This article deals with the design of an active fault‐tolerant control (AFTC) for a twin wind turbine consisting of two wind turbines mounted on the same tower. When one of the turbines is impacted by electrical faults, precisely a stator inter‐turn short circuits fault or a demagnetization fault, the sparse recovery diagnosis method is used for the detection, isolation and estimation of the active fault. An AFTC law is designed for the supervision of the faulty machine. Both methods, concerning diagnosis and control, are based on homogeneous theory and consequently converge in finite time. Simulation results highlighting the relevance of the proposed approach are also presented.