Closed-Form Expression to Estimate the Hydrogen Consumption of a Fuel Cell Hybrid Electric Vehicle

Optimizing the design of hybrid powertrains requires co-optimizing their plant and their control, and the complexity of combining a static and a time-varying problem naturally leads to methodologies that optimize both levels in a nested configuration. As an alternative, a method to estimate the fuel consumption over a driving cycle with a closed-form expression is available in the literature, the Fully-Analytical Fuel Consumption Estimation (FACE), reducing the co-optimization to a uni-level problem. This approach was also expanded to Fuel Cell Hybrid Electric Vehicles (FCHEV) by introducing theory-based models for the fuel cell system and the electric components, since the latter were oversimplified in the first FACE implementation. However, the resulting expressions were difficult to handle, and the component operating constraints were ignored. This article addresses the problems identified in the first implementation of FACE for FCHEVs, using the 2020 Toyota Mirai as a reference architecture. Simplified models of the powertrain components are introduced, and the steps required for development of a single closed-form expression for the hydrogen consumption are explained. The models are fitted and validated with experimental data obtained with a real vehicle on a roller test bench. The results show that the final model adequately estimates the hydrogen consumption over 5 different homologation cycles in both cold and hot starting conditions, with an overall error RMS of less than four percent.