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/Simulink^TM (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.

This paper focuses on the modeling, analysis, and design of grid-forming (GFM) inverter-based microgrids (MGs). It starts with the development of a mathematical model for three-phase voltage source inverters (VSI). The voltage and current controllers consist of two feedback loops: an outer feedback loop of the capacitance-voltage and an inner feedback loop of the output inductance current. The outer voltage loop is employed to enhance the controller’s response time. The inner current loop is used to provide active damping for the resonance created by the LCL filter. A two-layer control scheme is adopted for the GFM inverter control. The primary decentralized control uses droop control and virtual impedance loops to share active and reactive power. Simultaneously, the centralized secondary control addresses frequency and amplitude deviations induced by the droop control. Additionally, a synchronization loop is proposed for seamless reconnection of GFM inverters to the MG and to connect the GFM-controlled MG to the main grid. It has the advantage that the inverter operates in GFM mode even after the synchronization has occurred. The simulation results have shown that the voltage controller ensures a 0.005 s settling time and maintains the steady-state error at its minimum value of 0.1 V. Similarly, the current controller ensures a 0.006 s settling time with a 10⁻⁵ steady-state error. The system with the designed controller has a low total harmonic distortion (THD) of 1.46% and improved power quality of the output voltage. Furthermore, a quick restoration time is observed during load steps and tripping events, with a restoration time of 1 s with 10⁻¹⁰ steady-state error. Synchronization is achieved within 0.8 s for the incoming inverters and requires 3 s to synchronize the MG with the main grid, maintaining a steady-state error of 10⁻⁹.

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.