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LCL Filter for Grid Connected VSC Converter
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
= Inverter Side Inductor= Grid Side Inductor= Inverter Side Resistor= Grid Side Resistor= Input (inverter) voltage= 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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delta connected capacitors
Fig. 1 LCL Filter Per Phase Model
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LCL frequency response
Fig. 4 Bode Diagram
important transfer function
The insertion of a series resistance with the capacitor eliminates the gain spike, smoothing the overallresponse and rolling-off to −180◦ for high frequency, insteadof −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 procedureInput parameters
Calculate Base Values
Calculate and
Provide desired
Calculate
Check
Provide
Output and
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Filter Design procedure
𝑍 𝑏=𝐸𝑛
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𝑃𝑛Base Impedance
𝐶𝑏=1
𝜔𝑔𝑍𝑏Base 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:
𝐶 𝑓=0.05𝐶𝑏
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
= Inverter Side Inductor= DC Link Voltage
= 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 () for the design parameters is given by
∆ 𝐼 𝐿𝑚𝑎𝑥=0.1 𝐼𝑚𝑎𝑥
Where,
𝐼𝑚𝑎𝑥=𝑃𝑛 √23𝑉 h𝑝
Hence, becomes
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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 is the desired attenuation.
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 FILTER DESIGN EXAMPLEThe specifications are
, 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=𝐸𝑛
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𝑃𝑛=
(120√3)2
5000=8.64 ΩBase Impedance
𝐶𝑏=1
𝜔𝑔𝑍𝑏=307.16 μ FBase Capacitance
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Lcl FILTER DESIGN EXAMPLE
Using 10% allowed ripple
∆ 𝐼 𝐿𝑚𝑎𝑥=1.9641
𝐼𝑚𝑎𝑥=𝑃𝑛 √23𝑉 h𝑝
=19.641𝐴𝑚𝑝
For 5% power factor variation
(wye connected) (wye connected)
For =20%
(wye)
𝑓 𝑟𝑒𝑠=6.1897 𝑘𝐻𝑧 Satisfy criteria
(wye)
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Lcl FILTER DESIGN EXAMPLE
The damping resistor
𝑅 𝑓=0.55 h𝑜 𝑚(𝑤𝑦𝑒)
𝑅 𝑓=0.185 h𝑜 𝑚(𝑑𝑒𝑙𝑡𝑎)
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%.
GSC Converter Control
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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