Journal of Power Sources 134 (2004) 41–48 A new approach to empirical electrical modelling of a fuel cell, an electrolyser or a regenerative fuel cell S. Busquet ∗ , C.E. Hubert, J. Labbé, D. Mayer, R. Metkemeijer CENERG/E.N.S.M.P., Rue Claude Daunesse, Les Lucioles-BP 207, Sophia Antipolis Cedex 06904, France Received 27 May 2003; received in revised form 11 February 2004; accepted 16 February 2004 Available online 1 Jun 2004 Abstract In terms of fuel cell steady-state performance modelling, many electrical models have been developed either from a theoretical point of view or from an empirical point of view. The model described in this article is from the empirical point of view approach. This model enables to simulate both fuel cells and electrolysers V–J curves (cell voltage versus current density) in typical conditions. This model is particularly adapted to regenerative fuel cell (RFC) simulation. It is a four degree-of-freedom model and it is convergent near zero current. It depends on the stack temperature and the oxygen partial pressure. The regions where mass transfer limitations occur have not been modelled, because they are usually avoided for efficiency or thermal reasons. The parameters have been fitted with a 4kW e proton exchange membrane fuel cell (PEMFC) and a 3.6 kW e electrolyser. The electrical equations and the experimental data are well correlated. © 2004 Elsevier B.V. All rights reserved. Keywords: Fuel cell; Electrolyser; Regenerative fuel cell; Empirical model; Convergence 1. Introduction The Centre d’Energétique of Ecole des Mines de Paris at Sophia Antipolis has gained experience in fuel cell (FC) studies for 10 years, and particularly in proton exchange membrane fuel cell (PEMFC). Since the development of the first fuel cell stack test bench, many works have been achieved in terms of fuel cell integration, hydrogen genera- tion or storage and fuel cell modelling. For testing purposes, a dedicated fuel cell stack test bench is available, capable of testing fuel cells up to 15 kW e in various system configura- tions. The laboratory is also doing research concerning hybrid systems made up of a renewable energy generator (photo- voltaic field or PV), a back-up unit (diesel engine) and a storage system (batteries, fuel cell/gas storage/electrolyser). For these projects two test facilities have been set up. The first one is a PV–battery–diesel test bench and the second one is a PV–electrolyser-fuel cell test bench. This latter, constructed within the frame of the PVFC-SYS European project (ERK5-CT1999-00017) is an autonomous electricity generator including a PV field (3.6 kWp), an elec- trolyser (3.6 kW) splitting water into hydrogen and oxygen, ∗ Corresponding author. Tel.: +33-4-93-95-74-90; fax: +33-4-95-75-35. E-mail address: severine.busquet@ensmp.fr (S. Busquet). a gas storage unit (4 Nm 3 of H 2 and 2 Nm 3 of O 2 ) and a PEMFC (4 kW e ) to generate electricity during low sun shine periods. This test bench, described in different articles [1–3] en- ables us to validate the model of each component and finally of the complete system. Different approaches exist to simulate the electrical char- acteristics of a FC. There are roughly two kinds of fuel cell models. The first one is the theoretical model (also named mecha- nistic model), which describes the electrochemical reactions occurring in the cells. In the model of Metkemeijer [4], the cell voltage is the thermodynamical voltage, minus the dif- ferent overvoltages due to the ionic transfers at the anode and at the cathode, the resistive losses and the material transfer at high current density. Each term of the equation depends on the stack temperature and the partial pressure of hydro- gen and oxygen. This approach requires the knowledge of nine parameters, which are difficult to determine. The model of Amphlett [5], which is largely quoted in the literature, is also based on Nernst and Tafel equations. It considers all physical parameters in the system (effective pressure of oxygen and hydrogen, temperature, concentra- tion of oxygen, hydrogen, water, proton). Since all these parameters cannot be identified, the authors use empirical means to estimate their values [6]. 0378-7753/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jpowsour.2004.02.018