A wind farm consisting of doubly-fed wind turbines based on a virtual synchronous generator control strategy exacerbates the main shaft fatigue load of each unit in the farm in response to grid frequency variations. For this reason

a distributed allocation strategy for damping coefficient considering the main shaft fatigue load is proposed. Based on the derivation of a discrete model that quantitatively characterizes the relationship between the damping coefficient and the main shaft torque in the virtual synchronous generator (VSG) control strategy

the objective function is to minimize the fluctuation of the main shaft torque of each unit

and the constraints are set based on the frequency response capability of the wind farm and the operating status of each unit. In order to divert the computational pressure caused by the centralized objective function to the VSG field controller

a distributed solving architecture based on the alternating direction multiplier method is formed in which the VSG field controller interacts with the local controller to solve the damping coefficients received by each turbine online in real time. The case study shows that the proposed distributed allocation strategy for damping coefficient can reduce the sum of fatigue loads on the main shafts of each unit in the field by 6.72% while guaranteeing the responsiveness of the wind farm to frequency variations.