Tight and compact MILP formulation for a high-resolution of start-up costs in the medium-term unit commitment

L. Montero, G. Morales-España, A. Bello, J. Reneses

Sustainable Energy, Grids and Networks Vol. 44, pp. 101935

Summary:

Nowadays, most modern power systems are evolving towards a considerable capacity expansion in their energy storage and interconnection facilities. However, these great developments are not being accomplished fast enough to accommodate the high penetration of variable renewable energy sources. This situation raises demand variability, requiring more flexibility from thermal generators, especially due to their more frequent start-up and shut-down processes. Consequently, the unit commitment requires more accurate and detailed modeling while maintaining computational efficiency. This paper analyzes some of the best models to manage long-duration start-up costs according to the real fuel-consumption curves of a gas-fired generation portfolio. Moreover, we propose a tight and compact MILP piecewise formulation that enhances the resolution of start-up representations and achieves outstanding results compared to the literature benchmarks. The successful performance of this methodology is proven in several large-size case studies focusing on the medium term. Furthermore, conventional day-ahead problems are also run to demonstrate the overall competitiveness of the formulation.

Spanish layman's summary:

Este artículo presenta una formulación MILP que mejora el acotado de variables al representar los costes de arranque del unit commitment mediante linealizaciones piecewise, ofreciendo un mejor equilibrio entre tightness y compactness que finalmente se traduce en una mayor eficiencia computacional.

English layman's summary:

This paper presents a tight and compact MILP formulation that uses piecewise linearizations to represent start-up costs. The tightness improvement of this unit commitment model entails more efficient resolution processes.

Keywords: Start-up costs; Unit commitment; Medium-term models; Piecewise linearizatio;n; Mixed-integer linear programming

JCR-JIF Impact Factor and WoS quartile: 5,700 - Q1 (2025)

DOI reference: https://doi.org/10.1016/j.segan.2025.101935

Published on paper: December 2025.

Published on-line: August 2025.

Citation:
L. Montero, G. Morales-España, A. Bello, J. Reneses, "Tight and compact MILP formulation for a high-resolution of start-up costs in the medium-term unit commitment", Sustainable Energy, Grids and Networks, Vol. 44, pp. 101935, December 2025. [Online: August 2025] doi: 10.1016/j.segan.2025.101935