Optimal voltage control for loss minimization based on sequential convex programming

This paper focuses on the active power loss minimization by optimal voltage control in a power system using a new optimization algorithm. The cost function is assumed to be convex. The algorithm we propose to address the numerical solution of this problem is based on the exploitation of the convex problem structure using a sequential convex programming framework that linearizes the nonlinear power balance constraints at each iteration. The convex subproblem is then solved using a dual fast gradient method. We provide mathematical guarantees for the linear convergence of the algorithm towards a local solution. This approach allows an optimal voltage for each bus, while achieving the (local) economical optimum of the whole power grid. The newly developed algorithm can be run over large electricity networks, as we show on several numerical simulations using the classical IEEE bus test cases.