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MIP-based instantaneous control of mixed-integer PDE-constrained gas transport problems

COMPUTATIONAL optimization AND APPLICATIONS 2018年第1期70卷 267-294页

作者： Gugat, Martin Leugering, Gunter Martin, Alexander Schmidt, Martin Sirvent, Mathias Wintergerst, David Friedrich Alexander Univ Erlangen Nurnberg FAU Lehrstuhl Angew Math 2 Cauerstr 11 D-91058 Erlangen Germany Friedrich Alexander Univ Erlangen Nurnberg FAU Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany

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 on a graph. We propose an instantaneous control approach in which suitable Euler discretizations yield systems of ordinary differential equations on a graph. This networked system of ordinary differential equations is shown to be well-posed and affine-linear solutions of these systems are derived analytically. As a consequence, finite-dimensional mixed-integer linear optimization problems are obtained for every time step that can be solved to global optimality using general-purpose solvers. We illustrate our approach in practice by presenting numerical results on a realistic gas transport network.

关键词： mixed-integer optimal control Instantaneous control Partial differential equations on graphs Gas networks mixed-integer linear optimization

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Heuristics with performance guarantees for the minimum number of matches problem in heat recovery network design (Reprintede from Computers and Chemical Engineering, vol 113, pg 57-85, 2018)

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COMPUTERS & CHEMICAL ENGINEERING 2018年 116卷 422-450页

作者： Letsios, Dimitrios Kouyialis, Georgia Misener, Ruth Imperial Coll London Dept Comp South Kensington SW7 2AZ England

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an NP-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods. (C) 2018 The Author(s). Published by Elsevier Ltd.

关键词： Minimum number of matches Heat exchanger network design Heuristics Approximation algorithms mixed-integer linear optimization

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Heuristics with performance guarantees for the minimum number of matches problem in heat recovery network design

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COMPUTERS & CHEMICAL ENGINEERING 2018年 113卷 57-85页

作者： Letsios, Dimitrios Kouyialis, Georgia Misener, Ruth Imperial Coll London Dept Comp London SW7 2AZ South Kensingto England

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an N P-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods. (C) 2018 The Authors. Published by Elsevier Ltd.

关键词： Minimum number of matches Heat exchanger network design Heuristics Approximation algorithms mixed-integer linear optimization

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Energy supply modelling of a low-CO₂ emitting energy system: Case study of a Danish municipality

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APPLIED ENERGY 2017年 195卷 922-941页

作者： Sveinbjornsson, Dadi Ben Amer-Allam, Sara Hansen, Anders Bavnhoj Algren, Loui Pedersen, Allan Schroder Tech Univ Denmark Dept Energy Convers & Storage Frederiksborgvej 399 DK-4000 Roskilde Denmark Tech Univ Denmark Dept Management Engn Prod TorvetBldg 426 DK-2800 Lyngby Denmark Energinet Dk Tonne Kjaersvej 65 DK-7000 Fredericia Denmark

Municipal activities play an important role in national and global CO2-emission reduction efforts, with Nordic countries at the forefront thanks to their energy planning tradition and high penetration of renewable energy sources. In this work, we present a case study of the Danish municipality of Sonderborg, whose aim is to reach zero net CO2 emissions by 2029. Sonderborg has an official strategic plan towards 2029, which we compared with four alternative scenarios to investigate how the municipality could approach its target in the most energy-efficient and cost-effective way while simultaneously keeping biomass and waste consumption close to the limits of the locally available residual resources. We modelled all sectors of the energy system on the municipal scale, applying a broad range of energy conversion technologies, including advanced biomass conversion technologies and reversible electrolysis. We constructed five scenarios, each representing a different energy mix for Sonderborg's energy system in 2029. We modelled these scenarios using the mixed-integer linear optimization tool Sifre. We compared the results for the five scenarios using four indicators: annual total system cost, total energy system efficiency, annual net system CO2 emissions and total annual biomass consumption. The results show that scenarios with a high degree of electrification perform better on the selected indicators than scenarios with a high degree of biomass utilization. Moreover, the incorporation of advanced conversion technologies such as electrolysis, fuel cells and methanol production further reduces both the total system cost and net CO2 of the highly electrified energy system. Our sensitivity analysis demonstrates that scenarios with a low biomass consumption and a high degree of electrification are less dependent on changes in energy prices. We conclude that in order to achieve their CO2 emission goals in the most energy-efficient, cost-effective and sustainable way, municip

关键词： Energy system modelling Urban energy scenarios Renewable energy mixed-integer linear optimization Energy conversion Electrolysis

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PENALTY ALTERNATING DIRECTION METHODS FOR mixed-integer optimization: A NEW VIEW ON FEASIBILITY PUMPS

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SIAM JOURNAL ON optimization 2017年第3期27卷 1611-1636页

作者： Geissler, Bjorn Morsi, Antonio Schewe, Lars Schmid, Martin Friedrich Alexander Univ Erlangen Nurnberg FAU Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany

Feasibility pumps are highly effective primal heuristics for mixed-integer linear and nonlinear optimization. However, despite their success in practice there are only a few works considering their theoretical properties. We show that feasibility pumps can be seen as alternating direction methods applied to special reformulations of the original problem, inheriting the convergence theory of these methods. Moreover, we propose a novel penalty framework that encompasses this alternating direction method, which allows us to refrain from random perturbations that are applied in standard versions of feasibility pumps in case of failure. We present a convergence theory for the new penalty based alternating direction method and compare the new variant of the feasibility pump with existing versions in an extensive numerical study for mixed-integer linear and nonlinear problems.

关键词： mixed-integer nonlinear optimization mixed-integer linear optimization feasibility pump alternating direction methods penalty methods

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A mixed-integer linear optimization Model for Local Energy System Planning Based on Simplex and Branch-and-Bound Algorithms

A Mixed-Integer Linear Optimization Model for Local Energy S...

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International Conference on Life System Modeling and Simulation / International Conference on Intelligent Computing for Sustainable Energy and Environment (LSMS-ICSEE)

作者： Ren, Hongbo Zhou, Weisheng Gao, Weijun Wu, Qiong Ritsumeikan Univ Ritsumeikan Global Innovat Res Org Kyoto 6038577 Japan Ritsumeikan Univ Coll Policy Sci Kyoto 6038577 Japan Univ Kitakyushu Fac Environm Engn Kitakyushu Fukuoka 8080135 Japan

ISBN: (纸本)9783642156205

A mixed-integer linear optimization model is developed to support the decision making for the sustainable use of energy in the local area. It details exploitation of primary energy sources, electrical and thermal generation, end-use sectors and emissions. The model covers both the energy demand and energy supply sides, and can provide valuable information both on the technical options, and on the possible policy measures. By aiming to realize a low-carbon energy system, the proposed optimization process provides feasible generation settlements between utility grid and distributed generations, as well as optimal diffusion of energy efficiency technologies. Moreover, the mathematical methods for solving the developed model are discussed. The focus is paid on the general solution method for mixed-integer linear optimization model including simplex algorithm and branch-and-bound algorithm. By using the suggested solution methods, the local energy system optimization problem is expected to be resolved in a reasonable time with enough precision.

关键词： mixed-integer linear optimization local energy system low-carbon society simplex algorithm branch-and-bound algorithm

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Scheduling of a Constellation of Satellites: Improving a Simulated Annealing Model by Creating a mixed-integer linear Model

Scheduling of a Constellation of Satellites: Improving a Sim...

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作者： Monmousseau, Philippe KTH Royal Institute of Technology

学位级别：master

The purpose of this thesis is to provide a new scheduling model of a large constellation of imaging satellites that does not use a heuristic solving method. The objective is to create a mixed-integer linear model that would be competitive in speed and in its closeness to reality against a current model using simulated annealing, while trying to improve both models. Each satellite has the choice between a number of possible events, each event having a utility and a cost, and the chosen schedule must take into account numerous time-related constraints. The main difficulties appeared in modeling realistically a battery level and in handling infeasible configurations due to inaccurate parameters. The obtained linear model has enabled a better understanding of the performance of the simulated annealing solver, and could also be adapted to different real-world scheduling problems

关键词： Scheduling of a Constellation of Satellites mixed-integer linear optimization Natural Sciences Mathematics Naturvetenskap Matematik Civilingenj?rsexamen - Farkostteknik Master of Science in Engineering - Vehicle Engineering Systems Engineering Systemteknik

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A mixed-integer optimization model for the economic and environmental analysis of biomass production

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BIOMASS & BIOENERGY 2014年 67卷 8-23页

作者： Cobuloglu, Halil Ibrahim Bueyuektahtakin, I. Esra Wichita State Univ Dept Ind & Mfg Engn Wichita KS 67260 USA

Biofuel production from second-generation feedstock has become critical due to environmental concerns and the need for sustainable energy supply. This paper provides a unique optimization approach of quantifying and formulating the economic and environmental benefits of switchgrass production at the farm level. In particular, we propose a multi-objective mixed-integer programming model, which maximizes the revenue from harvested switchgrass biomass and the economic value obtained from the positive environmental impacts of switchgrass yield during a ten-year planning horizon. Environmental impacts include soil erosion prevention, sustainability of bird populations, carbon sequestration, and carbon emissions, while economic impacts are analyzed under various budget, yield, and sustainability scenarios. The proposed model is then applied to a case study in the state of Kansas. Results show that given the current market prices, switchgrass cultivation on grassland and cropland is highly profitable. The model results also suggest that if utilized by the government, conservation reserve program (CRP) incentives could make marginal land more favorable over cropland. We perform sensitivity analysis to address the uncertainty in budget, yield, and utilization of cropland, and present insights into the economic and environmental impacts of switchgrass production. This model can also be extended to biomass production from any other types of energy crops to identify the most efficient production planning strategies under various management scenarios. Published by Elsevier Ltd.

关键词： Switchgrass Biofuel and biomass production mixed-integer linear optimization Sustainability and biodiversity Carbon emissions and sequestration Soil erosion prevention

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Allocation of available transfer capability in planning horizon

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EUROPEAN TRANSACTIONS ON ELECTRICAL POWER 2011年第3期21卷 1437-1454页

作者： Rajabi-Ghahnavieh, A. Fotuhi-Firuzabad, M. Feuillet, R. ENS3E INPG Lab Genie Elect Grenoble F-38402 St Martin Dheres France Sharif Univ Technol Dept Energy Engn Tehran Iran Sharif Univ Technol Dept Elect Engn Tehran Iran

In the United States electricity market standard, when several transmission service requests (TSRs) are made for a specific pair of power injection/extraction points, the independent system operator (ISO) must allocate the available transmission capability (ATC) associated with the pair to the requests. An ATC allocation must determine the amount of accepted requests as well as the priority of the accepted requests during emergencies. The requests could have different types (recallable/non-recallable), tariffs, and time frames and these factors must be properly considered in ATC allocation. This paper proposes a method for optimal ATC allocation in the planning horizon which incorporates the type and tariffs of the requests in a mixed integer linear optimization programming for which the expected net revenue of ATC allocation on a seasonal base has to be maximized. The method also incorporates maintenance and forced outage of power system components as well as the load forecast uncertainty in ATC allocation problem. Once allocation accomplished by solving the optimization problem, the amount of the accepted requests and their priorities to the power system operator during emergencies are determined. The proposed method is applied to the modified IEEE reliability test system (IEEE-RTS) and its performance is evaluated. A comparison is made between the results obtained by the proposed method and those obtained using existing ATC allocation methods. Two approaches are finally presented and evaluated to apply the proposed method for allocating ATC to the requests with a yearly base. Copyright (C) 2010 John Wiley & Sons, Ltd.

关键词： available transfer capability allocation transmission services deregulated power system mixed-integer linear optimization

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Maximum savings approach for location and sizing of capacitors in distribution systems

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ELECTRIC POWER SYSTEMS RESEARCH 2008年第7期78卷 1192-1203页

作者： Khodr, H. M. Olsina, F. G. De Oliveira-De Jesus, P. M. Yusta, J. M. Univ Zaragoza Dept Elect Engn E-50018 Zaragoza Spain Univ Simon Bolivar Dept Energy Convers & Delivery INESC Porto Caracas Venezuela Univ Porto Fac Engn Dept Elect & Comp Engn Oporto Portugal

This paper proposes a computationally efficient methodology for the optimal location and sizing of static and switched shunt capacitors in radial distribution systems. The problem is formulated as the maximization of the savings produced by the reduction in energy losses and the avoided costs due to investment deferral in the expansion of the network. The proposed method selects the nodes to be compensated, as well as the optimal capacitor ratings and their operational characteristics, i.e. fixed or switched. After an appropriate linearization, the optimization problem was formulated as a mixed-integer linear problem, suitable for being solved by means of a widespread commercial package. Results of the proposed optimizing method are compared with another recent methodology reported in the literature using two test cases: a 15-bus and a 33-bus distribution network. For the both case's tested, the proposed methodology delivers better solutions indicated by higher loss savings, which are achieved with lower amounts of capacitive compensation. To calculate the energy savings and the deferral investment cost exactly, a load flow for radial distribution network is executed before and after the compensation. The proposed method has also been applied for compensating to an actual radial distribution network served by AES-Venezuela in the metropolitan area of Caracas. A convergence time of about 4 s after 22,298 iterations demonstrates the ability of the proposed methodology for efficiently handling compensation problems. (c) 2007 Elsevier B.V. All rights reserved.

关键词： capacitors distribution systems mixed-integer linear optimization

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