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School of Engineering & Applied Sciences,
Frederick University Nicosia, Cyprus
August, 2015

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 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.

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 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.

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 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.

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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

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Wye connected capacitors
Fig. 1 LCL Filter Per Phase Model

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Wye connected capacitors

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Wye connected capacitors

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deltaconnected capacitors
Fig. 1 LCL Filter Per Phase Model

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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◦.

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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.

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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

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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

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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)

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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

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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

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Lcl FILTERDESIGNEXAMPLE
𝐿1 = 𝑉𝐷𝐶 6𝑓𝑠𝑤∆𝐼𝐿𝑚𝑎𝑥 = 2.26𝑚𝐻
Using 10% allowed ripple
∆𝐼𝐿𝑚𝑎𝑥 = 1.9641
𝐼 𝑚𝑎𝑥 =
𝑃𝑛 2
3𝑉𝑝ℎ
= 19.641𝐴𝑚𝑝
For 5% power factor variation
𝐶𝑓 = 15μF (wye connected) 𝐶𝑓 = 45μF (wye connected)
For 𝑘 𝑎=20%
𝐿2 = 0.045𝑚𝐻 (wye)
𝑓𝑟𝑒𝑠 = 6.1897𝑘𝐻𝑧 Satisfy criteria
𝐿2 = 0.135𝑚𝐻 (wye)

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Lcl FILTERDESIGNEXAMPLE
The damping resistor
𝑅𝑓 = 0.55 𝑜ℎ𝑚 (𝑤𝑦𝑒)
𝑅𝑓 = 0.185 𝑜ℎ𝑚 (𝑑𝑒𝑙𝑡𝑎)

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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%.

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GSC Converter Control

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GSC Converter Control
The THD of injected current is higher in grid-connected mode, but
still less than the required specification of 5%

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Thank
You
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