LCL Filter for Grid Connected VSC Converter
Comprehensive analysis and modeling of the three-phase LCL filter for VSC converters, suitable for wind energy or photovoltaic applications.
1. 1
School of Engineering & Applied Sciences,
Frederick University Nicosia, Cyprus
August, 2015
2. 2
An LCL filter is often used to interconnect an inverter to the utility grid in order to
filter the harmonics produced by the inverter.
So far, there is lack of a state-space mathematical modeling approach that considers
practical cases of delta- and wye-connected capacitors
This paper describes a design methodology of an LCL filter for grid-
interconnected inverters along with a comprehensive study of how to mitigate
harmonics.
3. 3
Simple type of filter that can be used is a series inductor,
but its harmonic attenuation is not very pronounced
High voltage drop is produced, hence the size of inductor becomes bulky.
High Order LCL Filter is used as replacement of conventional L filter for
smoothing output current of VSC
Higher attenuation along with cost savings,
overall weight and size reduction of the components.
Good performance can be obtained using small values of inductors and
capacitors.
4. 4
Little information available describing the systematic design of LCL filters
In order to design an effective LCL filter, it is necessary to have an appropriate
mathematical model of the filter.
The objective of this paper is to conduct a comprehensive analysis and modeling
of the three-phase LCL filter for VSC converters, suitable for wind energy or
photovoltaic applications.
Two configurations of three-phase full-bridge dc/ac inverter are compared:
first, a set of wyeconnected filter capacitors with damping
second, a deltaconnected filter output connection.
5. 5
LCL Filter Modeling
Fig. 1 LCL Filter Per Phase Model
𝐿1= Inverter Side Inductor
𝐿2= Grid Side Inductor
𝑅1= Inverter Side Resistor
𝑅2= Grid Side Resistor
𝑣1= Input (inverter) voltage
𝐿2= output system voltage
Fig. 2 General schematic for grid-interconnected dc power source
10. 10
LCL frequency response
Fig. 4 Bode Diagram
𝐻𝐿𝐶𝐿 =
𝑖 𝑔
𝑣 𝑖 important transfer function
The insertion of a series resistance
with the capacitor eliminates the
gain spike, smoothing the overall
response and rolling-off to −180◦
for high frequency, instead
of −270◦.
11. 11
Filter Design procedure
Several characteristics must be considered in designing an LCL filter,
such as current ripple, filter size, and switching ripple attenuation.
The reactive power requirements may cause a resonance of the capacitor
interacting with the grid.
Therefore, passive or active damping must be added by including a resistor
in series with the capacitor.
The following parameters are needed for the filter design:
VLL, line-to-line RMS voltage (inverter output);
Vph, phase voltage (inverter output);
Pn, rated active power;
VDC, dc-link voltage;
fg, grid frequency;
fsw, switching frequency; and
fres, resonance frequency.
12. 12
Filter Design procedure
Input parameters
Calculate Base Values
Calculate 𝐶𝑓 and 𝐿1
Provide desired 𝑘 𝑎
Calculate 𝐿2
Check 𝑓𝑟𝑒𝑠
Provide 𝑅𝑓
Output 𝐶𝑓 and 𝑅𝑓
13. 13
Filter Design procedure
𝑍 𝑏 =
𝐸 𝑛
2
𝑃𝑛
Base Impedance
𝐶 𝑏 =
1
𝜔 𝑔 𝑍 𝑏
Base Capacitance
For the design of the filter capacitance, it is considered that the maximum power
factor variation seen by the grid is 5%, indicating that the base impedance of the
system is adjusted as follows:
𝐶𝑓 = 0.05𝐶 𝑏
The maximum current ripple at the output of dc/ac inverter is given by
It can be observed that the maximum peak-to-peak current ripple happens at m = 0.5, then
𝐿1= Inverter Side Inductor
𝑉𝐷𝐶= DC Link Voltage
𝐸 𝑛= Line-Line Grid Voltage
14. 14
Filter Design procedure
The LCL filter should reduce the expected current ripple to 20%, resulting in a ripple value of
2% of the output current.
A 10% ripple of the rated current (𝐼 𝑚𝑎𝑥) for the design parameters is given by
∆𝐼𝐿𝑚𝑎𝑥 = 0.1𝐼 𝑚𝑎𝑥
Where,
𝐼 𝑚𝑎𝑥 =
𝑃𝑛 2
3𝑉𝑝ℎ
Hence, 𝐿1 becomes
𝐿1 = 𝑉𝐷𝐶 (6𝑓𝑠𝑤∆𝐼𝐿𝑚𝑎𝑥)
15. 15
Filter Design procedure
Now harmonic mitigation, the harmonic current generated by inverter to that of current
injected in the grid is given by:
where 𝑘𝑎 is the desired attenuation. 𝐶𝑓 = 0.01 ÷ 0.05 𝐶 𝑏
A resistor in series (Rf ) with the capacitor attenuates part of the ripple on the switching
frequency in order to avoid the resonance.
The value of this resistor should be one third of the impedance of the filter capacitor at the
resonant frequency
The constant r is the ratio between the inductance at the inverter side and the one at the grid side
16. 16
Lcl FILTERDESIGNEXAMPLE
The specifications are
𝐸 𝑛 = 120 3, line-to-line RMS voltage;
Ps = Pn = 5 kW, rated active power;
VDC = 400 V, dc-link voltage;
ωg = 2π60, grid angular frequency;
fsw = 15 kHz, switching frequency;
x = 0.05, maximum power factor variation seen by the grid;
ka = 0.2 (20%), attenuation factor.
𝑍 𝑏 =
𝐸 𝑛
2
𝑃𝑛
=
(120 3)2
5000
= 8.64ΩBase Impedance
𝐶 𝑏 =
1
𝜔 𝑔 𝑍 𝑏
= 307.16μFBase Capacitance
19. GSC Converter Control
Various tests have been conducted stand-alone mode for a load with different power
factors; in all cases, the filter output voltage has THD less than 2%.