Algebraic Methods for Power Network Analysis and Design

Abstract:

We recall recent advances in the theory of positive polynomials, semidefinite programming and the sum of squares decomposition and describe how these tools can be used to address several questions for systems described by models with polynomial vector fields. We show how these tools can be extended to treat non-polynomial vector fields in two ways, approximation or recasting, and apply them to the analysis of simple power networks. In particular, we formulate and solve robust bifurcation analysis questions as well as how to estimate the region of attraction of the stable operating point. Finally, we discuss ways to scale these methods to bigger networks.