Scalable Multi-Level Optimization for Sequentially Cleared Energy Markets with a Case Study on Gas and Carbon Aware Unit Commitment

TL;DR

This paper introduces a scalable multi-level optimization approach for energy markets, integrating gas and carbon considerations into unit commitment decisions, with a case study demonstrating significant computational efficiency improvements.

Contribution

It develops a novel approximation method for complex multi-level problems and proposes a Benders decomposition technique tailored for energy market applications.

Findings

Achieved 32.23% reduction in computation time.

Reduced optimality gaps by 94.23%.

Successfully integrated gas and carbon market data into unit commitment.

Abstract

This paper examines Mixed-Integer Multi-Level problems with Sequential Followers (MIMLSF), a specialized optimization model aimed at enhancing upper-level decision-making by incorporating anticipated outcomes from lower-level sequential market-clearing processes. We introduce a novel approach that combines lexicographic optimization with a weighted-sum method to asymptotically approximate the MIMLSF as a single-level problem, capable of managing multi-level problems exceeding three levels. To enhance computational efficiency and scalability, we propose a dedicated Benders decomposition method with multi-level subproblem separability. To demonstrate the practical application of our MIMLSF solution technique, we tackle a unit commitment problem (UC) within an integrated electricity, gas, and carbon market clearing framework in the Northeastern United States, enabling the incorporation of anticipated costs and revenues from gas and carbon markets into UC decisions. This ensures that only profitable gas-fired power plants (GFPPs) are committed, allowing system operators to make informed decisions that prevent GFPP economic losses and reduce total operational costs under stressed electricity and gas systems. The case study not only demonstrates the applicability of the MIMLSF model but also highlights the computational benefits of the dedicated Benders decomposition technique, achieving average reductions of 32.23% in computing time and 94.23% in optimality gaps compared to state-of-the-art methods.