Application of the Newton–Raphson algorithm for enhanced harmonic reduction in seven-level packed U-cell multilevel inverters

Introduction. Recently, multilevel inverters (MLIs) have been widely investigated for industrial and renewable energy systems as they are valuable in applications where they can produce clean, high-fidelity electrical signals that minimize harmonic content and distortion. Problem. Among the modulation strategies, selective harmonic elimination pulse width modulation (SHE-PWM) is highly effective, but solving its nonlinear transcendental equations requires accurate numerical methods. Goal. To improve the performance of the 7-level packed U-cell (PUC) inverter by applying the Newton–Raphson method to compute optimal switching angles for SHE-PWM, thereby minimizing total harmonic distortion (THD), improving waveform quality, and achieving a more compact and cost-effective design with fewer components. Methodology. The Newton–Raphson iterative algorithm was implemented in MATLAB/Simulink to solve the nonlinear equations of SHE-PWM, and a hardware prototype of the 7-level PUC-MLI was fabricated and tested to validate real-world performance. Results. The application of the Newton–Raphson algorithm significantly improved the system’s performance. After implementation, the THD was reduced to 13.19 % in the simulation and 18.14 % in the hardware prototype, whereas both initially exhibited considerably higher THD levels. Scientific novelty. The proposed method demonstrates the capability of the Newton–Raphson algorithm as a reliable numerical solution for selective harmonic elimination in the 7-level PUC MLI, ensuring rapid convergence and precise determination of switching angles. Practical value. The study shows that significant harmonic reduction can be achieved without additional hardware or complex circuitry, making the approach applicable to other inverter topologies and suitable for advanced power electronic and renewable energy systems. References 22, tables 4, figures 9.