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Optimal design and operation of energy systems under uncertainty

JOURNAL OF PROCESS CONTROL 2015年 30卷 1-9页

作者： Li, Xiang Barton, Paul I. Queens Univ Dept Chem Engn Kingston ON K7L 3N6 Canada MIT Proc Syst Engn Lab Cambridge MA 02139 USA

This paper is concerned with integrated design and operation of energy systems that are subject to significant uncertainties. The problem is cast as a two-stage stochastic programming problem, which can be transformed into a large-scale nonconvex mixed-integer nonlinear programming problem (MINLP). The MINLP exhibits a decomposable structure that can be exploited by nonconvex generalized Benders decomposition (NGBD) for efficient global optimization. This paper extends the NGBD method developed by the authors recently, such that the method can handle non-separable functions and integer operational decisions. Both the standard NGBD algorithm and an enhanced one with piecewise convex relaxations are discussed. The advantages of the proposed formulation and solution method are demonstrated through case studies of two industrial energy systems, a natural gas production network and a polygeneration plant. The first example shows that the two-stage stochastic programming formulation can result in better expected economic performance than the deterministic formulation, and that NGBD is more efficient than a state-of-the-art global optimization solver. The second example shows that the integration of piecewise convex relaxations can improve the efficiency of NGBD by at least an order of magnitude. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Energy systems Design and operation Uncertainty Stochastic programming Global optimization mixed-integer nonlinear programming

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Energy loss reduction by optimal distributed generation allocation in distribution systems

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2015年第9期25卷 1673-1684页

作者： Haghighat, Hossein Islamic Azad Univ Jahrom Branch Jahrom Fars Iran

This paper presents a mixed-integer nonlinear optimization model for distributed generation (DG) placement in the distribution system. A multiperiod ac optimal power-flow model is developed for minimizing annual energy losses and determining the optimal site and size of DG units. Various system constraints and time-varying demands are incorporated in the model. A novel iterative method for solving the multiperiod DG placement problem based on the Benders decomposition technique is proposed, which reduces the computational burden and facilitates its practical application. Two case studies are presented to illustrate the efficacy of the proposed method. Copyright (C) 2014 John Wiley & Sons, Ltd.

关键词： distributed generation distribution system DG placement energy losses mixed-integer nonlinear programming

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Validation of nominations in gas network optimization: models, methods, and solutions

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OPTIMIZATION METHODS & SOFTWARE 2015年第1期30卷 15-53页

作者： Pfetsch, Marc E. Fuegenschuh, Armin Geissler, Bjoern Geissler, Nina Gollmer, Ralf Hiller, Benjamin Humpola, Jesco Koch, Thorsten Lehmann, Thomas Martin, Alexander Morsi, Antonio Roevekamp, Jessica Schewe, Lars Schmidt, Martin Schultz, Ruediger Schwarz, Robert Schweiger, Jonas Stangl, Claudia Steinbach, Marc C. Vigerske, Stefan Willert, Bernhard M. Tech Univ Darmstadt Dept Math Darmstadt Germany Helmut Schmidt Univ Dept Mech Engn Hamburg Germany Zuse Inst Berlin Berlin Germany Univ Erlangen Nurnberg Dept Math D-91054 Erlangen Germany Open Grid Europe GmbH Essen Germany Univ Duisburg Essen Dept Math Duisburg Germany Leibniz Univ Hannover Inst Appl Math D-30167 Hannover Germany

In this article, we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult nonconvex mixedinteger nonlinear feasibility problem. The first phase consists of four distinct algorithms applying mixedinteger linear, mixedinteger nonlinear, nonlinear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high-quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before.

关键词： gas network optimization nomination mixed-integer nonlinear programming gas transport optimization

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Convex reformulations for solving a nonlinear network design problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2015年第3期62卷 717-759页

作者： Humpola, Jesco Fuegenschuh, Armin Zuse Inst Berlin D-14195 Berlin Germany Univ Fed Armed Forces Hamburg Helmut Schmidt Univ D-22043 Hamburg Germany

We consider a nonlinear nonconvex network design problem that arises, for example, in natural gas or water transmission networks. Given is such a network with active and passive components, that is, valves, compressors, control valves (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes in the network. The active elements are associated with costs when used. Besides flow conservation constraints in the nodes, the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is to compute a cost minimal setting of the active components and numerical values for the flow and node potentials. We examine different (convex) relaxations for a subproblem of the design problem and benefit from them within a branch-and-bound approach. We compare different approaches based on nonlinear optimization numerically on a set of test instances.

关键词： nonlinear network flow mixed-integer nonlinear programming Relaxations Network design

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A COMPARISON BETWEEN MILP AND MINLP APPROACHES TO OPTIMAL SOLUTION OF nonlinear DISCRETE TRANSPORTATION PROBLEM

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TRANSPORT 2015年第2期30卷 135-144页

作者： Klansek, Uros Univ Maribor Fac Civil Engn Maribor Slovenia

Finding an exact optimal solution of the nonlinear Discrete Transportation Problem (NDTP) represents a challenging task in transportation science. Development of an adequate model formulation and selection of an appropriate optimization method are thus significant for attaining valuable solution of the NDTP. When nonlinearities appear within the criterion of optimization, the NDTP can be formulated directly as a mixed-integer nonlinear programming (MINLP) task or it can be linearized and converted into a mixed-integer Linear programming (MILP) problem. This paper presents a comparison between MILP and MINLP approaches to exact optimal solution of the NDTP. The comparison is based on obtained results of experiments executed on a set of reference test problems. The paper discusses advantages and limitations of both optimization approaches.

关键词： transportation problems discrete transporting flows nonlinear costs optimization methods mixed-integer linear programming mixed-integer nonlinear programming

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Using short-term resource scheduling for assessing effectiveness of CCS within electricity generation subsector

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AICHE JOURNAL 2015年第12期61卷 4210-4234页

作者： Alie, Colin Elkamel, Ali Croiset, Eric Douglas, Peter L. Univ Waterloo Dept Chem Engn Waterloo ON N2L 3G1 Canada

A new methodology for assessing the effectiveness of carbon capture and storage (CCS) that does explicitly consider the detailed operation of the target electricity system is proposed. The electricity system simulation consists of three phases, each one using a modified version of an economic dispatch problem that seeks to maximize the producers' and consumers' surplus while satisfying the technical constraints of the system. The economic dispatch is formulated as a dynamic mixed-integer nonlinear programming problem and implemented in general algebraic modelling system (GAMS). The generating unit with CCS is designed and simulated using Aspen Plus (R). In the first case study, the operation of the IEEE RTS '96 (Institute of Electrical and Electronics Engineers One-Area Reliability Test System1996) is simulated with greenhouse gas (GHG) regulation implemented in the form of CO2 permits that generators need to acquire for every unit of CO2 that it is emitted. In the second case study, CCS is added at one of the buses and the operation of the modified IEEE RTS '96 is again simulated with and without GHG regulation. The results suggest that the detailed operation of the target electricity system should be considered in future assessments of CCS and a general procedure for undertaking this for any GHG mitigation option is proposed. Future work will use the novel methodology for assessing the effectiveness of generating units with flexible CO2 capture. (c) 2015 American Institute of Chemical Engineers

关键词： process simulation energy environmental engineering optimization postcombustion CO2 capture carbon capture and storage greenhouse gas mitigation mixed-integer nonlinear programming short-term generation scheduling

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Multi-criteria optimisation approach to increase the delivered power in radial distribution networks

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IET GENERATION TRANSMISSION & DISTRIBUTION 2015年第16期9卷 2565-2574页

作者： Canizes, Bruno Soares, Joao Vale, Zita Lobo, Cristina Polytech Porto ISEP IPP GECAD Knowledge Engn & Decis Support Res Ctr P-4200072 Oporto Portugal

This study proposes a new methodology to increase the power delivered to any load point in a radial distribution network, through the identification of new investments in order to improve the repair time. This research work is innovative and consists in proposing a full optimisation model based on mixed-integer non-linear programming considering the Pareto front technique. The goal is to achieve a reduction in repair times of the distribution networks components, while minimising the costs of that reduction as well as non-supplied energy costs. The optimisation model considers the distribution network technical constraints, the substation transformer taps, and it is able to choose the capacitor banks size. A case study based on a 33-bus distribution network is presented in order to illustrate in detail the application of the proposed methodology.

关键词： distribution networks investment integer programming nonlinear programming Pareto optimisation cost reduction substations transformers power capacitors multicriteria optimisation approach power delivery radial distribution network investment optimisation model mixed-integer nonlinear programming Pareto front technique costs minimisation nonsupplied energy cost substation transformer tap capacitor bank 33-bus distribution network

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Delay-Constrained Shortest Paths: Approximation Algorithms and Second-Order Cone Models

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第3期164卷 1051-1077页

作者： Frangioni, Antonio Galli, Laura Scutella, Maria Grazia Univ Pisa Dipartimento Informat Largo B Pontecorvo 3 I-56127 Pisa Italy

Routing real-time traffic with maximum packet delay in contemporary telecommunication networks requires not only choosing a path but also reserving transmission capacity along its arcs, as the delay is a nonlinear function of both components. The problem is known to be solvable in polynomial time under quite restrictive assumptions, i.e., equal rate allocations (all arcs are reserved the same capacity) and identical reservation costs, whereas the general problem is -hard. We first extend the approaches to the equal rate allocation (ERA) version to a pseudo-polynomial Dynamic programming one for integer arc costs and a FPTAS for the case of general arc costs. We then show that the general problem can be formulated as a mixed-integer Second-Order Cone (SOCP) program and therefore solved with off-the-shelf technology. We compare two formulations: one based on standard big-M constraints and one where Perspective Reformulation techniques are used to tighten the continuous relaxation. Extensive computational experiments on both real-world networks and randomly generated realistic ones show that the ERA approach is fast and provides an effective heuristic for the general problem whenever it manages to find a solution at all, but it fails for a significant fraction of the instances that the SOCP models can solve. We therefore propose a three-pronged approach that combines the fast running time of the ERA algorithm and the effectiveness of the SOCP models, and show that it is capable of solving realistic-sized instances with high accuracy at different levels of network load in a time compatible with real-time usage in an operating environment.

关键词： Delay-constrained routing Approximation algorithms mixed-integer nonlinear programming Second-order cone model Perspective reformulation

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Algorithmic Approach for Improved mixed-integer Reformulations of Convex Generalized Disjunctive Programs

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INFORMS JOURNAL ON COMPUTING 2015年第1期27卷 59-74页

作者： Trespalacios, Francisco Grossmann, Ignacio E. Carnegie Mellon Univ Pittsburgh PA 15213 USA

In this work, we propose an algorithmic approach to improve mixed-integer models that are originally formulated as convex generalized disjunctive programs (GDPs). The algorithm seeks to obtain an improved continuous relaxation of the mixed-integer linear and mixed-integer nonlinear programming (MILP/MINLP) model reformulation of the GDP while limiting the growth in the problem size. There are three main stages that form the basis of the algorithm. The first one is a presolve, consequence of the logic nature of GDP, which allows us to reduce the problem size, find good relaxation bounds, and identify properties that help us determine where to apply a basic step. The second stage is the iterative application of basic steps, selecting where to apply them and monitoring the improvement of the formulation. Finally, we use a hybrid reformulation of GDP that seeks to exploit both of the advantages attributed to the two common GDP-to-MILP/MINLP transformations, the Big-M, and the Hull reformulation. We illustrate the application of this algorithm with several examples. The results show the improvement in the problem formulations by generating models with improved relaxed solutions and relatively small growth of continuous variables and constraints. The algorithm generally leads to reduction in the solution times.

关键词： generalized disjunctive programming mixed-integer nonlinear programming

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Multi-objective cell formation problem considering work-in-process minimization

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2015年第9-12期76卷 1947-1955页

作者： Rafiei, Hamed Rabbani, Masoud Nazaridoust, Babak Ramiyani, Sara Saeidi Univ Tehran Coll Engn Sch Ind & Syst Engn Tehran Iran

This paper addresses designing a dynamic cellular manufacturing system which considers optimizing batch sizes for inter-cell moves in order to pursue fundamentals of Just-In-Time production philosophy. To do so, a bi-objective mixed-integer nonlinear programming model is proposed with two conflicting objective functions: minimizing sum of machine purchasing, operating, inter-cell moves, machine relocation, and machine transferring cost, and minimizing work-in-process (WIP) with regard to inter-cell batch sizes. Also, the best time to sell unused machines is obtained by calculating their salvage values. Finally, the proposed model is validated using numerical experiments and hence, the resulted WIP inventories are assessed through the conducted numerical experiments, and sensitivity analysis is provided with respect to three major parameters (machine purchasing cost, inter-cell material handling cost, and part demand) applied in the proposed model.

关键词： Multi-objective optimization Dynamic cellular manufacturing Work-in-process mixed-integer nonlinear programming

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