Majed, C., Karaki, S., Jabr, R., and Panik, F., "Near Optimal Control of Fuel Cell Hybrid Electric Vehicles in Real-Time," SAE Technical Paper 2016-01-1390, 2016, doi:10.4271/2016-01-1390.
The development of an energy management system for a fuel cell hybrid electric vehicle (FCHEV) based on single step dynamic programming (SSDP) is described in this paper. The SSDP method is used to minimize a weighted cost of hydrogen and battery degradation with the latter being controlled to carry out charge-depleting (CD) as well as charge-sustaining (CS) strategies with simple lower bound enforcement or relaxation. The problem formulation accounts for the power balance at each stage, the fuel cell and battery power limits, the battery state-of-charge limits, and the ramp-rates constraints of the fuel cell and battery. Its chief advantage over forward dynamic programming (DP) or other formal optimization methods is that it does not require the speed forecast of the whole drive cycle but requires only a one-step-ahead speed forecast. As such it can readily be implemented in real-time to do a “near optimal” scheduling of the battery and fuel cell under CS or CD strategies without revising any rule base or program code. This paper will investigate the operational characteristics of the SSDP and will propose procedures to set the battery cost parameter which is theoretically the incremental cost of the fuel cell at average demand. In this work, the battery cost parameter is calculated based on a moving average method that calculates the average demand over a number of the previous observed demands. The paper also uses the same procedure as that of the DP to relax or tighten the battery state-of-charge lower bound in order to allow operation in CS or CD strategies. The results obtained by the SSDP method will be compared to those obtained by the DP in terms of fuel utilization and battery degradation over the Highway Fuel Economy Driving Schedule (HWFET) and the Urban Dynamometer Driving Schedule (UDDS) for different car designs.