Thermal-physical modeling and parameter identification method for dynamic model with unmeasurable state in 10-kW scale proton exchange membrane fuel cell system

Abstract

For proton exchange membrane fuel cell, the accurate physical modeling, involving dynamic modeling and parameter identification, plays a significant role in simulation and control. The literature presents many optimization algorithms, for instance, gradient-based and metaheuristic method, to identify the parameters of the steady-state model, whereas lack of an effective way to carry out the identification for the dynamic model with unmeasurable states, which is very typical for the control issue. This paper handles these issues for the thermal dynamic model at a 10 kW fuel cell system. It is the first time that the identification, for the dynamic temperature model with two states and one of it unmeasurable, is proposed using step integration with continued fractions to obtain the theoretical value and using the p-dimensional extremum seeking via simplex tuning to optimize the mean square error between the theoretical and sampled value. The fitness between the theoretical and real value reaches 0.89 for stack inlet temperature and 0.90 for outlet temperature. It makes more sense that the identified parameters are within their typical value range. In addition, the method-empowered model obtains good validation in the full power range, from 1.2 kW to 7.2 kW. Through the comparison with traditional gradient-based optimization method, genetic algorithm, differential evolution method, and particle swarm optimization method, the method proposed in this paper features much lower calculation cost and higher fit accuracy. The accuracy of the newly proposed dynamic thermal model, considering the real fuel cell thermal transfer behavior, is improved from 0.54 to 0.89. The method is a promising way to the simulation of inner mass transfer, water content estimation, and especially for the controller design.