Constrained model-based control for robust operation of a solid oxide fuel cell
Keywords:
Control, Fuel Cell, Identification, Model, MPC, OptimizationAbstract
Over the years, the Solid Oxide Fuel Cell (SOFC) has grown in popularity due to its high efficiency and fuel flexibility, low maintenance requirements and environmentally friendly features. Its durability and performance can be substantially enhanced through the implementation of optimal control strategies. However, controlling the SOFC is challenging due to its nonlinear behavior and the need to manage its operational constraints simultaneously. To come up with an effective control algorithm for a SOFC, it is necessary to understand its dynamic behavior. In this work, a Wiener model is developed for control purpose. This mathematical representation enables the use of an identification algorithm to estimate unknown parameters. Furthermore, the control-oriented model uncertainty is characterized and incorporated as bounds on the model parameters. The resulting model is integrated into a Model Predictive Control (MPC) framework, designed for both regulation and optimization objectives. This control scheme ensures robust constraint satisfaction for the whole set of characterized uncertain models. The simulation results show the benefits of the proposed model-based controller both for SOFC operation and performance enhancement.
Downloads
References
R.K. Ahluwalia, and X.Wang, “Fuel cell systems for transportation: Status and trends,” Journal of Power Sources, vol. 177, pp. 167-176, February, 2008. doi: 10.1016/j.jpowsour.2007.10.026
E. Ogungbemi, O. Ijaodola, F.N.Khatib, T. Wilberforce, Z. El Hassan, J. Thompson, M. Ramadan, and A.G. Olabi, “Fuel cell membranes – Pros and cons,” Energy, vol. 172, pp. 155–172, April, 2019. doi: 10.1016/j.energy.2019.01.034
H. Sethia, and A. Priyam, “Review on hydrogen fuel as an alternative fuel,” Next Energy, vol. 9, 100460, October, 2025. doi: 10.1016/j.nxener.2025.100460
M. Irshad, K. Siraj, R. Raza, A. Ali, P. Tiwari, B. Zhu, A. Rafique, A. Ali, M. Ullah, and A. Usman, “A brief description of high temperature solid oxide fuel cell's operation, materials, design, fabrication technologies and performance,” Applied Sciences, vol. 6, Art. no. 75, March, 2016. doi: 10.3390/app6030075
Z. Wu, P. Zhu, Y. Huang, J. Yao, F. Yang, Z. Zhang, and M. Ni, “A comprehensive review of modeling of solid oxide fuel cells: from large systems to fine electrodes,” Chem. Rev., vol. 125, pp. 2184-2268, February, 2025. doi: 10.1021/acs.chemrev.4c00614
W. Zhang, Y. Zeng, H. Zhang, R. Shi, N. Duan, L. Jia, and D. Yan, “Structural design and optimization for a 20-cell solid oxide fuel cell stack based on flow uniformity and pressure drop,” International Journal of Hydrogen Energy, vol. 48, pp. 36900-36917, 2023. doi: 10.1016/j.ijhydene.2023.05.325
M. Guo, D. Zhao, Q. Xu, Z. Li, H. Xu, and M. Ni, “New interconnector design optimization to balance electrical and mechanical performance of solid oxide fuel cell stack,” International Journal of Hydrogen Energy, vol. 48, pp. 3107-3121, 2023. doi: 10.1016/j.ijhydene.2022.10.147
B. Yang, Y. Li, J L, H. Shu, X. Zhai, Y. Ren and Q. Li, “Comprehensive Summary of Solid Oxide Fuel Cell Control: A State-of-the-art Review,” Protection and Control of Modern Power Systems, vol. 7, no. 36, pp. 1-31, July, 2022, doi: 10.1186/s41601-022-00251-0.
J. Braun, T. Vincent, H. Zhu, and R. Kee, “Analysis, optimization and control of solide-oxid fuel cell systems,” Advances in Chemical Engineering, vol. 41, pp. 383-446, 2012. doi: 10.1016/B978-0-12-386874-9.00011-7
R. Roberts, J. Brouwer, F. Jabbari, T. Junker, and H. Ghezel-Ayagh, “Control design of an atmospheric solid oxide fuel cell/gas turbine hybrid system: Variable versus fixed speed gas turbine operation,” Journal of Power Sources, vol.161, pp. 484-491, October, 2006. doi: 10.1016/j.jpowsour.2006.03.059
C. Stiller, B. Thorud, O. Bolland, R. Kandepu, and L. Imsland, “Control strategy for a solid oxide fuel cell and gas turbine hybrid system,” J. Power Sources, vol. 158, pp. 303–315, July 2006. doi: 10.1016/j.jpowsour.2005.09.010
Y. Li, S. Choi, and S. Rajakaruna, “An analysis of the control and operation of a solid oxide fuel-cell power plant in an isolated system,” IEEE Trans Energy Convers, vol. 20, pp. 381–387, June, 2005. doi: 10.1109/TEC.2005.847998
F. Jurado, “Predictive control of solid oxide fuel cells using fuzzy Hammerstein models,” J. Power Sources, vol. 158, pp. 245–253, July, 2006. doi: 10.1016/j.jpowsour.2005.08.041
M. Ławryńczuk, and D. Söffker, “Wiener structures for modeling and nonlinear predictive control of proton exchange membrane fuel cell,” Nonlinear Dyn. vol. 95, pp. 1639–1660, January, 2019. doi: 10.1007/s11071-018-4650-y
M. Ławryńczuk, “Modelling and MPC of the Proton Exchange Membrane Fuel Cell Using Wiener Models.” Nonlinear Predictive Control Using Wiener Models. Studies in Systems, Decision and Control, vol. 389, pp 251–281, Springer, 2022. Doi: 10.1007/978-3-030-83815-7_6
J. Padullés, G.W. Ault, and J.R. McDonald, “An integrated SOFC plant dynamic model for power systems simulation,” Journal of Power Sources, vol 86, pp. 495-500, March, 2000. doi: 10.1016/S0378-7753(99)00430-9
X.-J. Wu, X.-J. Zhu, G.-Y. Cao, and H.-Y. Tu, “Predictive control of SOFC based on a GA-RBF neural network model,” Journal of Power Sources, vol. 179, pp. 232–239, April, 2008. doi: 10.1016/j.jpowsour.2007.12.036
A.M. Omer Abbaker, H. Wang and Y. Tian, “Voltage control of solid oxide fuel cell power plant based on intelligent proportional integral-adaptive sliding mode control with anti-windup compensator,” Transactions of the Institute of Measurement and Control, vol. 42, pp. 116-130, August, 2019. doi: 10.1177/0142331219867779
M. Ławryńczuk, “Identification of Wiener models for dynamic and steady-state performance with application to solid oxide fuel cell,” Asian J. of Control, vol. 21, pp. 1836-1846, July, 2019. doi: 10.1002/asjc.2038
S.I. Biagiola, C. Schmidt, and J.L. Figueroa, “Model uncertainty estimation of a solid oxide fuel cell using a Volterra-type model,” Journal of the Franklin Institute, vol. 351, pp. 4183–4197, August, 2014. doi: 10.1016/j.jfranklin.2014.04.025
E.F. Camacho, and C. Bordons, Model Predictive Control. Second edition, Springer-Verlag, London, 2007. doi: 10.1007/978-0-85729-398-5
J.L. Figueroa, and S.I. Biagiola, “Modelling and uncertainties characterization for robust control,” Journal of Process Control, vol. 23, pp. 415– 428, March, 2013. doi: 10.1016/j.jprocont.2012.11.008
X.W. Zhang, S.H. Chan, H.K. Ho, J. Li, G. Li, and Z. Feng, “Nonlinear model predictive control based on the moving horizon state estimation for the solid oxide fuel cell,” International Journal of Hydrogen Energy, vol. 33, pp. 2355-2366, May, 2008. doi: 10.1016/j.ijhydene.2008.02.063
