Transmission Expansion Planning via Partitioning: Efficient Sensitivity Calculations

Transmission expansion planning is often approached via iterative partitioning, which involves a master problem and a subproblem. The master problem provides investment proposals, while the subproblem computes the resulting operation cost and the sensitivities of the investment proposals with respect to operation cost. These sensitivities are critical for the master problem to progressively refine its investment proposals. We propose an analytical procedure based on the Lagrangian function of the subproblem to compute these sensitivities, efficiently and accurately. The outcomes of the proposed analytical procedure are contrasted with those obtained from the common but cumbersome practice of using auxiliary constraints to fix investment variables to master problem investment proposals, and with those obtained by numerical perturbation.