Offline optimal energy management strategies considering high dynamics in batteries and constraints on fuel cell system power rate: From analytical derivation to validation on test bench

For a fuel cell hybrid train, offline optimal energy management strategies using the Pontryagin's minimum principle and dynamic programming are developed and presented in this contribution. The dynamics in the voltages over various parallel resistance-capacitor branches in the batteries are considered. In addition, dynamic limitation of the fuel cell power is taken into account by choosing the fuel cell power rate as the control variable instead of the fuel cell power, as found so far in all literature with related topics. The correctness of the Pontryagin's minimum principle and the dynamic programming-based strategies are mutually validated. The corresponding results provide more precise references than the offline strategies without the resistance-capacitor branches in batteries taken into account. A damping factor is then introduced into the cost function to reduce unnecessary high dynamic oscillations of the operating points of the fuel cell system without compromising fuel economy. Finally, the results of the offline strategies are validated with measurements on the test bench at the Center for Mobile Propulsion of the RWTH Aachen University. Only a difference of 0.15% was determined between the measured and the offline calculated hydrogen consumption.

Automated summary

This contribution introduces offline optimal energy management strategies for a fuel cell hybrid train, taking into account dynamics in batteries and introducing a damping factor to reduce unnecessary oscillations. The strategies, based on Pontryagin's minimum principle and dynamic programming, have been mutually validated for correctness and provide more precise references. Validation with measurements showed only a 0.15% difference in hydrogen consumption between calculated and measured values.