Restoring Solvability of the Electric Network Equations: An Approach Based on the Augmented Lagrangean Algorithm

This paper presents and discusses a new, robust approach for restoring solvability of the electric network equations in power systems. The unsolvable power flow is modelled as a constrained optimization problem. The cost function is the squared sum of the real and reactive power mismatches at the electric system buses which are subject to suffer load shedding. The equality constraints are the real and reactive power mismatches at null injection buses and/or at buses whose power demands must be integrality supplied due to technical and/or economical criteria. The mathematical model is solved using an algorithm based on Augmented Lagrangean function method which takes into account the special structure of the proposed problem. The inner iterations of the proposed methodology are solved using the Levenberg-Marquardt (LM) algorithm. Numerical results for both IEEE test systems and a real equivalent electric system corresponding to Brazil South-Southeast region are presented in order to analyze and test the performance of the proposed methodology.