Environmental Engineering Reference
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Block diagram of the voltage H repetitive control scheme
Figure 5.2
w
contains both the grid voltage u g and the voltage reference u ref , which are assumed to be
periodic with a fundamental frequency of 50 Hz.
5.2.1 State-space Model of the Control Plant P
The single-phase diagram of the system is shown in Figure 5.3. It consists of the inverter
bridge, an LC filter ( L f and C f ) and a grid interface inductor L g . The LC filter and the
grid interface inductor form an LCL filter. The series winding resistance of the inductors is
considered but the parallel resistance considered in Chapter 4 is not taken into account. The
circuit breaker S C is provided to facilitate the synchronisation and shut-down procedure and is
considered to be closed (i.e. the synchronisation process is omitted). 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 fundamental component of u f is
equal to u . As a result, the PWM block and the inverter bridge can be ignored when designing
the controller.
The currents of the two inductors and the voltage of the capacitor are chosen as state
variables x
[ u g u ref ] T consists of the grid voltage
u g and the reference voltage u ref , and the control input is u . The output signal from the plant
u c ] T . The external input
=
[ i 1
i 2
w =
Figure 5.3
Single phase representation of the plant P
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