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Solving Power-Constrained Gas Transportation Problems using an MIP-based Alternating Direction Method

Björn Geißler (bjoern.geissler***at***math.uni-erlangen.de)
Antonio Morsi (antonio.morsi***at***math.uni-erlangen.de)
Lars Schewe (lars.schewe***at***math.uni-erlangen.de)
Martin Schmidt (mar.schmidt***at***fau.de)

Abstract: We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to hard nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the nonlinearities and a tailored alternating direction method. In addition to most other publications in the field of gas transport optimization, we do not only consider pressure and flow as main physical quantities but further incorporate heat power supplies and demands as well as a mixing model for different gas qualities. We demonstrate the capabilities of our method on Germany's largest transport networks and hereby present numerical results on the largest instances that were ever reported in the literature for this problem class.

Keywords: Nonconvex Mixed-Integer Nonlinear Optimization, Alternating Direction Methods, Piecewise Linear Relaxations, Gas Transport Networks, Heat Power Supply and Demand

Category 1: Applications -- Science and Engineering

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Technical report, (a) Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Discrete Optimization, Cauerstraße 11, 91058 Erlangen, Germany; (b) Energie Campus Nürnberg, Fürther Straße 250, 90429 Nürnberg, Germany. November 2014.

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Entry Submitted: 11/24/2014
Entry Accepted: 11/24/2014
Entry Last Modified: 07/08/2015

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