Predictive Control of Three Phase AC/DC Converters

58 CHAPTER 4. PREDICTIVE DIRECT POWER CONTROL
4.7 Virtual Flux Based Constant Switching Frequency Predictive
Direct Power Control
This part of dissertation will be focused on implementation of Virtual Flux approach
into Constant Switching Frequency Predictive Direct Power Control (VF-
CSF-P-DPC) [48], [52].
4.7.1 Virtual Flux Based Predictive Model of the Instantaneous Power
Behavior
Principles of Virtual Flux concept have been presented in Section 3.5. For sinusoidal
and balanced voltage, neglecting grid side choke resistance R = 0, the instantaneous
power can be computed as (3.20), (3.21):
P = 3 2 ω L (Ψ Lα I Lβ − Ψ Lβ I Lα ) (4.48)
Q = 3 2 ω L (Ψ Lα I Lα + Ψ Lβ I Lβ ) (4.49)
The VF-CSF-P-DPC is based on instantaneous power time derivatives behavior
prediction. Variations of active and reactive power can be calculated from
following equations:
dP
dt = 3ω (
L dI Lβ
Ψ Lα
2 dt
dQ
dt = 3ω L
2
(
Ψ Lα
dI Lα
dt
+ dΨ Lα
d
I dI Lα
Lβ − Ψ Lβ
dt
+ dΨ Lα
d
I dI Lβ
Lα + Ψ Lβ
dt
− dΨ )
Lβ
d
I Lα
)
+ dΨ Lβ
d
I Lβ
(4.50)
(4.51)
where dI Lαβ
dt
is defined by (4.3).
If we consider sinusoidal and balanced line voltage, following expressions can
be taken into account:
Ψ Lα = U Lβ
ω L
(4.52)
Ψ Lβ = − U Lα
ω L
(4.53)
dΨ Lα
= −ω L Ψ Lβ (4.54)
dt
dΨ Lβ
= ω L Ψ Lα (4.55)
dt
Replacing (4.3), (4.52) – (4.55) into (4.50), (4.51) power derivatives can be
expressed as:
(
)
dP
dt
= 3 2 ω 1
L Ψ Lα L (U Lβ − U P β − RI Lβ ) − ω L Ψ Lβ I Lβ
(
)
− 3 2 ω 1
L Ψ Lβ L (U (4.56)
Lα − U P α − RI Lα ) + ω L Ψ Lα I Lα