Analytical approximate calculation of losses for modular multilevel converters

The voltages of the upper and lower arms per phase unit in a modular multilevel converter (MMC) are analysed. In addition, the enabled probabilities of each submodule (SM) in the upper and lower arms are proposed on the basis of the relationship between the arm voltage and the number of enabled SMs. Analytical models of the currents in the switches can be obtained from the current path and sign. Then, the average or root mean square (RMS) current can be obtained from the corresponding model. Therefore, the conduction and essential switching losses can be expressed by analytical formulas. In the inverter and rectifier modes, the two losses of the corresponding upper and lower switches of the SM are compared, and the sums of the two losses of the upper and lower switches are compared with the analytical method. Simulation studies are performed on a 1000 MW 320 kV MMC-high-voltage direct current system under typical operating conditions. The magnitudes of the compared losses are validated by the simulation results. Both the relative errors of the total conduction and essential switching losses are within ±2.5 and ±7%, respectively, and the comparison results demonstrate the effectiveness of the analytical method.