Stability Analysis and Improvement of the Capacitor Current Active Damping of the LCL Filters in Grid-Connected Applications

- Journal title : Journal of Power Electronics
- Volume 16, Issue 4, 2016, pp.1565-1577
- Publisher : The Korean Institute of Power Electronics
- DOI : 10.6113/JPE.2016.16.4.1565

Title & Authors

Stability Analysis and Improvement of the Capacitor Current Active Damping of the LCL Filters in Grid-Connected Applications

Xu, Jinming; Xie, Shaojun; Zhang, Binfeng;

Xu, Jinming; Xie, Shaojun; Zhang, Binfeng;

Abstract

For grid-connected LCL-filtered inverters, dual-loop current control with an inner-loop active damping (AD) based on capacitor current feedback is generally used for the sake of current quality. However, existing studies on capacitor current feedback AD with a control delay do not reveal the mathematical relation among the dual-loop stability, capacitor current feedback factor, delay time and LCL parameters. The robustness was not investigated through mathematical derivations. Thus, this paper aims to provide a systematic study of dual-loop current control in a digitally-controlled inverter. At first, the stable region of the inner-loop AD is derived. Then, the dual-loop stability and robustness are analyzed by mathematical derivations when the inner-loop AD is stable and unstable. Robust design principles for the inner-loop AD feedback factor and the outer-loop current controller are derived. Most importantly, ensuring the stability of the inner-loop AD is critical for achieving high robustness against a large grid impedance. Then, several improved approaches are proposed and synthesized. The limitations and benefits of all of the approaches are identified to help engineers apply capacitor current feedback AD in practice.

Keywords

Active damping;Capacitor current feedback;Control delay;LCL filter;Stability;

Language

English

Cited by

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References

1.

J. Dannehl, C. Wessels, and F. Fuchs, “Limitations of voltage-oriented pi current control of grid-connected PWM rectifiers with LCL filters,” IEEE Trans. Ind. Electron., Vol. 56, No. 2, pp. 380-388, Feb. 2009.

2.

X. Guo, X. You, X. Li, R. Hao, and D. Wang, “Design method for the LCL filters of three-phase voltage source PWM rectifiers,” Journal of Power Electronics, Vol. 12, No. 4, pp. 559-566, Jul. 2012.

3.

F. Liu, Y. Zhou, S. Duan, J. Yin, B. Liu, and F. Liu, “Parameter design of a two-current-loop controller used in a grid-connected inverter system with LCL filter,” IEEE Trans. Power Electron., Vol. 56, No. 11, pp. 4483-4491, Nov. 2009.

4.

Y. Tang, P. C. Loh, P. Wang, F. H. Choo, F. Gao, and F. Blaabjerg, “Generalized design of high performance shunt active power filter with output LCL filter,” IEEE Trans. Ind. Electron., Vol. 59, No. 3, pp. 1443-1452, Mar. 2012.

5.

J. Xu, S. Xie, and T. Tang, “Evaluations of current control in weak grid case for grid-connected LCL-filtered inverter,” IET Power Electron., Vol. 6, No. 2, pp. 227-234, Feb. 2013.

6.

Y. Han, P. Shen, and J. M. Guerrero, “Stationary frame current control evaluations for three-phase grid-connected inverters with PVR-based active damped LCL filters,” Journal of Power Electronics, Vol. 16, No. 1, pp. 297-309, Jan. 2016.

7.

J.B. Kwon, S.J. Yoon, and S. Choi, “Indirect current control for seamless transfer of three-phase utility interactive inverters,” IEEE Trans. Power Electron., Vol. 27, No. 2, pp. 773-781, Feb. 2012.

8.

M. Malinowski and S. Bernet, “A simple voltage sensorless active damping scheme for three-phase PWM converters with an LCL filter,” IEEE Trans. Ind. Electron., Vol. 55, No. 4, pp. 1876-1880, Apr. 2008.

9.

J. Xu, S. Xie, and T. Tang, “Active damping-based control for grid-connected LCL-filtered inverter with injected grid current feedback only,” IEEE Trans. Ind. Electron., Vol.61, No.9, pp. 4746-4758, Sep. 2014.

10.

X Wang, F. Blaabjerg, and P. Loh, “Grid-current-feedback active damping for LCL resonance in grid-connected voltage source converters,” IEEE Trans. Power Electron., Vol. 31, No. 1, pp. 213-223, Jan. 2016.

11.

L. A. Maccari Jr., J. R. Massing, L. Schuch, C. Rech, H. Pinheiro, R. C. L. F. Oliveira, and V. F. Montagner, “LMI-based control for grid-connected converters with LCL filters under uncertain parameters,” IEEE Trans. Power Electron., Vol. 29, No. 7, pp. 3776-3785, Jul, 2014.

12.

J. Xu, S. Xie, and T. Tang, “Systematic current control strategy with pole assignment for grid-connected LCL-filtered inverters,” Journal of Power Electronics, Vol. 13, No. 3, pp. 447-257, May 2013.

13.

J. Dannehl, F. W. Fuchs, S. Hansen, and P. B. Thøgersen, “Investigation of active damping approaches for PI-based current control of grid-connected pulse width modulation converters with LCL filters,” IEEE Trans. Ind. Appl., Vol. 46, No. 4, pp. 1509-1517, Jul./Aug. 2010.

14.

D. Pan, X. Ruan, C. Bao, W. Li, and X. Wang, “Capacitor-current-feedback active damping with reduced computation delay for improving robustness of LCL-type grid-connected inverter,” IEEE Trans. Power Electron., Vol. 29, No. 7, pp. 3414-3427, Jul. 2014.

15.

J. Xu, S. Xie, J. Kan, and B. Zhang, "Research on stability of grid-connected LCL-filtered inverter with capacitor current feedback active damping control," in Proc. ICPE-ECCE Asia, pp. 682-687, 2015.

16.

M. Orellana and R. Grino, "On the stability of discrete-time active damping methods for VSI converters with a LCL input filter," in Proc. IEEE IECON, pp.2378-2383, 2012.

17.

X. Li, X. Wu, Y. Geng, X. Yuan, C. Xia, and X. Zhang, “Wide damping region for LCL-type grid-connected inverter with an improved capacitor-current-feedback method,” IEEE Trans. Power Electron., Vol. 30, No. 9, pp. 5247-5259, Sep. 2015.

18.

R. Li, B. Liu, S. Duan, C. Zou, and L. Jiang, “Analysis and suppression of alias in digitally controlled inverters,” IEEE Trans. Ind. Informat., Vol. 10, No. 1, pp. 655-665, Feb. 2014.

19.

D. Yang, X. Ruan, and H. Wu, “A real-time computation method with dual sampling modes to improve the current control performances of the LCL-type grid-connected inverter,” IEEE Trans. Ind. Electron., Vol. 62, No. 7, pp. 4563-4572, Jul. 2015.

20.

Z. Zou, Z. Wang, and M. Cheng, “Modeling, analysis, and design of multifunction grid-interfaced inverters with output LCL filter,” IEEE Trans. Power Electron., Vol. 29, No. 7, pp. 3830-3839, Jul. 2014.

21.

M. Wagner, T. Barth, R. Alvarez, C. Ditmanson, and S. Bernet, “Discrete-time active damping of LCL-resonance by proportional capacitor current feedback,” IEEE Trans. Ind. Appl., Vol. 50, No. 6, pp. 3911-3920, Nov./Dec. 2014.

22.

W. Lu, N. Zhao, J. Wu, A. El Aroudi, and L. Zhou, “Filterbased perturbation control of low-frequency oscillation in voltage-mode H-bridge DC/AC inverter,” Int. J. Circ. Theor. Appl., Vol. 43, No.7, pp. 866-874, July 2015.

23.

B. Lei, G. Xiao, X. Wu, Y. Kafle and L. Zheng, “Bifurcation analysis in a digitally controlled H-bridge grid-connected inverter,” Int. J. Bifurcat. Chaos, Vol. 24, No. 1, pp. 1-15, Jan. 2014.

24.

X. Wu, G. Xiao, and B. Lei, “Simplified discrete-time modeling for convenient stability prediction and digital control design,” IEEE Trans. Power Electron., Vol. 28, No. 11, pp. 5333-5342, Nov. 2013.

25.

B. Lei, G. Xiao, X. Wu, and L. Zheng, “A unified “scalar” discrete-time model for enhancing bifurcation prediction in digitally controlled H-bridge grid-connected inverter,” Int. J. Bifurcat. Chaos, Vol. 23, No. 7, pp. 1-17, Jul. 2013.

26.

S. Yang, Q. Lei, F. Z. Peng, and Z. Qian, “A robust control scheme for grid-connected voltage-source inverters,” IEEE Trans. Ind. Electron., Vol. 58, No. 1, pp. 202-212, Jan. 2011.

27.

D. Pan, X. Ruan, and C. Bao, “Optimized controller design for LCL-Type grid-connected inverter to achieve high robustness against grid-impedance variation,” IEEE Trans. Ind. Electron., Vol. 62, No. 3, pp. 1537-1547, Mar. 2015.

28.

J. Xu, S. Xie, and T. Tang, “Improved control strategy with grid-voltage feedforward for LCL-filter-based inverter connected to weak grid,” IET Power Electron., Vol. 7, No. 10, pp. 2660-2671, Oct. 2014.

29.

P. Alemi, S.-Y. Jeong, and D.-C. Lee, “Active damping of LLCL filters using PR control for grid-connected threelevel T-type converters,” Journal of Power Electronics, Vol. 15, No. 3, pp.786-795, May 2015.

30.

J.M. Guerrero, M. Leetmaa, F. Briz, A. Zamarron, and R.D. Lorenz, “Inverter nonlinearity effects in high-frequency signal-injection-based sensorless control methods,” IEEE Trans. Ind. Appl., Vol. 41, No. 2, pp. 618-626, Mar./Apr. 2005.