A Wasserstein distributionally robust model for transmission expansion planning with renewable-based microgrid penetration

This article introduces a Wasserstein distance-based distributionally robust optimization model to address the transmission expansion planning considering renewable-based microgrids (MGs) under the impact of uncertainties. The primary objective of the presented methodology is to devise a robust expansion strategy that accounts for both long-term uncertainty and short-term variability over the planning horizon from the perspective of a central planner. In this framework, the central planner fosters the construction of appropriate transmission lines and the deployment of optimal MG-based generating units among profit-driven private investors. The Wasserstein distance uncertainty set is used to characterize the long-term uncertainty associated with future load demand. Short-term uncertainties, stemming from variations in load demands and production levels of stochastic units, are modeled through operating conditions. To ensure the tractability of the proposed planning model, the authors introduce a decomposition framework embedded with a modified application of Bender's method. To validate the efficiency and highlight the potential benefits of the proposed expansion planning methodology, two case studies based on simplified IEEE 6-bus and IEEE 118-bus systems are included. These case studies assess the effectiveness of the presented approach, its ability to navigate uncertainties, and its capacity to effectively optimize expansion decisions.