In this paper, an adaptive parallel charging system is designed for energy-storage urban rail vehicles. The main circuit of the charging system is chosen with two parallel buck converters. The state space model of the charging system is derived with averaging method. Then an adaptive model-free extremum seeking charging controller is designed. Different from existing model-based charging methods, the proposed strategy calls for no knowledge of urban rail vehicles and hence has a wider range of applications. We further show that the proposed charging method can suppress the current imbalance between two parallel buck converters efficiently. The effectiveness of the proposed charging strategy is proved with rigorous theoretical analysis. Moreover, experiment results from a prototype parallel charging system verify the theoretical analysis.
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