Analysis and Optimization of Carrier Phase Displacement Angles for Modular Multilevel Converters With PSC–PWM

In the conventional implementations of phase-shifted carrier pulsewidth modulation (PSC–PWM) for modular multilevel converters (MMCs), different phases normally adopt identical carrier arrangements, neglecting the phase-to-phase carrier phase displacement (P2PCPD). This article presents a comprehensive analysis of the P2PCPD angles, focusing on their effects on the harmonic characteristics of the line-to-line voltages (LLVs) and common mode voltage (CMV). The selection criteria of the P2PCPD angles are proposed for different conditions in terms of the modulation index and the number of submodules (SMs) per arm of the MMC. It is revealed that the LLV and CMV harmonics cannot be minimized simultaneously, while a trade-off can be achieved between these two control objectives: a proper set of P2PCPD angles can be obtained which minimizes the CMV/LLV harmonic distortion meanwhile keeping the LLV/CMV harmonic distortion below a preset threshold. Simulations and experiments are conducted, and their results validate the theoretical findings.