An enhanced efficient optimization algorithm (EINFO) for accurate extraction of proton exchange membrane fuel cell parameters

Proton exchange membrane fuel cell (PEMFC) is considered as propitious solution for an environmentally friendly energy source. A precise model of PEMFC for accurate identification of its polarization curve and in-depth understanding of all its operating characteristics attracted the interest of many researchers. In this paper, novel meta-heuristic optimization methods have been successfully applied to evaluate the unknown parameters of PEMFC models, particularly Harris Hawks’ optimization (HHO) and atom search optimization (ASO) techniques. The proposed optimization algorithms have been tested on three different commercial PEMFC stacks, namely BCS 500-W PEM, 500W SR-12PEM and 250W stack, under various operating conditions. The sum of square errors (SSE) between the results obtained by the application of the estimated parameters and the experimentally measured results of the fuel cell stacks was considered as the objective function of the optimization problem. In order to validate the effectiveness of the proposed methods, the results are compared with that obtained in studies. Moreover, the I/V curves obtained by the application of HHO and ASO showed a clear matching with data sheet curves for all the studied cases. Finally, PEMFC model based on HHO technique surpasses all compared algorithms in terms of the solution accuracy and the convergence speed.

Development and modeling of proton exchange membrane fuel cells (PEMFCs) need accurate identification of unknown factors affecting mathematical models. The trigonometric function-based sine cosine algorithm (SCA) may solve such problems, but it traps in local optima, making it inappropriate for larger optimization tasks. This paper introduces a novel multi-trial vector-based sine cosine algorithm (MTV-SCA) for the identification of seven unknown parameters of PEMFCs. The proposed MTV-SCA incorporates MTV methodology utilizing three control parameters to achieve the desired optimization targets. A key contribution of this work is the development of four distinct search strategies, to mitigating early convergence issues. These strategies leverage various sinusoidal and cosinusoidal factors to improve the algorithm. The optimization goal is to minimize sum square error (SSE) between measured and simulated stack voltages. Five PEMFC stack mode:250W, BCS 500W, SR-12, H-12, and Temasek 1 kW, validate the MTV-SCA algorithm’s efficacy and robustness Compared to previously established optimization approaches, MTV-SCA extracts optimum PEMFC parameters more accurately and reliably. Statistical testing further demonstrates the method’s durability and consistency. Analyzing PEMFC performance at different pressures and temperatures helps verify the adjusted parameters. Simulations show that the MTV-SCA solves difficult PEMFC parameter identification issues better than SCA and other approaches.

Proton Exchange Membrane (PEM) fuel cells represent a promising clean energy technology due to their high efficiency, environmental sustainability, and wide applicability in transportation and stationary power systems. Accurate parameter extraction from PEM fuel cell models is critical for reliable performance prediction, control, and optimization. However, this task is challenging because of the nonlinear, multimodal, and highly coupled characteristics of fuel cell models. To address this challenge, this paper proposes an Enhanced Elk Herd Optimizer (EEHO), incorporating a novel best-bull–guided differential reproduction mechanism to improve search accuracy, convergence speed, and robustness. The proposed enhancement enables a portion of offspring solutions to be generated by perturbing the global best solution using scaled differences between randomly selected herd members. This mechanism strengthens exploitation around promising regions while maintaining population diversity and preventing premature convergence. The EEHO is applied to extract seven unknown parameters of PEM fuel cell models by minimizing the sum of squared errors between experimental and simulated voltage data. The effectiveness of the proposed method is validated using two commercial PEM fuel cell stacks, namely a 250 W stack and a BCS 500 W stack. Extensive comparative evaluations against the conventional Elk Herd Optimizer and several well-established methods demonstrate that the EEHO achieves superior performance in terms of accuracy, convergence speed, robustness, and statistical consistency. The proposed algorithm attains lower error values, faster convergence, and more stable performance across multiple independent runs. Furthermore, the extracted parameters produce highly accurate voltage and power characteristics, closely matching experimental observations. The results confirm that the proposed EEHO provides an efficient, reliable, and robust optimization framework for PEM fuel cell parameter extraction and offers strong potential for broader applications in energy system modeling, intelligent optimization, and renewable energy optimization problems. Quantitatively, the proposed EEHO achieved a significant reduction in the averages of the Sum of Squared Errors (SSE) of up to 24.96% and 23.29% compared with the conventional EHO for the 250 W stack and a BCS 500 W stack, respectively, demonstrating its superior accuracy in parameter estimation. To further validate the robustness and generalization capability of the proposed EEHO, two additional commercial PEM fuel cell datasets, of Ballard Mark V and Modular SR-12, are investigated and compared against several state-of-the-art optimization algorithms. The results, supported by Wilcoxon and Friedman statistical tests and boxplot analyses, confirm that EEHO consistently achieves superior accuracy, stability, and convergence reliability across different operating conditions.

Precise models predicting fuel cell performance under different operating conditions require accurate parameter identification in a proton exchange membrane fuel cell (PEMFC). Most traditional parameter estimation methodologies depend on optimization algorithms which are limited in their efficiency, convergence speed, and robustness. Typically, existing algorithms fail to achieve a balance between precision and computational efficiency, leading to suboptimal modeling of the complex, nonlinear behavior of PEMFCs. In this paper, we present the two-stage differential evolution (TDE) algorithm, which fills these gaps by using a new mutation strategy that improves solution diversity and speeds up convergence. Seven critical unknown parameters ( and ) in PEMFC models are identified by using the proposed TDE algorithm. The optimization process is to minimize the sum of squared errors (SSE) between the experimentally measured and predicted cell voltages. TDE resulted in a 41% reduction in SSE (minimum SSE of 0.0255 compared to 0.0432), a 92% improvement in maximum SSE, and over 99.97% reduction in standard deviation compared to the HARD-DE algorithm. Furthermore, TDE was shown to be 98% more efficient than HARD-DE, with a runtime of 0.23 s, compared to HARD-DE’s runtime of 11.95 s. Extensive testing of these advancements was performed on six commercially available PEMFC stacks over twelve case studies, and I/V and P/V characteristics were confirmed to be consistent with experimental data. The results show that TDE has better accuracy, robustness and computational efficiency than the other methods, and therefore TDE can be used as a real time PEMFC parameter estimation tool.

Performance of rime-ice algorithm for estimating the PEM fuel cell parameters

Efficient fractional-order modified Harris hawks optimizer for proton exchange membrane fuel cell modeling

The use of proton exchange membrane fuel cells (PEMFCs) in sustainable energy applications depends on their high efficiency levels along with their ability to produce low emissions and operation without noise. The optimization of PEMFC design variables faces difficulties because of the complex nonlinear relationships which exist between activation overpotential and concentration overpotential and internal resistance. The optimization methods PSO, DE and WOA face three major setbacks which include their delayed convergence rates as well as their sensitiveness to initial parameter settings and their tendency to lock onto sub-optimal solutions. The study presents the Parrot Optimizer (PO) as a new metaheuristic algorithm which derives its inspiration from the adaptive behaviors of Pyrrhura Molinae parrots to overcome current optimization challenges. The PO serves to optimize six PEMFC stack design variables for BCS 500 W, Nedstack 600 W PS6, SR-12 W, Horizon H-12, Ballard Mark V, and STD 250 W. The research performs an extensive comparison between nine advanced algorithms to analyze their performance against PSO, DE, WOA, Rabbit Optimization Algorithm (ROA), Flamingo Herd Optimization (FHO), Arithmetic Optimization Algorithm (AOA), Sine Cosine Algorithm (SCA), Multi-Verse Optimizer (MVO) and Bat Algorithm (BA). The objective function Sum of Squared Error (SSE) for stack voltage is minimized using different algorithms for comparative analysis. Simulation results for I–V and V–P characteristics aligned closely with experimental data under varying temperature and pressure conditions. PO achieved the lowest Mean SSE values across all cases, with values of 0.025519, 0.275211, 0.242413, 0.102915, 0.148632, and 0.283774 for the BCS 500 W, Nedstack 600 W PS6, SR-12 W, Horizon H-12, Ballard Mark V, and STD 250 W stacks, respectively. Additionally, PO demonstrated the fastest runtime (RT) in all cases, with values as low as 0.116855 s for the Horizon H-12 stack. The results indicate that PO delivers better performance than existing algorithms because it reaches the lowest Sum of Squared Error for stack voltage outputs across every test scenario. I–V and V–P characteristic simulations match experimental results across different temperature and pressure values which proves the theoretical value and practical usage of PO in solving nonlinear optimization problems. The study demonstrates PO as a dependable optimization method which improves PEMFC design processes while enhancing operational reliability through future research that includes real-time control and algorithm combination and system scalability.

A new technique for optimal estimation of the circuit-based PEMFCs using developed Sunflower Optimization Algorithm

In this paper, an accurate model of proton exchange membrane fuel cell (PEMFC) for optimal identification of PEMFC parameters has been developed. The optimization methodology is based on the modified version of Manta Ray Foraging Optimization (MMRFO) technique for minimizing the sum of squared errors (SSE) between the Experimentally measured stack voltage and the estimated voltage produced by the optimized model. In the modified methodology, the sine-cosine method has been utilized to enhance the global searching capability in the exploration phase and the local searching capability in the exploitation phase of the MRFO algorithm. In order to validate the effectiveness of the suggested methodology, four different case studies comprising standard benchmark 250 W PEMFC, BCS-500 W PEMFC, SR-12 500 W FC, and 1 kW Temasek stacks were utilized, and the attainments have been compared with the measured polarization characteristics. The attainments have been intensively compared with several metaheuristic algorithms (MA) including Tree growth Algorithm (TGA), Grey wolf optimizer (GWO), Whale optimization algorithm (WOA), Salp swarm algorithm (SSA), and original Manta Ray Foraging Optimization (MRFO), to confirm the superiority of the MMRFO against the compared techniques. The obtained results give a satisfactory agreement between the MMRFO-based model and the experimentally measured data. Finally, the achievements confirmed the effectiveness of the MMRFO over the basic MRFO algorithm and other novel metaheuristic algorithms in identifying PEMFC parameters.

Model parameter estimation of the PEMFCs using improved Barnacles Mating Optimization algorithm

Proton Exchange Membrane Fuel Cells (PEMFC) is considered a propitious solution for an environmentally friendly energy source. A precise model of PEMFC for accurate identification of its polarization curve and an in-depth understanding of all its operating characteristics attracted the interest of many researchers. In this paper, recent meta-heuristic optimization methods have been successfully applied to evaluate the unknown parameters of PEMFC models, particularly Marine Predators Algorithm (MPA) and Political Optimizer (PO) techniques. The proposed optimization algorithms have been tested on three different commercial PEMFC stacks, namely BCS 500-W, SR-12PEM 500 W, and 250 W stack under various operating conditions. The sum of square errors (SSE) between the results obtained by the application of the estimated parameters and the experimentally measured results of the fuel cell stacks was considered as the objective function of the optimization problem. In order to validate the effectiveness of the proposed methods, the results are compared with those obtained in the literature. Moreover, the I/V curves obtained by the application of MPA and PO showed a clear matching with datasheet curves for all the studied cases. Statistical analysis has been performed to evaluate the robustness of the MPA and PO techniques. Finally, the PEMFC model based on the MPA technique surpasses all compared algorithms in terms of the solution accuracy and the convergence speed. The obtained results confirmed the superiority and reliability of the applied approach of the MPA algorithm. The results prove that the MPA algorithm has a superior performance based on its reliability.

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.

An efficient hybrid sine-cosine Harris hawks optimization for low and high-dimensional feature selection

The parameter extraction of the proton exchange membrane fuel cells (PEMFCs) is an active study area over the past few years to achieve accurate current/voltage (I/V) curves. This work proposes an advanced version of an improved gorilla troops technique (IGTT) to precisely estimate the PEMFC’s model parameters. The GTT's dual implementation of the migration approach enables boosting the exploitation phase and preventing becoming trapped in the local minima. Besides, a Tangent Flight Strategy (TFS) is incorporated with the exploitation stage for efficiently searching the search space. Using two common PEMFCs stacks of BCS 500W, and Modular SR-12, the developed IGTT is effectively applied. Furthermore, the two models are evaluated under varied partial temperature and pressure. In addition to this, different new recently inspired optimizers are employed for comparative validations namely supply demand optimization (SDO), flying foxes optimizer (FFO) and red fox optimizer (RFO). Also, a comparative assessment of the developed IGTT and the original GTT are tested to ten unconstrained benchmark functions following to the Congress on Evolutionary Computation (CEC) 2017. The proposed IGTT outperforms the standard GTT, grey wolf algorithm (GWA) and Particle swarm optimizer (PSO) in 92.5%, 87.5% and 92.5% of the statistical indices. Moreover, the viability of the IGTT is proved in comparison to various previously published frameworks-based parameter's identification of PEMFCs stacks. The obtained sum of squared errors (SSE) and the standard deviations (STD) are among the difficult approaches in this context and are quite competitive. For the PEMFCs stacks being studied, the developed IGTT achieves exceedingly small SSE values of 0.0117 and 0.000142 for BCS 500 and SR-12, respectively. Added to that, the IGTT gives superior performance compared to GTT, SDO, FFO and RFO obtaining the smallest SSE objective with the least STD ever.

Artificial ecosystem optimizer for parameters identification of proton exchange membrane fuel cells model