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Abstract— The constant increase of power generation provided by renewable energy source (RES) power plants is causing a progressive reduction of the overall inertia of the power systems. Especially in the case of small, isolated power networks, the replacement of conventional generation plants with RES power plants can affect significantly the frequency response of the system. The critical low-inertia conditions can be improved by the introduction of specific additional controls to the RES power converters. These control schemes are known as “synthetic inertia” or “virtual inertia” controls. The paper analyzes the impact of a derivative-based inertial control on a small, isolated power system, with a relevant share of power supplied by a wind power plant. The inertial response control is added to the standard IEC wind turbine active power controller of type WT4A. Simulations performed on the dynamic model of the system indicate the appearance of frequency oscillations in response to the applied power unbalance. A comprehensive analysis of the observed phenomenon is given, and a tuning of the inertial control parameters is then proposed. Simulations repeated with the proposed tuning of the controller prove the validity of the applied modifications, and show a satisfactory transient response of the system, even in the case of critical low-inertia conditions.