Experimental Evaluation of a Multifunctional System Single-Stage Pv-Shunt Active Filter Under Partial Shading Conditions

P. Robson M. Costa; Marcus R. de Castro; Isaac R. Machado; Edilson M. de Sá Junior

doi:10.18618/REP.2020.2.0020

Authors

P. Robson M. Costa Universidade Federal do Ceará (UFC), Sobral – CE, Brazil
Marcus R. de Castro Universidade Federal do Ceará (UFC), Sobral – CE, Brazil
Isaac R. Machado Universidade Federal do Ceará (UFC), Sobral – CE, Brazil
Edilson M. de Sá Junior Instituto Federal do Ceará (IFCE), Sobral – CE, Brazil

DOI:

https://doi.org/10.18618/REP.2020.2.0020

Keywords:

DC-AC power converters, Distributed power generation, Maximum power point trackers, Photovoltaic systems, Power conditioning, Shunt active filter

Abstract

Distributed solar photovoltaic (PV) generation is becoming more popular. Similarly, the number of electronic loads has increased along with the need to improve power quality. The PV-Shunt Active Filter (PV-SAF) is a system capable of injecting the PV power generated in the electrical grid and eliminating harmonics of current and reactive power of the local installation load. In the single-stage topology, the PV array is connected directly to the SAF DC bus, without the need for an intermediate DC-DC converter. In this paper, a three-phase single-stage PV-SAF system is evaluated in partial shading conditions. For this, a Global Maximum Power Point Tracking (GMPPT) technique capable of quickly tracking the point of maximum power even in the presence of several peaks in the power-voltage curve of the PV array is proposed. A night-time mode is implemented for the system operation when there is no PV generation. The instantaneous power theory and the adaptive hysteresis band current controller are used to control the SAF currents. The results obtained through an experimental prototype show that the PV-SAF system with the control strategies adopted is capable of simultaneously injecting into the grid the maximum power of the PV system and compensating harmonics and reactive power.

Downloads

Download data is not yet available.

Author Biographies

P. Robson M. Costa, Universidade Federal do Ceará (UFC), Sobral – CE, Brazil

was born in Guaraciaba do Norte, CE, Brazil in 1994. He received the B.S. and M.S. degrees in electrical engineering from the Federal University of Ceará, Sobral, Brazil, in 2016 and 2019, respectively. He is currently a substitute professor at Federal University of Ceará. His areas of interest are power electronics, electricity conversion quality, electronic control systems and electrical machine actuation. Prof. Costa is member of the SOBRAEP.

Marcus R. de Castro, Universidade Federal do Ceará (UFC), Sobral – CE, Brazil

was born in Fortaleza, Brazil. He received the B.S. and M.S. degrees in electrical engineering from the Federal University of Ceará, Fortaleza, Brazil, in 1999 and 2004, respectively, and the Ph.D. degree from the Université De Reims – Champagne Ardennes Reims, France, in 2010. Since 2011, he has been a Professor at the Federal University of Ceará, Sobral, Brazil. His research interests include static inverters, power factor correction circuits, dc-dc converters and their application to renewable energy systems.

Isaac R. Machado, Universidade Federal do Ceará (UFC), Sobral – CE, Brazil

was born in Parnaíba, state of Piauí, Brazil. He received the B.Sc. and M.Sc. degrees in electrical engineering from the Federal University of Ceará (UFC), Fortaleza, Brazil, in 2004 and 2007, respectively, and the D.Sc. degree from the Federal University of Rio de Janeiro, Rio de Janeiro (COPPE/UFRJ), Brazil, in 2013. Since 2011, he has been a Professor at the Federal University of Ceará and the Post Graduate Program in Electrical and Computer Engineering (PPGEEC/UFC), in Sobral city, Brazil. He coordinates research and development studies in power electronics, working mainly on the following topics: energy processing, electrical drives, renewable energy sources (solar, wind and waves), active filters and FACTS. Prof. Isaac Machado is a member of the Brazilian Power Electronics Society (SOBRAEP) and the Institute of Electrical and Electronic Engineers (IEEE).

Edilson M. de Sá Junior, Instituto Federal do Ceará (IFCE), Sobral – CE, Brazil

was born in Fortaleza, Brazil. He received the B.S. and M.S. degrees in electrical engineering
from the Federal University of Ceará, Fortaleza, Brazil, in 1999 and 2004, respectively, and the Ph.D. degree from the Federal University of Santa Catarina, Florianopolis, Brazil, in 2010. Since 2008, he has been a Professor at the Federal Institute of Ceará, Sobral, Brazil, where he coordinates the Mechatronics Research Group (GPEM). His research interests include electronic ballasts, power factor correction circuits, dc–dc converters and their application to renewable energy systems, and LED drivers. Prof. Sá is member of the SOBRAEP.

References

J. L. Sawin, J. Rutovitz, and F. Sverrisson, Renewables 2018 Global Status Report. Jun. 2018.

P. R. M. Costa, M. R. de Castro, I. R. Machado, and V. P. Pinto, "A hybrid PI-LQG robust servo control method for STATCOM performance improvement," Eletrônica de Potência, vol. 25, no. 1, pp. 1-12, Mar. 2020. https://doi.org/10.18618/REP.2020.1.0006 DOI: https://doi.org/10.18618/REP.2020.1.0006

R. K. Varma, V. Khadkikar, and R. Seethapathy, "Nighttime application of PV solar farm as STATCOM to regulate grid voltage," IEEE Trans. Energy Convers., vol. 24, no. 4, pp. 983-985, Dec. 2009. https://doi.org/10.1109/TEC.2009.2031814 DOI: https://doi.org/10.1109/TEC.2009.2031814

IEEE, "IEEE Standards for Interconnecting Distributed Resources with Electric Power System," IEEE Std1547-2003, Jul. 2003.

H. Markiewicz and A. Klajn, "Voltage Disturbances: Standard EN 50160," Power Qual. Appl. Guid., 2004.

E. Quitmann and E. Erdmann, "Power system needs -How grid codes should look ahead," IET Renew. Power Gener., vol. 9, no. 1, pp. 3-9, Dec. 2014. https://doi.org/10.1049/iet-rpg.2014.0107 DOI: https://doi.org/10.1049/iet-rpg.2014.0107

IEEE Recommended Practices and Requirements for Harmonic Control in Electric Power Systems, "IEEE std 519-1992," IEEE, pp. 1-9, Apr. 1992.

S. Ponnaluri, G. O. Linhofer, J. K. Steinke, and P. K. Steimer, "Comparison of single and two stage topologies for interface of BESS or fuel cell system using the ABB standard power electronics building blocks," in 2005 European Conference on Power Electronics and Applications, pp.9, Jan. 2005. https://doi.org/10.1109/EPE.2005.219502 DOI: https://doi.org/10.1109/EPE.2005.219502

A. K. Barnes, J. C. Balda, and C. M. Stewart, "Selection of converter topologies for distributed energy resources," Conf. Proc. -IEEE Appl. Power Electron. Conf. Expo. -APEC, pp. 1418-1423, Feb. 2012. https://doi.org/10.1109/APEC.2012.6166006 DOI: https://doi.org/10.1109/APEC.2012.6166006

S. Silva, L. Sampaio, F. Oliveira, and F. Durand, "Pso-based MPPT Technique Applied To A Grid-tied PV System With Active Power Line Conditioning Using A Feed-forward Dc-bus Control Loop," Eletrônica de Potência, vol. 21, no. 2, pp. 105-116, May 2016.

T. Esram and P. L. Chapman, "Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques," IEEE Trans. Energy Convers., vol. 22, no. 2, pp. 439-449, Jun. 2007. https://doi.org/10.1109/TEC.2006.874230 DOI: https://doi.org/10.1109/TEC.2006.874230

M. Aureliano Gomes de Brito, L. Poltronieri Sampaio, G. de Azevedo e Melo, and C. Alberto Canesin, "Contribution For The Study Of The Main Pv Maximum Power Point Tracking Methods," Eletrônica de Potência, vol. 17, no. 3, pp. 592-600, Aug. 2012. https://doi.org/10.18618/REP.2012.3.592600 DOI: https://doi.org/10.18618/REP.2012.3.592600

S. A. Papathanassiou, P. S. Georgilakis, and E. I. Batzelis, "Energy models for photovoltaic systems under partial shading conditions: a comprehensive review," IET Renew. Power Gener., vol. 9, no. 4, pp. 340-349, Nov. 2014. https://doi.org/10.1049/iet-rpg.2014.0207 DOI: https://doi.org/10.1049/iet-rpg.2014.0207

K. Chen, S. Tian, Y. Cheng, and L. Bai, "An Improved MPPT Controller for Photovoltaic System Under Partial Shading Condition," IEEE Trans. Sustain. Energy, vol. 5, no. 3, pp. 978-985, Jul. 2014. https://doi.org/10.1109/TSTE.2014.2315653 DOI: https://doi.org/10.1109/TSTE.2014.2315653

G.-J. Fang and K.-L. Lian, "A maximum power point tracking method based on multiple perturb-and-observe Fig. 11. Grid voltages and currents before (a) and after (b) the PV-SAF starts to act in the Night-time Mode obtained with the Minipa Power Quality Analyzer ET-5060C. The grid current THD before (c) and after (d) the switching start. method for overcoming solar partial shaded problems," in 2017 6th International Conference on Clean Electrical Power (ICCEP), Jun. 2017, pp. 68-73. https://doi.org/10.1109/ICCEP.2017.8004794 DOI: https://doi.org/10.1109/ICCEP.2017.8004794

M. A. Ghasemi, H. M. Foroushani, and M. Parniani, "Partial Shading Detection and Smooth Maximum Power Point Tracking of PV Arrays Under PSC," IEEE Trans. Power Electron., vol. 31, no. 9, pp. 6281-6292, Sep. 2016. https://doi.org/10.1109/TPEL.2015.2504515 DOI: https://doi.org/10.1109/TPEL.2015.2504515

Q. Zhu, X. Zhang, S. Li, C. Liu, and H. Ni, "Research and Test of Power-Loop-Based Dynamic Multi-Peak MPPT Algorithm," IEEE Trans. Ind. Electron., vol. 63, no. 12, pp. 7349-7359, Dec. 2016. https://doi.org/10.1109/TIE.2016.2594233 DOI: https://doi.org/10.1109/TIE.2016.2594233

A. Ramyar, H. Iman-Eini, and S. Farhangi, "Global Maximum Power Point Tracking Method for Photovoltaic Arrays Under Partial Shading Conditions," IEEE Trans. Ind. Electron., vol. 64, no. 4, pp. 2855-2864, Apr. 2017. https://doi.org/10.1109/TIE.2016.2632679 DOI: https://doi.org/10.1109/TIE.2016.2632679

S. A. O. da Silva, L. P. Sampaio, F. M. de Oliveira, and F. R. Durand, "Feed-forward DC-bus control loop applied to a single-phase grid-connected PV system operating with PSO-based MPPT technique and active power-line conditioning," IET Renew. Power Gener., vol. 11, no. 1, pp. 183-193, Jan. 2017. https://doi.org/10.1049/iet-rpg.2016.0120 DOI: https://doi.org/10.1049/iet-rpg.2016.0120

R. B. A. Koad, A. F. Zobaa, and A. El-Shahat, "A Novel MPPT Algorithm Based on Particle Swarm Optimization for Photovoltaic Systems," IEEE Trans. Sustain. Energy, vol. 8, no. 2, pp. 468-476, Apr. 2017. https://doi.org/10.1109/TSTE.2016.2606421 DOI: https://doi.org/10.1109/TSTE.2016.2606421

S. Rajendran and H. Srinivasan, "Simplified accelerated particle swarm optimisation algorithm for efficient maximum power point tracking in partially shaded photovoltaic systems," IET Renew. Power Gener., vol. 10, no. 9, pp. 1340-1347, Oct. 2016. https://doi.org/10.1049/iet-rpg.2016.0114 DOI: https://doi.org/10.1049/iet-rpg.2016.0114

N. Kumar, I. Hussain, B. Singh, and B. K. Panigrahi, "Rapid MPPT for Uniformly and Partial Shaded PV System by Using Jaya DE Algorithm in Highly Fluctuating Atmospheric Conditions," IEEE Trans. Ind. Informatics, vol. 13, no. 5, pp. 2406-2416, Oct. 2017. https://doi.org/10.1109/TII.2017.2700327 DOI: https://doi.org/10.1109/TII.2017.2700327

N. Pragallapati, T. Sen, and V. Agarwal, "Adaptive Velocity PSO for Global Maximum Power Control of a PV Array Under Nonuniform Irradiation Conditions," IEEE J. Photovoltaics, vol. 7, no. 2, pp. 624-639, Mar. 2017. https://doi.org/10.1109/JPHOTOV.2016.2629844 DOI: https://doi.org/10.1109/JPHOTOV.2016.2629844

N. Kumar, I. Hussain, B. Singh, and B. K. Panigrahi, "Peak power detection of PS solar PV panel by using WPSCO," IET Renew. Power Gener., vol. 11, no. 4, pp. 480-489, Mar. 2017. https://doi.org/10.1049/iet-rpg.2016.0733 DOI: https://doi.org/10.1049/iet-rpg.2016.0733

S. Mohanty, B. Subudhi, and P. K. Ray, "A New MPPT Design Using Grey Wolf Optimization Technique for Photovoltaic System Under Partial Shading Conditions," IEEE Trans. Sustain. Energy, vol. 7, no. 1, pp. 181-188, Jan. 2016. https://doi.org/10.1109/TSTE.2015.2482120 DOI: https://doi.org/10.1109/TSTE.2015.2482120

J. P. Ram and N. Rajasekar, "A Novel Flower J. P. Ram and N. Rajasekar, "A Novel Flower J. P. Ram and N. Ra Pollination Based Global Maximum Power Point Method for Solar Maximum Power Point Tracking," IEEE Trans. Power Electron., vol. 32, no. 11, pp. 8486-8499, Nov. 2017. https://doi.org/10.1109/TPEL.2016.2645449 DOI: https://doi.org/10.1109/TPEL.2016.2645449

D. F. Teshome, C. H. Lee, Y. W. Lin, and K. L. Lian, "A Modified Firefly Algorithm for Photovoltaic "A Modified Firefly Algorithm for Photovoltaic "A Mod if Maximum Power Point Tracking Control Under Partial Shading," IEEE J. Emerg. Sel. Top. Power Electron., vol. 5, no. 2, pp. 661-671, Jun. 2017. https://doi.org/10.1109/JESTPE.2016.2581858 DOI: https://doi.org/10.1109/JESTPE.2016.2581858

K. Sundareswaran, S. Pedappati, and S. Palani, "MPPT of PV Systems Under Partial Shaded Conditions Through a Colony of Flashing Fireflies," IEEE Trans. Energy Convers., vol. 29, no. 2, pp. 463-472, Jun. 2014. https://doi.org/10.1109/TEC.2014.2298237 DOI: https://doi.org/10.1109/TEC.2014.2298237

C. Manickam, G. P. Raman, G. R. Raman, S. I. Ganesan, and N. Chilakapati, "Fireworks Enriched P& O Algorithm for GMPPT and Detection of Partial Shading in PV Systems," IEEE Trans. Power Electron., vol. 32, no. 6, pp. 4432-4443, Jun. 2017. https://doi.org/10.1109/TPEL.2016.2604279 DOI: https://doi.org/10.1109/TPEL.2016.2604279

S. Mohanty, B. Subudhi, and P. K. Ray, "A Grey Wolf-S. Mohanty, B. Subudhi, and P. K. Ray, "A Grey Wolf-S. Mohanty, B. Subudhi, and P. K. Ray, "A Grey Wolf Assisted Perturb & Observe MPPT Algorithm for a PV System," IEEE Trans. Energy Convers., vol. 32, no. 1, pp. 340-347, Mar. 2017. https://doi.org/10.1109/TEC.2016.2633722 DOI: https://doi.org/10.1109/TEC.2016.2633722

.[31]A. Chandra, B. Singh, K. Al-Haddad, S. Kumar, and I. Hussain, "An Adaptive Control Scheme of SPV System Integrated to AC Distribution System," IEEE Trans. Ind. Appl., vol.53, no. 6, pp. 5173-5181, Dec. 2017. https://doi.org/10.1109/TIA.2017.2722978 DOI: https://doi.org/10.1109/TIA.2017.2722978

N. Beniwal, I. Hussain, and B. Singh, "Second-order Volterra-filter-based control of a solar PV-DSTATCOM system to achieve Lyapunov’s stability," IEEE Trans. Ind. Appl., vol. 55, no. 1, pp. 670-679, Feb. 2019. https://doi.org/10.1109/TIA.2018.2867324 DOI: https://doi.org/10.1109/TIA.2018.2867324

S. Devassy and B. Singh, "Design and Performance Analysis of Three-Phase Solar PV Integrated UPQC," in IEEE Transactions on Industry Applications,Feb.2018. https://doi.org/10.1109/TIA.2017.2754983 DOI: https://doi.org/10.1109/TIA.2017.2754983

R. K. Agarwal, I. Hussain, and B. Singh, "Three-phase single-stage grid tied solar PV ECS using PLL-less fast CTF control technique," IET Power Electron., vol. 10, no. 2, pp. 178-188, Feb. 2017. https://doi.org/10.1049/iet-pel.2016.0067 DOI: https://doi.org/10.1049/iet-pel.2016.0067

S. Pradhan, I. Hussain, B. Singh, and B. Ketan Panigrahi, "Performance improvement of grid-integrated solar PV system using DNLMS control algorithm," IEEE Trans. Ind. Appl., vol. 55, no. 1, pp. 78-91, Jan. 2019. https://doi.org/10.1109/TIA.2018.2863652 DOI: https://doi.org/10.1109/TIA.2018.2863652

V. Jain and B. Singh, "A Multiple Improved Notch Filter-Based Control for a Single-Stage PV System Tied to a Weak Grid," IEEE Trans. Sustain. Energy, vol. 10, no. 1, pp. 238-247, Jan. 2019. https://doi.org/10.1109/TSTE.2018.2831704 DOI: https://doi.org/10.1109/TSTE.2018.2831704

N. Beniwal, I. Hussain, and B. Singh, "Control and operation of a solar PV-battery-grid-tied system in fixed and variable power mode," IET Gener. Transm. Distrib., vol. 12, no. 11, pp. 2633-2641, Jun. 2018. https://doi.org/10.1049/iet-gtd.2017.1095 DOI: https://doi.org/10.1049/iet-gtd.2017.1095

N. D. Tuyen and G. Fujita, "PV-Active Power Filter Combination Supplies," IEEE Power Energy Technol. Syst. J., vol. 2, no. 1, pp. 32-42,Mar.2015. https://doi.org/10.1109/JPETS.2015.2404355 DOI: https://doi.org/10.1109/JPETS.2015.2404355

H. Akagi, E. H. Watanabe, and M. Aredes, Instantaneous Power Theory and Applications to Power Conditioning. Sept. 2006. https://doi.org/10.1002/0470118938 DOI: https://doi.org/10.1002/0470118938

B. Yahia, D. Hind, and C. Rachid, "The Application of an Active Power Filter on a Photovoltaic Power Generation System," Int. J. Renew. ENERGY Res. Djeghloud Hind al, vol. 2, no. 4,Jan.2012.

N. Shah and C. Rajagopalan, "Experimental investigation of a multifunctional grid interactive photovoltaic system operating in partial shading conditions," IET Renew. Power Gener., vol. 10, no. 9, pp. 1382-1392, Oct. 2016. https://doi.org/10.1049/iet-rpg.2015.0436 DOI: https://doi.org/10.1049/iet-rpg.2015.0436

S. Kumar and B. Singh, "A Multipurpose PV System Integrated to a Three-Phase Distribution System Using an LWDF-Based Approach," IEEE Trans. Power Electron., vol. 33, no. 1, pp. 739-748, Oct. 2018. https://doi.org/10.1109/TPEL.2017.2665526 DOI: https://doi.org/10.1109/TPEL.2017.2665526

F. J. Lin, K. H. Tan, Y. K. Lai, and W. C. Luo, "Intelligent PV Power System with Unbalanced Current Compensation Using CFNN-AMF," IEEE Trans. Power Electron., vol. PP, no. c, p. 1, Sept. 2019. https://doi.org/10.1109/TPEL.2018.2888732 DOI: https://doi.org/10.1109/TPEL.2018.2888732

P. K. Ray, S. R. Das, and A. Mohanty, "Fuzzy Controller Designed PV based Custom Power Device for Power Quality Enhancement," IEEE Trans. Energy Convers., vol. PP, no. c, p. 1, Nov. 2018. https://doi.org/10.1109/TEC.2018.2880593 DOI: https://doi.org/10.1109/TEC.2018.2880593

N. Kumar, B. Singh, B. K. Panigrahi, and L. Xu, "Leaky Least Logarithmic Absolute Difference Based Control Algorithm and Learning Based In C MPPT Technique for Grid Integrated PV System," IEEE Trans. Ind. Electron., vol. 0046, no. c, Nov. 2019. https://doi.org/10.1109/TIE.2018.2890497 DOI: https://doi.org/10.1109/TIE.2018.2890497

N. Kumar, B. Singh, and B. K. Panigrahi, "LLMLF based Control Approach and LPO MPPT Technique for Improving Performance of a Multifunctional Three-Phase Two-Stage Grid Integrated PV System," IEEE Trans. Sustain. Energy, vol. PP, no. c, pp. 1-1, Jan. 2020. https://doi.org/10.1109/TSTE.2019.2891558 DOI: https://doi.org/10.1109/TSTE.2019.2891558

S. Buso, L. Malesani, and P. Mattavelli, "Comparison of current control techniques for active filter applications," IEEE Trans. Ind. Electron. IEEE Trans. Ind. Electron. IEEE T, vol. 45, no. 5, pp. 722-729, Oct. 1998. https://doi.org/10.1109/41.720328 DOI: https://doi.org/10.1109/41.720328

B. K. Bose, "An adaptive hysteresis-band current control technique of a voltage-fed PWM inverter for machine drive system," IEEE Trans. Ind. Electron., vol. 37, no. 5, pp. 402-408, Oct. 1990. https://doi.org/10.1109/41.103436 DOI: https://doi.org/10.1109/41.103436

M. Kale and E. Ozdemir, "An adaptive hysteresis band current controller for shunt active power filter," Electr. Power Syst. Res., vol. 73, no. 2, pp. 113-119,Feb.2005. https://doi.org/10.1016/j.epsr.2004.06.006 DOI: https://doi.org/10.1016/j.epsr.2004.06.006

N. Gupta, S. Singh, and S. Dubey, "DSP based adaptive hysteresis-band current controlled active filter for power quality conditioning under non-sinusoidal supply voltages," Int. J. Eng. Sci. Technol., vol. 3, no. 4, pp. 236-252, Feb. 2011. https://doi.org/10.4314/ijest.v3i4.68556 DOI: https://doi.org/10.4314/ijest.v3i4.68556

L. Castañer and S. Silvestre, Modelling Photovoltaic Systems Using PSpice®. Wiley, Sept .2002. https://doi.org/10.1002/0470855541 DOI: https://doi.org/10.1002/0470855541

T. Markvart and L. Castañer, Practical Handbook of Photovoltaics. Elsevier, Oct. 2003.

H. Patel and V. Agarwal, "Maximum power point tracking scheme for PV systems operating under partially shaded conditions," IEEE Trans. Ind. Electron., Apr. 2008. https://doi.org/10.1109/TIE.2008.917118 DOI: https://doi.org/10.1109/TIE.2008.917118

J. Ahmed and Z. Salam, "An improved method to predict the position of maximum power point during partial shading for PV arrays," IEEE Trans. Ind. Informatics, vol. 11, no. 6, pp. 1378-1387, Dec. 2015. https://doi.org/10.1109/TII.2015.2489579 DOI: https://doi.org/10.1109/TII.2015.2489579

M. Rastogi, R. Naik, and N. Mohan, "A Comparative Evaluation of Harmonic Reduction Techniques in Three-Phase Utility Interface of Power Electronic Loads," IEEE Trans. Ind. Appl., vol. 30, no. 5, pp. 1149-1155, Oct. 1994. https://doi.org/10.1109/28.315225 DOI: https://doi.org/10.1109/28.315225

M. Karimi-Ghartemani, H. Karimi, and M. R. Iravani, "A Magnitude/Phase-Locked Loop System Based on Estimation of Frequency and In-Phase/Quadrature-Phase Amplitudes," IEEE Trans. Ind. Electron., vol. 51, no. 2, pp. 511-517, Apr. 2004. https://doi.org/10.1109/TIE.2004.825282 DOI: https://doi.org/10.1109/TIE.2004.825282

R. L. de A. Ribeiro, C. C. de Azevedo, and R. M. de Sousa, "A Robust Adaptive Control Strategy of Active Power Filters for Power-Factor Correction, Harmonic Compensation, and Balancing of Nonlinear Loads," IEEE Trans. Power Electron., vol. 27, no. 2, pp. 718-730, Feb. 2012. https://doi.org/10.1109/TPEL.2011.2161334 DOI: https://doi.org/10.1109/TPEL.2011.2161334