Journal of Power Sources 165 (2007) 224–231 Modelling a PEM fuel cell stack with a nonlinear equivalent circuit U. Reggiani, L. Sandrolini ∗ , G.L. Giuliattini Burbui Department of Electrical Engineering, Alma Mater Studiorum, University of Bologna, Viale del Risorgimento 2, I-40136 Bologna, Italy Received 16 February 2006; received in revised form 20 June 2006; accepted 18 November 2006 Available online 16 January 2007 Abstract A nonlinear circuit model of a polymer electrolyte membrane (PEM) fuel cell stack is presented. The model allows the simulation of both steady-state and dynamic behaviour of the stack on condition that the values of some of its parameters are changed in the two operating conditions. The circuit parameters can be obtained by means of simple experimental tests and calculations. A commercial PEM fuel cell stack is modelled as seen from the power conditioning system side, without requiring parameters necessary for complex mathematical models and not easily obtainable by the majority of users. A procedure of parameter determination is developed and a comparison between the simulated and experimental results for both steady-state and dynamic behaviour of the PEM stack is shown. © 2006 Elsevier B.V. All rights reserved. Keywords: Fuel cell; Polymer electrolyte membrane; Equivalent circuit; Voltage drop; Current interrupt method; Fitting 1. Introduction Rising crude oil prices (with highs over US$ 70 a barrel dur- ing the last year) pose the exploitation of alternative energy sources as a serious challenge for the next future. Fuel cells appear one of the most appealing renewable energy technolo- gies for their low environmental impact and high conversion efficiency. Their application ranges from stationary to portable power generation, including transportation. Modelling fuel cells is then necessary to simulate the behaviour of more complex systems (e.g., electric vehicles, or electric low-power plants or cogeneration systems), in which fuel cells are integrated as source of energy. Lots of papers present mathematical models for PEM fuel cells, in which their typical application require- ments of high specific power, rapid start-up, low-temperature operation and ease of construction are met. Different load con- ditions, temperature and pressure of gases, as well as spatial dimensions of the cell [1], can thus be taken into account at the design level and simulation results can be of help in setting up operational strategies. Most of these models are however ∗ Corresponding author. Tel.: +39 051 2093484; fax: +39 051 2093588. E-mail addresses: ugo.reggiani@mail.ing.unibo.it (U. Reggiani), leonardo.sandrolini@mail.ing.unibo.it (L. Sandrolini), gianlorenzo.giuliattini@mail.ing.unibo.it (G.L. Giuliattini Burbui). extremely complex, involving many partial differential equa- tions and their boundary conditions, and need a lot of expertise in identifying and estimating their large number of parameters as detailed information on the cell is essential [2–4]. The variety of material properties to know, such as porosity, permeability, effective diffusion and charge transfer coefficients, makes these models cumbersome, and not often easily exploitable. Simplified models have also been proposed, in which the reversible volt- age and the voltage drops are summarized in simpler equations [5–7]. On the other hand, complex mathematical models can be simplified with the introduction of some empirical equations instead of partial differential equations [8,9]. These equations use fitting coefficients obtained from experimental data and are therefore related to a particular operating condition. This means that the equations may fail to predict experimental data in dif- ferent conditions. The steady-state performance of a fuel cell stack can be represented by the majority of these models, result- ing in the so called polarisation curve, that is a plot of voltage versus current density for a given set of operating conditions. Besides, the dynamic behaviour of a fuel cell stack cannot be disregarded in all those applications where mechanical, thermal or electrical quantities have fast variations [9,10]. Commercial fuel cell systems are power modules that include also auxil- iary circuitry to control subsystems for fuel and air supply, and water disposal. This paper will be focused to model a commer- cial fuel cell stack as seen from the power conditioning system 0378-7753/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jpowsour.2006.11.062