Introduction - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 33

Figure 1.32 Circuit model of a passive LC filter

1.3.3 Output Filters
Since an inverter is operated with PWM signals, which contain harmonics often around the
multiples of the switching frequency, it is necessary to connect a low-pass filter to the output
of the inverter power switches so that the harmonics can be filtered out and the desired output
voltage is recovered. This can be done with conventional passive filters (Chang et al . 2006;
Das 2004; Hamadi et al . 2010), e.g. LC and LCL filters.

1.3.3.1 LC Filters

The circuit model of a passive LC filter is shown in Figure 1.32. The equivalent series resis-
tance (ESR) of the inductor and the capacitor may not be considered during the design process
because of their small values. In practice, the ESRs are able to dampen high-frequency oscil-
lations so it is good for performance. Ideally, the smaller the inductance and the capacitance,
the more cost-effective the system. However, the inductance and the capacitance should be big
enough in order to filter out the switching effects, taking into account several contradictory
factors (Pasterczyk et al . 2009), e.g. the cut-off frequency f c (Hatua et al . 2012; Michels et al .
2006), size, the voltage THD, the cost function (Dewan and Ziogas 1979; Dewan 1981; Kim
et al . 2000), the resonance damping, efficiency (Strom et al . 2011) and the power level, etc.
The cut-off frequency f c of the filter is

1

f c =

π √ LC .

(1.2)

2

This is the most important factor to be considered. In order to filter out the switching harmonics,
it should be much lower than the switching frequency while providing enough bandwidth for
the controller. It is recommended to position it within 3 ∼

1
2 of the switching frequency f s w

(Hatua et al . 2012), i.e.

f s 3 ≤ f s 2 .

f c ≤ (1.3)

It is worth noting that this causes resonance in the output impedance of the inverter around
the cut-off frequency. As will be discussed in Chapters 2 and 7, this actually amplifies the
harmonic current components around the cut-off frequency and might result in high THD in