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 .
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