Transmission Network Planning Under Uncertainty with Benders Decomposition

This paper treats the problem of the long term transmission expansion planning of an electrical network under uncertainty. A static form of this problem is considered; transmission constraints are represented in the DC approximation (linearized power flow). Uncertainty is taken into account to evaluate the operating cost (demand, availability); the investment variables are binary. The problem is therefore a large stochastic mixed integer one, requiring a considerable computational effort.This article proposes a new formulation of the problem, which is well suited to the application of the Benders Decomposition. Several ways of dealing with the cuts which are obtained at each iteration are described and compared. Numerical tests show the practical interest of the algorithm finally obtained.