Hybrid Methodology for Efficient on the Fly (Re)Parametrization of Proton Exchange Membrane Fuel Cells Electrochemical Model for Diagnostics and Control Applications
Authors: Kravos Andraz , Kregar Ambroz , Katrašnik Tomaž 
Published: December 2020

Prevention and diminution in effects of degradation phenomena under highly dynamic operation of proton exchange membrane fuel cells (PEMFC), while retaining sufficiently high efficiency and performance of the system, are considered significant obstacles toward their wider use in transport applications. Overcoming these obstacles calls for precise on-line monitoring and control tools such as coupled observers, which enable combined performance and service life optimizations. Models used in these applications should feature low computational effort, good extrapolation capabilities and should be easy to parametrize. The first requirement, which is obvious for on-line applications, in frequently in contradiction to the last two, which are heavily intertwined. Good extrapolation capabilities of the model significantly reduce the size of experimental data sets needed for successful parametrization, thus enabling the parametrization on small data sets, while retaining higher accuracy outside of trained variation space. This rationale motivates the use of the computationally-fast reduced-dimensionality electrochemical models e.g. [1, 2], featuring a more profound mechanistic basis; thus, exhibiting better prediction capability of the model.
To present significant progress in the aforementioned area, this contribution presents framework of computationally-fast electrochemical models that can be parametrized whether on experimental data from polarization curves or on data obtained by electrochemical impedance spectroscopy (EIS). This hybrid methodology consists of interchangeable thermodynamically consistent reduced-dimensionality electrochemical model for PEMFC [2] and newly developed analytical physical model for impedance spectra with the same set of calibration parameters. The latter is developed by applying electrochemical ansatzes for the cathode and anode reactions derived in [2] on the proposed modelling approach used for calculation of the cathode catalyst layer impedance in the inspiring work of Kulikovsky [3]. Profound modelling basis using the same set of calibration parameters enable enhanced identification of individual calibration parameters that are otherwise harder to be uniquely determined [4] on one hand, and enable parametrization of the model from either of the two separate measurements in time and frequency domains on the other.
Enhanced identifiability of calibration parameters using proposed hybrid methodology is especially pronounced in the case of parameters describing anodic and cathodic reaction rates and their activation energies, which are extremely hard to be uniquely determined based on the experimental data consisting of polarization curves only, due to coupling of their information with other calibration parameters. Additionally, proposed hybrid methodology also enables a significant reduction in the measurement time in the case of experimental data obtained by EIS, allowing the low frequency regions, where the transport phenomena could be otherwise characterized, to be omitted due to already uniquely determined calibration parameters from polarization curve measurements. Furthermore, to reduce the necessary amount of experiments for successful parametrization of the model even further, the optimal design of experiments (DoE) is used, based on D-optimal criterion applied onto Fisher information matrix.
To assess developed hybrid methodology calibration parameters, obtained by means of minimizing penalty function value with differential evolution algorithm on EIS data, are used for validation against polarization curves measured at the same RuL (remaining useful life). Furthermore, to confirm applicability of the methodology, the same procedure is also used for calibration on the measured polarization curves and validation on the EIS experimental data. Small discrepancy between the values of the root-mean-square errors show plausibility of the proposed hybrid methodology. On the other hand, Fisher information analysis is performed to assess increment in the information about individual calibration parameter when each experimental point from EIS data set is added to experimental space used for parametrization.
Results of this joint analysis offer unique insight into the information that data set obtained with the EIS measurements possess about individual calibration parameter in the individual frequency interval and intuitively confirm the results obtained by application of the optimal DoE for a synthetic space of EIS measurements. The latter extremely reduces experimental workload needed for successful calibration of the model in comparison with the full factorial. Innovative hybrid methodology of the measurements in time and frequency domains can thus be used for achieving reduced costs and efforts in initial parametrization and during operation in re-parametrization procedures of the modelling framework for virtual observers.
References:
[1] A. A. Kulikovsky, J. Electrochem. Soc., 2014, 161, F263 https://doi.org/10.1149/2.028403jes

[2] A. Kravos, D. Ritzberger, G. Tavcar, C. Hametner, S. Jakubek, T. Katrasnik, Journal of Power Sources, 454, 2020, 227930, https://doi.org/10.1016/j.jpowsour.2020.227930

[3] A.A. Kulikovsky, Electrochimica Acta, 147, 2014, 773-777, https://doi.org/10.1016/j.electacta.2014.09.145

[4] A. Kravos, D. Ritzberger, G. Tavcar, C. Hametner, S. Jakubek, T. Katrasnik, EFC19, 8th European Fuel Cell, Piero Lunghi Conference, Naples, 9-11 December, 2019. ENEA, 2019, 303-304, https://www.europeanfuelcell.it/media/book_of_proceedings_EFC19.pdf