Current H Repetitive Control - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 81

P

− s

W ( s ) e

d

u g

+

w

e

+

plant

i ref

internal model

u

M

stabilising
compensator

p

C

Block diagram of the H ∞ repetitive current control scheme Figure 3.2

function of the internal model. The internal model M is implemented with the frequency
adaptive mechanism discussed in Chapter 5. The external signal contains the grid voltage

u g and the current reference i ref . Both are assumed to be periodic with a fundamental frequency
of 50 Hz.

w

3.2.1 State-space Model of the Control Plant P
The control plant consists of the inverter bridge, an LC filter ( L f and C f ) and a grid interface
inductor L g ; see the single-phase diagram of the system shown in Figure 3.3. The PWM block
together with the inverter bridge 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 =

u g . The feed-forwarded grid voltage u g actually provides a base
output voltage and the same voltage appears on both sides of the LCL filter. It does not affect
the controller design and can be ignored during the design process. The only contribution
that needs to be considered during the design process is the output u of the repetitive current
controller; see Figures 3.1 and 3.2.
The currents of the two inductors and the voltage of the capacitor are chosen as state
variables x

u +

= i 1 u c T . The external input is w = u g i ref T

i 2 and the control input is

u . The output signal from the plant P is the tracking error e = i ref − i 2 , i.e., the difference

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 3.3 Single-phase representation of the plant P