Argonne National Laboratory

Mixed-Interger PDE-Constrained Optimal Control of Gas Networks

TitleMixed-Interger PDE-Constrained Optimal Control of Gas Networks
Publication TypeReport
Year of Publication2017
AuthorsHahn, M, Leyffer, S, Zavala, VM
Report NumberANL/MCS-P7095-0817

We develop a mixed-integer optimal control model with partial differential equation constraints for gas transport networks, designed for planning extreme state transitions, such as flow reversals. We use binary control variables to model different configurations of compressor stations. We model the flow of gas using a simplified variant of the Euler equations, which we discretize using a finite volume scheme, which obeys conservation of mass and average impulse independent of the direction of flow. The resulting large-scale mixed-integer nonlinear optimization is difficult to solve by using standard branch-and-bound solvers, and we propose several heuristics that allow us to solve realistic instances. We compare the performance of several solution schemes on ten test instances.