Analysis of Operating Range of the Capacitor Voltage Sorting Algorithm for iM2DCT Submodule Under Quasi Two-Level Modulation

The isolated modular multilevel DC-DC transformer (iM²DCT) offers advantages such as high voltage and large capacity, bidirectional power transfer, and fault isolation, making it a key device for connecting medium-voltage (MV) and low-voltage (LV) systems in DC distribution networks. However, the capacitor voltage balancing issue in its submodules (SMs) has been a challenge for the application of iM <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$^{2}$</tex> DCT. Sorting algorithms, known for their simplicity and ease of implementation, are applied in the capacitor voltage balancing strategies of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{iM}^{2} \text{DCT}$</tex> SMs. However, existing capacitor voltage sorting algorithms are unable to enable iM <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$^{\mathbf{2}}$</tex> DCT to operate under all working conditions. In this paper, through mathematical modeling of the capacitor voltages in the SMs, the operating range and limitations of the existing capacitor voltage sorting methods are analyzed and verified using MATLAB/Simulink.