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

2. Voltage Source Converters – VSC
I
= I S + I S I S ,
(2.59)
dc LA A LB B
+
LC
C
Hence, AC side of the VSR voltage equations in the three phase system can be
expressed as:
dI
L
dt
LA
dI
L
dt
LB
C
⎛ 1
+ RILA
= U
LA
−Udc⎜
S
A
− ∑ S
⎝ 3 k = A
C
⎛ 1
+ RI
LB
= U
LB
−U
dc⎜
SB
− ∑ S
⎝ 3 k = A
k
⎞
⎟ = U
⎠
k
LA
⎞
⎟ = U
⎠
LB
−U
dc
−U
⎛
⎜ S
⎝
dc
A
⎛
⎜ S
⎝
B
1
⎞
− ( S
A
+ SB
+ SC
)⎟
3
⎠
(2.60)
1
⎞
− ( S
A
+ SB
+ SC
)⎟
3
⎠
(2.61)
dI
L
dt
LC
C
⎛ 1
+ RI
LC
= U
LC
−U
dc⎜
SC
− ∑ S
⎝ 3 k = A
Where the line voltages are expressed by:
U
LA
= U
Lm
sin
k
⎞
⎟ = U
⎠
LC
−U
dc
⎛
⎜ S
⎝
C
1
⎞
− ( S
A
+ SB
+ SC
)⎟
3
⎠
(2.62)
( ω t) , U = U sin( ω t − 2 π / 3) , U = U sin( ω t + 2π
/ 3)
L
LB
Also DC-link side equation of the VSR can be modeled by:
dU
C
dt
dc
C
= ∑ I
Lk
k = A
S
k
− I
load
= I
The above expressions can be written as:
d
( L
dt
Lm
LA
S
A
+ I
L
LB
C
⎛ 1
+ R )I
Lk
= U
Lk
−U
dc⎜
Sk
− ∑ S
⎝ 3 k=
A
k=
A
S
k
B
⎞
⎟
⎠
+ I
LC
S
C
LC
− I
load
Lm
L
(2.63)
(2.64)
(2.65)
C
dU
dc
C = ∑ I
Lk
Sk
− Iload
(2.66)
dt
The equations (2.65) and (2.66) can be represented as a block diagram in Fig. 2. 15
[13], [16].
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