Tight MIP Formulation for Pipeline Gas Flow with Linepack

TL;DR

This paper introduces a tight piecewise linearization method for pipeline gas flow with linepack in integrated energy system models, significantly improving computational efficiency over existing approaches.

Contribution

It proposes a novel tight linearization technique that reduces problem complexity and enhances solver speed in mixed-integer linear programming models for gas pipeline flow.

Findings

Achieves an average speed-up of 2.83 times in computational performance.

Demonstrates effectiveness on IEEE Reliability Test System and a 12-node gas system.

Provides theoretical and practical validation of the proposed method.

Abstract

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 programing, 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 2.83 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.