MODELING OF A PEM FUEL CELL POLARIZATION CURVE BY LOW-ORDER POLYNOMIALS FOR THE OUTPUT POWER CALCULATION ALGORITHMS
DOI:
https://doi.org/10.59277/RRST-EE.2024.2.22Keywords:
Proton exchange membrane (PEM) fuel cell, Parameter estimation, Low-order model, Maximum power extraction, Energy managementAbstract
The control and energy algorithms that govern the operation of a PEM fuel cell within an energy system must account for the nonlinear phenomena in the cell; it is often captured by the polarization curve. However, the modeling approaches used for simulation studies could be more suitable for the abovementioned algorithms due to their higher computational burden. That leads to the development of simplified approaches. Our study focuses on the algorithms used for the fuel cell output power calculation. Many of them are directed towards the maximum power point operation of the cell. We propose that the fuel cell representation for the algorithms can be used in the low-order polynomial form, thus decreasing the computational load compared to the other approaches. For the maximum power point prediction, we propose using the truncated form of polarization curve input data (ignoring the activation loss region). Our study has demonstrated that based on the same input data and MATLAB curve fitting commands, the 3rd-order polynomial provides the comparable RMSE 3.5…3.9 for the power curve approximation vs. 3.9 for the 5th-order polynomial representation. The value of the maximum PowerPoint is obtained with a 1.3 % relative error with the 2nd-order polynomial using the truncated input data compared to 1.2 % for the 5th-order polynomial representation.
References
(1) Y.A. Zúñiga-Ventura et al., Nonlinear voltage regulation strategy for a fuel cell/supercapacitor power source system, IECON 2018 - 44th Ann. Conf. IEEE Ind. Electron. Soc., pp. 2373–2378 (2018).
(2) J.T. Pukrushpan, H. Peng, A.G. Stefanopoulou, Control-oriented modeling and analysis for automotive fuel cell systems, J. Dyn. Syst., Meas. Contr., 126, 1, pp. 14-25 (2004).
(3) J. Kim, S. Lee, S. Srinivasan, C.E. Chamberlin, Modeling of proton exchange membrane fuel cell performance with an empirical equation, J. Electrochem. Soc., 142, 8, pp. 2670–2674 (1995).
(4) A. Shahin et al., High voltage ratio dc-dc converter for fuel-cell applications, IEEE Trans. Ind. Electron., 57, 12, pp. 3944–3955 (2010).
(5) G. Squadrito et al., An empirical equation for polymer electrolyte fuel cell (PEFC) behaviour, J. Appl. Electrochem., 29, pp. 1449–1455 (1999).
(6) ***Hydrogen roadmap Europe: A sustainable pathway for the European energy transition, 2019.
(7) T. Jamal et al., Fuelling the future: An in-depth review of recent trends, challenges and opportunities of hydrogen fuel cell for a sustainable hydrogen economy, Energy Rep., 10, pp. 2103-2127 (2023).
(8) M.A. Aminudin et al., An overview: Current progress on hydrogen fuel cell vehicles, Int. J. Hydrogen Energy, 48, 11, pp. 4371-4388 (2023).
(9) M. Waseem et al., Fuel cell-based hybrid electric vehicles: An integrated review of current status, key challenges, recommended policies, and future prospects, Green Energy Intell. Transp., 2, 6, 100121 (2023).
(10) V. Martini, F. Mocera, A. Somà, Numerical investigation of a fuel cell-powered agricultural tractor, Energies, 15, 23, 8818 (2022).
(11) X. Wang, J. Zhu, M. Han, Industrial Development status and prospects of the marine fuel cell: A review, J. Marine Sci. Eng., 11, 2, 238 (2023).
(12) H. Peng et al., Offline optimal energy management strategies considering high dynamics in batteries and constraints on fuel cell system power rate: From analytical derivation to validation on test bench, Appl. Energy, 282, 116152 (2021).
(13) S. Quan et al., Real-time energy management for fuel cell electric vehicle using speed prediction-based model predictive control considering performance degradation, Appl. Energy, 304, 117845 (2021).
(14) T. Teng, X. Zhang, H. Dong, Q. Xue, A comprehensive review of energy management optimization strategies for fuel cell passenger vehicle, Int. J. Hydrogen Energy, 45, 39, pp. 20293-20303 (2020).
(15) N. Zidane, S.L. Belaid, A new fuzzy logic solution for energy management of hybrid photovoltaic/battery/hydrogen system, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg, 67, 1, 21-26 (2022).
(16) X. Wei et al., Co-optimization method of speed planning and energy management for fuel cell vehicles through signalized intersections, J. Pow. Sources, 518, 230598 (2022).
(17) B. Gou, W. Na, B. Diong, Fuel Cells. Dynamic Modeling and Control with Power Electronics Applications, 2nd ed., CRC Press, 2016.
(18) G.R. Molaeimanesh, F. Torabi, Fuel Cell Modeling and Simulation: From Microscale to Macroscale, Elsevier, 2022.
(19) A. Benaissa, B. Rabhi, M.F. Benkhoris, L. Zellouma, Linear quadratic controller for two-interleaved boost converter associated with PEMFC emulator, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg, 66, 2, 125-130 (2021).
(20) J.F Z. Zerhouni, M. Telidjane, Direct connection of a proton exchange membrane fuel cell to a load and modelling, (in French), Rev. Roum. Sci. Techn. – Électrotechn. et Énerg, 60, 4, 387–396 (2015).
(21) A. Kravos et al., Thermodynamically consistent reduced dimensionality electrochemical model for proton exchange membrane fuel cell performance modelling and control, J. Pow. Sources, 454, 227930 (2020)
(22) M. Derbeli, O. Barambones, M.Y. Silaa, C. Napole, Real-time implementation of a new MPPT control method for a DC-DC boost converter used in a PEM fuel cell power system, Actuators, 9, 4, 105 (2020).
(23) D. Hao et al., An improved empirical fuel cell polarization curve model based on review analysis, Int. J. Chem. Eng., 2016, pp. 1–10 (2016).
(24) A. Saadi, M. Becherif, A. Aboubou, M.Y. Ayad, Comparison of proton exchange membrane fuel cell static models, Ren. Energy, 56, 64-71 (2013).
(25) J.C. Amphlett et al., Performance modeling of the Ballard-Mark-IV solid polymer electrolyte fuel cell, I. Mechanistic model development, J. Electrochem. Soc., 142, 1, 1-8 (1995).
(26) Y.A. Zúñiga-Ventura et al., Adaptive backstepping control for a fuel cell/boost converter system, IEEE J. Emerg. Select. Topics Pow. Electron., 6, 2, pp. 686-695 (2018).
(27) K. Ettihir, M.H. Cano, L. Boulon, K. Agbossou, Design of an adaptive EMS for fuel cell vehicles, Int. J. Hydrogen Energy, 42, 2, pp. 1481-1489 (2017).
(28) A. Abaza et al., Optimal estimation of proton exchange membrane fuel cells parameter based on coyote optimization algorithm, Appl. Sci., 11, 5, 2052 (2021).
(29) A. Shaheen, R. El-Sehiemy, A. El-Fergany, A. Ginidi, Fuel-cell parameter estimation based on improved gorilla troops technique, Sci. Rep., 13, 8685 (2023).
(30) A.M. Agwa et al., MPPT of PEM fuel cell using PI-PD controller based on golden jackal optimization algorithm, Biomimetics, 8, 5, 426 (2023).
(31) N. Karami, R. Outbib, N. Moubayed, Maximum power point tracking with reactant flow optimization of proton exchange membrane fuel cell, J. Fuel Cell Sci. Techn., 10, 5, 051008, (2013).
(32) Y. Wang, X. Yang, Z. Sun, Z. Chen, A systematic review of system modeling and control strategy of proton exchange membrane fuel cell, Energy Rev., 3, 1, 100054 (2024).
(33) L. Fan, X. Ma, Maximum power point tracking of PEMFC based on hybrid artificial bee colony algorithm with fuzzy control, Sci Rep 12, 4316 (2022).
(34) P. Bayat, A. Baghramian, A novel self-tuning type-2 fuzzy maximum power point tracking technique for efficiency enhancement of fuel cell based battery chargers, Int. J. Hydrogen Energy, 45, 43, 23275-23293 (2020)
(35) A.W. Leedy, K.M. Miller, E. Rafferty, M.A. Karanja, Approximation of fuel cell characteristic curves for maximum power point tracking, 2023 IEEE 2nd Ind. Electron. Soc. Ann. On-Line Conf. (ONCON), SC, USA, 1-6 (2023).
(36) R.F. Mann et al., Development and application of a generalized steady-state electrochemical model for a PEM fuel cell, J. Pow. Sources, 86, 1–2, 173-180 (2000).
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