Convex Relaxations for Gas Expansion Planning

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal soluutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solutions

Mathematical properties of formulations of the gas transmission problem

The paper presents the mathematical properties of several formulations for the gas transmission problem that account for the nonlinear flow pressure relations. The form of the nonlinear flow pressure relations is such that the model is in general nonconvex. However, we show here that under a restrictive condition (gas inlet or gas pressure fixed at every entry/outgoing node) the problem becomes convex. This result is obtained by use of the variational inequality theory. We also give a computational method to find a feasible solution to the problem and give a physical interpretation to this feasible solution

Design and operations of gas transmission networks

Problems dealing with the design and the operations of gas transmission networks are challenging. The difficulty mainly arises from the simultaneous modeling of gas transmission laws and of the investment costs. The combination of the two yields a non- linear non-convex optimization problem. To obviate this shortcoming, we propose a new formulation as a multi-objective problem, with two objectives. The first one is the investment cost function or a suitable approximation of it; the second is the cost of energy that is required to transmit the gas. This energy cost is approximated by the total energy dissipated into the network. This bi-criterion problem turns out to be convex and easily solvable by convex optimization solvers. Our continuous optimization formulation can be used as an efficient continuous relaxation for problems with non-divisible restrictions such as a limited number of available commercial pipe dimensions.gas transmission networks, reinforcement, convex optimization

A cost function for the natural gas transmission industry: further considerations

This article studies the cost function for the natural gas transmission industry. In addition to a tribute to H.B. Chenery, it firstly offers some further comments on a recent contribution (Yépez, 2008): a statistical characterization of long-run scale economies, and a simple reformulation of the long-run problem. An extension is then proposed to analyze how the presence of seasonally-varying flows modifies the optimal design of a transmission infrastructure. Lastly, the case of a firm that anticipates a possible random rise in its future output is also studied to discuss the optimal degree of excess capacity to be built into a new transmission infrastructure

Flow-pressure analysis of loop gas networks

This paper proposes a mathematical model underlying a computer program for flow-pressure analysis of loop gas pipe networks. The method is used on a test case with four nodes. The HAPN application for flow-pressure analyses of low pressure gas pipe networks is completely designed in object-oriented programming technology. The equations, which describe the physical flow-pressure conditions through every cross point are assumed to be continuous and the energy of every closed loop of analyzed network conserved. The system of non-linear equations was linearized by LTM (Linear Theory Method). The algorithm for numerical module LTM and the method for solution of sparse matrix are developed at the Faculty of Chemistry and Chemical Engineering, University of Maribor, Slovenia

The technology and cost structure of a natural gas pipeline: Insights for costs and rate-of-return regulation

This note details a complete microeconomic characterization of the physical relationships between input use and the level of output of a simple point-to-point gas pipeline system and uses it to contribute to the public policy discussions pertaining to the economic regulation of natural gas pipelines. We show that the engineering equations governing the design and operations of that infrastructure can be approximated by a single production equation of the Cobb-Douglas type. We use that result to inform three public policy debates. First, we prove that the long-run cost function of the infrastructure formally verifies the condition for a natural monopoly, thereby justifying the need of regulatory intervention in that industry. Second, we examine the conditions for cost-recovery in the short-run and contribute to the emerging European discussions on the implementation of short-run marginal cost pricing on interconnector pipelines. Lastly, we analyze the performance of rate-of-return regulation in that industry and inform the regulatory policy debates on the selection of an appropriate authorized rate of return. We highlight that, contrary to popular belief, the socially desirable rate of return can be larger than the market price of capital for that industry

Global optimization of pipe networks by the interval analysis approach: the Belgium network case

We show that global optimization techniques, based on interval analysis and constraint propagation, succeed in solving the classical problem of optimization of the Belgium gas network.Nous montrons que les techniques d'optimisation globale, basées sur l'analsye par intervalles et la propagation de contraintes, réussissent à résoudre le problème classique de l'optimisation du réseau belge de gaz