Efficient Benders cuts for transmission expansion planning

Abstract

This paper studies the problem of optimal transmission grid expansion planning. Deterministic formulations are developed for a single time period planning problem, while the operation costs (including total energy, reserve procurement, and load and wind curtailment costs) and N-1 security constraints are taken into consideration. Benders decomposition approach is employed to decompose the large optimization problem into smaller subproblems. New and more efficient Benders cuts are proposed, which are specifically tailored to the binary decision variables of transmission planning problem. The advantages of the proposed Benders cuts to the regular cuts used in the literature are demonstrated, in terms of the increase in convergence speed, decrease in the computational time and required number of iterations, and the scalability of the solution approach. Besides, the proposed Benders cuts are extended to include multiple operation scenarios (similar to stochastic formulations), where the optimization problem considers multiple power demand and wind production scenarios. The proposed optimization models are investigated using Graver's 6-bus, IEEE 24-bus, IEEE 73-bus, and IEEE 118-bus test systems and compared to ones reported in the literature.