A fast sorting strategy based on a two-way merge sort for balancing the capacitor voltages in modular multilevel converters

The Modular Multilevel Converter (MMC) is particularly attractive for medium and high power applications such as High-Voltage Direct Current (HVDC) systems. In order to reach a high voltage, the number of cascaded submodules (SMs) is generally very large. Thus, in the applications with hundreds or even thousands of SMs such as MMC-HVDCs, the sorting algorithm of the conventional voltage balancing strategy is extremely slow. This complicates the controller design and increases the hardware cost tremendously. This paper presents a Two-Way Merge Sort (TWMS) strategy based on the prediction of the capacitor voltages under ideal conditions. It also proposes an innovative Insertion Sort Correction for the TWMS (ISC-TWMS) to solve issues in practical engineering under non-ideal conditions. The proposed sorting methods are combined with the features of the MMC-HVDC control strategy, which significantly accelerates the sorting process and reduces the implementation efforts. In comparison with the commonly used quicksort algorithm, it saves at least two-thirds of the sorting execution time in one arm with 100 SMs, and saves more with a higher number of SMs. A 501-level MMC-HVDC simulation model in PSCAD/EMTDC has been built to verify the validity of the proposed strategies. The fast speed and high efficiency of the algorithms are demonstrated by experiments with a DSP controller (TMS320F28335).