lcl filter design

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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


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delta connected capacitors


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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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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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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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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%.


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