Modelling and Simulation of Fuel Cells

  • Ranjan Vepa
Part of the Lecture Notes in Energy book series (LNEN, volume 20)


 Chap. 6 is about the electrochemical and dynamic modelling of fuel cells. The highlights of the chapter are the control-oriented modelling of fuel cells and the application of H2 norm and H norm, minimizing optimal controllers to the control and tracking of the power output of fuel cells.


Fuel Cell Solid Oxide Fuel Cell Polymer Electrolyte Membrane Unscented Kalman Filter Fuel Cell System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Adzakpa KP, Agbossous K, Dube Y, Dostie M, Fournier M, Poulin A (2008) PEM fuel cells modeling and analysis through current and voltage transients behaviors. IEEE Trans Energy Convers 23(2):581–591CrossRefGoogle Scholar
  2. Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge RR, Rodrigues A (1993) The effect of carbon monoxide contamination on anode efficiency in PEM fuel cells. Am Chem Div Fuel Chem 38:1477–1482Google Scholar
  3. Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge RR, Rodrigues A (1994) Parametric modeling of the performance of a 5 kW proton exchange membrane fuel cell stack. J Power Sources 49:349–356CrossRefGoogle Scholar
  4. Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge RR (1995) Performance modeling of the Ballard mark IV solid polymer electrolyte fuel cell: empirical model development. J Electrochem Soc 145:1–8CrossRefGoogle Scholar
  5. Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge RR, Rodrigues A (1996) A model predicting transient responses of proton exchange membrane fuel cells. J Power Sources 61:183–188CrossRefGoogle Scholar
  6. Arcak M, Görgün H, Pedersen LM, Varigonda S (2004) A nonlinear observer design for fuel cell hydrogen estimation. IEEE Trans Control Syst Technol 12:101–110CrossRefGoogle Scholar
  7. Badrinarayanan P, Ramaswamy S, Eggert A, Moore R (2001) Fuel cell stack water and thermal management: impact of variable system power operation. SAE Paper 2001-01-0537Google Scholar
  8. Bernardi D (1990) Water balance calculations for solid polymer electrolyte fuel cells. J Electrochem Soc 137(11):3344–3350MathSciNetCrossRefGoogle Scholar
  9. Bove R, Ubertini S (2006) Modeling solid oxide fuel cell operation: approaches, techniques and results. J Power Sources 159(1):543–559CrossRefGoogle Scholar
  10. Bryson AE, Ho Y-C (1975) Applied optimal control. Hemisphere Publishing Co., New YorkGoogle Scholar
  11. Burl JB (1999) Linear optimal control: H2 and H methods, Addison Wesley Longman, IncGoogle Scholar
  12. Calise F, d’Accadia MD, Palombo A, Vanoli L, Vanoli R (2004) Modelling, simulation and energy analysis of a hybrid SOFC-gas turbine system. 3rd international symposium on energy and environment, SorrentoGoogle Scholar
  13. Calise F, d’Accadia MD, Palombo A, Vanoli L (2006) Simulation and energy analysis of a SOFC-gas turbine system. Energy Int J 31(15):3278–3299CrossRefGoogle Scholar
  14. Calise F, d’Accadia MD, Palombo A, Vanoli L (2007) A detailed one dimensional finite-volume simulation model of a tubular SOFC and a pre-reformer. Int J Thermodyn 10(3):87–96Google Scholar
  15. Carnes B, Djilali N (2005) Systematic parameter estimation for PEM fuel cell models. J Power Sources 144:83–93CrossRefGoogle Scholar
  16. Ceraolo M, Miulli C, Pozio A (2003) Modeling static and dynamic behavior of proton exchange membrane fuel cells on the basis of electro-chemical description. J Power Sources 113:131–144CrossRefGoogle Scholar
  17. Chen S, Xue Z, Wang D, Xiang W (2012) An integrated system combining chemical looping hydrogen generation process and solid oxide fuel cell/gas turbine cycle for power production with CO2 capture. J Power Sources 215:89–98CrossRefGoogle Scholar
  18. Chia E-S (2006) A chemical reaction engineering perspective of polymer electrolyte membrane fuel cells. Dissertation, Faculty of Chemical Engineering, Princeton UniversityGoogle Scholar
  19. Chu D, Jiang R (1999) Performance of polymer electrolyte membrane fuel cell (PEMFC) stacks. Part I. Evaluation and simulation of an air-breathing PEMFC stack. J Power Sources 83:128–133CrossRefGoogle Scholar
  20. del Real AJ, Arce A, Bordons C (2007) Development and experimental validation of a PEM fuel cell dynamic model. J Power Sources 173:310–324CrossRefGoogle Scholar
  21. Doyle JC, Glover K, Khargonekar PP, Francis B (1989) State-space solutions to the standard H2 and H control problems. IEEE Trans Automat Contr 34:831–847MathSciNetCrossRefMATHGoogle Scholar
  22. El-Sharkh MY, Rahman A, Alam MS, Byrne PC, Sakla AA, Thomas T (2004) A dynamic model for a stand-alone PEM fuel cell power plant for residential applications. J Power Sources 138:199–204CrossRefGoogle Scholar
  23. Fishtik I, Callaghan CA, Datta R (2004a) Reaction route graphs. I. Theory and algorithm. J Phys Chem B 108(18):5671–5682CrossRefGoogle Scholar
  24. Fishtik I, Callaghan CA, Datta R (2004b) Reaction route graphs. II. Examples of enzyme- and surface-catalyzed single overall reactions. J Phys Chem B 108(18):5683–5697CrossRefGoogle Scholar
  25. Fishtik I, Callaghan CA, Datta R (2004c) Reaction route graphs. III. Non-minimal kinetic mechanisms. J Phys Chem B 109(7):2710–2722CrossRefGoogle Scholar
  26. Fontes G, Turpin C, Astier S (2010) A large signal dynamic circuit model of a H2/O2 PEM fuel cell. IEEE Trans Ind Electron 57(6):1874–1881CrossRefGoogle Scholar
  27. Fronk M, Wetter D, Masten D, Bosco A (2000) PEM fuel cell system solutions for transportation. SAE paper 2000-01-0373Google Scholar
  28. Gahinet P, Apkarian P (1994) A linear matrix inequality approach to H control. Int J Robust Nonlinear Control 4:421–448MathSciNetCrossRefMATHGoogle Scholar
  29. Garnier S, Pera M-C, Hissel D, De Bernardinis A, Kauffmann J-M, Coquery G (2004) Dynamic behavior of a proton exchange membrane fuel cell under transportation cycle load. Proceeding of international symposium on industrial elect 1, pp 329–333Google Scholar
  30. Glover K, Doyle JC (1988) State space formulae for all stabilizing controllers that satisfy an H -norm bound and relations to risk sensitivity. Syst Control Lett 11:167–172MathSciNetCrossRefMATHGoogle Scholar
  31. Görgün H, Arcak M, Barbir F (2006) An algorithm for estimation of membrane water content in PEM fuel cells. J Power Sources 157:389–394CrossRefGoogle Scholar
  32. Grasser F (2005) An analytical, control-oriented state-space model for a PEM fuel cell system, Ph.D. Dissertation, Ecole Polytechnique Fédérale de Lausanne, Lausanne, SwitzerlandGoogle Scholar
  33. Grasser F, Rufer A (2007) A fully analytical PEM fuel cell system model for control applications. IEEE Trans Ind Appl 43(6):1499–1506CrossRefGoogle Scholar
  34. Haschka M, Weickert T, Krebs V (2006) Application of a sigma-point Kalman-filter for the online estimation of fractional order impedance m Fractional Differentiation and its Applications. Proceeding of the second IFAC workshop on fractional differentiation and its applications 2(1):194:199Google Scholar
  35. Hinaje M, Nguyen D, Rael S, Davat B (2008) Modelling of the proton exchange membrane fuel cell in steady state. Proceeding of IEEE power electronics specialists conference 3550–3556Google Scholar
  36. Ingimundarson A, Stefanopoulou A, McKay DA (2008) Model-based detection of hydrogen leaks in a fuel cell stack. IEEE Trans Control Syst Technol 16(5):1004–1012CrossRefGoogle Scholar
  37. Janardhanan VM, Deutschmann O (2006) CFD analysis of a solid oxide fuel cell with internal reforming: coupled interactions of transport, heterogeneous catalysis and electrochemical processes. J Power Sources 162:1192–1202CrossRefGoogle Scholar
  38. Ju H, Meng H, Wang C (2005) A single phase, non isothermal model for PEM fuel cells. Int J Heat Mass Transfer 48:1303–1315CrossRefMATHGoogle Scholar
  39. Julier SJ (2002) The scaled unscented transformation. Proceeding of the American control conference, vol 6, pp 4555–4559Google Scholar
  40. Julier SJ, Uhlmann J (2000) Unscented filtering and nonlinear estimation. Proc IEEE 92(3):401–422MathSciNetCrossRefGoogle Scholar
  41. Julier SJ, Uhlmann J, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Auto Cont 45(3):477–482MathSciNetCrossRefMATHGoogle Scholar
  42. Kalhammer F, Prokopius P, Roan V, Voecks G (1998) Status and prospects of fuel cells as automotive engines. State of California Air Resources Board, Ca., USAGoogle Scholar
  43. Kandepu R, Imsland L, Foss BA, Stiller C, Thorud B, Bolland O (2005) Control-relevant SOFC modeling and model evaluation. Proceedings of ECOS 5Google Scholar
  44. Kandepu R, Foss BA, Imsland L (2006) Integrated modeling and control of a load-connected SOFC-GT autonomous power system. Proceeding of the American control conference 6:5Google Scholar
  45. Kandepu R, Imsland L, Stiller C, Foss BA, Kariwala V (2006b) Control-relevant modeling and simulation of a SOFC-GT hybrid system. Model Ident Control 27(3):143–156CrossRefGoogle Scholar
  46. Kandepu R, Huang B, Imsland L, Foss BA (2007) Comparative study of state estimation of fuel cell hybrid system using UKF and EKF. IEEE international conference on control and automation, ICCAGoogle Scholar
  47. Kandepu R, Imsland L, Foss BA, Stiller C, Thorud B, Bolland O (2007b) Modeling and control of a SOFC-GT-based autonomous power system. Energy 32(4):406–417CrossRefGoogle Scholar
  48. Kandepu R, Foss BA, Imsland L (2008a) Applying the unscented Kalman filter for nonlinear state estimation. J Process Control 18(7):753–768CrossRefGoogle Scholar
  49. Kandepu R, Imsland L, Foss BA (2008) Constrained state estimation using the unscented Kalman filter. 16th Mediterranean conference on control and automation, pp 1453–1458Google Scholar
  50. Khargonekar PP, Rotea MA (1991) Mixed H2 /H Control: a convex optimization approach. IEEE Trans Auto Contr 36(7):824–837MathSciNetCrossRefMATHGoogle Scholar
  51. Laffly E, Pera M-C, Hissel D (2007) Polymer electrolyte membrane fuel cell modeling and parameters estimation for ageing consideration. Proceeding IEEE international symposium on industrial elect, pp 180–185Google Scholar
  52. Lee J, Lalk T (1998) Modeling fuel cell stack systems. J Power Sources 73:229–241CrossRefGoogle Scholar
  53. Mann RF, Amphlett JC, Hooper MAI, Jensen HM, Peppley BA, Roberge RR (2000) Development and application of a generalized steady state electrochemical model for a PEM fuel cell. J Power Sources 86:173–180CrossRefGoogle Scholar
  54. Master J (2010) Kinetics, catalysis and mechanism of methane steam reforming, Thesis Submitted to the Faculty of the Worcester Polytechnic Institute Department of Chemical EngineeringGoogle Scholar
  55. McKay D, Stefanopoulou AG (2004) Parameterization and validation of a lumped parameter diffusion model for fuel cell stack membrane humidity estimation. Proceeding of American control conferences 816–821Google Scholar
  56. Methekar RN, Patwardhan SC, Rengaswamy R, Gudi RD, Prasad V (2010) Control of proton exchange membrane fuel cells using data driven state space models. Chem Eng Res Des 88(7):861–874CrossRefGoogle Scholar
  57. Morner SO, Klein SA (2001) Experimental evaluation of the dynamic behavior of an air-breathing fuel cell stack. J Solar Energy Eng 123:225–231CrossRefGoogle Scholar
  58. O’Hayre R, Cha SW, Colella W, Prinz FB (2006) Fuel cell fundamentals. Wiley, New YorkGoogle Scholar
  59. Ogata K (2001) Modern control engineering, 4th edn. Prentice Hall, Chapters 11 and 12Google Scholar
  60. Pakalapati SR (2006) A new reduced order model for solid oxide fuel cells, Ph.D. Thesis, West Virginia University, Morgantown, WVGoogle Scholar
  61. Pakalapati SR, Yavuz I, Elizalde-Blancas F, Celik I, Shahnam M (2006) Comparison of a multidimensional model with a reduced order pseudo three-dimensional model for simulation of solid oxide fuel cells. Proceeding of the 4th international conference on fuel cell science, engineering and technology, Irvine, CAGoogle Scholar
  62. Pan S, Su H, Wang H, Chu J (2010) The study of joint input and state estimation with Kalman filtering, Trans Inst Meas Control. ISSN: 01423312. doi: 10.1177/0142331210361551
  63. Pasricha S, Shaw SRD (2006) A dynamic PEM fuel cell model. IEEE Trans Energy Convers 21:484–490CrossRefGoogle Scholar
  64. Pasricha S, Keppler M, Shaw SR, Nehrir MH (2007) Comparison and identification of static electrical terminal fuel cell models. IEEE Trans Energy Convers 22(3):746–754CrossRefGoogle Scholar
  65. Pukrushpan JT, Peng H, Stefanopoulou A (2004a) Control-oriented modeling and analysis for automotive fuel cell systems. ASME J Dyn Syst Measure Control 126(1):14–25CrossRefGoogle Scholar
  66. Pukrushpan JT, Stefanopoulou AG, Peng H (2004b) Control of fuel cell power systems: principles, modeling and analysis and feedback design. In series on advances in industrial control. SpringerGoogle Scholar
  67. Pukrushpan JT, Stefanopoulou AG, Peng H (2004c) Control of fuel cell breathing. IEEE Control Syst Mag 30–46Google Scholar
  68. Puranik SV, Keyhani A, Khorrami F (2010) State-space modeling of proton exchange membrane fuel cell. IEEE Trans Energy Convers 25(3):804–813CrossRefGoogle Scholar
  69. Ramousse J, Deseure J, Lottin O, Didierjean S, Maillet D (2005) Modelling of heat, mass and charge transfer in a PEMFC single cell. J Power Sources 145(6):416–427CrossRefGoogle Scholar
  70. Rowe A, Li X (2001) Mathematical modeling of proton exchange membrane fuel cells. J Power Sources 102:82–96CrossRefGoogle Scholar
  71. Shan Y, Choe S-Y (2005) A high dynamic PEM fuel cell model with temperature effects. J Power Sources 145:30–39CrossRefGoogle Scholar
  72. Springer T, Zawodzinski T, Gottesfeld S (1991) Polymer electrolyte fuel cell model. J Electrochem Soc 138(8):2334–2342CrossRefGoogle Scholar
  73. Stanton K (2005) A thermally dependent fuel cell model for power electronics design. Proceeding of IEEE power electronics specialists conference, pp 1647–1651Google Scholar
  74. Stiller C, Thorud B, Bolland O, Kandepu R, Imsland L (2006) Control strategy for a solid oxide fuel cell and gas turbine hybrid system. J Power Sources 158(1):303–315CrossRefGoogle Scholar
  75. Suares GE, Hoo KA (2000) Parameter estimation of a proton-exchange-membrane fuel cell using voltage-current data. Chem Eng Sci 55:2237–2247CrossRefGoogle Scholar
  76. Thanapalan K, Wang B, Williams JG, Liu GP and Rees D (2008) Modeling, parameter estimation and validation of a 300 W PEM fuel cell system. Proceeding of UKACC’08, international conference on control 2008, Manchester, UKGoogle Scholar
  77. Tumuluri U (2008) Nonlinear state estimation in polymer electrolyte membrane fuel cells. Master’s Thesis, Chemical Engineering, Cleveland State UniversityGoogle Scholar
  78. Turner W, Parten M, Vines D, Jones J, Maxwell T (1999) Modeling a PEM fuel cell for use in a hybrid electric vehicle. IEEE 49th vehicular technology conference 2, pp 1385–1388Google Scholar
  79. Uzunoglu M, Alam MS (2006) Dynamic modeling, design, and simulation of a combined PEM fuel cell and ultracapacitor system for stand-alone residential applications. IEEE Trans Energy Convers 21:767–775CrossRefGoogle Scholar
  80. Vahidi A, Stefanopoulou AG, Peng H (2006) Current management in a hybrid fuel cell power system: a model-predictive control approach. IEEE Trans Control Syst Technol 14(6):047–1057CrossRefGoogle Scholar
  81. Vepa R (2012) Adaptive state estimation of a PEM fuel cell. IEEE Trans Energy Convers 27:457–467CrossRefGoogle Scholar
  82. Wang C (2004) Fundamental models for fuel cell engineering. Chem Rev 104(10):4727–4766CrossRefGoogle Scholar
  83. Wang Y, Wang C (2005) Transient analysis of polymer electrolyte fuel cells. J Electrochemica Acta 50:1307–1315CrossRefGoogle Scholar
  84. Williams JG, Liu GP, Thanapalan K, Rees D (2007) Design and implementation of on-line self-tuning control for PEM fuel cells. Proceeding of EVS-23; sustainability- the future of transportation, Ca. USA, pp 359–375Google Scholar
  85. Wohr M, Bolwin K, Schnurnberger W, Fischer M, Neubrand W, Eigenberger G (1998) Dynamic modeling and simulation of a polymer membrane fuel cell including mass transport limitation. Int J Hydrogen Energy 23(3):213–218CrossRefGoogle Scholar
  86. Xu JG, Froment GF (1989a) Methane steam reforming, methanation and water-gas shift. 1. Intrinsic kinetics. AIChE J 35(1):88–96CrossRefGoogle Scholar
  87. Xu JG, Froment GF (1989b) Methane steam reforming, 2. Diffusional limitations and reactor simulation. AIChE J 35(1):97–103CrossRefGoogle Scholar
  88. Xue X, Tang J, Sammes N, Ding Y (2006) Model-based condition monitoring of PEM fuel cell using Hotelling T2 control limit. J Power Sources 162:388–399CrossRefGoogle Scholar
  89. Yalcinoz T, Alam MS (2008) Dynamic modeling and simulation of air-breathing proton exchange membrane fuel cell. J Power Sources 182:168–174CrossRefGoogle Scholar
  90. Yang W, Bates B, Fletcher N, Pow R (1998) Control challenges and methodologies in fuel cell vehicle development. SAE paper 98C054Google Scholar
  91. Yang CR, Srinivasan S, Bocarsly AB, Tulyani S, Benziger JB (2004) A comparison of physical properties and fuel cell performance of Nafion and Zirconium Phosphate/Nafion composite membranes. J Membr Sci 237:145–161CrossRefGoogle Scholar
  92. Yu D, Yuvarajan S (2004) A novel circuit model for PEM fuel cells. Proceeding of IEEE APEC, Anaheim, Ca. 1:362–366Google Scholar
  93. Zhang Z, Huang X, Jiang J, Wu B (2006) An improved dynamic model considering effects of temperature and equivalent internal resistance for PEM fuel cell power models. J Power Sources 161:1062–1068CrossRefGoogle Scholar
  94. Zhang H, Wang L, Weng S, Su M (2008) Performance research on the compact heat exchange reformer used for high temperature fuel cell systems. J Power Sources 183(1):282–294CrossRefGoogle Scholar
  95. Zhu H, Kee RJ, Janardhanan VM, Deutschmann O, Goodwin DG (2005) Modeling elementary heterogeneous chemistry and electrochemistry in solid-oxide fuel cells. J Electrochem Soc 152:A2427CrossRefGoogle Scholar
  96. Ziogou C, Voutetakis S, Papadopoulou S, Georgiadis MC (2011) Modeling, simulation and experimental validation of a PEM fuel cell system. Comput Chem Eng 35(9):1886–1900CrossRefGoogle Scholar

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© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.University of LondonLondonUK

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