A Novel Adaptive Newton-Raphson Algorithm for Harmonic Reduction in Cascaded Multilevel Inverters for Grid-Connected SPV Systems

Background: Inverter outputs are the main sources of harmonic distortions in the network, with cascaded multilevel inverters contributing significantly. Harmonic distortions severely impact power quality and reliability. Objective: Developing an Adaptive Newton-Raphson (ANR) algorithm for harmonic reduction in SPV-integrated cascaded multilevel inverters for grid-connected systems using SHE-PWM. Methods: This paper presents an adaptive Newton-Raphson algorithm for the Selective Harmonic Elimination method to improve harmonic suppression and waveform quality in PV-integrated 7- level cascaded inverters. This algorithm improves upon the classical Newton-Raphson method through two key innovations: dynamic selection of initial guesses based on modulation index trends, a self-adjusting initialization mechanism, stabilization of the Jacobian matrix under nearsingular conditions, and improved convergence logic. These enhancements address typical problems encountered in solving nonlinear transcendental equations for SHE-PWM, including convergence failures and sensitivity to initial values. The algorithm computed three optimal switching angles to successfully eliminate the 3rd, 5th, and 7th harmonic components while keeping the desired fundamental voltage. Results: Simulation results demonstrate the algorithm’s effectiveness. At a modulation index of 1.0, the overall voltage total harmonic distortion (THD) is reduced to 11.70% and current THD to 4.70%, showing significant improvement in power quality. The proposed method also showed stable performance under varying environmental conditions, such as changes in solar irradiance and temperature. Discussion: The proposed ANR algorithm confirms that selective elimination of dominant lower- order harmonics in PV-integrated cascaded MLIs significantly improves power quality while maintaining computational efficiency. The method offers a practical, real-time control solution for renewable energy systems, highlighting its potential for grid-connected applications where waveform quality and embedded feasibility are critical. Conclusion: The proposed ANR algorithm is computationally efficient and feasible for real-time embedded control in PV-integrated multilevel inverters. It has strong practical potential, especially for renewable energy systems requiring reliable harmonic elimination and high-quality power conversion.