Complete mathematical model derivation for modular multilevel converter based on successive approximation approach

Considering the voltage difference between the neutral points of the DC side and the AC side, this study first establishes the differential mathematical model of the modular multilevel converter (MMC). Then, through the proposed successive approximation approach, the analytical expressions of the electrical quantities are derived, including the arm voltage and current, the output voltage and current, the capacitor voltage and current, the voltage difference between two neutral points, the instantaneous active and reactive power, the arm reactance voltage and the current of switching devices. The proposed successive approximation approach contains three main steps. In step 1, the preliminary analytical expressions of the MMC's electrical quantities based on the ideal step wave of the arm voltage with constant SM's capacitor voltage is deduced; step 2 is to derive the final analytical expressions of the MMC's electrical quantities according to the time-varying SM's capacitor voltage expression which is derived in the first step; and the convergence is analysed in step 3. A simulation model of the MMC is realised in PSCAD/EMTDC and the results show that the complete analytical model coincides well with the simulation results and has a higher accuracy than the traditional model.