A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

TL;DR

This paper introduces a new strong duality-based reformulation for trilevel energy system models, enabling more efficient and globally optimal solutions for complex power market problems involving emissions and policy impacts.

Contribution

It presents a novel single-level reformulation based on strong duality for trilevel problems, improving upon existing methods in model size and computational efficiency.

Findings

Successfully applied to a Nordic power market case study.

Achieved globally optimal solutions for emission reduction scenarios.

Analyzed the impact of carbon tax on electricity production.

Abstract

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed methods, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio.