Sub-module capacitors of the modular multilevel converter(MMC)are steadily charged and discharged during normal operation. Every sub-module is inserted and bypassed randomly to keep all the capacitor voltages balanced

which resulting in high complexity in MMC loss calculation. Based on the duty ratio concept of the inserted sub-module on a bridge arm

the analytical formulas of average and effective values of current flowing through the four switching devices are deduced in the whole power operation region. Taking the influence of capacitor voltage and gate resistor into account

the formulas of conducting loss and switching loss are deduced. Furthermore

since average junction temperature does not truly reflect the real working condition of switching devices

an approximation method for estimating the maximum operating junction temperature is proposed based on the detailed analysis of junction temperature ripple characteristics in every fundamental frequency cycle. Finally

an example analysis shows that the loss and junction temperature calculating results are in good agreement with the MMC operation characteristics

the method proposed is simple and effective.