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This paper presents a model of voltage source converters (VSC) based transmission that can be used for wide range of stability studies and controller design with MATLAB software. The model is intended for analytical studies in the frequency domain above 5 Hz. The system model has modular structure and includes three separate units in state-space form: AC rectifier model, AC inverter and DC system model. The converters, controllers and phased locked loop (PLL) units are included in the DC model and the model is linked with other units using input-output matrices in the state-space models. The converter non-linear model is linearized assuming small deviations around the steady-state. The model is tested against the PSCAD/EMTDC non-linear model and the results show satisfactory accuracy. The tests also confirm that the analytical model well represents multivariable system properties. An example of the model used is given showing the eigenvalue study of the influence of PLL gains on the system stability. It is concluded that increased PLL gains deteriorate system stability.
Jovcic et al. (Tue,) studied this question.