Available online at www.sciencedirect.com Journal of Power Sources 175 (2008) 773–778 Short communication Surrogate model for proton exchange membrane fuel cell (PEMFC) R. Tirnovan, S. Giurgea ∗ , A. Miraoui, M. Cirrincione Institut FC LAB, UTBM Laboratory, University of Technology of Belfort-Montb´ eliard (UTBM), Thierry Mieg 90010, Belfort Cedex, France Received 22 June 2007; received in revised form 20 September 2007; accepted 23 September 2007 Available online 5 October 2007 Abstract The main goal of this work is to realize a PEMFC model that can be used efficiently for the global modelling of the fuel cell system. The modelling method proposed in the paper is an approach from an empirical point of view that allows a PEMFC model of “black-box” class to be developed. Moving least squares (MLS) have therefore been employed to approximate the cell voltage characteristics V, using an experimental dataset measured in determinate conditions. The MLS approach appears to present a good balance of response surface accuracy, smoothness, robustness, and ease of use. This kind of numerical model offers good perspectives for the systems identification, the simulation of the systems, the design and the optimization of process control, etc. The results prove that the method is suitable for predicting and describing the fuel cell behaviour in all the points of the approximation domain. The proposed model can be included in a numerical application to optimize the operation of an existing fuel cell system. © 2007 Elsevier B.V. All rights reserved. Keywords: Fuel cell; Moving least squares; Surrogate model; Performance; Prediction 1. Introduction Fuel cells power generating systems represent a solution to replace traditional distributed power sources because of their high efficiency, clean operation and multiple applications (trans- port, residential, portable) [1,2]. Fuel cell based power plants are currently under rapid development and first plants are expected by the next few years with size ranging from 20 to 250 kW, up to 1 MW [2]. In particular, proton exchange membrane fuel cells (PEMFC) are most suitable for automotive applications because of their low operation temperature, providing a fast start-up, and high power density. The design and analysis of a complete fuel cell system demand the correct modelling of the fuel cell stack and of the other sub-systems around. Over the last 17 years, many PEMFC models, either theo- retical or empirical, from simple zero-dimensional to complex three-dimensional models, have been developed (analytical models, mechanistic models, semi-empirical and empirical models). There are several papers which review some of the work about PEMFC modelling, for example [3,4]. Semi-empirical approaches combine theoretically derived differential and alge- ∗ Corresponding author. Tel.: +33 384 58 36 40; fax: +33 384 58 34 13. E-mail address: stefan.giurgea@utbm.fr (S. Giurgea). braic equations with empirically determined relationships [5–9]. The empirical approaches develop algebraic models based on experimental datasets. They describe the performance of a true system working in given conditions. Such models can be based on analytical expressions [10] or they can be described by pure numerical approaches. The main goal of this work is to realize a PEMFC model that can be used efficiently for the global modelling of the fuel cell system. The modelling method proposed in the paper is an approach from an empirical point of view that allows PEMFC model of “black-box” class to be developed. The MLS approx- imation method is the core of the proposed method. The MLS method is widely used in meshless methods but it has been suc- cessfully applied for response surface generation in the context of optimization [11]. The MLS algorithm uses an experimental dataset, cell voltage versus current density, measured in determi- nate experimental conditions (pure hydrogen fuel, air as oxidant, cell temperature, pressure, membrane humidity, reactants stoi- chiometry), in order to create the PEMFC numeric model. Such numerical models are extensively employed in various areas of the science and of the technology offering good perspectives in the systems identification, the simulation of the systems, the design and the optimization of process control, etc. The proposed model can be included in a numerical application to optimize the operation of an existing fuel cell system. 0378-7753/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jpowsour.2007.09.097