The $\alpha\beta$ Impedance Modeling with Small Disturbances of Any Form for Three-phase Power-Electronics-Based Power Systems

Many methods have been proposed for small-signal stability analysis of power-electronic-based power systems. As one common method, the sequence impedance model stands on that the disturbances are in the form of harmonics, which seems not consistent with the basic small-signal stability theory. In this paper, firstly small disturbances of any forms are applied to the three-phase voltage. By a rigorous Laplace transform, the $\alpha\beta$ impedance of the power electronic device is obtained, both in the form of transfer function matrix and complex transfer function. Then, the equivalence between the proposed model, the sequence impedance model, and the complex transfer function model are obtained. Finally, the open-loop response of a voltage source converter (VSC) and the stability of its grid connected system are verified by simulation. Based on the detailed analysis in the paper, it has been proved that the sequence impedance model is suitable for small-signal stability analysis of power-electronic-based power systems under not only harmonic disturbances but also any forms of disturbances, standing on a more rigorous mathematical basis.