The simulation method is not applicable to rapidly assessing the power loss of hybrid modular multilevel converter（HMMC） at initial design stage

and existing analytical models mainly focus on the modular multilevel converter（MMC） constituted by submodules（SMs） with the same structure

without taking into account the impacts of active redundancy. Therefore

we proposed an analytical power loss model for HMMC with active redundancy. Firstly

both fixed level（FL） and voltage sharing（VS） redundancy modes were taken into consideration

and the modulation strategies of half-and full-bridge SMs were analyzed. Then

according to the conduction and switching states of power devices in SMs

the analytical approach to power loss of HMMC with different redundancy modes was derived. Finally

by taking a 10 MW and 10 kV MMC as an example

the efficacy of the proposed model was verified through simulations. Moreover

the influences of different redundancy modes and SM structures on power loss were analyzed and compared. The results show that

at the rated wind speed

the total loss of HMMC almost linearly increases with the increase of redundant half-bridge SMs（HBSMs） or full-bridge SMs（FBSMs）. Compared with that in the FL mode

the total loss change with redundant HBSMs is slighter in the VS mode

which becomes greater with redundant FBSMs. The research can provide a theoretical basis for the loss calculation of grid-connected MMC for offshore DC wind turbine.