Control of Inverter Output Impedance - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 152

7.4.4 Special Case III: to Minimise the 5th Harmonic Component
In this case, the optimal C o is

1

C o =

(5 ω ∗ ) 2 L

and the corresponding impedance is

ω ∗ L ω

ω ∗
ω

25

ω =

ω ∗ −

.

Z o ( j ) j

The gain factor ω ∗ −

25 ω ∗

ω

of the imaginary part with respect to the normalised frequency ω ∗ is

ω = ω ∗ . At the fundamental

also shown in Figure 7.5. It changes from negative to positive at 5

ω = ω ∗ , the output impedance is

frequency, i.e., when

ω ∗ L ω ∗ L

Z o =− j 24 ≈− j 24 .

This is capacitive as well.

7.5 Simulation Results for R-, L- and C-inverters
Simulations were carried out on a single-phase inverter powered by a 42 V DC voltage
supply. The inverter was equipped with an outer-loop controller, as shown in Figure 7.6, to
regulate the output voltage. This outer-loop controller is actually the robust droop controller
(Zhong 2012c) for C-inverters to be discussed in detail in Chapter 19. The parameters were
n i = 5 kHz and the frequency

of the system was 50 Hz. The rated voltage was 12 V. The filter capacitance was 22

2 . 2, m i = 0 . 14 and K e = 20. The switching frequency was 7 .

μ F

E *

-

K

RMS e

+

E i 1

P i

n i

s

v o

v ri

+

1 i

m i

s Q i

ω i t+ δ i

*

ω

Figure 7.6 Outer-loop controller to generate the voltage reference v r for C-inverters. See Chapter 19
for more details