# Capacitor Voltage Ripple Reduction for Modular Multilevel Converter with 2nd order Current Injection and Over Modulation

The structure of MMC is shown in Fig.1. Each phase of MMC contains two arms, which consists of submodules and one arm inductor. The number of submodules can be an arbitrary value, N. The topology of the submodule can be half bridge or full bridge. The arm current can contain harmonics beside DC and 1st order terms:

Under traditional control, the harmonic is suppressed, where modules offer 2nd power to the AC load besides a 1st order oscillating power between two arms. The capacitor voltage is shown in Fig. 2. To avoid the 2nd power in modules, a proper 2nd harmonic current can be injected in both arm currents, where the DC source would offer that 2nd power to the AC load and the oscillating power contains a dominated 1st order part and a small 3rd order part. The capacitor voltage is shown in Fig. 3.

The definition of modulation index is introduced for further power analysis,

When M=1.15, the significant 1st or-der power is also eliminated. Over modulation is realized with full bridge modules. The capacitor voltage is shown in Fig. 4.