Introduction - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 34

the output voltage. Hence, the cut-off frequency should not be chosen within the band where
the major harmonic components of the load current reside.
According to (Dewan and Ziogas 1979; Dewan 1981; Kim et al . 2000), the cost function of
the filter can be defined as

2 Q L + Q c

h = 1 , odd |

COST =

V oh I h | ,

(1.4)

with

n

2 X Lh ,

Q L =

, odd |

I h |

h = 1

n

2
X Ch .

| V Ch |

Q c =

h =

, odd

1

The weight of the reactive power for the inductor is taken as twice that of the capacitor,
considering the real price. Intuitively, the capacitance C size should be small for high-voltage
applications and the inductance L should be small for high-current applications (while keeping
the same cut-off frequency). Moreover, the inductance L should be small for applications with
significant amount of current harmonics and the capacitance C should be small for applications
with a significant amount of voltage harmonics, e.g. when the switching frequency is low.
When the ESRs R L and R C are considered or intentionally increased, the LC resonance
around the cut-off frequency is dampened. However, the increase of R C and/or R L results
in excessive power losses, which might cause difficulties in the LC design, in particular, for
high-power applications (Strom et al . 2011). One possible option is to adopt control strategies
to add virtual resistors to achieve the same purpose (Dahono 2003; Dahono et al . 2001; Guo
and Liu 2011); see Chapter 7 for more details.
Of course, the current rating of the inductor and the voltage rating of the capacitor should
be chosen to meet the requirement of the current and voltage levels of the inverter.

1.3.3.2 LCL Filters

Passive LCL filters, of which the circuit model is shown in Figure 1.33, are often adopted
in grid-connected inverters. Adding the grid-side inductor L g increases the order of the filter
by 1 and, hence, an LCL filter is able to attenuate the harmonics better than an LC filter.

Figure 1.33 Circuit model of a passive LCL filter