Global polynomial approximation of static voltage stability region boundaries considering inequality constraints

An approach for approximating the static voltage stability region boundaries (SVSRBs) considering inequality constraints is proposed. The mathematical model of the SVSRB is formulated as a parametric optimization, and Galerkin method is applied by projecting the Karush-Kuhn-Tucker conditions of the optimization model based on an interior point method scheme onto a set of basis functions of parameters. The result of the approximation is in polynomial form and the precision is globally high in the whole domain of parameters, which can be controlled by the degree of polynomial basis functions. Case studies in New England 39-bus system exhibit the validity, accuracy and flexibility of the proposed method.