Optimal reactive dispatch through primal-dual method

This paper presents an algorithm for the optimal reactive dispatch problem. The algorithm is based on Newton's method which it works with an augmented Lagrangian function associated with the original problem. The function aggregates all the equality and inequality constraints. The first order necessary conditions for optimality are reached by Newton's method, and by updating the dual variables and the penalty terms associated with the inequality constraints. The proposed approach does not have to identify the set of binding constraints and can be utilized for an infeasible starting point. The sparsity of the Hessian matrix of the augmented Lagrangian is completely exploited in the computational implementation. Tests results are presented to show the good performance of this algorithm.