Distribution system planning through a generalized Benders decomposition approach

In this paper the authors introduce a model to specify the distribution system for electrical power industry. The objective function includes maintenance and investment costs of substations, feeders and voltage regulators along with cost associated with energy loss in the feeders. In addition to the standard constraints to specify the network design and the power flow, additional constraints related to power drops in the feeders are taken into account. The model has a nonlinear objective function and nonlinear constraints. The authors first specify an equivalent formulation where the constraints are linear. The generalized Benders decomposition is used to deal with this model. Simple procedures are introduced to solve the subproblems and generate the cuts. To deal with the nonlinearity of the objective function of the master problem, and equivalent mixed-integer linear problem is introduced and solved by branch and bound.