Exchange Membrane Fuel Cell Model Research Articles

A levy chaotic horizontal vertical crossover based artificial hummingbird algorithm for precise PEMFC parameter estimation

In this research, enhanced versions of the Artificial Hummingbird Algorithm are used to accurately identify unknown parameters in Proton Exchange Membrane Fuel Cell (PEMFC) models. In particular, we propose a multi strategy variant, the Lévy Chaotic Artificial Hummingbird Algorithm (LCAHA), which combines sinusoidal chaotic mapping, Lévy flights and a new cross update foraging strategy. The combination of this method with PEMFC parameters results in a significantly improved performance compared to traditional methods, such as Particle Swarm Optimization (PSO), Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Sparrow Search Algorithm (SSA), which we use as baselines to validate PEMFC parameters. The quantitative results demonstrate that LCAHA attains a minimum Sum of Squared Errors (SSE) of 0.0254 and standard deviation of 4.59E−08 for the BCS 500W PEMFC model, which is much lower than the SSE values obtained for PSO (0.1924) and GWO (0.0364), thereby validating the superior accuracy and stability of LCAHA. Moreover, LCAHA converges faster than DE and SSA, reducing runtime by about 47%. The robustness and reliability of LCAHA-simulated and actual I–V curves across six PEMFC stacks are shown to be in close alignment.

Precision parameter estimation in Proton Exchange Membrane Fuel Cells using depth information enhanced Differential Evolution

Proton Exchange Membrane Fuel Cell (PEMFC) models require parameter tuning for their design and performance improvement. In this study, Depth Information-Based Differential Evolution (Di-DE) algorithm, a novel and efficient metaheuristic approach, is applied to the complex, nonlinear optimization problem of PEMFC parameter estimation. The Di-DE algorithm was tested on twelve PEMFCs (BCS 500 W PEMFC, Nedstack 600 W PS6 PEMFC, SR-12 500 W PEMFC, H-12 PEMFC, STD 250 W PEMFC, HORIZON 500 W PEMFC and four 250W PEMFC and two H-12 12W PEMFC) and showed excellent accuracy. The Di-DE algorithm is was compared with other advanced evolutionary algorithms like iwPSO, CLPSO, DNLPSO, SLPSO, SaDE, SHADE, JADE, QUATRE, LSA, QUATRE-EMS and C-QUATRE, which obtained a minimum objective function value of 0.0255 and an average runtime improvement of 98.8%. The optimized parameters of the proposed method yielded the Sum of Squared Errors (SSE) as low as 0.00002 in some cases, which indicates better precision and stability. Moreover, the voltage–current (V–I) and power–voltage (P–V) characteristics predicted by Di-DE were within 1% error relative to the experimental data for all tested PEMFCs. The results of this work highlight the potential of the Di-DE algorithm to enable more sophisticated modelling and optimization of PEMFCs, which in turn will help to broaden the use of PEMFCs in clean energy applications.

Novel reinforcement learning technique based parameter estimation for proton exchange membrane fuel cell model

Proton Exchange Membrane Fuel Cells (PEMFCs) offer a clean and sustainable alternative to traditional engines. PEMFCs play a vital role in progressing hydrogen-based energy solutions. Accurate modeling of PEMFC performance is essential for enhancing their efficiency. This paper introduces a novel reinforcement learning (RL) approach for estimating PEMFC parameters, addressing the challenges of the complex and nonlinear dynamics of the PEMFCs. The proposed RL method minimizes the sum of squared errors between measured and simulated voltages and provides an adaptive and self-improving RL-based Estimation that learns continuously from system feedback. The RL-based approach demonstrates superior accuracy and performance compared with traditional metaheuristic techniques. It has been validated through theoretical and experimental comparisons and tested on commercial PEMFCs, including the Temasek 1 kW, the 6 kW Nedstack PS6, and the Horizon H-12 12 W. The dataset used in this study comes from experimental data. This research contributes to the precise modeling of PEMFCs, improving their efficiency, and developing wider adoption of PEMFCs in sustainable energy solutions.

Application of chaotic teaching-learning-based optimization technique for estimating unknown parameters of proton exchange membrane fuel cell model.

Proton exchange membrane fuel cells (PEMFC) possess features like high specific power density, low operating temperature, and low operating pressure and thus are most widely used. The performance of PEMFC highly depends on its output voltage which further affects its efficiency. This research paper aims to improve this output voltage by minimizing the losses through parameter estimation technique for three well-known commercial PEMFC stacks, namely, 250W, BCS 500W, and Ballard Mark V. The multiobjective function framed for optimization serves two goals. One is to extract the unknown parameters of FC, and second is to achieve the minimum sum of squared errors (SSE) that occur due to the difference between experimental voltage and estimated voltage. Chaotic teaching-learning-based optimization (CTLBO) algorithm is used for optimization process. SSE values obtained for three commercial PEMFC stacks 250W, BCS 500W, and Ballard Mark V are 7.02267, 4.00150, and 0.8100, respectively. The applicability of this technique is further checked for different operating conditions of each model. The I-P (current-power) curve and I-V (current-voltage) curve obtained using estimated data closely matched the experimental data that showed the practical relevance and efficacy of the algorithm. A comparison is done among the SSE results obtained using CTLBO to other competitive algorithms mentioned in the literature. CTLBO showed its superiority over other algorithms in estimating the unknown parameters of PEMFC stack parameters.

Performance Investigation of PEM Fuel Cell with Three-Pass Serpentine Flow Fields under Varying Operating Voltages

The fuel cells performance is significantly impacted by both design and operational factors. The effective distribution of reactants within the flow fields is facilitated by the design of the flow channels. Therefore, the geometry of the flow channels and the overall design of the flow field play a crucial role in determining the fuel cells performance. Among various flow field designs, the serpentine flow field demonstrates superior performance compared to others. In this research, a three-dimensional proton exchange membrane fuel cell model was developed and used to study the influence of three-pass serpentine flow field on cell performance across varying operating voltages (0.9 V, 0.7 V and 0.5 V). The purpose of this research is to simulate and evaluate the comportment of the three-pass serpentine flow channels configuration by analyzing several parameters such as channels velocity distribution, oxygen mole fraction, pressure distribution and electrolyte current density along the z-axis at the cathode under different operating voltages. Numerical simulations were conducted using the COMSOL Multiphysics software. Therefore, this software is used to solve numerically the complete three-dimensional model with the governing equations of charge conservation, species transport, momentum, and continuity. The obtained results indicate that among different operating voltages, the cell voltage of 0.5 V demonstrated the highest channels velocity distribution, pressure distribution, and electrolyte current density. Moreover, it is found that at an operating voltage of 0.5 V, there is an important decrease in oxygen concentrations indicating a significant oxygen consumption in the fuel cell which improves the overall efficiency. This work contributes valuable insights to the optimization of fuel cell performance, specifically highlighting the favorable outcomes associated with the three-pass serpentine flow field design at lower operating voltages

Extracting Accurate Parameters from a Proton Exchange Membrane Fuel Cell Model Using the Differential Evolution Ameliorated Meta-Heuristics Algorithm

The electrochemical proton exchange membrane fuel cell (PEMFC) is an electrical generator that utilizes a chemical reaction mechanism to produce electricity, serving as a sustainable and environmentally friendly energy source. To thoroughly analyze and develop the features and performance of a PEMFC, it is essential to use a precise model that incorporates exact parameters to effectively suit the polarization curve. In addition, parameter extraction plays a crucial role in the simulation analysis, evaluation, optimum control, and fault detection of the proton exchange membrane fuel cell (PEMFC) system. Despite the development of many algorithms for parameter extraction in PEMFC, obtaining accurate and trustworthy results rapidly remains a challenge. This study presents a hybridized algorithm, namely differential evolution ameliorated (DEA) for reliably estimating PEMFC model parameters. To evaluate the proposed DEA-based parameter identification, a comparison analysis with previously published methods is conducted using MATLAB/SimulinkTM (R2016b, MathWorks, Natick, MA, USA) in terms of system correctness and convergence process. The proposed DEA algorithm is tested to extract the parameters of two PEMFC models: SR-12 500 W and 250 W. The sum of the squared errors (SSE) between the experimental and the obtained voltage data is defined as an objective function. The simulation results prove that the suggested DEA algorithm is capable of identifying the optimal PEMFC parameters rapidly and accurately in comparison with other optimization algorithms.

Randomness effect of platinum loading distribution in a proton exchange membrane fuel cell: A numerical simulation

The platinum loading is randomly distributed within catalyst layers because of the fabrication way, whereas the platinum loading is considered to follow the homogeneous distribution in the traditional catalyst layer model. The cell performance and heat and species transport laws of the fuel cell with platinum loading random distribution within catalyst layers are not yet clear. Therefore, in this work, a two-dimensional, non-isothermal proton exchange membrane fuel cell model considering the two-phase flow and agglomerate structure of catalyst layers is established to simulate the fuel cell having the catalyst layer where platinum loading is random distribution in a way that is closer to the actual structure. The effect of random distribution of platinum loading on the electrical property, species transfer and temperature distribution is analyzed. Results suggest that the randomness influence needs to be considered when the local distributions of parameters are studied and the research accuracy of parameters is relatively high. In contrast with the homogeneous distribution of platinum loading, the cell performance for the normal random distribution and uniform random distribution cases is reduced. The effects of catalyst loading random patterns on cell performance, species and temperature distributions are different, and the decrease of cell performance for the uniform random distribution case is more obvious. Furthermore, the influence degree of randomness on each parameter is different. The distributions of electrochemical reaction rate, oxygen concentration and temperature display random characteristics, while the liquid water saturation distribution is less influenced by randomness and does not show an obvious random change. These findings can provide a reference for the randomness verification in random simulations and deepen the understanding of species and heat transfer laws in the catalyst layer which is closer to the reality to improve the accuracy of fuel cell simulations.

Research of Proton Exchange Membrane Fuel Cell Modeling on Concentration Polarization under Variable-Temperature Operating Conditions

In this study, a concentration overvoltage model that focuses on describing variable-temperature operating condition properties for PEMFCs is established. Sensitivity analysis and a quantification study of oxygen transport resistance are carried out based on the oxygen transport resistance model and measurement data. By analyzing the influence of temperature on cathode oxygen transport resistance, the key structural parameters of the cathode oxygen transport resistance models are estimated, and the parameter modification method of fuel cell limiting current density under variable temperatures is proposed. Based on the polarization curve test experiments under variable-temperature conditions, it is demonstrated that the newly developed concentration overvoltage model reduces the relative error of simulation for a low Pt loading fuel cell in the high current region by 2.97% and 10.06% at 60 °C and 80 °C, respectively. The newly established concentration overvoltage model of a PEMFC solves the problem that the parameter of limiting current density is set without considering the influence of fuel cell temperature fluctuation, which leads to the poor simulation accuracy of the concentration overvoltage model in the high current region.

Parameters Estimation of Proton Exchange Membrane Fuel Cell Model Based on an Improved Walrus Optimization Algorithm

Parameters Estimation of Proton Exchange Membrane Fuel Cell Model Based on an Improved Walrus Optimization Algorithm

Comprehensive analysis of shutdown purge influencing factors of proton exchange membrane fuel cell based on water heat transfer and water vapor phase change mechanism

A two-dimensional multiphase proton exchange membrane fuel cell model is established to study the effect mechanism of temperature, pressure, humidity, and flow rate on the purge rate and ionomer dissolved water content at the end of purging on the basis of water heat transfer and water vapor phase change mechanism. The numerical model is analyzed by COMSOL Multiphysics 6.0 software, and the polarization curve and high-frequency impedance curve obtained under the same operating conditions are used to verify the validity of the model. Results show that ionomer dissolved water content increases and then decreases slightly due to the liquid water dissolved phase transfer in the slow-change step of the purge. Temperature, pressure, and humidity can effectively improve the purge rate and reduce the ionomer dissolved water content of the purge end. However, flow rate has little impact on both, but it can shorten the duration of the first stage and improve the effectiveness of the purge by effectively removing liquid water. This study provides a basis for revealing the influence of shutdown purge and formulating a reasonable shutdown purge strategy.

Low stoichiometry operation of the anode side of a low-temperature proton exchange membrane fuel cell – A modeling study

A single-channel proton exchange membrane fuel cell model (anode side) based on computational fluid dynamics is used to investigate the possibility of operating a fuel cell at low stoichiometric flow ratios using completely dry inlet hydrogen. A case study of three different stoichiometric flow ratios (ξ = 1.01, ξ = 1.03, ξ = 1.05), three different operating temperatures (343.15 K, 347.15 K, 353.15 K), and three different operating pressures (1 atm, 1.2 atm and 1.5 atm) are presented. It is found that the predicted hydrogen concentration and relative humidity (RH) in the catalyst layer (CL) have opposite trends: the RH in CL decreases with increasing stoichiometric flow ratios, but it reaches 100% at the outlet. While hydrogen concentration in CL increases with increasing stoichiometric flow ratios and the largest difference is at the inlet, with a maximum of 3.6%. The results also suggest that PEM fuel cells may be operated in a stoichiometric flow ratio as low as ξ = 1.01 at the anode side. This cell operation would allow open-ended anode operation without a recirculation system, thus significantly reducing system complexity and cost. The CFD code is disclosed to provide a starting point for more complex model development.

Adaptive Estimation of Quasi-Empirical Proton Exchange Membrane Fuel Cell Models Based on Coot Bird Optimizer and Data Accumulation

The ambitious spread of fuel cell usage is facing the aging problem, which has a significant impact on the cells’ output power. Therefore, it is necessary to develop reliable techniques that are capable of accurately characterizing the cell throughout its life. This paper proposes an adaptive parameter estimation technique to develop a robust proton exchange membrane fuel cell (PEMFC) model over its lifespan. This is useful for accurate monitoring, analysis, design, and control of the PEMFC and increasing its life. For this purpose, fair comparisons of nine recent optimization algorithms were made by implementing them for a typical quasi-empirical PEMFC model estimation problem. Investigating the best competitors relied on two conceptual factors, the solution accuracy and computational burden (as a novel assessment factor in this study). The computational burden plays a great role in accelerating the model parameters’ update process. The proposed techniques were applied to five commercial PEMFCs. Moreover, a necessary statistical analysis of the results was performed to make a solid comparison with the competitors. Among them, the proposed coot-bird-algorithm (CBO)-based technique achieved a superior and balanced performance. It surpassed the closest competitors by a difference of 16.01% and 62.53% in the accuracy and computational speed, respectively.

Open-source Computational Model for Polymer Electrolyte Fuel Cells

Open-source fuel cell models outmatch commercial codes in many important aspects. By providing the source code, reuse, modification and extension of the model and comparison with other codes becomes possible. With this motivation, we present a three-dimensional, steady-state, non-isothermal proton exchange membrane fuel cell model, implemented in the open-source finite volume library OpenFOAM® . At every stage of implementation, special care was taken to ensure a well documented, organised, and modular structure of the software. The resulting model suite can, and should, be extended with new sub-modules by the user. The main field of application, modelling of fuel cells from an engineering perspective, is demonstrated by simulating two different conventional polymer electrolyte fuel cells, operated at CIEMAT and Forschungszentrum Jülich, respectively.

Optimal estimation of proton exchange membrane fuel cell model parameters based on an improved chicken swarm optimization algorithm

ABSTRACT Proton exchange membrane fuel cell (PEMFC) has been gradually applied in new energy vehicles, aviation and other industries, attracting widespread attention. Accurately identifying unknown parameters in the mathematical model of PEMFC is beneficial to the simulation, control and prediction of its output Current-Voltage curve. In order to identify the optimal unknown parameters, based on basic Chicken Swarm Optimization, this paper introduces positive/negative learning strategies for roosters and positive learning strategies for hens and chicks. An Improved Chicken Swarm Optimization algorithm is proposed. Compared with Particle Swarm Optimization, Salp Swarm Algorithm, Whale Optimization Algorithm and basic CSO algorithm, the proposed algorithm shows better convergence and accuracy. The five algorithms are applied to three common stacks (250W PEMFC, NedStack PS6 PEMFC, Ballard Mark V) and PEMFC monomer for model unknown parameter identification and optimization. The results show that, the ICSO algorithm obtains the minimum integral of absolute error of the actual stack voltage and the simulated stack voltage in the three test stacks and a PEMFC monomer, which are 2.288, 5.857, 2.407 and 0.408, the ICSO algorithm has a maximum increase of 8.63%, 4.52%, 6.20% and 64.83% in accuracy, respectively. The simulation data agrees well with the experimental data. These indicating that the mathematical model of PEMFC based on ICSO algorithm can accurately simulate the polarization curve at different temperatures and partial pressures, and it can be obtained that with the increase of temperature and partial pressure, the output performance of the PEMFC is also getting better.

A novel robust reset controller implemented through field programmable gate array for oxygen ratio regulation of proton exchange membrane fuel cell

This paper considers the nonlinear proton exchange membrane fuel cell model to precisely describe the system dynamics and presents a robust reset control method for regulating oxygen rate and optimizing the operation of the fuel cell system during fast load variations. The proposed reset law eliminates overshoot, shortens settling time, and thus improves the behavior of the closed-loop system, while achieving these goals is impossible by any linear controller. Due to the ability of field programmable gate array (FPGA) in providing high speed and efficient processing through software as well as near-real-time performance verification, the proposed control method is implemented through FPGA to confirm operational capability and high speed flexibility of controller. The results of the implementation of the proposed method and comparison with the hybrid fuzzy proportional integral derivative method exhibit smooth dynamic response, error reduction in terms of various criteria and better capability in tracking the desired oxygen rate despite the drastic changes in load current.

Correlating electrochemical active surface area with humidity and its application in proton exchange membrane fuel cell modeling

The electrochemical active surface area has a vital influence on the performance of proton exchange membrane fuel cells. In this study, a universal semi-empirical equation of the electrochemical active surface area in the catalyst layer of fuel cells is proposed based on self-designed experiments, aiming to improve the predictive accuracy of numerical models under low humidity conditions. The generalization of this equation is also verified with the other nine catalyst layers of different compositions. At very low water content corresponding to low inlet humidification operations, the electrochemical active surface area is generally low and increases sharply with the increment of water content. When the water content exceeds a certain threshold value, the electrochemical active surface area becomes independent of water content. In addition, the electrochemical active surface area significantly decreases as the operating temperature increases. Consequently, including this newly proposed electrochemical active surface area equation in conventional full-cell models is of significant importance to accurately predict the activation loss and performance of fuel cells under both cold-start and normal operation conditions, especially at low humidification, which is validated against experimental data. In contrast with the conventional constant electrochemical active surface area assumption, this equation improves the model accuracy from about 70% to be higher than 90% under low humidity conditions.

Three-Dimensional CFD Modeling of Serpentine Flow Field Configurations for PEM Fuel Cell Performance

A complete three-dimensional Proton Exchange Membrane Fuel Cell (PEMFC) model is proposed to study the influence of right-angle turn single serpentine (RAT1S), right-angle turn double serpentine (RAT2S), right-angle turn triple serpentine (RAT3S), and right-angle turn 3–2–1 serpentine (RAT321S) flow fields configuration on PEMFC performance with a commercial CFD code (ANSYS FLUENT). Simulations have been performed to envisage the pressure drop in the channel, the mass fraction of H2 and O2 along the anode and cathode channels, current flux density dispersion on the catalyst layer (CL), the membrane water content and proton conductivity as well as cell performance for proposed 4 flow field designs. A comparison of the simulation results of the four models was carried out. It has been found that the output of RAT321S flow field has improved compared to the RAT1S, RAT2S, and RAT3S flow field designs for the flow of the fixed-flow reactants, and RAT321S flow field model has been validated with experimental literature evidence. The results also show that the pressure drop losses are reduced as the number of passes increases.

A comprehensive two-phase proton exchange membrane fuel cell model coupled with anisotropic properties and mechanical deformation of the gas diffusion layer

Adequate mechanical compression applied to a proton exchange membrane fuel cell is essential for enhancing performance and durability. The compression not only improves the intimate contact between each layer component, but also causes significant deformation of the gas diffusion layer (GDL). As a result, the level of compression results in changes of electrical and thermal contact resistances, and anisotropic distribution of porosity and tortuosity in the GDL. To improve the fundamental understanding of the compression effect, a comprehensive two-phase model coupling solid mechanics, heat and mass transfer, and electrochemical reactions is developed. First, the model results are validated and show good agreement with the experimental data at baseline operating conditions of 80 °C, 200 kPa, 80% relative humidity, and 20% compression strain ratio with hydrogen and air. Then, oxygen, temperature and liquid saturation distribution at low, intermediate and high current densities are studied at the baseline compression level (20% strain). Finally, five compression strain ratios ranging from 5%, 10%, 15%, 20% and 25% are investigated to study the effect on stress distribution, transport properties, and fuel cell performance. Our results indicate that significant GDL deformation and channel intrusion are caused by land and rib distribution. As a combined effect from heat and mass transport, the liquid water condensation tends to initiate near the rib/GDL interface and can reach near 30% saturation at high current density. In addition, significant difference of in-plane temperature, oxygen, current, and load distributions can be observed due to the geometric aspect ratio and anisotropic GDL properties. A compression strain ratio of 20% is found to have an optimal performance balancing between high contact resistance caused by low compression and high transport resistance due to high compression. The findings of this study provide a new insight to the understanding the complicated coupling effect between mechanical, thermal, mass transport, and electrochemical multiphysics.

Performance analysis of Pt/TiO2/C catalyst using a multi-scale and two-phase proton exchange membrane fuel cell model

We present a detailed theoretical investigation into the effect of using titanium dioxide (TiO2) as support for Pt nanoparticles in proton-exchange membrane fuel cells (PEMFCs). In this context, TiO2 was exhibited excellent resistance towards carbon corrosion and Pt particle agglomeration despite being a semi-conductive metal with poor electric conductivity. The major focus of this study is on elucidating the merits and demerits of using a TiO2 support material in terms of PEMFC performance and durability. For the first time, the micro-scale catalyst model was improved and used to analyze the effects of electron transport in Pt/TiO2/C catalyst structure. The new model is coupled with a three-dimensional two-phase PEMFC model and multi-scale simulations are carried out for various PEMFCs, designed with both Pt/TiO2/C and traditional Pt/C catalysts, for comparison. The model predictions highlight that the suppression of Pt particle growth via the Pt/TiO2/C catalyst structure is clearly advantageous to maintain good catalyst performance during long-term PEMFC operations. However, the additional electronic ohmic loss by the TiO2 particles can be significant during high current density operations (e.g. 20 mV at 1.0 A/cm2). This study illustrates that the present multi-scale PEMFC model is a valuable instrument for designing and optimizing porous catalyst structures with various candidate catalyst support materials.

Proton exchange membrane fuel cell model parameter identification based on dynamic differential evolution with collective guidance factor algorithm

This paper firstly proposes a dynamic differential evolution algorithm (DDE-CGF) with a collective guiding factor to solve the problem of parameter identification and optimization of proton exchange membrane fuel cell (PEMFC) model. Inspired by the swarm intelligence scheme, a collective guidance factor is designed to accelerate the convergence speed without affecting the convergence accuracy. Moreover, a dynamic scaling factor and the dynamic crossover probability based on evolutionary mechanism are introduced to enhance the diversity of population as well as improve the global searching performance. Through testing eight benchmark functions, the DDE-CGF algorithm exhibits superior performance in both convergence accuracy and speed. Based on the excellent global performance, applying DDE-CGF algorithm to the parameter identification of the PEMFC model, and more accurate parameter values are obtained. Comparing with other algorithms, the result proves that the DDE-CGF algorithm could accurately estimate model parameters and the identified model could greatly describe the dynamical characteristic of the PEMFC model.