Bypassing Harmonic Current Components - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 161

1 1 1 16

1+K 3
1+K 5
1+K 7

8

90

45

0

−45

3ω 5ω 7ω

−90

10 2 10 3 10 4

Frequency (rad/sec)

Figure 8.3 Bode plot of a typical 1 + K R ( s ) with ξ = 0 . 01

The block K R ( s ) in Figure 8.2 can be designed to have small gains at low frequencies and
high gains at high frequencies so that the output impedance is resistive at low frequencies (in
particular at the fundamental frequency) for other purposes, e.g. power sharing, and is small at
harmonic frequencies for the purpose of improving the voltage THD. There are many ways to
achieve this. One option is to adopt the resonant harmonic compensators (Castilla et al. 2009;
Shen et al. 2010)

2 ξ h ω s

K R ( s ) =

) 2 ×

K h , (8.3)

h = 3 , 5 ,... s 2 + 2 ξ h ω s + ( h ω

of which the gain at frequency h ω is K h with zero phase; see the Bode plot of a typical

1 01 shown in Figure 8.3. It is more or less 1 everywhere apart from at the

frequencies around the harmonics. This is equivalent to reducing the inductance L to

+ K R ( s ) with ξ = 0 .

L
1 + K h

at

K i

the frequency h ω (and also the output resistance to

K h ), which is able to improve the THD

1 +

of the output voltage 01 to accommodate

frequency variations and h can be chosen to cover the major harmonic components in the
current, e.g. the 3rd, 5th and 7th harmonics.

v o . The damping factor ξ can be chosen as ξ = 0 .

8.2 Physical Interpretation of the Controller
As explained in the previous section, the strategy is able to reduce the output impedance of the
inverter at the h -th harmonic frequency by

1

K h . As a matter of fact, this inner-loop controller
is equivalent to the block diagram shown in Figure 8.4(a), that is, it is equivalent to the feedback
of current i L =

1 +

K R ( s )

K i v o , which is the sum of the original current i and the current flowing
through the admittance K R ( s )
K i

i +

that is connected across the output terminals. Since the reference

voltage v r only contains the fundamental component, it is the same after passing through

the block K R ( s ) 1. Hence, the structure is in principle the same as a proportional current

feedback adopted to achieve R-inverters discussed in Chapter 7 but the inductor current i L has
an additional component

+

K R ( s )

K i v o . The corresponding equivalent circuit diagram is shown in
Figure 8.4(b), where the admittance block K R ( s )
K i

is connected in parallel with the filter capacitor