Control system design for proton exchange membrane fuel cell based on a common rail (II): Optimization and schedule scheme for the common rail

•Minimum nozzle configuration scheme decreases the number of valves in common rail.•Circular queue schedule strategy is presented to equalise workload of each valve.•Circular queue with random rotation lowers switching frequency to optimise workload.•The lifespan of the common rail increases using the proposed strategy.•Average switching frequency is accurately estimated by the stack current profile.

Conduction ratio and switching frequency are two main factors influencing the reliability and durability of high-speed solenoid valves in common rail hydrogen injection systems. Excessive conduction ratio may result in valve overheating, while the switching frequency determines the lifespan of the valve, which should be scheduled evenly for each valve. In this paper, first, a minimum nozzle configuration scheme is presented to optimise a given common rail for the minimum number of valves. Second, two strategies to equalise and optimise the workload (conduction ratio and switching frequency) of each valve are developed: 1) the circular queue schedule strategy ensures uniform workload of each valve and 2) the circular queue with random rotation schedule strategy can further decrease the switching frequency drastically by introducing randomness. Finally, both the minimum nozzle configuration scheme and the schedule strategies are elaborately analysed and verified via simulations. The circular queue with random rotation strategy with a probability of 0.99 shows superior performance.