Convex Relaxations for Gas Expansion Planning

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal soluutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solutions

Shift factor-based SCOPF topology control MIP formulations with substation configurations

Topology control (TC) is an effective tool for managing congestion, contingency events, and overload control. The majority of TC research has focused on line and transformer switching. Substation reconfiguration is an additional TC action, which consists of opening or closing breakers not in series with lines or transformers. Some reconfiguration actions can be simpler to implement than branch opening, seen as a less invasive action. This paper introduces two formulations that incorporate substation reconfiguration with branch opening in a unified TC framework. The first method starts from a topology with all candidate breakers open, and breaker closing is emulated and optimized using virtual transactions. The second method takes the opposite approach, starting from a fully closed topology and optimizing breaker openings. We provide a theoretical framework for both methods and formulate security-constrained shift factor MIP TC formulations that incorporate both breaker and branch switching. By maintaining the shift factor formulation, we take advantage of its compactness, especially in the context of contingency constraints, and by focusing on reconfiguring substations, we hope to provide system operators additional flexibility in their TC decision processes. Simulation results on a subarea of PJM illustrate the application of the two formulations to realistic systems.The work was supported in part by the Advanced Research Projects Agency-Energy, U.S. Department of Energy, under Grant DE-AR0000223 and in part by the U.S. National Science Foundation Emerging Frontiers in Research and Innovation under Grant 1038230. Paper no. TPWRS-01497-2015. (DE-AR0000223 - Advanced Research Projects Agency-Energy, U.S. Department of Energy; 1038230 - U.S. National Science Foundation Emerging Frontiers in Research and Innovation)http://buprimo.hosted.exlibrisgroup.com/primo_library/libweb/action/openurl?date=2017&issue=2&isSerivcesPage=true&spage=1179&dscnt=2&url_ctx_fmt=null&vid=BU&volume=32&institution=bosu&issn=0885-8950&id=doi:10.1109/TPWRS.2016.2574324&dstmp=1522778516872&fromLogin=truePublished versio

An Improved Mathematical Formulation For the Carbon Capture and Storage (CCS) Problem

abstract: Carbon Capture and Storage (CCS) is a climate stabilization strategy that prevents CO2 emissions from entering the atmosphere. Despite its benefits, impactful CCS projects require large investments in infrastructure, which could deter governments from implementing this strategy. In this sense, the development of innovative tools to support large-scale cost-efficient CCS deployment decisions is critical for climate change mitigation. This thesis proposes an improved mathematical formulation for the scalable infrastructure model for CCS (SimCCS), whose main objective is to design a minimum-cost pipe network to capture, transport, and store a target amount of CO2. Model decisions include source, reservoir, and pipe selection, as well as CO2 amounts to capture, store, and transport. By studying the SimCCS optimal solution and the subjacent network topology, new valid inequalities (VI) are proposed to strengthen the existing mathematical formulation. These constraints seek to improve the quality of the linear relaxation solutions in the branch and bound algorithm used to solve SimCCS. Each VI is explained with its intuitive description, mathematical structure and examples of resulting improvements. Further, all VIs are validated by assessing the impact of their elimination from the new formulation. The validated new formulation solves the 72-nodes Alberta problem up to 7 times faster than the original model. The upgraded model reduces the computation time required to solve SimCCS in 72% of randomly generated test instances, solving SimCCS up to 200 times faster. These formulations can be tested and then applied to enhance variants of the SimCCS and general fixed-charge network flow problems. Finally, an experience from testing a Benders decomposition approach for SimCCS is discussed and future scope of probable efficient solution-methods is outlined.Dissertation/ThesisMasters Thesis Industrial Engineering 201

Using Functional Programming to recognize Named Structure in an Optimization Problem: Application to Pooling

Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems

Exact and Approximate Schemes for Robust Optimization Problems with Decision Dependent Information Discovery

Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed sequentially based on a prescribed filtration. This problem class is useful in a wide range of applications, however, its assimilation is partly limited by the lack of efficient solution schemes. In this paper we study two-stage robust optimization problems with decision dependent information discovery where uncertainty appears in the objective function. The contributions of the paper are twofold: (i) we develop an exact solution scheme based on a nested decomposition algorithm, and (ii) we improve upon the existing K-adaptability approximate by strengthening its formulation using techniques from the integer programming literature. Throughout the paper we use the orienteering problem as our working example, a challenging problem from the logistics literature which naturally fits within this framework. The complex structure of the routing recourse problem forms a challenging test bed for the proposed solution schemes, in which we show that exact solution method outperforms at times the K-adaptability approximation, however, the strengthened K-adaptability formulation can provide good quality solutions in larger instances while significantly outperforming existing approximation schemes even in the decision independent information discovery setting. We leverage the effectiveness of the proposed solution schemes and the orienteering problem in a case study from Alrijne hospital in the Netherlands, where we try to improve the collection process of empty medicine delivery crates by co-optimizing sensor placement and routing decisions

A mathematical framework for modelling and evaluating natural gas pipeline networks under hydrogen injection

This article presents the framework of a mathematical formulation for modelling and evaluating natural gas pipeline networks under hydrogen injection. The model development is based on gas transport through pipelines and compressors which compensate for the pressure drops by implying mainly the mass and energy balances on the basic elements of the network. The model was initially implemented for natural gas transport and the principle of extension for hydrogen-natural gas mixtures is presented. The objective is the treatment of the classical fuel minimizing problem in compressor stations. The optimization procedure has been formulated by means of a nonlinear technique within the General Algebraic Modelling System (GAMS) environment. This work deals with the adaptation of the current transmission networks of natural gas to the transport of hydrogen-natural gas mixtures. More precisely, the quantitative amount of hydrogen that can be added to natural gas can be determined. The studied pipeline network,initially proposed by Abbaspour et al. (2005) is revisited here for the case of hydrogen-natural gas mixtures. Typical quantitative results are presented, showing that the addition of hydrogen to natural gas decreases significantly the transmitted power : the maximum fraction of hydrogen that can be added to natural gas is around 6 mass percent for this example

Simultaneous mixed-integer disjunctive optimization for synthesis of petroleum refinery topology Processing Alternatives for Naphtha Produced from Atmospheric Distillation Unit

In this work, we propose a logic-based modeling technique within a mixed-integer disjunctive superstructure optimization framework on the topological optimization problem for determining the optimal petroleum refinery configuration. We are interested to investigate the use of logic cuts that are linear inequality/equality constraints to the conceptual process synthesis problem of the design of a refinery configuration. The logic cuts are employed in two ways using 0-l variables: ( l) to enforce certain design specifications based on past design experience, engineering knowledge, and heuristics; and (2) to enforce certain structural specifications on the interconnections of the process units. The overall modeling framework conventionally gives rise to a mixedinteger optimization framework, in this case, a mixed-integer linear programming model (because of the linearity of the constraints). But in this work, we elect to adopt a disjunctive programming framework, specifically generalized disjunctive programming (GDP) proposed by Grossmann and co-workers (Grossmann, l. E. (2002). Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques. Optimization & Engineering, 3, 227.) The proposed GOP-based modeling technique is illustrated on a case study to determine the optimal processing route of naphtha in a refinery using the GAMS/LogMIP platform, which yields practically-acceptable solution. The use of LogMIP obviates the need to reformulate the logic propositions and the overall disjunctive problem into algebraic representations, hence reducing the time involved in the typically time-consuming problem formulation. LogMIP typically leads to less computational time and number of iterations in its computational effort because the associated GDP formulation involves less equations and variables compared to MILP. From the computational experiments, it is found that logical constraints of design specifications and structural specifications potentially play an important role to determine the optimal selection of process units and streams. Hence, in general, the GDP formulation can be improved by adding or eliminating constraits that can accelerate or slow-down the problem solution respectively

Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics

The second MFO Oberwolfach Workshop on Mixed-Integer Nonlinear Programming (MINLP) took place between 2nd and 8th June 2019. MINLP refers to one of the hardest Mathematical Programming (MP) problem classes, involving both nonlinear functions as well as continuous and integer decision variables. MP is a formal language for describing optimization problems, and is traditionally part of Operations Research (OR), which is itself at the intersection of mathematics, computer science, engineering and econometrics. The scientific program has covered the three announced areas (hierarchies of approximation, mixed-integer nonlinear optimal control, and dealing with uncertainties) with a variety of tutorials, talks, short research announcements, and a special "open problems'' session