Models for Control Applications

  • Dario Marra
  • Cesare Pianese
  • Pierpaolo Polverino
  • Marco Sorrentino
Part of the Green Energy and Technology book series (GREEN)


Real-world deployment of SOFC systems entails developing suitable control strategies, which particularly have to guarantee meeting electrical load demand, while limiting as much as possible thermal stresses for ceramic components. In this way, undesirable excessive degradation can be prevented and, in turn, longer lifetime can be achieved. Therefore, the main targets are to control the operating load and manage air and fuel inlet flows so as not to induce severe thermal gradients across fuel cell length, as well as to reduce temperature derivative during both cold-start and shutdown phases. Of course, such control goals are to be pursued taking into account the final application of the SOFC system, depending on which load demand fluctuations considerably vary (e.g., compared to stationary generation, transportation applications exhibit more fluctuating load demand). Therefore, depending on how much articulated is the designed SOFC system, which can particularly include hybridizing components (e.g., batteries and fly wheels) to enable limited power rate operation of the SOFC stack, different control levels must be developed to ensure desired control targets be appropriately met. The current chapter initially focuses on the analysis of the physical relationship between main control and controlled variables, depending on which the multilevel control structure can be appropriately defined. Then, specific analyses are presented and discussed to demonstrate the great potential offered by the model-based approach, to ensure appropriate control strategies be developed for on-field energy-efficient and safe operation of SOFC systems.


Internal Combustion Engine Power Demand Load Demand Fuel Cell System Battery Pack 
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. Aguiar P, Adjiman CS, Brandon NP (2004) Anode-supported intermediate temperature direct internal reforming solid oxide fuel cell. I: model-based steady-state performance. J Power Sour 138:120–136CrossRefGoogle Scholar
  2. Aguiar P, Adjiman CS, Brandon NP (2005) Anode-supported intermediate-temperature direct internal reforming solid oxide fuel cell: II. Model-based dynamic performance and control. J Power Sour 147:136–147CrossRefGoogle Scholar
  3. Allgöwer F, Findeisen R, Nagy ZK (2004) Nonlinear Model Predictive Control: From Theory to Application. J Chin Inst Chem Eng 35:299–315Google Scholar
  4. Apfel H, Rzepka M, Tua H, Stimming U (2006) Thermal start-up behaviour and thermal management of SOFC’s. J Power Sour 154:370–378CrossRefGoogle Scholar
  5. Arsie I, Di Domenico A, Pappalardo L, Pianese C, Sorrentino M (2006) Steady-State Analysis and Energetic Comparison of Air Compressors for PEM Fuel Cell Systems. In: Proceedings of 4th ASME international conference on fuel cell science, engineering and technology, Irvine (CA), USAGoogle Scholar
  6. Arsie I, Di_Domenico A, Pianese C, Sorrentino M (2007) Modeling and Analysis of Transient Behavior of Polymer Electrolyte Membrane Fuel Cell Hybrid Vehicles. ASME Trans J Fuel Cell Sci Technol 4:261–271CrossRefGoogle Scholar
  7. Arsie I, Pianese C, Sorrentino M (2004) Nonlinear recurrent neural networks for air fuel ratio control in SI engines. SAE Technical Paper 2004-01-1364, doi: 10.4271/2004-01-1364
  8. Ataer OE (2006) Storage of thermal energy, in energy storage systems. In Gogus YA (ed) Encyclopedia of life support systems (EOLSS), Developed under the auspices of the UNESCO, Eolss Publishers, OxfordGoogle Scholar
  9. Bolton W (2002) Control system. First Edition Elsevier LtdGoogle Scholar
  10. Botti JJ, Grieve MJ, MacBain JA (2005) Electric vehicle range extension using an SOFC APU. SAE Technical Paper 2005-01-1172. doi: 10.4271/2005-01-1172
  11. Brandon N (2014) SOFCs for power plants—current status and future perspectives. In: 1st Symposium “solid oxide fuel cells for next generation power plants”, June 23rd 2011, Delft University of Technology, The Netherlands.
  12. Braun RJ (2002) Optimal design and operation of solid oxide fuel cell systems for small-scale stationary applications. Ph.D. Thesis, University of Wisconsin, Madison, WIGoogle Scholar
  13. Choi TY, Guezennec YG, Rizzoni G (2003) Supervisory control of a fuel cell SUV hybridized with supercapacitors. In: Proceedings of 4th international conference on control and diagnostic in automotive applications, June 18–20, Sestri Levante, ItalyGoogle Scholar
  14. FCLAB, Fuel Cell Laboratory University of Perugia (2014)
  15. Ferrari ML, Traverso A, Magistri L, Massardo AF (2005) Influence of the anodic recirculation transient behavior on the SOFC hybrid system performance. J Power Sour 149:22–32CrossRefGoogle Scholar
  16. Franklin G, Powell J, Emami-Naeini A (2006) Feedback control of dynamic systems, 5th edn. Prentice Hall, New JerseyMATHGoogle Scholar
  17. Gaynor R, Mueller F, Jabbari F, Brouwer J (2008) On control concepts to prevent fuel starvation in solid oxide fuel cells. J Power Sour 180:330–342CrossRefGoogle Scholar
  18. Guezennec Y, Choi TY, Paganelli G, Rizzoni G (2003) Supervisory control of fuel cell vehicles and its link to overall system efficiency and low-level control requirements. In: Proceedings of 2003 American control conference, June 4–6, vol 3, pp 2055–2061. Denver, CO (USA)Google Scholar
  19. Hussain MA (1999) Review of the applications of neural networks in chemical process control simulation and online implementation. Artif Intell Eng 13:55–68CrossRefGoogle Scholar
  20. Johnson VH (2002) Battery performance models in ADVISOR. J Power Sour 110:321–329CrossRefGoogle Scholar
  21. Larminie J, Dicks A (2003) Fuel cell systems explained. Wiley, ChichesterCrossRefGoogle Scholar
  22. Lutsey N, Wallace J, Brodrick CJ, Dwyer HA, Sperling D (2004) Modeling stationary power for heavy-duty trucks: engine idling vs. fuel cell APUs. SAE Technical paper 2004-01-1479. doi: 10.4271/2004-01-1479
  23. Markel T, Brooker A, Hendricks T, Johnson V, Kelly K, Kramer B, O’Keefe M, Sprik S, Wipke K (2002) ADVISOR: a systems analysis tool for advanced vehicle modeling. J Power Sour 110:255–266CrossRefGoogle Scholar
  24. Nørgaard M, Ravn O, Poulsen NL, Hansen LK (2000) Neural networks for modelling and control of dynamic systems. Springer, LondonCrossRefMATHGoogle Scholar
  25. Ormerod RM (2003) Solid oxide fuel cells. Chem Soc Rev 32:17–28CrossRefGoogle Scholar
  26. Passino KM, Yurkovich S (1998) Fuzzy control. Addison Wesley Longman, Menlo ParkMATHGoogle Scholar
  27. Rancruel D, von Spakovsky M (2005) Investigation of the start-up strategy for a solid oxide fuel cell based auxiliary power unit under transient conditions. Int J Thermodyn 8:103–113Google Scholar
  28. Rizzo G, Sorrentino M, Arsie I (2014) Numerical analysis of the benefits achievable by after-market mild hybridization of conventional cars. Int J Powertrains (in press)Google Scholar
  29. Sorrentino M, Pianese C (2009) Control oriented modeling of solid oxide fuel cell auxiliary power unit for transportation applications. ASME Trans J Fuel Cell Sci Technol 6:041011–04101112CrossRefGoogle Scholar
  30. Sorrentino M, Pianese C (2011) Model-based development of low-level control strategies for transient operation of solid oxide fuel cell systems. J Power Sour 196:9036–9045CrossRefGoogle Scholar
  31. Sorrentino M, Pianese C, Guezennec YG (2008) A hierarchical modeling approach to the simulation and control of planar solid oxide fuel cells. J Power Sour 180:380–392CrossRefGoogle Scholar
  32. Staffell I, Green R, Kendall K (2008) Cost targets for domestic fuel cell CHP. J Power Sour 181:331–349CrossRefGoogle Scholar
  33. Sundström O, Guzzella L, Soltic P (2010) Torque-assist hybrid electric powertrain sizing: from optimal control towards a sizing law. IEEE Trans Control Syst Technol 18:837–849CrossRefGoogle Scholar
  34. Valdivia V, Barrado A, Lázaro A, Sanz M, del Moral DL, Raga C (2014) Black-box behavioral modeling and identification of DC–DC converters with input current control for fuel cell power conditioning. IEEE Trans Industr Electron 61:1891–1903CrossRefGoogle Scholar
  35. Weber A, Ivers-Tiffée E (2004) Materials and concepts for solid oxide fuel cells (SOFCs) in stationary and mobile applications. J Power Sour 127:273–283CrossRefGoogle Scholar
  36. Weber A, Sauer B, Muller A, Herbstritt D, Ivers-Tiffée E (2002) Oxidation of H2, CO and methane in SOFCs with Ni/YSZ-cermet anodes. Solid State Ionics 152:543–550CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • Dario Marra
    • 1
  • Cesare Pianese
    • 1
  • Pierpaolo Polverino
    • 1
  • Marco Sorrentino
    • 1
  1. 1.Department of Industrial EngineeringUniversity of SalernoFiscianoItaly

Personalised recommendations