Operation and control of MMC station with constraints of internal variables under unbalanced grid conditions

Modular multilevel converter (MMC) station is expected to be able to operate under unbalanced grid conditions (UGCs) and to satisfy all kinds of limits under UGC. To investigate the allowable region of MMC under UGC, this study presents a point-scanning method, which directly solves the steady-state values of MMC from non-linear dynamic equations for each possible operating point, and therefore, can access the constraints of internal variables including the sub-module capacitor voltage, arm current and modulation index. First, the complete 28th-order dynamic model of MMC, which contains the zero-sequence second-order modulation signal is derived. Next, as the premise to solve the steady state of MMC, point of common coupling voltages are solved from a proposed unbalanced grid model, which incorporates the effect of ac fault. Following that, a peak-value seeking algorithm is proposed to seek the peak values of internal dynamics of irregular waveforms to implement the constraint of internal dynamics. Next, the allowable region of MMC under UGC is depicted and analysed. Also, the power limiting control is proposed to avoid MMC under UGC, violating the limits of internal dynamics. Finally, the simulation validates the effectiveness and correctness of the proposed point-scanning method and power limiting control.