IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 1, JANUARY 2009 139 Solid Oxide Fuel Cell Modeling Abraham Gebregergis, Member, IEEE, Pragasen Pillay, Fellow, IEEE, Debangsu Bhattacharyya, and Raghunathan Rengaswemy Abstract—This paper discusses the modeling of a solid oxide fuel cell using both lumped and distributed modeling approaches. In particular, the focus of this paper is on the development of a computationally efficient lumped-parameter model for real-time emulation and control. The performance of this model is compared with a detailed distributed model and experimental results. The fundamental relations that govern a fuel cell operation are utilized in both approaches. However, the partial pressure of the species (fuel, air, and water) in the distributed model is assumed to vary through the length of the fuel cell. The lumped model approach uses the partial pressure of the species at the exit point of the fuel cell. The partial pressure of the species is represented by an equivalent RC circuit in the lumped model. Index Terms—Fuel cells, modeling, simulation. I. I NTRODUCTION A SOLID OXIDE fuel cell (SOFC) converts chemi- cal energy into electrical energy at high temperature (800 ◦ C–1000 ◦ C), in contrast to a PEM fuel cell that op- erates at a lower temperature (80 ◦ C–100 ◦ C). The SOFC is a promising technology for distributed power generation with high efficiency and no moving parts. The transient and static model of an SOFC, which takes into account the effect of electrochemical, thermal, and mass flow, is proposed in [1]. In [2]–[4], dynamic models of SOFCs are developed for analyzing power system performance and fuel cells. A more compre- hensive mathematical model of an SOFC is conducted in [5]. It estimates the parameters for a 1-D cathode microstructure SOFC model, such as the composition and particle size. A zero- dimensional model is presented in [6] to show the limitation of the empirical assumptions derived from observation and measurements of physical process. The Butler–Volmer equation analysis for approximating the activation losses in SOFC mod- els is presented in [7]. These papers do not include a detailed analysis of all the losses in a fuel cell. A dynamic fuel cell model, which uses a similar approach to that in [2], is proposed in [8]. Reference [9] focuses only on the effect of polarization losses of an anode-supported SOFC for various cell parameters such as the geometry of the cell. A dynamic model of the SOFC, where a single cell is divided into small control volumes (CVs), is presented in [10]. It is a detailed model that accounts for both Manuscript received November 9, 2006; revised May 1, 2008. First pub- lished November 18, 2008; current version published December 30, 2008. This work was supported by NanoDynamics, Inc. A. Gebregergis and P. Pillay are with the Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY 13699-5720 USA (e-mail: natiabraham@gmail.com; pillayp@clarkson.edu). D. Bhattacharyya and R. Rengaswemy are with the Department of Chemical Engineering, Clarkson University, Potsdam, NY 13699-5707 USA (e-mail: debangsu@clarkson.edu; raghu@clarkson.edu). Digital Object Identifier 10.1109/TIE.2008.2009516 the effects of heat/mass transfer and electrochemical reactions in each CV. Detailed analyses of interconnecting a fuel cell to a grid are presented in [11]–[15]. References [11]–[14] focus on the design and control algorithms of the power conditioning system only. Reference [15] includes the fuel cell model based on empirical equations derived from experimental data of an actual fuel cell. However, the complexity and computation time associated with these models are the drawbacks for real-time emula- tion and control applications. This paper therefore focuses on a lumped-modeling approach using electrical components in PSpice and/or Matlab/Simulink for real-time applications, and parameter estimation. It also allows the study of the performance and reliability of the SOFC under various flow rates and load conditions. Moreover, the modeling takes into consideration the effects of reactant and product concentrations, polarization losses, and the effects of internal (inherent) resis- tances. Steady-state simulation results of the SOFC model were compared with experimental data to validate the model. This paper is organized as follows. Section II is a background study of fuel cell operation, in particular SOFC, followed by two modeling approaches—a distributed model incorporating detailed calculation of all phenomena and a lumped model us- ing electrical components in Section III. The simulation results and experimental data are presented in Section IV. Finally, Section V discusses the conclusions. II. SOFC OPERATION A fuel cell (SOFC) generates electrical power by contin- uously converting chemical energy of a fuel into electrical energy through an electrochemical reaction. The fuel cell itself has no moving parts, making it quiet and reliable. Fuel cells typically utilize hydrogen as the fuel and oxygen (usually from air) as the oxidant in the electrochemical reaction. It generates electricity, and its by-products are water and heat. The system has higher efficiency compared to conventional combustion engines [16], because it is not limited by Carnot efficiencies. The electrochemical reactions that occur in an SOFC that utilize fuel (hydrogen) and air (oxygen) [1]–[10] are as follows. Anode: H 2 + O 2− − > H 2 O +2e − . (1) Cathode: 1 2 O 2 +2e − > O 2− . (2) 0278-0046/$25.00 © 2008 IEEE Authorized licensed use limited to: CONCORDIA UNIVERSITY LIBRARIES. Downloaded on March 18,2010 at 09:27:28 EDT from IEEE Xplore. Restrictions apply.