Restoring Solution of Electric Network Equations: An Approach Using the Augmented Lagrangean Algorithm

This paper presents and discuss a new, robust approach to restore the solution of electric network equations in electric power systems. The unsolvable power flow is modelled as an constrained optimization problem. The objective function is the sum of squared real and reactive power mismatches at the system buses that are available to 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 method that considers the special structure of the proposed problem. The inner iterations of the proposed approach are solved using the Levenberg-Marquardt algorithm. Numerical results for both IEEE test systems and a real equivalent power system from South-Southeast region of Brazil are presented to analyze and the performance of the proposed methodology.