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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 487596, 17 pages
Research Article

Singular Perturbation Theory-Based Qualitative Dynamics Investigation of Flywheel Energy Storage System in Discharge Mode

1Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China
2School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Received 16 January 2014; Accepted 5 June 2014; Published 3 August 2014

Academic Editor: H. D. Chiang

Copyright © 2014 Weiya Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An investigation on qualitative dynamics in a voltage-current dual-loop controlled flywheel energy storage system (FESS) operating in discharge mode is presented in this paper, providing novel insights into the effect of two-timescale characteristics on the safety and stability of energy transmission of FESS. Based on singular perturbation theory, a two-timescale approach is proposed to separate the FESS into the fast and slow subsystems. Stability analysis of the transient fixed points confirms the effects of systemic parameters on FESS’s dynamics and indicates that the FESS shifts from the spiking state to the quiescent state when the slow variable crosses the bifurcation point of the fast subsystem. Mechanism analysis reveals that the root cause of the qualitative dynamics is the voltage instability of the FESS. Moreover, the feasibility boundaries of key parameters are derived, and application requirements of the proposed approach are also discussed, guiding the extension of the approach to engineering applications and solving the dynamics analysis problem to some extent at a theoretical analysis level. Constant voltage discharge experiment is performed based on the FESS test bench built in Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, which validates the theoretical results.