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As part of a system model, a PEM fuel cell stack model is presented for functional tests and pre-calibration of control units on hardware-in-the-loop (HiL) test benches. From the basic idea to couple a 1-D membrane model with a spatially distributed abstraction of the gas channel, a real-time capable 1-D+1-D PEM FC stack model is constructed. Fundament for the HiL usage is an explicit formulation of the commonly implicit model equations. With that, not only calculation time can be reduced, but also model accuracy is preserved. A validation using test bench data emphasizes the accuracy of the model. Finally, a runtime and eigenvalue analysis of the stack model proves the real-time capability.

An optimal design methodology is developed in this paper for fuel cell hybrid electric vehicles (FCHEV) based on ordinal optimization (OO) and dynamic programming (DP); the optimal design aims to determine the appropriate sizes of the hydrogen tank, fuel cell, battery, and motor for the purpose of minimizing investment and operational cost given some specification of the car range, the road type and its gradeability. The DP simulates the operation of the vehicle for a set of specified components' sizes for given driving cycles and provides the total vehicle cost per year. The OO method offers an efficient approach for optimization by focusing on ranking and selecting a finite set of “good enough” alternatives through two models: a simple model and an accurate model. The OO program uses the specified sizes of the components that uniformly sample the search space and evaluates these designs using a simple but fast model.

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.