Analytical forms of boundaries of static voltage stability region with nonlinear terms

Knowledge of the stability boundary geometrical configuration is important to analyze the robustness of operating points and gives guidance for the development of control strategies and decision-making. This paper proposes a method to deeply exploit the quadratic properties of the boundary structure of static voltage stability region, which is also called power flow feasible region, in power injection space. By making quadratic Taylor series expansion of the Jacobian matrix determinant of power flow equations near critical operating points, nonlinear terms are included in the analytical boundary approximation. Eigenvalue and eigenvector sensitivities are introduced into the analysis of power flow equations and employed to the boundary approximation. An advantage of the method is that no iterative solution of nonlinear equations is required. This nonlinear analytical expression closely matches the real boundary over a wide range and greatly promotes the accuracy of present linearization method which only gives an approximation of the local part. Various examples of IEEE power systems give an illustration of the effectiveness and accuracy of the method.