Equivalent model of nearest level modulation for fast electromagnetic transient simulation based on DC voltage control loops of sub-modules in modular multilevel converter

The nearest level modulation (NLM) is used to automatically generate ac side voltages of sub-modules in modular multilevel converter (MMC). Existing literature seldom presents models that describe complex NLM processes. This paper proposes an equivalent model of the NLM to simply describe and simulate the complex NLM process. The main contribution of this study is to build the model of NLM with fast simulation speed for the application focuses on the simulation accuracy at the millisecond level. The duty cycle of the average model generated by the NLM in sub-modules of the MMC is divided into two components, which are the stable component for generating the bridge arm voltage and the fluctuation component for balancing the dc side voltage of sub-modules, respectively. The stable component is generated by the modulation wave of the MMC control system. By adding a voltage control closed loop to the sub-module, the fluctuation component for balancing the dc side voltages of sub-modules can automatically adjust the ac side voltages of sub-modules. The proposed equivalent model of NLM improves the simulation speed and has the same effect with the traditional NLM within the low-frequency range or with the time step of millisecond level.