A Rational Fractional Representation Method for Wind Power Integrated Power System Parametric Stability Analysis

A method based on the rational fractional representation is developed for parametric stability analysis of power systems, such as wind power integrated power systems. A fitted parametric state matrix with its parameters in rational fractions rather than traditional polynomials is shown to enjoy improved accuracy. The generalized linear fractional transformation is used to develop the standard linear M (s)-Δ feedback system for robust stability analysis. The mapping theorem is then applied to compute the value set plots of the determinant of the return difference matrix, i.e., det (I - M (s) Δ) for the M (s)-Δ model, and the celebrated zero exclusion principle is directly extended to the value set plots of det (I - M ( s) Δ), which reveals the robust stability of the power system with rational fractional uncertainty. The performance of the proposed method is tested on several systems with integrated wind powers including a classic four-generator 11-bus test power system and a 547-machine 8647-bus model of the actual North China system.