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This paper introduces a small-signal dynamic model of a fixed-frequency (induction machine based) wind farm connected to an electrical power system. The model represents the system small-signal dynamics in the frequency range of a fraction of Hz to 50/60 Hz. The model includes the dynamics of the wind energy capturing mechanism, the rotating shaft system, the generator electrical system of each wind energy unit, the wind farm collector system, and the utility grid. Based on the proposed model, two performance indices are introduced to i) investigate sensitivity of the system modes, e.g., torsional modes, to the system parameters, and ii) evaluate the system capability to reject electrical and mechanical disturbances, e.g., a wind gust. The application of the model to the analysis of a system with two wind units is presented and the study results are validated based on comparison with the time-domain simulation results obtained in the PSCAD/EMTDC environment.