IEEE Transactions on Energy Conversion, Vol. 14, No. 3, September 1999

149

Transient Modeling and Simulation of a Tubular Solid Oxide Fuel CellDavid J. Hall, Senior Member, IEEE Westinghouse Science and Technology Center Pittsburgh, PA 15235 USAAbstract: This paper describes the development of a computer model for simulating the transient operation of a tubular solid oxide fuel cell (SOFC). model includes the electrochemical, thermal, The and mass flow elements that affect SOFC electrical output. The electrochemical and thermal parts of the model were developed and verified separately before they were combined to form the transientmodel. The results of model verification tests are presented. Transient simulations were conducted with constant reactant flows and constant inlet temperatures. The transient electrical response of the cell to a load change is described.

R.Gerald Colclaser, Fellow, IEEEDepartment of Electrical Engineering University of Pittsburgh Pittsburgh, PA 15261 USA terminal voltage. Changes in the load circuit or its demand for power change the operating conditions for the SOFC. For example, an increased demand for power out of the SOFC must eventually be met with increased flow of reactants. Changing mass flows change the SOFC temperature and electrochemical processes. Models to predict the transient response and operation of SOFCs in electrical circuits need to be developed to determine how such devices may be controlled. The models should include the electrochemical, thermal, and mass flow aspects of fuel cell operation that affect the output power produced. The results from detailed single cell models can be used in more general SOFC system models that in turn can be used in electrical power system models. This paper describes the development of a transient model for a tubular Solid Oxide Fuel Cell. The theory and solution techniques are summarized and examples of the computation results are presented. More detailed information is found in [Ill.

Keywords: Computer Program, Energy, Fuel Cells, High Temperature, Modeling, Simulation, Solid Oxide, Transient, Tubular

I. INTRODUCTION

Solid Oxide Fuel Cells (SOFCs) are a highly efficient, environmentally benign method of electric power production. SOFC systems have been proposed for electric utility power generation in both large central station power plants and distributed generation stationst 1,2]. Tubular SOFC modeling for these applications has focused on steady state electric power generation[3-81. Understanding the transient behavior of SOFCs is important for control of stationary utility generators during power system faults, surges, and switching. More recently, SOFCs have been proposed as power sources in electric drive systems for transportation applications[9,10]. In transportation applications, transient and partial load operation predominate. In order to continue the development of SOFCs for transportation applications, the transient operation of SOFCs in electrical systems must also be understood and modeled. Solid oxide fuel cells produce dc electric power from fuel and oxidant via an electrochemical process. The cell dc voltage and current depend on conditions that include fuel flow, oxidant flow, pressure, temperature, and the demands of the load circuit. These parameters affect the electrochemical processes that ultimately determine the generated power andPE-100-EC-0-04-1998 A paper recommended and approved by the IEEE Energy Development and Power Generation Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Energy Conversion. Manuscript submitted September 16, 1997; made available forprinting April 24, 1998.

11. OPERATING PRINCIPLES OF SOLID OXIDE FUEL CELLSThe solid oxide fuel cell consists of two porous ceramic electrodes separated by a dense ceramic electrolyte (see Fig. 1). The cell produces electricity by the electrochemical reaction of fuel (hydrogen and/or carbon monoxide) and oxidant (oxygen) across the solid electrolyte. Oxygen fed to the air electrode (cathode) accepts electrons from the external circuit to form oxygen ions. The ions are conducted through the solid electrolyte to the fuel electrode (anode). At the fuel electrode, the ions combine with hydrogen and/or carbon monoxide in the fuel to form water andlor carbon dioxide. This reaction also releases electrons. Electrons flow from the fuel electrode (anode) through the external circuit back to the air electrode (cathode). The overall reactions within the SOFC are listed in Table 1. Since the overall reactions are exothermic, the cell produces heat in addition to electricity. TABLE 1 SOFC ELECTROCHEMICAL REACTIONS Air Electrode (cathode) Fuel Electrode (anode) Overall Cell Reaction O2 + 4e- -+ 20= H2 + 0 -+ HtO + 2e CO + O= CO2 + 2ei H2 + CO + 0 2 --f HzO + CO2

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The electrochemical model includes the driving Nernst potential, cell electrical resistance, activation polarization, and concentration polarization. Activation polarization is related to the conversion of oxygen molecules to oxygen ions at the fuel electrode. It is combined with the cell resistance to produce an overall resistance factor for the cell. Diffusion polarization includes losses related to the diffusion of oxygen into the air electrode and diffusion of fuel and reaction products through the fuel electrode. The model includes separate concentration loss terms for each electrode. The electrochemical model was verified using test data from [12]. Table 2 lists the test parameters and Fig. 4 shows a sample plot of terminal voltage versus cell current density for the test and simulation. The difference between the electrochemical model and the test data was always less than 5%.Interconnection

Fig. 1 Basic SOFC Operation. Typical SOFC materials are stabilized zirconia for the electrolyte, nickelhirconia cermet for the fuel electrode, and doped lanthanum manganite for the air electrode. SOFC's operate in a temperature range from 800 to 1100 "C and at atmospheric or elevated pressures. The SOFC configuration simulated is the air electrode supported tubular cell described in [I21 (see Fig. 2). Air is provided to the inside of the cell via an air feed tube as shown in Fig. 3. Air enters the feed tube at the top and travels to the closed end of the cell at the bottom. Fuel enters on the outside at the closed end. The air and fuel both flow along the cell in the same direction from the closed end toward the open end. This is known as a coflow configuration.1 1 ELECTROCHEMICAL MODELING 1.Air In

Fig. 2 Cross-Section of a Tubular SOFC:

Practical fuel cell performance is usually described in terms of cell terminal voltage and current density. The cell terminal voltage is equal to the voltage difference between the cathode (air electrode) and anode (fuel electrode). Both electrodes are typically good conductors and therefore each electrode surface is at a constant voltage. The cell terminal voltage is constant along the length of the tubular cell shown in Figures 2 and 3. The terminal voltage is given by:

A

where V, is the cell terminal voltage, E is the driving Nernst potential, J is the current density, A is the active cell area, R is the resistance in Ohms, and q is the sum of the other loss mechanisms (often referred to as polarizations). The local conditions within the cell may vary greatly. The local Nerust potential, current density, and polarizations all vary along the length of the cell. E, J, and 1 are subject to the condition that their sum at any specific location equals the terminal voltage as shown in equation (1).

Fuel In

Fig. 3 Gas Flows in a Tubular SOFC.

751 TABLE 2 CELL PARAMETERS FOR ELECTROCHEMICAL SIMULATIONS Cell Temperature: Fuel: Fuel Utilization: Excess Air: where p is the mass density, C the specific heat, AV the v elemental volume, Tis temperature, t is time, and q,o,uris the sum of all the heat transfer and source terms. A difference equation for each node was developed from (2). The difference equations have the following form:

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where T, is the temperature at time t, T,+,is the temperature at time t + At, and At is the time step. The difference equations were solved using an electrical circuit analogy and the finite difference method described by Clausing[131. Results from the transient thermal model indicated that radiation heat transfer between the fuel cell and air feed tube was a significant mode of cell cooling[ll].

V. TRANSIENT MODEL AND RESULTS

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Fig. 4 Calculation and Test Data at T = 1223 K.

1V. THERMAL MODELINGSince the driving Nernst potential and loss mechanisms are temperature sensitive, the temperature throughout the cell must be known to accurately determine the cell's electrical performance. During normal operation, the predominant variation in cell temperature occurs along the length of tubular cells. Heat transfer occurs by thermal conduction, convection and radiation. Conduction occurs in the solid cell materials and the air feed tube. Axial conduction in the solids was neglected due to long conduction paths and reduced areas. Convection occurs between solid surfaces and the various gas streams (see Fig. 3). Radiation transfers heat between the cell and air feed tube and also between adjacent cells. There are also heat sources due to the exothermic reaction of fuel and oxygen. In addition to the various types of heat transfer and sources, the thermal model also includes the variation of material properties with temperature. The solids and gas flow spaces were divided into elemental volumes with nodes for solution of the transient thermal model. The following differential equation describes the energy balance at each node:

The combined transient model includes both the electrochemicaland thermal aspects of cell performance. The electrochemical part of the model accepts cell temperature from the thermal part and calculates cell electrical output and cell heat sources. The relationship shown in equation (1) is used to determine the cell local current densities and cell terminal voltage. The local cell currents are summed to form the total cell current. Cell heat sources are calculated from the enthalpy of the fuel-oxidant reaction, and are applied to thermal nodes within the solid cell material. The thermal part of the model accepts the cell heat sources and calculates new cell temperatures by solving equation (3) at each thermal node. The transient model steps back and forth between electrochemical and thermal calculations to produce transient electrical and thermal data. Fig. 5 shows a flow chart of this process. The combined model can also be used to determine steady state operating points by running transient simulations until the transients decay to a level below a specified amount. Simulations were conducted to determine the transient response of the cell to electrical load changes. The cell was subjected to a step increases in current density with all of input the gas flows held constant. Table 3 lists the initial conditions and parameters for the simulation. Fig. 6 shows the step increase in current density and Fig. 7 shows the electrical transient response of the cell to this change in load current. The cell terminal voltage overshoots and then decays back to the new steady state load condition. Fig. 8 shows the effect of the load change on cell maximum and minimum temperature. The transient results show the same general response and trends previously published for a planar SOFC model[ 1 1 4.

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TABLE 3 INITIAL CONDITIONS AND PARAMETERS FOR TRANSIENT SIMULATION A. Input G s Flows (Constant) a UH2= 5.83 X moles/sec U H ~= 7.21 X 10. moledsec O U,, = 1.08 x 10 moles/sec U,, = 4.06 X moledsec

+READ Initial Temperatures

B. Fuel and Air Inlet Temperatures (Constant)T,i, = 673 K True, 673 K = C. Initial Conditions J1 = 0.35 A/cm2 VT = 0.6342 Volts Max Cell Temperature = 1169 K Min Cell Temperature = 1059 K Fuel Utilization = 0.595 Excess Air Flow = 6.21 times Stoichiometric

Data (Flows, Currents, Voltage Electrical Power, Heat Sources)

D. Final Conditions

CALCULATENew Temperatures

52 = 0.5 A/cm2 V, = 0.6190 Volts Max Cell Temperature = 1347 K Min Cell Temperature = 1144 K Fuel Utilization = 0.85 Excess Air Flow = 4.35 times Stoichiometric

Properties and Resistances

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Fig. 5 Flowchart of Transient Solution Technique VI. CONCLUSIONS The newly developed transient model provides both steady state operating points and the SOFC transient response in moving between them. Understanding the transient behavior of SOFCs is important for control of stationary utility generators during power system faults, surges, and switching. It is also important for continued development of SOFCs for transportation applications where transients and partial load operation dominate. The model provides a foundation for continued work in transient modeling and simulation for tubular SOFCs.

Fig. 6 Step Increase in Cell Current Density.

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Fig. 7 Cell Terminal Voltage During a Load Change.

153Norman F. Bessette 11, A Mathematical Model of a Tubular Solid Oxide Fuel Cell, M.S. Thesis, School of Mechanical Engineering, Georgia Institute of Technology, 1992.

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Norman Frederic Bessette 11, Modeling und Simulation for Solid Oxide Fuel Cell Power Systems, Ph.D. Dissertation, School of Mechanical Engineering, Georgia Institute of Technology, 1994. V. Antonucci, N. Giordano, P. L. Antonucci, E. Amto, P. Costamagna, G. Rocchini. and A. Demin, Partial Oxidation of CHI for SOFC: Performance Analysis, Proceedings of the Fourth International Symposium on Solid Oxide Fuel Cells, Pennington, NJ: The Electrochemical Society, Inc.. Proceedings Volume 95-1, 1995, pp. 820-828. Owen S . Taylor, Donald W. Brown, David J. Hall, John W. Wiss, Wayne L. Lundberg, John I. Ykema, and Victor Temple, Hybrid Electric Maritime Power Systems (HEMPS), Proceedings of the ASNE 1994 Technical Innovation Symposium, Alexandria, VA. American Society of Naval Engineers, 1994, pp, 287-308.

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Fig. 8 Cell Temperatures During a Load Change. VII. FUTURE! WORK Solid Oxide Fuel Cells can operate on hydrogen, carbon monoxide, or a mixture of both fuels. The capability to operate on carbon monoxide allows SOFCs to operate directly on reformed hydrocarbon fuels. A transient reformation model could be incorporated into the model described in this paper. The steam (water) necessary for reformation can be obtained by recirculating a portion of the depleted fuel as it exits the cell. Reforming of natural gas should be investigated for utility applications of SOFCs. Reforming of liquid fuels such as methanol, gasoline, and diesel fuel should be modeled for transportation applications. VIII. ACKNOWLEDGMENTS This work was completed in partial fulfillment of the requirements for the Ph.D. degree at the University of Pittsburgh. The funding support of the Westinghouse Electric Corporation under the Westinghouse B.G. Lamme scholarship is gratefully acknowledged. IX. REFERENCESJ. H. Hirschenhofer, D. E.Stauffer, and R.R. Engelman, Fuel Cells A Handbook (Revision 3j, DOE Publication DOE/METC-94/1006 (DE94004072), January 1994, pp. 1-20 to 1-21.

R. Knmar, M. Krumpelt, and K. M. Myles, Solid Oxide Fuel Cells for Transportation: A Clean, Efficient Alternative for Propulsion, Proceedings o the Third International Symposium on Solid Oxide f Fuel Cells, Pennington, N J The Electrochemical Society, Inc., Proceedings Volume 93-4, 1993, pp. 948-956.David Jonathan Hall, Transient Modeling and Simulation of a Solid Oxide Fuel Cell, unpublished Ph.D. Dissertation, School of Engineering, University of Pittsburgh, 1997.

S . C. Singhal, Advances in Tubular Solid Oxide Fuel CellTechnology, Proceedings of the Fourth International Symposium on Solid Oxide Fuel Cells, Pennington, NJ: The Electrochemical Society, Inc., Proceedings Volume 95-1, 1995, pp. 195-207.

A. M. Clausing, Numerical Methods in Heat Transfer, Advanced Hear Transfer, E.T. Chao, editor, Chicago, U University of Illinois Press, 1969, pp. 157-213.E. Achenbach, Three-Dimensional and Time-Dependent Simulation of a Planar Solid Oxide Fuel Cell Stack, Journal of Power Sources, Vol. 49, 1994, pp. 333-348.

IX. BIOGRAPHIESDavid J. Hall (M 83, SM 97) received a BSEE from Cmegie-Mellon University in 1983 and a MSEE from the Air Force Institute of Technology in 1984. He served as an officer in the United States Air Force from 1983 through 1988. He conducted pulsed power and plasma physics experiments at the Air Force Weapons Laboratory (AFWL), in Albuquerque, NM. He joined the Westinghouse Science and Technology Center in 1989 and was awarded the Westinghouse E.G. Lnmme Scholarship in 1996. He received a PhDEE from the University of Pittsburgh in 1997. His current research interests are in the areas of power system transients, pulse power, and hybrid solid oxide fuel cell power systems for transportation.

A. J. Appleby and F. R. Foulks, Fuel Cell Handbook, New York Van Nostrand Reinhold, 1989, pp. 583-587. Akira Hirano, Minoru Suzuki, Masamichi Ippommatsu, Evaluation of a New Solid Oxide Fuel Cell System by Non-isothermal f Modeling, Journal o the Electrochemical Society, Vol. 139, no. 10, October 1992, pp. 2744-2751. W. J. Wepfer and M. H. Woolsey, High-Temperature Fuel Cells for Power Generation, Energy Conver.sion and Management, Vol. 25, no. 4,1985, pp. 477-486. Kiyoshi Kanamura, Shoji Yoshioka, and Zen-ichiro Takehara, Temperature Distribution in Tubular Solid Oxide Fuel Cell, Proceedings of the First International Symposium on Solid Oxide Fuel Cells, Pennington, NJ: The Electrochemical Society, Inc., Proceedings Volume 89-11. 1989, pp. 293-303.

R. Gerald Colclaser, Jr. (M 53, 65, F 70) received a BSEE from the SM University of Cincinnati in 1956, and MSEE and DScEE degrees from the University of Pittsburgh in 1961 and 1968 respectively. He was awarded the Westinghouse B. G. Lamme Scholarship in 1962 and attended Stanford University. He joined the Westinghouse Power Circuit Breaker division in 1956, specializing in breaker development and high power testing, and contributed to the development and testing of the first commercial high power SF6 circuit breakers. He is the inventor or co-inventor of 21 U. S. patents in the fields of interrupter design, breaker design, and test circuits. In 1970 Dr. Colclaser joined the Electrical Engineering Department of the University of Pittsburgh, serving as Chairman from 1974 through 1984. .He is active in teaching and research at Pitt, and consults in the field of electrical transients.