Journal of Power Sources 152 (2005) 210–217 Short communication Electrical coupling in proton exchange membrane fuel cell stacks  G.-S. Kim a , J. St-Pierre a, ∗ , K. Promislow b , B. Wetton c a Ballard Power Systems, Inc., 4343 North Fraser Way, Burnaby, BC V5J 5J9, Canada b Michigan State University, Department of Mathematics, East Lansing, MI 48824, USA c University of British Columbia, Department of Mathematics, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada Received 27 January 2005; accepted 27 January 2005 Available online 9 March 2005 Abstract Stack models require consideration of interactions between cells owing to practical variation of cell model parameters and different location/environment in the stack leading to thermal, electrical and mass transfer gradients. A previously developed voltage/current distribution model (electrical interaction) was extended and validated using two types of anomalies (bus plate material change, partially inactive cell located at the stack center), two anomaly locations and one or two anomalies within the stack. A measurement method for the principal cell interaction damping factor is discussed which can be used to easily and approximately predict the number of cells that are impacted by an anomaly. © 2005 Elsevier B.V. All rights reserved. Keywords: Polymer electrolyte fuel cell; Stack; Model; Voltage/current distribution; Cell anomaly 1. Introduction The development of proton exchange membrane fuel cells for automotive, stationary and portable electrical power has received considerable attention in recent years. Computa- tional design tools have kept pace with these advances, rang- ing from simple algebraic equations to fully coupled mass and thermal transport in three dimensions [1]. These models strive to describe all significant processes affecting the per- formance of a unit cell including electrical/electrochemical phenomena, which offer significant cost savings in terms of testing and design cycle time. Fuel cells generally comprise an assembly of single cells. These single cells are not identical from a manufacturing standpoint or have a different location/environment in the stack which can lead to performance inequalities during op- eration resulting in thermal, electrical (via shared bipolar plates) and mass transfer gradients between cells, and there-  This paper was presented at the 2004 Fuel Cell Seminar, San Antonio, TX, USA. ∗ Corresponding author. Tel.: +1 604 412 3186; fax: +1 604 453 3782. E-mail address: jean.st-pierre@ballard.com (J. St-Pierre). fore in cell interactions or coupling. This terminology is pre- ferred, for example, over the more common term of cur- rent/voltage distribution to emphasize the potential ‘infec- tion’ of healthy cells located near an anomalous cell. Cell interaction is an important model feature, for example, to define manufacturing tolerances for cell components, to ac- curately predict stack behavior or to assess series reliability. Most fuel cell stack models do not completely address in- teractions between cells and little information is available. From this standpoint, reactant flow distribution was briefly discussed [2] and, a stack model including temperature and prescribed reactant flow distributions was derived for a solid oxide fuel cell [3]. A first attempt was made to evaluate the character and im- portance of these effects for thermal interactions in proton exchange membrane fuel cells with particular emphasis on simplicity to achieve rapid computational convergence [4,5]. More recently, a similar electrical interaction model was de- veloped for the same application including an efficient nu- merical method to solve the nonlinear coupled system [6,7]. Validation of the full model and an asymptotic solution are presented here. The unit cells are described by simple, steady- state, 1 + 1-dimensional models appropriate for straight reac- 0378-7753/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jpowsour.2005.01.029