Modeling Analysis for Species, Pressure, and Temperature Regulation in Proton Exchange Membrane Fuel Cells

  • Zhaohui Wang


The performance degradation of proton exchange membrane or polymer electrolyte membrane fuel cell (PEMFC) stems from air starvation and water flooding. In the mathematical modeling, the conservation equations were applied for momentum, mass, species, charge, and energy, to investigate the heat transfer and temperature distribution in the cathode along with the multiphase and multi-species transport under the steady-state condition. This model shows the effect of stoichiometry of reactants and relative humidity on the water saturation. The back-diffusion of water from the cathode to the anode is considered to reduce possible flooding. The feedback controls are used to address the transient water, pressure, and temperature management problems of a PEMFC system. An anode recirculation system measures the feedback signals to regulate the anode and cathode humidities and the pressure difference between the anode and cathode compartments. It was found that the robust nonlinear controller is insensitive to parametric uncertainty, maintaining performance around any equilibrium point.



The author thanks Dr. Jingbo Liu and Dr. Bashir for their support and encouragement to finish this review chapter.


  1. 1.
    M. Schultze, J. Horn, Modeling, state estimation and nonlinear model predictive control of cathode exhaust gas mass flow for PEM fuel cells. Control. Eng. Pract. 49, 76–86 (2016)CrossRefGoogle Scholar
  2. 2.
    R.T. Meyer, B. Yao, Modeling and simulation of a modern PEM fuel cell system, in ASME 2006 4th International Conference on Fuel Cell Science, Engineering and Technology (American Society of Mechanical Engineers, 2006), pp. 133–150Google Scholar
  3. 3.
    A.Y. Karnik, J. Sun, A.G. Stefanopoulou, J.H. Buckland, Humidity and pressure regulation in a PEM fuel cell using a gain-scheduled static feedback controller. IEEE Trans. Control Syst Technol 17(2), 283–297 (2009)CrossRefGoogle Scholar
  4. 4.
    Peraza, C., Diaz, J. G., Arteaga-Bravo, F. J., Villanueva, C., Francisco Gonzalez-Longatt, F., Modeling and simulation of PEM fuel cell with bond graph and 20sim, in American Control Conference (2008), pp. 5104–5108Google Scholar
  5. 5.
    R. Urbanczyk, S. Peil, D. Bathen, C. Heßke, J. Burfeind, K. Hauschild, M. Felderhoff, F. Schüth, HT-PEM fuel cell system with integrated complex metal hydride storage tank. Fuel Cells 11(6), 911–920 (2011)CrossRefGoogle Scholar
  6. 6.
    Y.B. Kim, Study on the effect of humidity and stoichiometry on the water saturation of PEM fuel cells. Int. J. Energy Res. 36, 509–522 (2012)CrossRefGoogle Scholar
  7. 7.
    Z. Shi, X. Wang (2008). Two-dimensional PEM fuel cells modeling using COMSOL Multiphysics, in Modelling and Simulation, ed. by G. Petrone, G. Cammarata, pp. 677–688. Retrieved from: and_simulation/twodimensional_pem_fuel_cells_modeling_using_comsol_multiphysics
  8. 8.
    E. Robalinho, Z. Ahmed, E. Cekinski, M. Linardi, Advances in PEM fuel cells with CFD techniques, in Proceedings of the 5th International Workshop on Hydrogen and Fuel Cells (2010)Google Scholar
  9. 9.
    C. Siegel, G. Bandlamudi, A. Heinzel, Systematic characterization of a PBI/H 3 PO 4 sol–gel membrane–modeling and simulation. J. Power Sources 196(5), 2735–2749 (2011)CrossRefGoogle Scholar
  10. 10.
    T. Sousa, M. Mamlouk, K. Scott, An isothermal model of a laboratory intermediate temperature fuel cell using PBI doped phosphoric acid membranes. Chem. Eng. Sci. 65(8), 2513–2530 (2010)CrossRefGoogle Scholar
  11. 11.
    K. Klinedinst, J.A.S. Bett, J. Macdonald, P. Stonehart, Oxygen solubility and diffusivity in hot concentrated H3PO4. J. Electroanal. Chem. Interfacial Electrochem. 57(3), 281–289 (1974)CrossRefGoogle Scholar
  12. 12.
    A.A. Kulikovsky, H.F. Oetjen, C. Wannek, A simple and accurate method for high-temperature PEM fuel cell characterization. Fuel Cells 10(3), 363–368 (2010)CrossRefGoogle Scholar
  13. 13.
    N. Zamel, X. Li, Non-isothermal multi-phase modeling of PEM fuel cell cathode. Int. J. Energy Res. 34, 568–584 (2010)Google Scholar
  14. 14.
    E.L. Cussler, Diffusion-Mass Transfer in Fluid Systems (Cambridge University Press, London, 1969)Google Scholar
  15. 15.
    T. Henriques, B. César, P.C. Branco, Increasing the efficiency of a portable PEM fuel cell by altering the cathode channel geometry: a numerical and experimental study. Appl. Energy 87(4), 1400–1409 (2010)CrossRefGoogle Scholar
  16. 16.
    H. Wu, X. Li, P. Berg, Numerical analysis of dynamic processes in fully humidified PEM fuel cells. Int. J. Hydrog. Energy 32(12), 2022–2031 (2007)CrossRefGoogle Scholar
  17. 17.
    I. Matraji, S. Laghrouche, M. Wack, Pressure control in a PEM fuel cell via second order sliding mode. Int. J. Hydrog. Energy 37(21), 16104–16116 (2012)CrossRefGoogle Scholar
  18. 18.
    Z. Shi, X. Wang, Comparison of Darcy’s law, the Brinkman equation, the modified NS equation and the pure diffusion equation in PEM fuel cell modeling, in COMSOL Conference, (2007)Google Scholar
  19. 19.
    N. Zamel, X. Li, A parametric study of multi-phase and multi-species transport in the cathode of PEM fuel cells. Int. J. Energy Res. 32, 698–721 (2008)CrossRefGoogle Scholar
  20. 20.
    R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts (Academic, New York, 1978)Google Scholar
  21. 21.
    P.C. Chen, The dynamics analysis and controller design for the PEM fuel cell under gas flow rate constraints. Int. J. Hydrog. Energy 36, 3110–3122 (2011)CrossRefGoogle Scholar
  22. 22.
    P.C. Chen, Output-feedback voltage tracking control for input-constrained PEM fuel cell systems. Int. J. Hydrog. Energy 36(22), 14608–14621 (2011)CrossRefGoogle Scholar
  23. 23.
    J. Liu, W. Lin, F. Alsaadi, T. Hayat, Nonlinear observer design for PEM fuel cell power systems via second order sliding mode technique. Neurocomputing 168, 145–151 (2015)CrossRefGoogle Scholar
  24. 24.
    A.J. Real, A. Arce, C. Bordons, Development and experimental validation of a PEM fuel cell dynamic model. J. Power Sources 173, 310–324 (2007)CrossRefGoogle Scholar
  25. 25.
    D. Li, C. Li, Z. Gao, Q. Jin, On active disturbance rejection in temperature regulation of the proton exchange membrane fuel cells. J. Power Sources 283, 452–463 (2015)CrossRefGoogle Scholar
  26. 26.
    I.S. Hussaini, C.Y. Wang, Dynamic water management of polymer electrolyte membrane fuel cells using intermittent RH control. J. Power Sources 195(12), 3822–3829 (2010)CrossRefGoogle Scholar
  27. 27.
    M. Coppo, N.P. Siegel, M.R. Spakovsky, On the influence of temperature on PEM fuel cell operation. J. Power Sources 159(1), 560–569 (2006)CrossRefGoogle Scholar
  28. 28.
    M. Cai, M.S. Ruthkosky, B. Merzougui, S. Swathirajan, M.P. Balogh, S.H. Oh, Investigation of thermal and electrochemical degradation of fuel cell catalysts. J. Power Sources 160(2), 977–986 (2006)CrossRefGoogle Scholar
  29. 29.
    Z. Lua, S.G. Kandlikara, C. Ratha, M. Grimma, W. Domigana, A.D. Whitea, M. Hardbargera, J.P. Owejanb, T.A. Traboldb, Water management studies in PEM fuel cells, part II: Ex situ investigation of flow maldistribution, pressure drop and two-phase flow pattern in gas channels. Int. J. Hydrog. Energy 34, 3445–3456 (2009)CrossRefGoogle Scholar
  30. 30.
    P. Concus, R. Finn, On the behavior of a capillary surface in a wedge. Appl. Math. Sci. 63, 292–299 (1969)Google Scholar
  31. 31.
    R.W. Lockhart, R.C. Martinelli, Proposed correlation of data for isothermal two-phase, two-component flow in pipes. Chem. Eng. Prog. 45, 39–48 (1949)Google Scholar
  32. 32.
    C. Lee, W. Mérida, Gas diffusion layer durability under steady-state and freezing conditions. J. Power Sources 164, 141–153 (2007)CrossRefGoogle Scholar
  33. 33.
    W.K. Lee, C.H. Ho, J.W.V. Zee, M. Murthy, The effects of compression and gas diffusion layers on the performance of a PEM fuel cell. J. Power Sources 84, 45–51 (1999)CrossRefGoogle Scholar
  34. 34.
    I. Nitta, O. Himanen, M. Mikkola, Thermal conductivity and contact resistance of compressed gas diffusion layer of PEM fuel cell. Fuel Cells 8(2), 111–119 (2008)CrossRefGoogle Scholar
  35. 35.
    F. Barbir, PEM Fuel Cells Theory and Practice (Academic Press, 2012)Google Scholar
  36. 36.
    V. Gurau, H. Liu, S. Kakac, A two-dimensional model for proton exchange membrane fuel cells. AIChE J. 44(11), 2410–2422 (1998)CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer ScienceTexas A&M University-KingsvilleKingsvilleUSA

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