Linear time complexity sorting algorithms for electromagnetic transient simulation of MMC‐HVdc system

Abstract

In the electromagnetic transient (EMT) simulation programs, the candidate integration methods backward Euler (BE) method and Trapezoidal rule (TR) are normally used to discretise the submodule capacitors in modular multilevel converter (MMCs). This study proposes linear time complexity sorting algorithms for nearest level control-based BE and TR MMC models to further accelerate the EMT simulation of the equivalent MMC-HVdc models. First, the capacitor voltage increments in the charging and discharging processes are investigated from an EMT point of view. Second, for both BE and TR methods, although the actual capacitor voltage increments are not identical at each time step, the voltage ranking of the capacitors from the same inserted/bypassed category at each control period are proved to be unchanged. Taking this advantage, when preparing the entire ranked voltage table for the next control period, the sorting can be significantly simplified since one only needs to compare the capacitor voltages from capacitor categories of ascending orders. Third, when implementing the sorting algorithms, at most ( N -1) comparisons for BE model and (2 N -3) comparisons for TR model are required, showing that the proposed sorting algorithms have linear time complexities. Finally, all the proposed approaches are validated by EMT simulations on MATLAB/Simulink.