Because of the complexity and severity of the marine environment, the probability of failure of offshore wind farms is much higher than that of onshore wind farms. The original control might fail under a single-machine and the network communication faults of wind turbines. In this study, centralized control is replaced with distributed control, the leader-follower distributed control strategy under two types of fault conditions is proposed to reduce the adverse effect of failure on the system and improve the tolerance of the system. First, the single-machine system is expanded into a wind turbine cluster system model based on Hamiltonian energy theory. Then, a leader-follower distributed control strategy is proposed to ensure the stable operation of wind turbines under a single-machine fault of the leader or follower unit. Next, considering communication failure, the leader-follower control strategy in the weakly connected topology is designed to make the system and the active power output stable. Finally, the simulation results confirm that the leader-follower control strategy system can enhance the stability and reliability of the system in the case of a unit shut down and network communication faults.