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

• Published in: IET power electronics Vol. 8; no. 12; pp. 2396 - 2410
• Main Authors: Xiao, Huangqing, Xu, Zheng, Tang, Geng, Xue, Yinglin
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 01.12.2015
• Subjects: AC side neutral point; Approximation; approximation theory; arm current; arm reactance voltage; capacitor current; capacitor voltage; Capacitors; complete mathematical model derivation; DC side neutral point; differential equations; differential mathematical model; Electric potential; Exact solutions; instantaneous active power; instantaneous reactive power; Mathematical analysis; Metal matrix composites; MMC electrical quantity; Modular; modular multilevel converter; output current; output voltage; PSCAD‐EMTDC; simulation model; successive approximation approach; switching convertors; switching device current; time‐varying SM capacitor voltage expression; Voltage; voltage difference; AC side neutral point; approximation theory; instantaneous reactive power; arm current; switching device current; output current; differential mathematical model; differential equations; capacitor voltage; switching convertors; arm reactance voltage; complete mathematical model derivation; voltage difference; capacitor current; MMC electrical quantity; simulation model; modular multilevel converter; DC side neutral point; successive approximation approach; output voltage; time-varying SM capacitor voltage expression; PSCAD-EMTDC; instantaneous active power
• ISSN: 1755-4535; 1755-4543; 1755-4543
• DOI: 10.1049/iet-pel.2014.0892

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.