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With increasing wind penetration, it is likely that wind power plant will be expected to provide frequency response in support of the power system, in particular some form of inertial response. In these circumstances it is important to accurately quantify the type of inertial response available from wind plant (typically a wind farm) and how it is affected by varying wind conditions. Two different control schemes to provide this “synthetic” inertial response are investigated. The benefits of the non-standard control scheme are demonstrated by comparing the response with the conventional “ideal” inertial control scheme that exactly emulates synchronous generators in terms of their provision of inertial response. This paper proposes a novel probabilistic approach for estimation of the aggregate inertial response available from a wind farm by using a Gaussian probability distribution to model wind turbulence. The aggregate inertial response calculated in this way has been examined at various mean wind speed levels and has the advantage that it automatically takes into account wind speed variations during the transient event itself.