Critical Solutions of Maximum Loadability Via Direct Methods

Abstract

This work proposes a direct method for determination of the saddle-node bifurcation point corresponding to the maximum loadability of the power system. This problem is stated as a static optimization model, whose solution is obtained through an extended version of Newton’s method. The power flow equations are expressed in rectangular coordinates, which allows both to use second-order information (tensor calculation) as well as to handle directly the generated reactive power constraints. Sensitivity relationships between the power system variables at the maximum loadability point are computed as a by-product of the optimization process. Numerical results obtained with power systems of different sizes are used to illustrate the main features of the proposed methodology.