A Multistage Robust Transmission Expansion Planning Model Based on Mixed Binary Linear Decision Rules—Part I

This two-paper series introduces a new multistage robust approach for solving the transmission expansion planning (TEP) problem under the uncertainty of loads and wind power productions. The proposed multistage robust TEP model is formulated using mixed binary and linear decision rules, which aims at finding a solution withstanding any realization of the uncertain parameters belonging to a set-based uncertainty model. The robustness of the optimal expansion plan can be adjusted by the budget of uncertainty. The first part of this two-paper series presents the extended and compact formulations for a deterministic TEP problem. Then, the compact formulation of the TEP problem under the uncertainty of loads and wind power productions is introduced as a multistage robust optimization problem, which is reformulated using mixed binary and linear decision rules. The extended formulation of these decision rules, as functions of uncertain parameters, is presented in this part as well.