Robust Transmission Network Expansion Planning under Correlated Uncertainty

TL;DR

This paper introduces a robust transmission network expansion planning method that explicitly considers correlated uncertainties in demand and generation capacity using an ellipsoidal uncertainty set, improving planning accuracy under uncertainty.

Contribution

It presents a novel nested decomposition algorithm for solving the robust optimization problem with correlated uncertainties, incorporating a probabilistic interpretation and structural reliability analogy.

Findings

Effectively captures correlated uncertainties in planning.

Improves robustness of transmission expansion solutions.

Demonstrates superior performance on case studies.

Abstract

This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for under a given user-defined uncertainty set. This work differs from previously reported robust solutions in two respects. First, the typically disregarded correlation of uncertainty sources is explicitly considered through an ellipsoidal uncertainty set relying on their variance-covariance matrix. In addition, we describe the analogy between the corresponding second-stage problem and a certain class of mathematical programs arising in structural reliability. This analogy gives rise to a relevant probabilistic interpretation of the second stage, thereby revealing an undisclosed feature of the worst-case setting characterizing robust optimization with ellipsoidal uncertainty sets. More importantly, a novel nested decomposition approach based on results from structural reliability is devised to solve the proposed robust counterpart, which is cast as an instance of mixed-integer trilevel programming. Numerical results from several case studies demonstrate that the effect of correlated uncertainty can be captured by the proposed robust approach.