Capacitor Placement in Radial Distribution Networks through a Linear Deterministic Optimization Model

The classical optimization problem for reducing investment costs and energy loss in radial distribution systems is addressed through a strategy of linear approximations and new variable representation. The linear approximation of the problem is performed in two main aspects: one is by using Support Hipper-planes (SH) allowing the approximation of the loss function in each branch of the distribution system. The other is related to the treatment given to the product of integer variables and continuous variables. The classical problem is then transformed into a new mixed linear integer optimization problem, easy to solve by traditional large scale robust solvers. Rigid upper and lower limits to the voltage variables, instead of using penalty functions to prevent violation of limits, allow evaluating voltage profile improvement against corresponding cost savings. Examples on several distribution networks and planning periods show the robustness and performance indexes which indicate this method as an appealing alternative to utilities interested in planning radial distribution networks.