A scalable, causal, adaptive energy management strategy based on optimal control theory for a fuel cell hybrid railway vehicle

A scalable, causal, adaptive optimal control-based energy management strategy for the fuel cell hybrid train is designed. As learned from the results of offline Pontryagin's minimum principle (PMP)-based strategies, the convexity of the specific consumption curve is emphasized to improve the fuel economy. More important is that the dependency of the co-state on the state of charge (SoC) of batteries and the average fuel cell power is identified the first time. With the help of using the optimal control theory in a reverse way, a quantitative analytical formula is derived to determine the co-state based on the SoC and the average fuel cell power. The accuracy of the estimates, and the effectiveness of this strategy, under different weather, driving, and aging conditions, is validated by comparison to the results of offline PMP-based strategies. Thereby, a maximal deviation of the co-state average value compared to the offline results is 1.8%. An excellent fuel economy under a typical driving cycle of regional railway transports in Berlin, with only 0.03% more consumption for both summer and winter conditions, compared to the results of offline PMP, is resulted. Due to the model-based characteristics, the strategy can be scaled or transferred to other configuration systems or driving conditions without the loss of effectiveness.