Karaki, S., Jabr, R., Chedid, R., and Panik, F., "Optimal Energy Management of Hybrid Fuel Cell Electric Vehicles," SAE Technical Paper 2015-01-1359, 2015, doi:10.4271/2015-01-1359.
An optimal energy management system is presented to minimize hydrogen utilization over driving cycles using forward dynamic programming (FDP). The objective is to minimize the cost of hydrogen with the battery cost being used as a parameter to carry out charge-depleting as well as charge-sustaining strategies along with bound enforcement or relaxation. The problem formulation accounts for the power balance at each stage, the power limits, the state-of-charge limits, and the ramp rates constraints of the fuel cell and battery. FDP is selected because it can easily cater for non-linearity in system cost and constraints. It employs heuristic rules to limit the number of states at each stage and is shown to be a very fast algorithm using simple computations and thus may easily lend itself for real-time implementation. Charge sustained operation is obtained by enforcement of the lower bound on the SOC, and charge depletion operation is obtained by lowering the bound to the required depletion level. In both cases a battery cost parameter is set to a value lower than the incremental cost of the fuel cell calculated at the average load of the car for the given drive cycle. Verification of the code is provided by comparing it to results obtained using quadratic programming. Results on practical vehicle designs proposed in the literature are presented for the UDDS and HWFET standard driving cycles.