Robust transmission expansion planning using pair-based convex hull uncertainty sets under high penetration of renewable energy generation

Abstract

Robust optimization is a practical and effective mathematical framework for coping with uncertainty in the transmission expansion planning (TEP) process, while computing the full convex hull is an outstanding data-driven means of searching for robust boundaries in the uncertainty sets employed in robust TEP processes. However, computing the full convex hull becomes intractable as the number of uncertain factors increases. This study addresses this issue by proposing a two-stage, four-level robust TEP model with uncertainty sets constructed using pair-based convex hulls. Employing a pair-based convex hull enables high-dimensional uncertainty to be characterized by constructing multiple low-dimensional uncertainty sets, and thereby decreases the computational burden associated with solving the robust TEP model while reducing the conservativeness of planning solutions. The model is then solved by means of a parallel column and constraint generation method. The proposed model is demonstrated to characterize the high-dimensional uncertainty efficiently and provide TEP solutions with relatively low conservativeness and high robustness based on numerical simulations of Garver’s 6-bus and IEEE 118-bus test systems.

Keywords

• High-dimensional uncertainty
• Robust optimization
• Transmission expansion planning
• Pair-based convex hull
• Two-loop column and constraint generation method