Convex Relaxations for Gas Expansion Planning

Abstract

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the nonconvex 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 solutions. 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.

Optimizing natural gas pipeline transmission with nonuniform elevation: A new initialization approach

“…Convex relaxation is another good way to deal with nonconvex problems. Borraz‐Sánchez, Bent, Backhaus, Hijazi, and Hentenryck () use the convex relaxation to transform (F‐P) to a convex constraint, and Xue et al () use the iterative two‐stage convex relaxation approach to make the model much easier to solve. Geißler et al () apply the penalty alternating direction method to solve the MINLP problem.…”

GasLib—A Library of Gas Network Instances

“…The entries equally provide the gas; that is, the inflow at every entry is 660 Nm 3 /h. Numerical results for these instances can be found in [11][12][13][14]. …”

Joint Expansion Planning for Natural Gas and Electric Transmission with Endogenous Market Feedbacks

“…For compressors (the set A g c ), these values are typically 1 and for control valves (the set A g v ) these values are typically ≤ 1. Control valves also include on/off variables to turn off these constraints and set x = 0 (see [6]). Finally, flexible consumption, production, and pressures are bound by the following constraints…”

“…To address this complexity, we use the exact disjunctive formulation to model the flow direction of gas and the subsequent second order cone relaxation as discussed in [6].…”

“…Coordination in planning will become increasingly important as power grids continue to move towards natural gas and plants powered by other fuels retire. The model in the present paper represents an extension of previous work in [6,7,8,9], in which spot price feedbacks from expansion decisions are endogenized and incorporated into the planning objective function. We illustrate this modeling approach using an integrated test system composed of the IEEE 36-bus NPCC electric power system [10] with marginal costs for coal, nuclear, hydro, wind, oil and refuse generation as reported in [11] and a multi-company gas transmission network covering the Pennsylvania-To-Northeast New England area in the US [8].…”