0
Research Papers

SOFC Stack Model for Integration Into a Hybrid System: Stack Response to Control Variables

[+] Author and Article Information
Michael M. Whiston

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
3700 O'Hara Street,
Pittsburgh, PA 15261
e-mail: mmw66@pitt.edu

Melissa M. Bilec

Associate Professor
Department of Civil
and Environmental Engineering,
University of Pittsburgh,
3700 O'Hara Street,
Pittsburgh, PA 15261
e-mail: mbilec@pitt.edu

Laura A. Schaefer

Professor
Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
3700 O'Hara Street,
Pittsburgh, PA 15261
e-mail: las149@pitt.edu

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received November 11, 2014; final manuscript received December 18, 2014; published online March 10, 2015. Editor: Nigel M. Sammes.

J. Fuel Cell Sci. Technol 12(3), 031006 (Jun 01, 2015) (11 pages) Paper No: FC-14-1133; doi: 10.1115/1.4029877 History: Received November 11, 2014; Revised December 18, 2014; Online March 10, 2015

Due to the tight coupling of physical processes inside solid oxide fuel cells (SOFCs), efficient control of these devices depends largely on the proper pairing of controlled and manipulated variables. The present study investigates the uncontrolled, dynamic behavior of an SOFC stack that is intended for use in a hybrid SOFC-gas turbine (GT) system. A numerical fuel cell model is developed based on charge, species mass, energy, and momentum balances, and an equivalent circuit is used to combine the fuel cell's irreversibilities. The model is then verified on electrochemical, mass, and thermal timescales. The open-loop response of the average positive electrode-electrolyte-negative electrode (PEN) temperature, fuel utilization, and SOFC power to step changes in the inlet fuel flow rate, current density, and inlet air flow rate is simulated on different timescales. Results indicate that manipulating the current density is the quickest and most efficient way to change the SOFC power. Meanwhile, manipulating the fuel flow is found to be the most efficient way to change the fuel utilization. In future work, it is recommended that such control strategies be further analyzed and compared in the context of a complete SOFC-GT system model.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Campanari, S., 2000, “Full Load and Part-Load Performance Prediction for Integrated SOFC and Microturbine Systems,” ASME J. Eng. Gas Turbines Power, 122(2), pp. 239–246. [CrossRef]
Chan, S. H., Ho, H. K., and Tian, Y., 2002, “Modelling of Simple Hybrid Solid Oxide Fuel Cell and Gas Turbine Power Plant,” J. Power Sources, 109(1), pp. 111–120. [CrossRef]
Chan, S. H., Ho, H. K., and Tian, Y., 2003, “Modelling for Part-Load Operation of Solid Oxide Fuel Cell-Gas Turbine Hybrid Power Plant,” J. Power Sources, 114(2), pp. 213–227. [CrossRef]
Chan, S. H., Ho, H. K., and Tian, Y., 2003, “Multi-Level Modeling of SOFC–Gas Turbine Hybrid System,” Int. J. Hydrogen Energy, 28(8), pp. 889–900. [CrossRef]
Martinez, A. S., Brouwer, J., and Samuelsen, G. S., 2012, “Feasibility Study for SOFC-GT Hybrid Locomotive Power: Part I. Development of a Dynamic 3.5 MW SOFC-GT FORTRAN Model,” J. Power Sources, 213, pp. 203–217. [CrossRef]
Liese, E. A., Ferrari, M. L., Van Osdol, J., Tucker, D., and Gemmen, R. S., 2008, “Modeling of Combined SOFC and Turbine Power Systems,” Modeling Solid Oxide Fuel Cells: Methods, Procedures and Techniques, Vol. 1, R.Bove, and S.Ubertini, eds., Springer Science+Business Media, B.V., Dordrecht, The Netherlands, pp. 239–268.
Parker, D. S., 2003, “Research Highlights From a Large Scale Residential Monitoring Study in a Hot Climate,” Energy Build., 35(9), pp. 863–876. [CrossRef]
Collinge, W. O., 2014, University of Pittsburgh, Pittsburgh, PA, personal communication.
National Action Plan for Energy Efficiency, 2008, “Sector Collaborative on Energy Efficiency Accomplishments and Next Steps,” ICF International, pp. 3-1–3-5.
Aguiar, P., Adjiman, C. S., and Brandon, N. P., 2004, “Anode-Supported Intermediate Temperature Direct Internal Reforming Solid Oxide Fuel Cell. I: Model-Based Steady-State Performance,” J. Power Sources, 138(1–2), pp. 120–136. [CrossRef]
Aguiar, P., Adjiman, C. S., and Brandon, N. P., 2005, “Anode-Supported Intermediate-Temperature Direct Internal Reforming Solid Oxide Fuel Cell: II. Model-Based Dynamic Performance and Control,” J. Power Sources, 147(1–2), pp. 136–147. [CrossRef]
Bhattacharyya, D., Rengaswamy, R., and Finnerty, C., 2009, “Dynamic Modeling and Validation Studies of a Tubular Solid Oxide Fuel Cell,” Chem. Eng. Sci., 64(9), pp. 2158–2172. [CrossRef]
Wang, C., and Nehrir, M. H., 2007, “A Physically Based Dynamic Model for Solid Oxide Fuel Cells,” IEEE Trans. Energy Conv., 22(4), pp. 887–897. [CrossRef]
Mueller, F., Gaynor, R., Auld, A. E., Brouwer, J., Jabbari, F., and Samuelsen, G. S., 2008, “Synergistic Integration of a Gas Turbine and Solid Oxide Fuel Cell for Improved Transient Capability,” J. Power Sources, 176(1), pp. 229–239. [CrossRef]
Stiller, C., Thorud, B., Bolland, O., Kandepu, R., and Imsland, L., 2006, “Control Strategy for a Solid Oxide Fuel Cell and Gas Turbine Hybrid System,” J. Power Sources, 158(1), pp. 303–315. [CrossRef]
Leucht, F., Bessler, W. G., Kallo, J., Friedrich, K. A., and Müller-Steinhagen, H., 2011, “Fuel Cell System Modeling for Solid Oxide Fuel Cell/Gas Turbine Hybrid Power Plants. Part I: Modeling and Simulation Framework,” J. Power Sources, 196(3), pp. 1205–1215. [CrossRef]
Braun, R. J., 2002, “Optimal Design and Operation of Solid Oxide Fuel Cell Systems for Small-Scale Stationary Applications,” Ph.D. thesis, University of Wisconsin-Madison, Madison, WI.
Matsuzaki, Y., and Yasuda, I., 2000, “Electrochemical Oxidation of H2 and CO in a H2–H2O–CO–CO2 System at the Interface of a Ni–YSZ Cermet Electrode and YSZ Electrolyte,” J. Electrochem. Soc., 147(5), pp. 1630–1635. [CrossRef]
Larminie, J., and Dicks, A., 2003, Fuel Cell Systems Explained, Wiley, Chichester, UK.
O'Hayre, R. P., Cha, S.-W., Colella, W. G., and Prinz, F. B., 2009, Fuel Cell Fundamentals, Wiley, Hoboken, NJ.
Costamagna, P., and Honegger, K., 1998, “Modeling of Solid Oxide Heat Exchanger Integrated Stacks and Simulation at High Fuel Utilization,” J. Electrochem. Soc., 145(11), pp. 3995–4007. [CrossRef]
Costamagna, P., Selimovic, A., Del Borghi, M., and Agnew, G., 2004, “Electrochemical Model of the Integrated Planar Solid Oxide Fuel Cell (IP-SOFC),” Chem. Eng. J., 102(1), pp. 61–69. [CrossRef]
Ubertini, S., and Bove, R., 2008, “Mathematical Models: A General Overview,” Modeling Solid Oxide Fuel Cells: Methods, Procedures and Techniques, Vol. 1, R.Bove, and S.Ubertini, eds., Springer Science+Business Media, B.V., Dordrecht, The Netherlands, pp. 51–93.
Achenbach, E., 1994, “Three-Dimensional and Time-Dependent Simulation of a Planar Solid Oxide Fuel Cell Stack,” J. Power Sources, 49(1–3), pp. 333–348. [CrossRef]
Mogensen, M., and Lindegaard, T., 1993, “The Kinetics of Hydrogen Oxidation on a Ni-YSZ SOFC Electrode at 1000 °C,” Solid Oxide Fuel Cells III ( The Electrochemical Society Proceedings Series), S. C.Singal and T.Iwahara, eds., Electrochemical Society, Pennington, NJ, pp. 484–493.
Mogensen, M., 1993, “Electrode Kinetics of SOFC Anodes and Cathodes,” High Temperature Electrochemical Behaviour of Fast Ion and Mixed Conductors, 14th Risø International Symposium on Material Science, Risø National Laboratory, Roskilde, Denmark, pp. 117–135.
Incropera, F. P., DeWitt, D. P., Bergman, T. L., and Lavine, A. S., 2007, Fundamentals of Heat and Mass Transfer, Wiley, Hoboken, NJ.
Cussler, E. L., 1997, Diffusion: Mass Transfer in Fluid Systems, Cambridge University Press, Cambridge, UK, p. 173.
Chan, S. H., Khor, K. A., and Xia, Z. T., 2001, “A Complete Polarization Model of a Solid Oxide Fuel Cell and Its Sensitivity to the Change of Cell Component Thickness,” J. Power Sources, 93(1–2), pp. 130–140. [CrossRef]
Mills, A. F., 2001, Mass Transfer, Prentice-Hall Inc., Upper Saddle River, NJ, pp. 68–69.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 2007, Transport Phenomena, Wiley, New York, pp. 526–527.
Koide, H., Someya, Y., Yoshida, T., and Maruyama, T., 2000, “Properties of Ni/YSZ Cermet as Anode for SOFC,” Solid State Ionics, 132(3–4), pp. 253–260. [CrossRef]
Nehrir, M. H., and Wang, C., 2009, Modeling and Control of Fuel Cells: Distributed Generation Applications, Wiley, Hoboken, NJ, pp. 53–55.
Wang, C., Nehrir, M. H., and Shaw, S. R., 2005, “Dynamic Models and Model Validation for PEM Fuel Cells Using Electrical Circuits,” IEEE Trans. Energy Conv., 20(2), pp. 442–451. [CrossRef]
Esfandiari, R. S., and Lu, B., 2010, Modeling and Analysis of Dynamic Systems, Taylor and Francis, Boca Raton, FL.
Moran, M. J., Shapiro, H. N., Boettner, D. D., and Bailey, M. B., 2011, Fundamentals of Engineering Thermodynamics, Wiley, Hoboken, NJ, p. 854.
Achenbach, E., and Riensche, E., 1994, “Methane/Steam Reforming Kinetics for Solid Oxide Fuel Cells,” J. Power Sources, 52(2), pp. 283–288. [CrossRef]
Treybal, R. E., 1980, Mass-Transfer Operations, McGraw-Hill, New York, pp. 29–30.
Bossel, U. G., 1992, “Facts & Figures: Final Report on SOFC Data,” International Energy Agency and Swiss Federal Office of Energy, Berne, Switzerland.
Bhattacharyya, D., and Rengaswamy, R., 2009, “A Review of Solid Oxide Fuel Cell (SOFC) Dynamic Models,” Ind. Eng. Chem. Res., 48(13), pp. 6068–6086. [CrossRef]
Jia, J., Jiang, R., Shen, S., and Abudula, A., 2008, “Effect of Operation Parameters on Performance of Tubular Solid Oxide Fuel Cell,” AIChE J., 54(2), pp. 554–564. [CrossRef]
Shah, R. K., and London, A. L., 1978, Advances in Heat Transfer, Supplement I: Laminar Flow Forced Convection in Ducts, Academic Press, New York, pp. 199–203.
Poling, B. E., Prausnitz, J. M., and O'Connell, J. P., 2001, The Properties of Gases and Liquids, McGraw-Hill, New York.
Iora, P., Aguiar, P., Adjiman, C. S., and Brandon, N. P., 2005, “Comparison of Two IT DIR-SOFC Models: Impact of Variable Thermodynamic, Physical, and Flow Properties. Steady-State and Dynamic Analysis,” Chem. Eng. Sci., 60(11), pp. 2963–2975. [CrossRef]
White, F., 2006, Viscous Fluid Flow, McGraw-Hill, New York.
Çengel, Y. A., and Cimbala, J. M., 2010, Fluid Mechanics: Fundamentals and Applications, McGraw-Hill, New York, p. 345.
Kee, R. J., Korada, P., Walters, K., and Pavol, M., 2002, “A Generalized Model of the Flow Distribution in Channel Networks of Planar Fuel Cells,” J. Power Sources, 109(1), pp. 148–159. [CrossRef]
Kays, W. M., and London, A. L., 1984, Compact Heat Exchangers, McGraw-Hill, New York, pp. 35–38.
Achenbach, E., 1996, “Annex II: Modelling and Evaluation of Advanced Solid Oxide Fuel Cells: SOFC Stack Modelling (Final Report of Activity A2),” International Energy Agency, Germany.
Rohr, F. J., ABB Research Center, Heidelberg, Germany, personal communication.
Fergus, J. W., 2005, “Sealants for Solid Oxide Fuel Cells,” J. Power Sources, 147(1–2), pp. 46–57. [CrossRef]
Judkins, R. R., Singh, P., and Sikka, V. K., 2000, “Iron Aluminide Alloy Container for Solid Oxide Fuel Cells,” U.S. Patent No. US6114058 A.
Burt, A. C., Celik, I. B., Gemmen, R. S., and Smirnov, A. V., 2004, “A Numerical Study of Cell-to-Cell Variations in a SOFC Stack,” J. Power Sources, 126(1–2), pp. 76–87. [CrossRef]
Celik, I. B., and Pakalapati, S. R., 2008, “From a Single Cell to a Stack Modeling,” Modeling Solid Oxide Fuel Cells: Methods, Procedures and Techniques, Vol. 1, R.Bove, and S.Ubertini, eds., Springer Science+Business Media, B.V., Dordrecht, The Netherlands, pp. 123–182.
Goldstein, L., Hedman, B., Knowles, D., Freedman, S. I., Woods, R., and Schweizer, T., 2003, “Gas-Fired Distributed Energy Resource Technology Characterizations (Microturbine Systems),” Gas Research Institute and the National Renewable Energy Laboratory, Golden, CO, Technical Report No. NREL/TP-620-34783.
Chapra, S. C., and Canale, R. P., 2010, Numerical Methods for Engineers, McGraw-Hill, New York.
Klein, S. A., 2014, “engineering equation solver (EES),” V9.207, V9.715, F-Chart Software, Madison, WI.

Figures

Grahic Jump Location
Fig. 1

SOFC model: (a) SOFC with channel highlighted, (b) channel with computational segment highlighted (CVs are indicated by dashed lines)

Grahic Jump Location
Fig. 2

Representation of irreversible processes inside the SOFC: (a) equivalent circuit (adapted from Refs. [13,19,20,34]), (b) possible charge double layer in the SOFC (adapted from Ref. [20]), and (c) simplified equivalent circuit used to calculate the SOFC operating voltage (adapted from Refs. [19] and [33])

Grahic Jump Location
Fig. 3

Electrochemical voltage response. The dashed line indicates the estimated electrochemical voltage settling time based on Wang and Nehrir's results. The double layer polarization (axially averaged) is shown for Cdbl = 10 mF.

Grahic Jump Location
Fig. 4

Mass flow voltage response. The dashed line indicates the estimated mass flow voltage settling time based on Wang and Nehrir's results. The hydrogen mole fraction (axially averaged) is also shown.

Grahic Jump Location
Fig. 5

Thermal voltage response. The dashed line indicates the estimated thermal voltage settling time based on Wang and Nehrir's results. The PEN temperature (axially averaged) is also shown.

Grahic Jump Location
Fig. 6

SOFC stack's response to a step change in the fuel flow rate: (a) millisecond timescale, (b) second timescale, and (c) minute timescale

Grahic Jump Location
Fig. 7

SOFC stack's response to a step change in fuel flow rate assuming constant fuel utilization (Uf,2 = 85%)

Grahic Jump Location
Fig. 8

SOFC stack's response to a step change in the current density: (a) millisecond timescale, (b) second timescale, and (c) minute timescale

Grahic Jump Location
Fig. 9

SOFC stack's response to a step change in the air flow rate: (a) millisecond timescale, (b) second timescale, and (c) minute timescale

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In