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# Lcl filter design

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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.

Publié dans : Ingénierie
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### Lcl filter design

1. 1. 1 School of Engineering & Applied Sciences, Frederick University Nicosia, Cyprus August, 2015
2. 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. 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. 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. 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
6. 6. 6 Wye connected capacitors Fig. 1 LCL Filter Per Phase Model
7. 7. 7 Wye connected capacitors
8. 8. 8 Wye connected capacitors
9. 9. 9 deltaconnected capacitors Fig. 1 LCL Filter Per Phase Model
10. 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. 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. 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. 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. 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. 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. 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
17. 17. 17 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)
18. 18. 18 Lcl FILTERDESIGNEXAMPLE The damping resistor 𝑅𝑓 = 0.55 𝑜ℎ𝑚 (𝑤𝑦𝑒) 𝑅𝑓 = 0.185 𝑜ℎ𝑚 (𝑑𝑒𝑙𝑡𝑎)
19. 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%.
20. 20. GSC Converter Control
21. 21. GSC Converter Control The THD of injected current is higher in grid-connected mode, but still less than the required specification of 5%
22. 22. Thank You 22