Bond graph model of a solid oxide fuel cell with a C-field for mixture of two gas species

Abstract

A true bond graph model of a solid oxide fuel cell (SOFC) is presented in this paper. The constitutive relations of a C-field for two species of gases are formulated in order to model the cathode and the anode channels of the fuel cell. Moreover, an existing R-field model has been extended for modelling of forced convection of a mixture of two gas species. For given values of system operating pressure, the air source and hydrogen source pressures, the outlet pressures and the inlet gas compositions, the fuel utilization (FU), and air utilization (AU) are interpreted in terms of the partial pressures of the gases in the anode channel and cathode channel. The model is simulated and various static and dynamic characteristic curves for the SOFC are obtained. It is found that the model is capable of capturing all the essential dynamics of the SOFC. Availability of this bond graph model will aid in designing robust model-based control strategies for the fuel cell system and also for performing exergy analysis of the system.

Keywords

Solid oxide fuel cell bond graph thermodynamics electrochemical reaction

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References

Karnopp

D. C.

Margolis

D. L.

Rosenberg

R. C.

System dynamics: modeling and simulation of mechatronic systems, 2006 (Wiley, New York).

Mukherjee

Karmakar

Samantaray

A. K.

Bond graph in modeling, simulation and fault identification, 2006 (CRC Press, Florida).

Thoma

Ould Bouamama

Modelling and simulation in thermal and chemical engineering, 2000 (Springer-Verlag, New York).

Borutzky

Bond graph modeling from an object oriented modeling point of view. Simulation Practice and Theory, 1999, 7(5), 439–461.

Borutzky

Barnard

Thoma

J. U.

Describing bond graph models of hydraulic components in Modelica. Math. and Computers in Simulation, 2000, 53(4-6), 381–387.

Bouamama

B. O.

Bond graph approach as analysis tool in thermofluid model library conception. J. Franklin Inst., 2003, 340(1), 1–25.

Bouamama

B. O.

Medjaher

Samantaray

A. K.

Staroswiecki

Supervision of an industrial steam generator. Part I: Bond graph modeling. Control Engng Practice, 2006, 14(1), 71–83.

Brown

F. T.

Simulating distributed-parameter multiphase thermodynamic systems using bond graphs. ASME Dynamic Systems Control, 2002, 71, 545–553.

Brown

F. T.

Non-iterative evaluation of multiphase thermal compliances in bond graphs. Proc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 2002, 216(I1), 13–19.

10.

Karnopp

D. C.

State variables and pseudo-bond graphs for compressible thermo-fluid systems. J. Dynamic Systems, Measmt Control, 1979, 101, 201–204.

11.

Shoureshi

McLaughlin

Modeling and dynamics of two-phase flow heat exchangers using temperature—entropy bond graphs. In Proceedings of Amer control conference, Boston, Massachusetts, 1984, Vol. 1, 93–98.

12.

Hubbard

Brewer

J. W.

Pseudo bond graphs of circulating fluids with application to solar heating design. J. Franklin Inst., 1981, 311(6), 339–354.

13.

Nakrachi

Dauphin-Tanguy

A distributed parameter pseudo bond graph for heat conduction modeling: Notion of cellular bond graph. ASME, Dynamic Systems Control Div., 2003 DSC, 72(2), 911–916.

14.

Granda

J. J.

Tang

Computer simulation of heat transfer models using a pseudo bond graph network. Trans. Soc. Computer Simulation Int., 1989, 5(4), 265–283.

15.

Gawthrop

P. J.

Thermal modelling using mixed energy and pseudo bond graphs. Proc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 1999, 213(I3), 201–216.

16.

Singhal

S. C.

Advances in solid oxide fuel cell technology. Solid State Ionics, 2000, 135, 305–313.

17.

Mueller

Brouwer

Jabbari

Samuelsen

Dynamic simulation of an integrated solid oxide fuel cell system including current-based fuel flow control. J. Fuel Cell Sci. Technol., 2006, 3, 144–154.

18.

Aguiar

Adjiman

C. S.

Brandon

N. P.

Anode-supported intermediate-temperature direct internal reforming solid oxide fuel cell I. Model-based steady-state performance. J. Power Sources, 2004, 138, 120–136.

19.

Huang

Chuang

K. T.

Dynamic modeling of solid oxide fuel cell: The effect of diffusion and inherent impedance. J. Power Sources, 2005, 150, 32–47.

20.

Wang

Huang

Chen

Data driven predictive control of solid oxide fuel cells. J. Power Sources, 2007, 17, 103–114.

21.

Aguiar

Adjiman

C. S.

Brandon

N. P.

Anode-supported intermediate-temperature direct internal reforming solid oxide fuel cell II. Model-based dynamic performance and control. J. Power Sources, 2005, 147, 136–147.

22.

Franco

A. A.

Schott

Jallut

Maschke

A dynamic mechanistic model of an electrochemical interface. J. The Electrochem. Soc., 2006, 153(6), A1053–A1061.

23.

Franco

A. A.

Schott

Jallut

Maschke

Multi-scale bond graph model of the electrochemical dynamics in a fuel cell. In Proceedings of 3rd European PEFC Forum, Lucerne, Switzerland, 2005 paper no. B063.

24.

Franco

A. A.

Schott

Jallut

Maschke

Multi-scale bond graph model of the electrochemical dynamics in a fuel cell. In Proceedings of the 5th MATHMOD Conference, Vienna, Austria, 2005.

25.

Fahrenthold

E. P.

Venkataraman

System dynamics modeling of porous media. J. Dynamic Systems, Measmt Control, 1997, 119, 251–259.

26.

Choi

Howze

Jo. W.

Enjeti

Development of an equivalent circuit model of a fuel cell to evaluate the effects of inverter ripple current. J. Power Sources, 2006, 158, 1324–1332.

27.

Singhal

S. C.

Kendall

High temperature solid oxide fuel cells: fundamentals, design and applications, 2003 (Elsevier).

28.

Karnopp

Bond graph models for electrochemical energy storage: Electrical, chemical and thermal effects. J. Franklin Inst., 1990, 327(6), 983–992.

29.

Esperilla

J. J.

Felez

Vera

Thermal model for lead-acid batteries. Proc. ICBGM'03, 2003, 35, 293–299.

30.

Esperilla

J. J.

Vera

Felez

Mera

J. M.

Electrochemical cells modeling by means of the bond graph technique: Application of lead-acid batteries using the bond graph technique. Proc. ICBGM'05, New Orleans, Louisiana, 2005, pp. 255–261.

31.

Thoma

Electric batteries and fuel cells modeled by bond graphs. Simulation Practice and Theory, 1999, 7(5-6), 613–622.

32.

Saisset

Fontes

Turpin

Astier

Bond graph model of a PEM fuel cell. J. Power Sources, 2006, 156, 100–107.

33.

Bruun

Pedersen

Bond graph model of a high temperature fuel cell. Proc. ICBGM'07, San Diego, California, 2007, 39(1), 256–263.

34.

Heny

Simanca

Delgado

Pseudo-bond graph model and simulation of a continuous stirred tank reactor. J. Franklin Inst., 2000, 337, 21–42.

35.

Thomas

Simulation of industrial processes for control engineer, 1999 (Butterworth Heinemann, London).

36.

Feenstra

P. J.

A library of port-based thermo-fluid submodels. MSc Thesis, Twente University, Enschede, 2000.

37.

Breedveld

P. C.

Physical systems theory in terms of bond graphs. PhD Thesis, Twente University, Enschede, 1984.

38.

Breedveld

P. C.

Beaman

J. J.

Physical systems modelling with Eulerian frames and bondgraphs. Proc. ASME Winter Meeting, Miami, USA, 1985.

39.

Zemansky

M. W.

Dittman

D. H.

Heat and thermodynamics, 1997 (McGraw-Hill, Singapore).

40.

Benson

R. S.

Advanced engineering thermodynamics, 1977 (Pergamon Press).

41.

Brown

F. T.

Engineering system dynamics — a unified graph centered approach, 2007 (Taylor & Francis Group, FL).

42.

Bejan

Advanced engineering thermodynamics, 1988 (Wiley, Singapore).

43.

Liebhafsky

H. A.

Cairns

E. J.

Fuel cells and fuel batteries: a guide to their research and development, 1968 (Wiley, New York).

44.

Petruzzi

Cocchi

Fineschi

A global thermo-electrochemical model for SOFC systems design and engineering. J. Power Sources, 2003, 118, 96–107.

45.

Achenbach

Response of a solid oxide fuel cell to load change. J. Power Sources, 1995, 57, 105–109.

46.

Huang

Luo

Dynamic modeling of solid oxide fuel cell: The effect of transport dynamics. Chem. Engng Sci., 2006, 61, 6057–6076.

47.

Oster

Perelson

Katchalsky

Network thermodynamics. Nature, 1971, 234, 393–399.

48.

Perelson

A. S.

Network thermodynamics - an overview. Biophys. J., 1975, 15, 667–685.

49.

Saidi

M. H.

Ehyaei

M. A.

Abbasi

Optimization of a combined heat and power PEFC by exergy analysis. J. Power Sources, 2005, 143, 179–184.