ψ sβ
Figure 5.15. Torque control loop with PI controller.
Based on the equation (5.9a-b and 5.10a-b) the stator flux errors in α,
β coordinates can
be calculated as:
∆Ψ
α
= Ψ cos( θ + ∆δ ) − Ψ cos θ = Ψ [cos( θ + ∆δ ) − cos θ ]
s s_ ref Ψs Ψ s_ ref Ψs s_
ref Ψs Ψ Ψs
(5.21a)
∆Ψ
β
= Ψ sin( θ +∆δ ) − Ψ sin θ = Ψ [sin( θ +∆δ ) − sin θ ]
s s_ ref Ψs Ψ s_ ref Ψs s_
ref Ψs Ψ Ψs
(5.21b)
Assuming that for small changes of ∆δ Ψ
the cos ∆δ Ψ
≅ 1and sin ∆δ Ψ
≅∆ δ
Ψ
, the equations
(5.21a) and (5.21b) are given by:
∆Ψ
α _
= − Ψ
_
∆ δ sinθ
(5.22a)
s ref s ref Ψ Ψs
∆Ψ
β _
= Ψ
_
∆ δ cosθ
(5.22b)
s ref s ref Ψ Ψs
In order to design the PI torque controller the following assumption are made:
• stator flux vector position θ Ψ s
and rotor flux vector position θ
r
are equal zero. It
correspond to situation, when those two flux vectors lie along theα axis,
• the reference stator flux amplitude is equal value of permanent magnet flux
Ψ
s _ ref
=Ψ
PM
,
• stator resistance is neglected.
Therefore, the error stator fluxes in α,
β coordinates are calculated as:
∆Ψ = , (5.23a)
sα
_ ref
0
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