On the Solution of Large-Scale Robust Transmission Network Expansion Planning under Uncertain Demand and Generation Capacity

TL;DR

This paper introduces a novel column-and-constraint generation algorithm with a coordinate descent method for large-scale robust transmission network expansion planning under uncertainty, avoiding complex transformations and reducing computational effort.

Contribution

It proposes a new solution approach that handles large-scale problems efficiently without transforming the second-stage problem into a single-level form.

Findings

Successfully applied to a 2383-bus system benchmark

Reduces computational effort compared to existing methods

Avoids complex bilinear term linearizations

Abstract

Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, available solution methodologies for the resulting trilevel robust counterpart are unsuitable for large-scale problems. In order to overcome this shortcoming, this paper presents an alternative column-and-constraint generation algorithm wherein the max-min problem associated with the second stage is solved by a novel coordinate descent method. As a major salient feature, the proposed approach does not rely on the transformation of the second-stage problem to a single-level equivalent. As a consequence, bilinear terms involving dual variables or Lagrange multipliers do not arise, thereby precluding the use of computationally expensive big-M-based linearization schemes. Thus, not only is the computational effort reduced, but also the typically overlooked non-trivial tuning of bounding parameters for dual variables or Lagrange multipliers is avoided. The practical applicability of the proposed methodology is confirmed by numerical testing on several benchmarks including a case based on the Polish 2383-bus system, which is well beyond the capability of the robust methods available in the literature.