Environmental Engineering Reference
In-Depth Information
the phase shift and gain attenuation caused by the computational delay, PWM modulation, the
inverter bridge and the LC filter. It also attenuates the harmonics in the feed-forwarded grid
voltages and improves the dynamics during grid voltage fluctuations (Timbus
et al
. 2009).
16.2.2 Equivalent Controller in the abc Frame
As mentioned before, the PR controllers can easily be implemented in the
abc
frame. Actually,
it is straightforward to do so. Instead of using the
abc
transformation, each phase can
be equipped with a PR controller, with the current reference generated from
I
d
and
I
q
with
the
dq
→
αβ
abc
transformation. According to (Timbus
et al
. 2009), the controller matrix in the
abc
frame isgiven as
→
⎡
⎤
s
K
p
+
K
i
0
0
s
2
+
ω
2
⎣
s
⎦
.
C
PR
abc
(
s
)
=
0
K
p
+
K
i
0
(16.3)
s
2
+
ω
2
s
0
0
K
p
+
K
i
s
2
+
ω
2
Because of this, the PR controller can be designed for each phase and then applied to the
stationary reference frame.
16.3 Controller Design
16.3.1 Model of the Plant
The model of the control plant can be derived from the single-phase diagram of the inverter
shown inFigure 16.2, which mainly consists of the LCL filter of the inverter. The inverter is
operated so that the average of
u
f
over a switching period is the same as
u
and, hence, the
effect of the PWM conversion and the switching isnegligible.
According to Kirchhoff's current law (KCL), there is
i
c
=
i
1
−
i
2
.
(16.4)
V
DC
-
+
S
c
u
f
u
o
Inverter
bridge
PWM
u
g
u
L
f
i
1
i
c
L
g
i
2
R
f
R
g
C
f
filter inductor
grid interface inductor
u
c
grid
R
d
neutral
Figure 16.2
Single-phase representation of an inverter
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