Determination of the optimal design of experiments that enables efficient parametrisation of fuel cell (FC) model with a minimum parametrisation data-set is one of the key prerequisites for ...minimizing costs and effort of the parametrisation procedure. To efficiently tackle this challenge, the paper present an innovative methodology based on the electrochemical FC model, parameter sensitivity analysis and application of D-optimal design plan. Relying on this consistent methodological basis the paper answers fundamental questions: a) on a minimum required data-set to optimally parametrise the FC model and b) on the impact of reduced space of operational points on identifiability of individual calibration parameters. Results reveal that application of D-optimal DoE enables enhancement of calibration parameters information resulting in up to order of magnitude lower relative standard errors on smaller data-sets. In addition, it was shown that increased information and thus identifiability, inherently leads to improved robustness of the FC electrochemical model.
•Analysis is based on a thermodynamically consistent electrochemical fuel cell model.•Optimal set of fuel cell model parameters is determined by sensitivity analysis.•D-optimal criterion is used to determine the optimal design of experiments.•Enhanced parameter information results in up to few orders of magnitude lower RSE.•It is shown that variation of inlet pressure significantly increases information.
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•Coupled system-level model of fuel cell operation and degradation is developed.•Operation of fuel cell is simulated with a mechanistic spatially and temporally resolved ...model.•Transient platinum degradation modeling framework simulates particle size redistribution.•Platinum oxidation, dissolution, precipitation, detachment and agglomeration is modeled.•Credibility of the model is confirmed by remarkable agreement with the experimental data.
High temperature proton exchange membrane fuel cells (HT-PEMFCs) are a promising and emerging technology, which enable highly efficient, low-emission, small-scale electricity and heat generation. The simultaneous reduction in production costs and prolongation of service life are considered as major challenges toward their wider market adoption, which calls for the application of predictive virtual tools during their development process. To present significant progress in the addressed area, this paper introduces an innovative real-time capable system-level modeling framework based on the following: (a) a mechanistic spatially and temporally resolved model of HT-PEMFC operation, and (b) a degradation modeling framework based on interacting individual cathode platinum degradation mechanisms. Additional innovative contributions arise from a consistent consideration of the varying particle size distribution in the transient fuel cell operating regime. The degradation modeling framework interactively considers the carbon and platinum oxidation phenomena, and platinum dissolution, redeposition, detachment, and agglomeration; hence, covering the entire causal chain of these phenomena. Presented results confirm capability of the modeling framework to accurately simulate the platinum particle size redistribution. Results clearly indicate more pronounced platinum particle growth towards the end of the channel since humidity is the main precursor of oxidation reactions. In addition, innovative modeling framework elucidate contributions of agglomeration, which is more pronounced at voltage cycling, and Ostwald ripening, which is more pronounced at higher voltages, to the platinum particles growth. These functionalities position the proposed modeling framework as a beyond state-of-the-art tool for model-supported development of the advanced clean energy conversion technologies.
Optimal control of liquid water dynamics plays an instrumental role in achieving optimised performance and prolonged lifetime of PEM Fuel Cells (PEMFC). Tackling these challenges calls for precise ...on-line monitoring and control tools such as coupled virtual observers taking into consideration also liquid water dynamics. The latter proves to be especially challenging to model due to varying retention and removal rates of liquid and gaseous water depending on the operating conditions thus representing a longstanding knowledge gap. To fill this gap, this contribution presents derivation of a 1D+1D system level physically motivated two-phase model of PEMFC, which enables consistent treatment of liquid water dynamics on the system level in all seven most influential regions of the PEMFC, namely membrane, anode and cathode channels, GDLs, and catalyst layers, while exhibiting real-time readiness with real-time factor of 0.0449. The model is extensively tested on single-cell data, which consists of five sets of experiments with different operating regimes and durations. Overall results exhibit good agreement with experimental data in all of the performed tests with R2 factors larger than 0.95. Newly developed features of the model enable its use in development of advanced control methodologies and hardware-in-the-loop as well as digital twin applications.
•System-level physically motivated two-phase PEMFC model is derived.•Model considers retention and removal rates of liquid and gaseous water.•Identifiability of calibration parameters was proven by sensitivity analysis.•Model exhibits good extrapolation capabilities beyond calibrated operational area.•Newly derived model is applicable in on-line monitoring and control applications.
Achieving efficient solid oxide fuel cell operation and simultaneous prevention of degradation effects calls for the development of precise on-line monitoring and control tools based on predictive, ...computationally fast models. The originality of the proposed modelling approach originates from the hypothesis that the innovative derivation procedure enables the development of a thermodynamically consistent multi-species electrochemical model that considers the electrochemical co-oxidation of carbon monoxide and hydrogen in a closed-form. The latter is achieved by coupling the equations for anodic reaction rates with the equation for anodic potential. Furthermore, the newly derived model is capable of accommodating the diffusive transport of gaseous species through the gas diffusion layer, yielding a computationally efficient quasi-one-dimensional model. This resolves a persistent knowledge gap, as the proposed modelling approach enables the modelling of multi-species fuels in a closed form, resulting in very high computational efficiency, and thus enable the model’s real-time capability. Multiple validation steps against polarisation curves with different fuel mixtures confirm the capability of the newly developed model to replicate experimental data. Furthermore, the presented results confirm the capability of the model to accurately simulate outside the calibrated variation space under different operating conditions and reformate mixtures. These functionalities position the proposed model as a beyond state-of-the-art tool for model supported development and control applications.
The detrimental effects of the catalyst degradation on the overall envisaged lifetime of low-temperature proton-exchange membrane fuel cells (LT-PEMFCs) represent a significant challenge towards ...further lowering platinum loadings and simultaneously achieving a long cycle life. The elaborated physically based modeling of the degradation processes is thus an invaluable step in elucidating causal interaction between fuel cell design, its operating conditions, and degradation phenomena. However, many parameters need to be determined based on experimental data to ensure plausible simulation results of the catalyst degradation models, which proves to be challenging with the in situ measurements. To fill this knowledge gap, this paper demonstrates the application of a mechanistically based PEMFC modeling framework, comprising real-time capable fuel cell performance, and platinum and carbon support degradation models, to model transient CO2 release rates in the LT-PEMFCs with the consistent calibration of reaction rate parameters under multiple different accelerated stress tests at once. The results confirm the credibility of the physical and chemical modeling basis of the proposed modeling framework, as well as its prediction and extrapolation capabilities. This is confirmed by an increase of only 29% of root mean square deviations values when using a model calibrated on all three data sets at once in comparison to a model calibrated on only one data set. Furthermore, the unique identifiability and interconnection of individual model calibration parameters are determined via Fisher information matrix analysis. This analysis enables optimal reduction of the set of calibration parameters, which results in the speed up of both the calibration process and the general simulation time while retaining the full extrapolation capabilities of the framework.
The use of hydrogen fuel cells as a mobile source of electricity could prove key to the future decarbonisation of heavy-duty road and marine transportation. Due to the complex interplay of various ...physicochemical processes in fuel cells, further development of these devices will depend on concerted efforts by researchers from various fields, who often lack in-depth knowledge of different aspects of fuel cell operation. These knowledge gaps can be filled by information that is scattered in a wide range of literature, but is rarely covered in a concise and condensed manner. To address this issue, we propose an educational-scale-bridging approach towards the modelling of most relevant processes in the fuel cell that aims to adequately describe the causal relations between the processes involved in fuel cell operation. The derivation of the model equations provides an intuitive understanding of the electric and chemical potentials acting on protons at the microscopic level and relates this knowledge to the terminology commonly used in fuel cell research, such as catalyst electric overpotential and internal membrane resistance. The results of the model agreed well with the experimental data, indicating that the proposed simple mathematical description is sufficient for an intuitive understanding of fuel cell operation.
Polymer electrolyte membrane fuel cells (PEMFCs) are prone to membrane dehydration and liquid water flooding, negatively impacting their performance and lifetime. Therefore, PEMFCs require ...appropriate water management, which makes accurate water modeling indispensable. Unfortunately, available control-oriented models only replicate individual water-related aspects or use oversimplistic approximations. This paper resolves this challenge by proposing, for the first time, a control-oriented PEMFC stack model focusing on physically motivated water modeling, which covers phase change, liquid water removal, membrane water uptake, and water flooding effects on the electrochemical reaction. Parametrizing the resulting model with measurement data yielded the fitted model. The parameterized model delivers valuable insight into the water mechanisms, which were thoroughly analyzed. In summary, the proposed model enables the derivation of advanced control strategies for efficient water management and mitigation of the degradation phenomena of PEMFCs. Additionally, the model provides the required accuracy for control applications while maintaining the necessary computational efficiency.
High temperature polymer electrolyte membrane fuel cells (HT-PEMFCs) are a promising and emerging technology that allow for highly efficient low emission small scale electricity and heat generation. ...Simultaneous reduction of production costs and prolongation of the service life is considered as a significant challenge towards their wider market adoptions, which calls for application of predictive virtual tools during the development process of HT-PEMFC systems. To present a significant progress in the addressed area, this paper presents an innovative modelling framework based on: a) mechanistically based spatially and temporally resolved HT-PEMFC performance model and b) modular degradation modelling framework based on interacting partial platinum degradation mechanisms. Proposed innovative tool chain thus allows for - compared to the current state of the art – more efficient and systematic model supported design of FCs and in-depth understanding of cause and effect chain from FC operation to its degradation. This merit of the proposed modelling framework arises from systematic reflection of FC control parameters in operational parameters of the FC, which are inputs to degradation modelling framework that considers in an interacting manner carbon and Pt oxidation phenomena and Pt dissolution, redeposition, detachment and agglomeration phenomena thereby adequately modelling the causal chain.
The reduction and prevention of degradation effects of proton exchange membrane fuel cells calls for precise on-line monitoring and control tools such as coupled virtual observers. To present ...significant progress in the area of computationally fast electrochemical models used in observer applications, this paper provides the derivation of a zero-dimensional thermodynamically consistent electrochemical model for proton exchange membrane fuel cells performance modelling and control. The model is further extended to accommodate the transport of gaseous species along the channel and through gas diffusion layer, yielding a quasi-one-dimensional electrochemical model. In addition, the presented work features the determination of an optimal set of calibration parameters proposed and based on mathematical and physical rationale, which is further supported with parameter sensitivity analysis. Multiple validation steps against polarisation curves at different operational points confirm the capability of the newly developed model to replicate experimental data. Furthermore, investigation in models generalisation capabilities shows that the model exhibits very good extrapolation capabilities for operation points outside the calibrated variation space of parameters. Additionally, the newly developed model can be successfully parametrised with little effort on a small calibration data set. These features position the proposed modelling framework as a beyond state-of-the-art model for virtual observers.
•Advanced 0D thermodynamically consistent electrochemical model of PEMFC is derived.•Identifiability of calibration parameters was proven by sensitivity analysis.•Ease of parametrisation on the small calibration data is achieved.•Model exhibit good extrapolation capabilities beyond calibrated operational area.•Newly derived model is applicable in on-line monitoring and control applications.
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