Control of Inverter Output Impedance - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 151

6

4

2

0

−2

Original inductor

−4

3rd only

−6

−8

3rd and 5th

−10

−12

5th only

−14

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

*

ω / ω

Figure 7.5 Gain factors to meet different criteria

17 ω ∗

The gain factor ω ∗ −

225

of the imaginary part with respect to the normalised frequency

ω

ω
ω ∗

ω
ω ∗

= .

is shown in Figure 7.5. It changes from negative to positive at around 3 638. At the

ω = ω ∗ , the output impedance is

fundamental frequency, i.e., when

j 208

17 ω ∗ L

ω ∗ L Z o =− ≈− j 12 . 23 .

It is capacitive as expected.

7.4.3 Special Case II: to Minimise the 3rd Harmonic Component
In this case, the optimal C o is

1

C o =

ω ∗ ) 2 L

(3

and the corresponding impedance is

ω ∗ L ω

ω ∗
ω

9

Z o ( j ω ) = j

ω ∗ −

.

9 ω ∗
ω

The gain factor ω ∗ − of the imaginary part with respect to the normalised frequency ω ∗

is

ω ∗ . At the fundamental also shown in Figure 7.5. It changes from negative to positive at ω = 3

ω = ω ∗ , the output impedance is frequency, i.e., when

ω ∗ L ω ∗ L

Z o =− j 8 ≈− j 8 ,

which is capacitive as well.