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Chin. Phys. B, 2013, Vol. 22(9): 098401    DOI: 10.1088/1674-1056/22/9/098401

Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode

Zhang Wei-Ya (张玮亚), Li Yong-Li (李永丽), Chang Xiao-Yong (常晓勇), Wang Nan (王楠)
Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China; School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China
Abstract  In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system (FESS) with a permanent magnet (PM) brushless direct-current (DC) motor (BLDCM) is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments.
Keywords:  flywheel energy storage system      Hopf bifurcation mechanism      Routh stability criterion      parameter stability regions  
Received:  20 February 2013      Revised:  21 March 2013      Accepted manuscript online: 
PACS:  84.50.+d (Electric motors)  
  84.60.Ve (Energy storage systems, including capacitor banks)  
  05.45.-a (Nonlinear dynamics and chaos)  
Fund: Project supported by the National Basic Research Program of China (Grant No. 2009CB2197), the National Natural Science Foundation of China (Grant No. 51177108), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110032110066).
Corresponding Authors:  Zhang Wei-Ya     E-mail:

Cite this article: 

Zhang Wei-Ya (张玮亚), Li Yong-Li (李永丽), Chang Xiao-Yong (常晓勇), Wang Nan (王楠) Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode 2013 Chin. Phys. B 22 098401

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