A Computational Method for the Calculation of the Feasibility Boundary and Clustering in DifferentialAlgebraic Systems

A clustering approach is presented to calculate the limits of parametric stability for a stable equilibrium of the power systems modeled by differential algebraic equations (DAEs) , the so-called “feasibility boundary.” The underlying algorithm for calculation is based on the sensitivities of the eigenvalues of the DA system. The procedure is illustrated with several examples based on the standard nine-bus system and test beds formed by connecting sets of two and four nine-bus systems together.