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Future power＇ system faces several challenges, one of them is the high penetration level of intermittent wind power generation, providing small or even no inertial response and being not contributing to the frequency stability. The effect of shaft stiffness on inertial response of fixed speed wind turbines is presented. Four different drive-train models based on the multi-body system are developed. The small-signal analysis demonstrates no significant differences between models in terms of electro-mechanical eigen-values for increasing shaft stiffness. The natural resonance frequency of drive-train torsion modes shows slightly different values between damped and undamped models, but no significant differences are found in the number-mass models. Time-domain simulations show the changes in the active power contribution of a wind farm based on a fixed speed wind turbine during the system frequency disturbance. The changes in the kinetic energy during the dynamic process are calculated and their contribution to the inertia constant is small and effective. The largest contribution of the kinetic energy is provided at the beginning of the system frequency disturbance to reduce the rate of the frequency change, it is positive for the frequency stability.