Iterative LP-Based Methods for the Multiperiod Optimal Electricity and Gas Flow Problem

Abstract

In light of the increasing coupling between electricity and gas networks, this paper introduces two novel iterative methods for efficiently solving the multiperiod optimal electricity and gas flow (MOEGF) problem. The first is an iterative MILP-based method and the second is an iterative LP-based method with an elaborate procedure for ensuring an integral solution. The convergence of the two approaches is founded on two key features. The first is a penalty term with a single, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">automatically tuned</i> , parameter for controlling the step size of the gas network iterates. The second is a sequence of supporting hyperplanes and halfspaces for controlling the convergence of the electricity network iterates. Moreover, the two proposed algorithms use as a warm start the solution from a novel polyhedral relaxation of the MOEGF problem, for a noticeable improvement in computation time as compared to a cold start. Unlike the first method, which invokes a branch-and-bound algorithm to find an integral solution, the second method implements an elaborate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">steering</i> procedure that guides the continuous variables to take integral values at the solution. Numerical evaluation demonstrates that the two proposed methods can converge to high-quality <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasible</i> solutions in computation times at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">two orders of magnitude faster</i> than both a state-of-the-art nonlinear branch-and-bound (NLBB) MINLP solver and a mixed-integer convex programming (MICP) relaxation of the MOEGF problem. The experimental setup consists of five test cases, three of which involve the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">real</i> electricity and gas transmission networks of the state of Victoria with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">actual</i> linepack and demand profiles.