Optimal Switching Frequency Selection for Nine-Level Cascaded Multilevel Inverters: A Trade-Off Between Efficiency, Harmonic Performance, and Thermal Management

Cascaded Multilevel Inverters (CMIs) play a crucial role in renewable and medium-voltage systems due to their high efficiency and excellent harmonic performance. However, selecting the proper switching frequency remains a critical design challenge, as it directly affects converter efficiency, harmonic distortion, and semiconductor thermal reliability. This paper presents a comprehensive analyticalsimulation framework developed in MATLAB/Simulink to determine the optimal switching frequency range for a nine-level cascaded H-bridge inverter. The methodology integrates loss modeling, harmonic spectrum analysis, and electro-thermal evaluation within a unified platform, enabling quantitative correlation between switching frequency, total efficiency, total harmonic distortion (THD), and device junction temperature. Simulation results demonstrate that at an optimal switching frequency of $2.7-3.0 \mathrm{kHz}$, the inverter achieves a balanced trade-off between key performance metrics: efficiency improves to approximately 96.8%, voltage THD decreases to 1.7%, and the average junction temperature rise is limited to $58{ }^{\circ} \mathrm{C}$, representing a thermal stress reduction of nearly 22% compared to higher-frequency operation. The novel contribution of this work lies in establishing a multi-criteria optimization-based frequency selection approach that simultaneously considers efficiency, harmonic quality, and thermal constraints. This integrated methodology provides a practical design guideline for grid-connected and renewable-energy CMI applications, enhancing both performance and long-term reliability. Simulation results validate the analytical trends, showing that the optimal operating range lies between $2.7-3.0 \mathrm{kHz}$, where efficiency ($\approx 96-97 {\%}$) and THD ($\approx 1.7 {\%}$) achieve a balanced trade-off without excessive thermal stress. The novelty of this study lies in formulating a multi-criteria optimization-based frequency selection methodology that simultaneously considers efficiency, harmonic quality, and thermal reliability-providing a practical design guideline for CMI-based power systems.