IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 24, NO. 1, MARCH 2009 283 Modeling and Dynamic Characteristic Simulation of a Proton Exchange Membrane Fuel Cell J. Jia, Member, IEEE, Q. Li, Y. Wang, Senior Member, IEEE, Y. T. Cham, Senior Member, IEEE, and M. Han Abstract—In order to investigate the output characteristic of a proton exchange membrane fuel cell (PEMFC) based on the elec- trical empirical model, a novel dynamic model of the PEMFC has been developed with MATLAB/Simulink, which is distinct from the models that have been published previously. By using a fuel cell test system of the Fuel Cell Application Centre (FAC) at Temasek Polytechnic, the transient electrical responses of PEMFC were con- ducted and analyzed under various operating conditions. A good match is found between simulation results and experimental data. The comprehensive results of simulation manifested that the model is effective and operational. This model will be very useful to op- timize the structure design, improve the operation performance, and develop the real-time control system of PEMFC. Index Terms—Dynamic model, dynamic simulation, proton ex- change membrane fuel cell (PEMFC), transient electrical response. NOMENCLATURE A Activation area of the membrane. B Constant determined by the proton ex- change membrane fuel cell (PEMFC) and its working status. C Equivalent capacitance. C H + Liquid phase concentration of H + . C H 2 Liquid phase concentration of hydrogen. C H 2 O Liquid phase concentration of water. C O 2 Dissolved oxygen concentration in the in- terface of the cathode catalyst. E Nernst Thermodynamic potential. F Faraday’s constant. ΔG Gibbs free energy change. ΔG c Gibbs free energy change of the chemical sorption under standard status. i Current of the equivalent circuit. i C Current of the equivalent capacitance C. J Current density. J max Maximum current density. K 0 a Inherent velocity constant of anode reaction. Manuscript received January 4, 2008; revised August 8, 2008. First published January 27, 2009; current version published February 19, 2009. Paper no. TEC-00508-2007. J. Jia and Y. Wang are with the School of Electrical and Electronic Engineer- ing, Nanyang Technological University, Singapore 639798, Singapore (e-mail: jiajunbo@tp.edu.sg; eyywang@ntu.edu.sg). Q. Li is with the School of Electrical Engineering, Southwest Jiaotong Uni- versity, Chengdu 610031, China (e-mail: liqi0800@gmail.com). Y. T. Cham and M. Han are with the School of Engineering, Temasek Polytechnic, Singapore 529757, Singapore (e-mail: chamyt@tp.edu.sg; minghan@tp.edu.sg). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEC.2008.2011837 K 0 c Inherent velocity constant of cathode reaction. l Thickness of the membrane. N Number of cells. P consumed Power consumed by stack. P H 2 Effective partial pressure of hydrogen. P O 2 Effective partial pressure of oxygen. P stack Output power of stack. r M Resistivity of Nafion series proton ex- change membrane. R Gaseous constant. R a Equivalent resistance. R act Activation equivalent resistance. R c Contact resistances both between the mem- brane and electrodes as well as the elec- trodes and the bipolar plates. R con Concentration equivalent resistance. R M Equivalent membrane impedance. R total Equivalent resistance of fuel cell stack. ΔS Standard mole entropy change. t Time in seconds. T Temperature in Kelvin. T ref Reference temperature. ν d Overall voltage drop across R a . V act Activation losses. V con Concentration losses. V ohmic Ohmic losses. V stack Output voltage of stack. α c Activation coefficient. λ Water content of the membrane. τ Time constant of the equivalent circuit. ξ i (i =1,..., 4) Model coefficients obtained by exper- imental data fitting based on electro- chemistry, thermodynamics, and fluid mechanics. I. INTRODUCTION W ITH the world facing the global warming problem, fuel cells are one of the promising energy technologies for sustainable future due to their high energy efficiency and en- vironment friendliness. Compared with the other types of fuel cells, a proton exchange membrane fuel cell (PEMFC) shows promising results with its advantages such as low temperature, high power density, fast response, and zero emission if it is run with pure hydrogen, and it is suitable for use in portable power supply, vehicles, and residential and distributed power plants. For a better understanding of the characteristics and evalua- tion of the performance of PEMFCs, and therefore, optimization 0885-8969/$25.00 © 2009 IEEE