Comparative analysis of numerical, evolutionary and metaheuristic methods for experimental implementation of selective harmonic elimination in a five-level emerging inverter

Introduction. Multilevel inverters (MLIs) are widely used in renewable energy conversion and high-performance power applications due to their ability to generate output voltages with low harmonic distortion and reduced switching stress. Selective harmonic elimination (SHE) remains one of the most effective modulation strategies for suppressing low-order harmonics; however, its practical implementation relies on solving nonlinear transcendental equations that often require robust and efficient computational methods. Problem. Determining optimal switching angles for SHE in MLIs remains a challenging optimization problem because of the nonlinear, non-convex nature of the governing equations and the need to simultaneously preserve the fundamental voltage component while eliminating selected harmonics. The choice of an appropriate numerical or optimization-based solution method directly affects computational efficiency, robustness, and practical implementability. The goal of the work is the reducing harmonic distortion of output voltage and determining optimal switching angles of a single-phase 5-level inverter using the Newton-Raphson (NR) method, particle swarm optimization (PSO) and genetic algorithm (GA). Methodology. The operating principle and harmonic model of the inverter are first established using Fourier series analysis. The SHE problem is formulated as a system of nonlinear equations subject to ordering constraints. The NR method is used as a fast numerical solver, while PSO and GA are employed as evolutionary and metaheuristic optimization techniques capable of handling non-convex search spaces. All algorithms are implemented in MATLAB/Simulink over a range of modulation indices. Experimental validation is carried out using an Arduino Mega 2560-based prototype, where the optimized switching patterns are executed in real time and the output voltage is analyzed using oscilloscope and harmonic measurement tools. Results. The three approaches converge to identical switching-angle solutions over the investigated modulation range, confirming the consistency of the formulation. Simulation results demonstrate effective elimination of the 3rd harmonic and its multiples, with the total harmonic distortion of the output voltage decreasing from 28.42 % at M = 0.55, f = 1 kHz to 14.88 % at M = 0.55, f = 10 kHz. In terms of computational efficiency, NR-SHE achieves the shortest execution time (0.516 s), while PSO-SHE (10.237 s) and GA-SHE (23.289 s) require longer computation. Experimental waveforms and harmonic spectra closely match the simulation results, validating the proposed approach. Scientific novelty. This work provides a unified comparative analysis of numerical, evolutionary and metaheuristic methods for SHE applied to a 5-level emerging inverter with a reduced switch count (6 switches instead of 8 in a conventional 5-level H-bridge). In addition, it demonstrates the feasibility of executing SHE-based modulation schemes on a low-cost Arduino microcontroller. Practical value. The presented results offer practical guidance for selecting suitable computational methods for SHE in MLIs and confirm that efficient harmonic control can be achieved using inexpensive embedded platforms. The findings are relevant for research, prototyping and educational applications in industrial electronics and power conversion systems. References 21, tables 5, figures 12.