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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. [ABSTRACT FROM AUTHOR]

This paper presents a systematic approach to develop a dynamic model for a matrix converter. The matrix converter interfaces two three-phase ac systems that can be at different voltages and/or frequencies, e.g., a high-speed micro-turbine generator and a utility distribution system. The model is developed by (i) transferring the abc frame equations to a newly defined switching reference frame and then (ii) transferring the resultant equations to a rotating dqo frame. The model is then linearized and the concept of "sequential loop closing" is used to design a controller for the matrix converter as a multi-input multi-output system. The accuracy of the developed model and performance of the controller are evaluated based on comparing the study results with those obtained from digital time-domain simulations in the PSCAD/EMTDC software environment. [ABSTRACT FROM AUTHOR]

This paper introduces a frequency-domain approach for investigation of the phenomenon of torsional dynamics. The Nyquist criterion is adopted by the proposed method to identify stability regions with respect to torsional oscillations. This paper also introduces two performance indices to evaluate torsional dampings and propensity of the system to experience torsional oscillations. The proposed method is an alternative approach to the eigenvalue analysis method and the complex torque method for investigation of torsional dynamics. The salient features of the method as compared with the aforementioned two methods are:1) its computational efficiency since it utilizes the open-loop transfer-function matrix of the system and inherently more advantages for large size systems; 2) its performance indices that readily reveal "damping of' and "propensity to" a torsional oscillatory mode; and 3) its capability to formulate a multimachine system which includes both induction and synchronous machines. The proposed method is applied to the First IEEE Benchmark Systems for SSR studies and the results are verified based on comparison with those obtained from eigenvalue studies and digital-computer time-domain simulation. [ABSTRACT FROM AUTHOR]