With the increasing penetration of wind power, using wind turbines to participate in the frequency regulation to support power system has become a clear consensus. To accurately quantify the inertia provided by the doubly-fed induction generator (DFIG) based wind farm, the frequency response model of DFIG with additional frequency control is established, and then by using Routh approximation, the explicit expression of the virtual moment of inertia is derived for the DFIG gridconnected system. To further enhance the availability of the expression, an estimation method is proposed based on the matrix pencil method and the least squares algorithm for estimating the virtual moment of inertia provided by the wind farm. Finally, numerical results tested by a DFIG grid-connected system and a modified IEEE 30-bus system verify the derived expression of the virtual moment of inertia and the proposed estimation method.Index Terms--Doubly-fed induction generator (DFIG), additional frequency control, virtual moment of inertia, matrix pencil method, least squares algorithm.

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