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

2. Voltage Source Converters – VSC
U LA
+
−
1
sL + R
I LA
+
I load
−
1
sC
U dc
U pA
S A
f A
+
−
U LB
S B
+
−
U pB
1
sL + R
f B
I LB
+
+
+
+
+
+
+
1
3
−
U LC
+
−
U pC
1
sL + R
I LC
S C
f C
+
−
Fig. 2. 15. Block diagram of the VSR in three-phase ABC coordinates
Where:
f
A
⎛ 1
⎞ ⎛ 1
⎞ ⎛ 1
= ⎜ S
A
−
A B C ⎟ B ⎜ B A B C ⎟ C ⎜ C A B C
⎝ 3
⎠ ⎝ 3
⎠ ⎝ 3
⎞
( S + S + S ) , f = S − ( S + S + S ) , f = S − ( S + S + S )⎟
⎠
(2.67)
2.5.3. VSR Model in Stationary αβ Coordinates
In some studies is useful to present the VSR model in two axis coordinates
system. Equations (2.60) - (2.62) and Eq. (2.64) after transformation into stationary
αβ coordinates (Appendix A.2) can be described using the complex space vector
notation as:
dI
L
dt
L
dU
C
dt
+ RI
= U −U
(2. 68)
dc
L
L
dcS 1
*
[
LS
] − Iload
3
= Re I
1
(2. 69)
2
Further, those equations can be decomposed in α and β components:
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