Analytical line-voltage THD formulation and optimization for sine- and third harmonic injection PWM in three-phase cascaded H-bridge multilevel inverters with fixed and variable DC supply ratios

This paper presents novel analytical formulations for Line-voltage Total Harmonic Distortion (LTHD) in three-phase Cascaded H-bridge (CHB) Multilevel Inverters with variable DC supply ratios. While LTHD minimization has been well-studied for fundamental-frequency modulation techniques, this work extends such optimization to high-frequency Pulse Width Modulation (PWM) schemes, specifically the popular sine-PWM (SPWM) and Third Harmonic injection sine-PWM (THISPWM). Comprehensive LTHD expressions for fixed (symmetric) and variable (asymmetric) DC source ratios were developed using time-domain-based asymptotic analysis. These formulations enable Optimal Minimization of LTHD (OMLTHD) for both modulation techniques. The proposed approach is validated through theoretical analysis, digital simulations across multiple voltage levels (N = 5, 7, 9, 11), and hardware-in-the-loop experiments for a 7-level inverter. Results demonstrate significant LTHD improvements, particularly in challenging low and medium Modulation Index (MI) ranges, achieving relative LTHD reductions of 3.5 % and 75 % compared to conventional SPWM for MI values of 1.0 and 0.1, respectively. MATLAB functions implementing these THD expressions are provided as supplementary material.