Abstract: The virtual controllable inertia of doubly fed wind turbines significantly affect the dynamic characteristics of the regional power grid when they are synchronized with the grid. It is still necessary to reduce the additional operation risk through optimal control to give full play to its control potential.Firstly,the dynamic model of DFIG is established,and the coupling coefficient is introduced to analyze the virtual synchronous operation mechanism between DFIG and synchronous generator. Secondly,the energy function of DFIG synchronous grid-connected system is established. Based on the coupling relationship, the variable inertia optimal control strategy of DFIG is proposed,and the reasonable range of virtual inertia is designed through analyzing the influence of control parameters on system stability. Finally,a simulation system is built to verify that the DFIG needs to provide virtual inertia response within a reasonable range in order to provide reliable dynamic stability support for the grid connected system.