Environmental Engineering Reference
In-Depth Information
6.3 Design of the Voltage Controller
The design of the voltage controller is outlined below, following the detailed procedures
presented in (Hornik and Zhong 2010b) and Chapters 4 and 5. A prominent feature different
from what is known is that the control plant of the voltage controller is no longer the whole
LCL filter but just the LC filter, as shown in Figure 6.2.
The block diagram of the voltage
H
∞
repetitive control scheme is shown in Figure 6.5,
where
P
u
is the transfer function of the plant (i.e. the LC filter here),
C
u
is the transfer function
of the stabilising compensator and
M
u
is the transfer function of the internal model.
6.3.1 State-space Model of the Plant P
u
The corresponding control plant shown in Figure 6.2 for the voltage controller consists of the
inverter bridge and the LC filter (
L
f
and
C
f
). The filter inductor is modelled with a series
winding resistance. The PWM block together with the inverter are modelled by using an
average voltage approach with the limits of the available DC-link voltage (Weiss
et al.
2004)
so that the average value of
u
f
over a sampling period is equal to
u
u
. As a result, the PWM
block and the inverter bridge can be ignored when designing the controller.
The filter inductor current
i
1
and the capacitor voltage
u
c
are chosen as state variables
w
u
=
i
2
u
ref
T
consists of the grid current
i
2
and the
reference voltage
u
ref
. The control input is
u
u
. The output signal from the plant
P
u
is the
tracking error
e
u
=
x
u
=
i
1
u
c
T
. The external input
u
ref
−
u
o
, where
u
o
=
u
c
+
R
d
(
i
1
−
i
2
) is the inverter local load voltage.
The plant
P
u
can be described by the state equation
x
u
=
A
u
x
u
+
B
u
1
w
u
+
B
u
2
u
u
(6.1)
and the output equation
y
u
=
e
u
=
C
u
1
x
u
+
D
u
1
w
u
+
D
u
2
u
u
(6.2)
P
u
W
(
s
)
e
−
s
d
u
i
2
+
w
u
e
u
+
plant
u
ref
internal model
M
u
u
u
stabilising
compensator
C
u
Block diagram of the
H
∞
repetitive voltage control scheme
Figure 6.5
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