Topology Influence on Loss Reduction as a Mixed Integer Linear Programming Problem

This paper attempts to show the influence of network topological changes on the resistive losses for a significant period. As the problem for a long period is not tractable in a mixed integer non-linear programming approach, a piece-wise linear formulation is presented in order to find a convenient relation between active losses and real flows for each branch. Subsequently, a mixed integer linear formulation is developed to find an optimal topology that tends to minimize the active losses. Considered topological configurations concern the splits or mergers of electric nodes and the taps of phase shifting transformers. A practical example based on several hundreds of observations (snapshots) of the French national grid is presented. Obtained result confirms the interest of the method.