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Comprehensive analysis and modeling of the three-phase LCL filter for VSC converters, suitable for wind energy or photovoltaic applications.

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- 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
- 6. 6 Wye connected capacitors Fig. 1 LCL Filter Per Phase Model
- 7. 7 Wye connected capacitors
- 8. 8 Wye connected capacitors
- 9. 9 deltaconnected capacitors Fig. 1 LCL Filter Per Phase Model
- 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
- 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 Lcl FILTERDESIGNEXAMPLE The damping resistor 𝑅𝑓 = 0.55 𝑜ℎ𝑚 (𝑤𝑦𝑒) 𝑅𝑓 = 0.185 𝑜ℎ𝑚 (𝑑𝑒𝑙𝑡𝑎)
- 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. GSC Converter Control
- 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. Thank You 22

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