Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more

Nonoverlapping Domain Decomposition for Optimal Control Problems governed by Semilinear Models for Gas Flow in Networks

We consider optimal control problems for gas flow in pipeline networks. The equations of motion are taken to be represented by a first-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order … Read more

Global optimization of mixed-integer ODE constrained network problems using the example of stationary gas transport

In this paper we propose a new approach for finding global solutions of mixed-integer nonlinear optimization problems with ordinary differential equation constraints on networks. Instead of using a first discretize then optimize approach, we combine spatial and variable branching with appropriate discretizations of the differential equations to derive relaxations of the original problem. To construct … Read more

A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities

Many mixed-integer optimization problems are constrained by nonlinear functions that do not possess desirable analytical properties like convexity or factorability or cannot even be evaluated exactly. This is, e.g., the case for problems constrained by differential equations or for models that rely on black-box simulation runs. For these problem classes, we present, analyze, and test … Read more

MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems

We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations … Read more

Computational Optimization of Gas Compressor Stations: MINLP Models vs. Continuous Reformulations

When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to complicated mixed-integer nonlinear and nonconvex optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several … Read more

High Detail Stationary Optimization Models for Gas Networks: Validation and Results

Due to strict regulatory rules in combination with complex nonlinear physics, major gas network operators in Germany and Europe face hard planning problems that call for optimization. In part 1 of this paper we have developed a suitable model hierarchy for that purpose. Here we consider the more practical aspects of modeling. We validate individual … Read more