Bilevel Transmission Expansion Planning with Joint Chance-Constrained Dispatch

TL;DR

This paper presents a novel bilevel transmission expansion planning framework that incorporates joint chance-constrained market clearing under wind uncertainty, using a strengthened linear approximation for efficient and reliable solutions.

Contribution

It introduces a new bilevel TEP model with joint chance constraints and a SLA technique for robust, efficient solution of complex distributionally robust problems.

Findings

Achieves desired constraint satisfaction probability in case studies.

Provides up to 26x computational speedup over existing methods.

Maintains high solution quality with improved efficiency.

Abstract

In transmission expansion planning (TEP), network planners make long-term investment decisions while anticipating market clearing outcomes that are increasingly affected by renewable generation uncertainty. Additionally, market participants' sensitivity to network charges and the requirement for cost recovery by the network planner introduce further complexity. Since the day-ahead market clears before uncertainty realizes, explicitly modelling these uncertainties at the lower-level market clearing becomes important in bilevel TEP problems. In this paper, we introduce a novel bilevel TEP framework with lower-level joint chance-constrained market clearing that manages line flow constraints under wind uncertainty and accounts for the effect of network tariffs on participants' actual marginal costs and utility. To solve this complex problem, we propose a Strengthened Linear Approximation (SLA) technique for handling Wasserstein distributionally robust joint chance constraints with right-hand-side uncertainties (RHS-WDRJCC). The proposed method offers more efficient approximations without additional conservativeness and avoids the numerical issues encountered in existing approaches by introducing valid inequalities. The case study demonstrates that the proposed model achieves the desired out-of-sample constraint satisfaction probability. Moreover, the numerical results highlight the significant computational advantage of SLA, achieving up to a 26x speedup compared to existing methods such as worst-case conditional value-at-risk, while maintaining high solution quality.