Environmental Engineering Reference
In-Depth Information
Block diagram of a voltage-controlled VSI with a voltage
H
∞
repetitive controller in the
Figure 5.1
natural frame
is equivalent to increasing the inductor resistance. Hence, it does not affect the design of the
voltage controller and will be omitted when designing the voltage controller.
A PLL is adopted to provide the phase information of the grid voltage so that the power
controller can generate the voltage reference
u
ref
while regulating the active power
P
and the
reactive power
Q
according to the grid current references
I
d
and
I
q
. The inverter is assumed
to be powered by a constant DC power source and, hence, no controller is needed to regulate
the DC-link voltage. Otherwise, a controller can be introduced to regulate the DC-link voltage
and to generate
I
d
. The main objective in this chapter is to design the voltage controller so the
power controllers for
P
and
Q
are simply chosen as PI controllers. More details about power
flow control can be found in Part III.
5.2 Controller Design
In this section, a voltage controller based on the
H
∞
and repetitive control techniques is
designed. Its main objective is to maintain a clean and balanced local load voltage in the
presence of non-linear loads and/or grid distortion. The block diagram of the
H
∞
repetitive
control scheme is shown in Figure 5.2, where
P
is the transfer function of the plant,
C
is the
transfer function of the stabilising compensator and
M
is the transfer function of the internal
model. The stabilising compensator
C
and internal model
M
are the two components of the
controller. The stabilising compensator
C
, designed by solving a weighted sensitivity
H
∞
problem (Weiss
et al.
1998), assures the exponential stability of the entire system, which
implies that the tracking error
e
e
u
between the voltage reference and the inverter output
voltage converges to a small steady-state error (Weiss and Hafele 1999). The external signal
=
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