Online Superstructure Optimization for Energy Saving of an Industrial Gas Distribution System

Mixed-integer optimization is a common approach to handle decision-making problems. Nevertheless, such an approach still presents certain operational limitations, especially for online superstructures. One of these limitations is given by Jacobian singularity, which arises for certain combinations of the set of Boolean variables and which easily leads to possible infeasible numerical solutions. This paper proposes a novel approach to overcome this problem, ensuring the use of mixed-integer optimization also to solve online issues. The case of nitrogen supply for the Thyssen-Krupp steel mill placed in Terni (Italy) is considered as validation case

Bookings in the European Gas Market: Characterisation of Feasibility and Computational Complexity Results

International audienceAs a consequence of the liberalisation of the European gas market in the last decades, gas trading and transport have been decoupled. At the core of this decoupling are so-called bookings and nominations. Bookings are special long-term capacity right contracts that guarantee that a specified amount of gas can be supplied or withdrawn at certain entry or exit nodes of the network. These supplies and withdrawals are nominated at the day-ahead. The special property of bookings then is that they need to be feasible, i.e., every nomination that complies with the given bookings can be transported. While checking the feasibility of a nomination can typically be done by solving a mixed-integer nonlinear feasibility problem, the verification of feasibility of a set of bookings is much harder. The reason is the robust nature of feasibility of bookings-namely that for a set of bookings to be feasible, all compliant nominations, i.e., infinitely many, need to be checked for feasibility. In this paper, we consider the question of how to verify the feasibility of given bookings for a number of special cases. For our physics model we impose a steady-state potential-based flow model and disregard controllable network elements. For this case we derive a characterisation of feasible bookings, which is then used to show that the problem is in coNP for the general case but can be solved in polynomial time for linear potential-based flow models. Moreover, we present a dynamic programming approach for deciding the feasibility of a booking in tree-shaped networks even for nonlinear flow models. It turns out that the hardness of the problem mainly depends on the combination of the chosen physics model as well as the specific network structure under consideration. Thus, we give an overview over all settings for which the hardness of the problem is known and finally present a list of open problems

Co-optimized analysis of electric and natural gas infrastructures

This dissertation proposes and implements a long-term capacity expansion model for the co-optimization of electric and natural gas infrastructures. It allows to determine the required investments in generation units, transmission lines and pipelines for meeting future demands, while representing electricity and natural gas flows using steady state equations. A Mixed Integer Nonlinear Programming problem is developed, from which a linearized version is derived. A twenty six node integrated electric-gas system for the Eastern Region of the United States is used to demonstrate the model\u27s capabilities. Results show that the model provides an accurate operational representation of the integrated system, and therefore, enhances the expansion planning process

Mixed Integer Linear Programming Formulation Techniques

A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art solvers. In this survey we review advanced MIP formulation techniques that result in stronger and/or smaller formulations for a wide class of problems

Global optimization with piecewise linear approximation

textGlobal optimization deals with the development of solution methodologies for nonlinear nonconvex optimization problems. These problems, which could arise in diverse situations ranging from optimizing hydro-power generation schedules to estimating coefficients of non-linear regression models, are difficult for traditional nonlinear solvers that iteratively search the neighborhood around a starting point. The Piecewise Linear Approximation (PLA) method that we study in this dissertation seeks to generate ‘good’ starting points, hopefully ones that lie in the basin of attraction of the globally optimal solution. In this approach, we approximate the non-linear functions in the optimization problem by piecewise linear functions defined over the vertices of a grid that partitions the domain of each nonlinear function into cells. Based on this approximation, we convert the original nonlinear program into a mixed integer program (MIP) and use the solution to this MIP as a starting point for a local nonlinear solver. In this dissertation, we validate the effectiveness of the PLA approach as a global optimization approach by applying it to a diverse set of continuous and discrete nonlinear optimization problems. Further, we develop various modeling and algorithmic strategies for enhancing the basic approach. Our computational results demonstrate that the PLA approach works well on non-convex problems and can, in some cases, provide better solutions than those provided by existing nonlinear solvers.Information, Risk, and Operations Management (IROM

Validation of nominations in gas networks and properties of technical capacities

[no abstract