Natural Gas Flow Solvers using Convex Relaxation
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by
Manish Kumar Singh, Vassilis Kekatos
2020
Abstract
The vast infrastructure development, gas flow dynamics, and complex
interdependence of gas with electric power networks call for advanced
computational tools. Solving the equations relating gas injections to pressures
and pipeline flows lies at the heart of natural gas network (NGN) operation,
yet existing solvers require careful initialization and uniqueness has been an
open question. In this context, this work considers the nonlinear steady-state
version of the gas flow (GF) problem. It first establishes that the solution to
the GF problem is unique under arbitrary NGN topologies, compressor types, and
sets of specifications. For GF setups where pressure is specified on a single
(reference) node and compressors do no appear in cycles, the GF task is posed
as an convex minimization. To handle more general setups, a GF solver relying
on a mixed-integer quadratically-constrained quadratic program (MI-QCQP) is
also devised. This solver can be used for any GF setup at any NGN. It
introduces binary variables to capture flow directions; relaxes the pressure
drop equations to quadratic inequality constraints; and uses a carefully
selected objective to promote the exactness of this relaxation. The relaxation
is provably exact in NGNs with non-overlapping cycles and a single
fixed-pressure node. The solver handles efficiently the involved bilinear terms
through McCormick linearization. Numerical tests validate our claims,
demonstrate that the MI-QCQP solver scales well, and that the relaxation is
exact even when the sufficient conditions are violated, such as in NGNs with
overlapping cycles and multiple fixed-pressure nodes.
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