Loss reduction as a Mixed Integer optimization problem

This paper deals with the influence of network topological changes on the resistive losses for a significant period. It is based on a previous work where the goal was to reduce power losses on a peak load situation. The second part of the work, presented here, attempts to reduce the energy losses of transmission network by implementing a cyclic search of topology changes and phase shifting adjustments over a week time period. As the whole problem for such a long period is not tractable in a mixed integer non-linear programming approach, a piecewise-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 splitting or merging of electric buses and the line switching. Once the new topology has been identified, the interactions between real and reactive power are handled to adjust the taps of phase shifting transformers through a mathematical program with equilibrium constraints (MPEC). A practical example based on several hundreds of observations (snapshots) of the French national grid is presented. Obtained results confirm the interest of the method.