Environmental Engineering Reference
In-Depth Information
converter loss, the active power of the AC side is equal to the active power of the
DC side, i.e.,
P
ac
¼
P
dc
ð
3
:
13
Þ
The active power of AC and DC sides can be calculated by:
P
ac
¼
e
d
i
d
þ
e
q
i
q
ð
3
:
14
Þ
P
dc
¼
u
dc
i
dc
¼
u
dc
ð
C u
dc
þ
i
L
Þ
ð
3
:
15
Þ
Based on Eqs. (
3.13
)-(
3.15
), it can be obtained:
u
dc
ð
C u
dc
þ
i
L
Þ¼
e
d
i
d
þ
e
q
i
q
ð
3
:
16
Þ
Define a new variable u
¼
u
dc
. Equation (
3.16
) can be simplified as:
p
u
u
¼
2
C
ð
e
d
i
d
þ
e
q
i
q
Þ
2
i
L
ð
3
:
17
Þ
C
Now from Eqs. (
3.12
) and (
3.17
), new dynamic model of the converter in d-
q synchronous rotating reference frame can be expressed as:
8
<
:
Li
d
¼
Ri
d
þ
xLi
q
þ
e
d
u
d
Li
q
¼
Ri
q
xLi
d
þ
e
q
u
q
u
¼
C
ð
e
d
i
d
þ
e
q
i
q
Þ
C
ð
3
:
18
Þ
p
i
L
where u
d
= s
d
u
dc
, u
q
= s
q
u
dc
.
As the d-axis of the synchronously rotating d-q frame is aligned with the grid
voltage vector, d- and q-axis components of grid voltage can be obtained as
follows:
e
d
¼
E
s
e
q
¼
0
ð
3
:
19
Þ
where E
s
is equal to the grid voltage vector. So Eq. (
3.18
) can be further simplified
as:
8
<
:
Li
d
¼
Ri
d
þ
xLi
q
þ
E
s
u
d
Li
q
¼
Ri
q
xLi
d
u
q
u
¼
C
E
s
i
d
C
ð
3
:
20
Þ
p
i
L
It can be seen from Eq. (
3.20
) that the DC-link voltage, u
dc
¼
u
p
, can be
controlled using the q-axis current, i
d
.