Tight MILP formulation for pipeline gas flow with linepack

T. Klatzer, S. Wogrin, D.A. Tejada, G. Morales-España

International Journal of Electrical Power & Energy Systems Vol. 169, pp. 110734-1 - 110734-12

Summary:

In integrated power and gas energy system optimization models (ESOMs), pipeline gas transmission with linepack is a particularly complex problem due to its non-linear and non-convex character. For ESOMs based on mixed-integer linear programming, piecewise linearization is a well-established convexification approach for this problem, which, however, requires binary variables to model feasible combinations of linear gas flow and pressure segments and thus can quickly become computationally challenging. In order to improve computational performance, this paper proposes a piecewise linearization method specifically designed to be tight, resulting in a reduced problem space a solver can explore faster. We provide numerical results comparing the proposed formulation against two piecewise linearizations from the literature, both from a theoretical point of view and in terms of practical computational performance, with results showing an average speed-up of 2.57 times for our case study. Test cases are carried out on a modified 24-bus IEEE Reliability Test System and a 12-node gas system, considering discrete unit commitment decisions.

Spanish layman's summary:

Comparamos linealizaciones por partes, con un enfoque novedoso y demostramos su rigor calculando los vértices fraccionarios de su región factible de PL relajada. Los experimentos muestran una aceleración promedio de 2,57 veces en nuestro caso de estudio de un sistema con energía eléctrica y gas.

English layman's summary:

We compare piecewise linearizations, propose a novel approach, and demonstrate its tightness by computing the fractional vertices of its relaxed LP feasible region. Numerical experiments show an average speed-up of 2.57 times for our case study of an integrated power and gas energy system.

Keywords: Integrated energy system modeling; Gas flow; Linepack; Piecewise linearization; MILP

JCR-JIF Impact Factor and WoS quartile: 5,000 - Q1 (2023)

DOI reference: https://doi.org/10.1016/j.ijepes.2025.110734

Published on paper: August 2025.

Published on-line: May 2025.

Citation:
T. Klatzer, S. Wogrin, D.A. Tejada, G. Morales-España, Tight MILP formulation for pipeline gas flow with linepack. International Journal of Electrical Power & Energy Systems. Vol. 169, pp. 110734-1 - 110734-12, August 2025. [Online: May 2025]