Precise estimation of fuel cell parameters is critical for optimizing performance and developing energy systems. However, experimental data are often affected by outliers stemming from inaccurate measurements, transient operating conditions, or environmental variations. In this line, this study proposes a robust approach for estimating proton exchange membrane fuel cell (PEMFC) parameters. This study focuses on the steady-state current–voltage (I–V) characteristics and performs parameter extraction for a semi-empirical model. The proposed estimation framework employs the collaboration of the Huber loss function (HLF) in conjunction with adaptive hyperparameter and the metaheuristic Wild Horse Optimizer (WHO) to compute seven unknown PEMFC parameters. The impact of different hyperparameter (δ) values is examined on the performance of the HLF while estimating key fuel cell parameters. The sensitivity of the estimating process to the δ-value is explored using measured and estimated datasets, including accuracy, convergence rate, and resilience. The WHO-based approach is adopted to address and mitigate issues such as premature convergence and entrapment in local optima, which are common challenges in existing optimization strategies. The proposed model has been tested and verified through three test samples of standard commercial PEMFC units as benchmarks. The simulation results demonstrate that the WHO exhibits robust performance across the three benchmark PEMFC systems. Furthermore, the proposed model's generalization capability is validated under a range of operating conditions using polarization curves generated at different temperatures and cathode stoichiometries. A single globally specified parameter set reliably predicts fuel cell performance across these diverse conditions, as evidenced by its consistent ability to deliver high-quality solutions with an extraordinary level of precision under predefined experimental conditions. The proposed estimation framework outperforms three commercial PEMFC units (NedStack-PS6, Horizon-500 W, and BCS-500W), achieving Huber loss values of 1.03277845, 0.00562094, and 0.00584889, respectively. The adaptive HLF with hyperparameter (δ) ranging from 0.5 to 2.0 efficiently tackles outliers and improves convergence speed. While the hyperparameter (δ) in previous studies was kept constant, δ = 1. The proposed estimation framework closely matches the experimental data and offers significantly higher accuracy compared to existing competing methods in the literature. The results reveal that the suggested HLF enhances the robustness and immunity of the WHO optimizer, and it outperforms traditional approaches such as steady-state error.

The accurate modeling of PV modules is critical for enhancing performance of electrical grids during simulations. However, modeling PV systems requires dealing with a nonlinear current–voltage curve with unknown parameters, which is frequently due to the restricted data available in cell datasheets. This paper presents a unique optimization technique known as the Human Evolutionary Optimizer Algorithm (HEOA) for correctly predicting the parameters of triple- diode model (TDM). In this study, the HEOA optimizer minimizes the root mean square error function in order to precisely find the TDM's ideal parameters. The simulation outcomes clearly demonstrate the effectiveness of HEOA in accurately extracting model parameters. Throughout the optimization process, the HEOA consistently achieved the lowest ideal fitness values when compared to other state-of-the-art optimization algorithms, indicating superior performance. The results further confirm that the HEOA offers faster convergence rates and higher estimation accuracy, highlighting its efficiency and precision in solving complex parameter identification problems. In addition, comprehensive statistical analysis supports the robustness and consistency of the HEOA across multiple trials, reinforcing its reliability as an optimization tool. For further validation, the proposed approach will be tested using standard benchmark cases, including the RTC France Solar Cell and the KC200GT PV module, to ensure comparability with existing methods. Moreover, real-world validation will be conducted under dynamic climate conditions using the Trina Solar Monocrystalline. Then, the TDM for solar cells/modules is notable for its excellent accuracy, which accounts for both electrical and non-electrical losses. The HEOA-based TDM system achieved parameter extraction performance which matched the benchmark results and practical PV test results. The HEOA method produced the best RMSE result of 8.1307E−04 for the RTC France solar cell, which surpassed multiple recent optimization techniques. The KC200GT PV module achieved an RMSE result of 3.32E−04 which demonstrated that the method accurately reconstructed the nonlinear I–V and P–V characteristics through its extremely small pointwise current and power errors. The experimental validation showed that Trina Solar 290 W monocrystalline modules performed accurately under real operational environments, which included testing single-cell, five-cell, and six-cell configurations to achieve minimum RMSE values of 0.0 and mean RMSE values of 0.0141, 0.0059, and 0.0521. The results demonstrate that HEOA produces precise and dependable parameter estimation for PV cells and modules.