A Study of the SPWM High-Frequency Harmonic Circulating Currents in Modular Inverters

  • Xu, Sheng (Department of Mechanical and Electrical Engineering, Taizhou University) ;
  • Ji, Zhendong (School of Automation, Nanjing University of Science and Technology)
  • Received : 2016.02.05
  • Accepted : 2016.07.22
  • Published : 2016.11.20


Due to detection and control errors, some high-frequency harmonics with voltage-source characteristics cause circulating currents in modular inverters. Moreover, the circulating currents are usually affected by the output filters (OF) of each module due to their filter and resonance properties. The interaction among the circulating currents in the modules increase the power loss and reduce system stability and control precision. Therefore, this paper reports the results of a study on the SPWM high-frequency harmonics circulating currents for a double-module VSI. In the paper, an analysis of the circulating-current circuits is briefly described. Next, a mathematic model of the single-module output voltage based on the carrier frequency of SPWM is built. On this basis, through mathematic modeling of high-frequency harmonic circulating currents, the formation mechanism and distribution characteristics of circular currents and their influences are studied in detail. Finally, the influences of the OF on the circulating currents are studied by mainly taking an LC-type filter as an example. A theoretical analysis and experimental results demonstrate some important characteristics. First, the carrier phase shifting of the SPWM for each module is the major cause of the SPWM harmonic circulating currents, and the circulating currents are in an odd distribution around n-times the carrier frequency $n{\omega}_s$, where n = 1, 2, 3, ${\ldots}$. Second, the harmonic circular currents do not flow into the parallel system. Third, the OF can effectively suppress the non-circulating part of the high-frequency harmonic currents but is ineffective for the circulation part, and actually reduces system stability.


Supported by : National Natural Science Foundation of China, Natural Science Foundation of the Jiangsu Higher Education Institutions of China, China Postdoctoral Science Foundation


  1. K. Ilves, A. Antonopoulos, L. Harnefors, S. Norrga, and H. P. Nee, "Circulating current control in modular multilevel converters with fundamental switching frequency," in 7th International Power Electronics and Motion Control Conference (IPEMC), pp. 249-256, Jun. 2012.
  2. Y. Zhang, S. Duan, Y. Kang, and J. Chen, "The restrain of harmonic circulating currents between parallel inverters," in CES/IEEE 5th International Power Electronics and Motion Control Conference (IPEMC), pp. 1-5, Aug. 2006.
  3. J. A. P. Lopes, C. L. Moreira, and A. G. Madureira, "Defining control strategies for microgrid island operation," IEEE Trans. Power Syst., Vol. 21, No. 2, pp. 916-924, May 2006.
  4. Y. A. R. I. Mohamed and E. F. El Saadany, "Adaptive decentralized droop controller to preserve power sharing stability of paralleled inverters in distributed generation microgrids," IEEE Trans. Power Electron., Vol. 23, No. 6, pp. 2806-2816, Nov. 2008.
  5. Z. He and Y. Xing, "Distributed control for UPS modules in parallel operation with rms voltage regulation," IEEE Trans. Ind. Electron., Vol. 55, No. 8, pp. 2860-2869, Aug. 2008.
  6. X. Sun, Y. S. Lee, and D. Xu, "Modeling, analysis, and implementation of parallel multi-inverter systems with instantaneous average-current-sharing scheme," IEEE Trans. Power Electron., Vol. 18, No. 3, pp. 844-856, May 2003.
  7. L. Chen, L. Xiao, C. Gong, and Y. Yan, "Circulating current's characteristics analysis and the control strategy of parallel system based on double close-loop controlled VSI," in IEEE 35th Annual Power Electronics Specialists Conference (PESC), pp. 4791-4797, Jun. 2004.
  8. K. D. Brabandere, B. Bolsens, J. V. D. Keybus, A. Woyte, J. Driesen, and R. Belmans, "A voltage and frequency droop control method for parallel inverters," IEEE Trans. Power Electron., Vol. 22, No. 4, pp. 1107-1115, Jul. 2007.
  9. J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. D. Vicuna, and M. Castilla, "Hierarchical control of droop-controlled ac and dc microgrids-a general approach toward standardization," IEEE Trans. Ind. Electron., Vol. 58, No. 1, pp. 158-172, Jan. 2011.
  10. A. Tuladhar, H. Jin, T. Unger, and K. Mauch, "Control of parallel inverters in distributed AC power systems with consideration of line impedance effect," IEEE Trans. Ind. Appl., Vol. 36, No. 1, pp. 131-138, Jan./Feb. 2000.
  11. F. Xu, B. Guo, Z. Xu, L. M. Tolbert, F. Wang, and B. J. Blalock, "SiC based current source rectifier paralleling and circulating current suppression," in 28th Annual IEEE Applied Power Electronics Conference and Exposition (APEC), pp. 402-409, Mar. 2013.
  12. X. Zhang, W. Zhang, J. Chen, and D. Xu, "Deadbeat control strategy of circulating currents in parallel connection system of three-phase PWM converter," IEEE Trans. Energy Convers., Vol. 29, No. 2, pp. 406-417, Jun. 2014.
  13. T. Itkonen, J. Luukko, A. Sankala, T. Laakkonen, and R. Pollanen, "Modeling and analysis of the dead-time effects in parallel PWM two-level three-phase voltage-source Inverters," IEEE Trans. Power Electron., Vol. 24, No. 11, pp. 2446-2455, Nov. 2009.
  14. J. B. Liu, H. Lin, and X. Qin, "Study on restraint of circulating current in parallel inverters system with SPWM modulation by adjusting phases of triangular carrier waves," in 2nd International Symposium on Instrumentation and Measurement, Sensor Network and Automation (IMSNA), pp. 477-480, Dec. 2013.
  15. X. Bao, F. Zhuo, B. Liu, and Y. Tian, "Suppressing switching frequency circulating current in parallel inverters with Carrier Phase-Shifted SPWM technique," in IEEE International Symposium on Industrial Electronics (ISIE), pp. 555-559, May 2012.
  16. C. Xie, Y. Wang, X. Zhong, and G. Chen, "A novel active damping method for LCL-filter-based shunt active power filter," in IEEE International Symposium on Industrial Electronics (ISIE), pp. 64-69, May 2012.
  17. D. Pan, X. Ruan, X. Wang, C. Bao, and W. Li, "Magnetic integration of an LCL filter for the single-phase grid-connected inverter," in IEEE Energy Conversion Congress and Exposition (ECCE), pp. 573-578, Sep. 2012.

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