Direct Power and Torque Control of AC/DC/AC Converter-Fed ...

2. Voltage Source Converters – VSC
dI
L
L
dt
dI
L
L
dt
α
β
dU
C
dt
dc
+ RI = U −U
S ,
(2.70)
Lα
Lα
dc
α
+ RI = U −U
S ,
(2.71)
Lβ
β
= ∑ I
S
Lβ
− I
dc
β
3
=
Lk k load
k = α 2
( I S + I S ) − I .
Lα
α
Where, appropriate switching states are expressed as:
S
=
f
⎛
= S
⎝
1
−
3
⎞
Lβ
β
load
( S + S + S ) , S = ( S − S )
(2.72)
α A ⎜ A A B C ⎟ β
B C
(2.73)
⎠
Equations (2.70) - (2.72) can be represented as a block diagram in stationary αβ
coordinates as in Fig. 2. 16.
1
3
U pα
S α
I load
U Lα
+
−
1
sL + R
I Lα
+
+
3
2
+
−
1 U
dc
sC
U Lβ
+
−
1
sL + R
I Lβ
U pβ
S β
Fig. 2. 16. Model of a three-phase VSR in stationary αβ coordinates
2.5.4. VSR Model in Synchronously Rotating xy Coordinates
The two-phase model in stationary αβ coordinates (Eqs. (2.70) - (2.72)), can be
transformed into a two-phase model in synchronously rotating xy coordinates using
the appropriate transformation (see Subsection A.2.3.). Therefore, xy model using
the complex space vector notation can be expressed as:
dI
L
dt
Lxy
+ RI
= U −U
S1 + jω
LI
(2.74)
Lxy
Lxy
dc
xy
L
Lxy
30