Modeling and ZVS Operation of the Isolated Modular Multilevel DC–DC Converter With a Unified Trapezoidal Wave Modulation

This article introduces a unified trapezoidal wave (UTW) modulation scheme for the isolated modular multilevel dc–dc (IM2dc) converter, which consolidates multiple existing modulation strategies for the IM2dc converter, including the quasi-square wave (QSW) modulation, trapezoidal wave modulation, and sinusoidal wave modulation, into a unified framework. Furthermore, this article introduces the harmonic state-space (HSS) equations to model the IM2dc converter based on the UTW modulation method. The HSS model operates in the frequency domain, enabling it to circumvent the complexities associated with time-domain analysis and seamlessly integrate with the UTW modulation. This article proceeds to analyze the real and reactive power transfer characteristics of the IM2dc converter, as well as the power factor, considering the influence of multiple modulation parameters. Subsequently, it delves into the examination of zero voltage switching (ZVS) conditions for the IM2dc converter based on the UTW modulation and the HSS model. The complete ZVS boundaries of the IM2dc converter, taking various voltage ratios into account, are derived. This article also illustrates the effects of including harmonic orders in the modeling process, modulation parameters, and internal harmonic ripples on the ZVS boundaries. Finally, experimental validation of the analyses is conducted on a down-scaled prototype.