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Peak Shaving Model for Coordinated Hydro-Wind-Solar System Serving Local and Multiple Receiving Power Grids via HVDC Transmission Lines

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IEEE ACCESS 2020年 8卷 60689-60703页

作者： Liu, Benxi Lund, Jay R. Liao, Shengli Jin, Xiaoyu Liu, Lingjun Cheng, Chuntian Dalian Univ Technol Inst Hydropower & Hydroinformat Dalian 116024 Peoples R China Dalian Univ Technol Key Lab Ocean Energy Utilizat & Energy Conservat Minist Educ Dalian 116024 Peoples R China Univ Calif Davis Dept Civil & Environm Engn Davis CA 95616 USA

To meet the rapid growth of electricity demand and reduce carbon intensity, China is developing renewable energies rapidly including hydropower, wind and solar power. Due to the geographical mismatch of energy sources and demands in China, many long-distance and large-scale UHVDC and HVDC transmission projects have been built to transmit electric power from the western renewable bases to eastern coastal load centers. Some provincial power sources serve both local demands and deliver power to multiple regional power grids via HVDC transmission lines. As large capacity HVDC power transmission projects have great impacts on receiving-end power grids. Thus, the local exporting power grid should consider both local demands and energy importing area demands. A mixed-integer linear programming day-ahead peak shaving model to minimize the peak-valley difference in residual load after renewable generation of multiple power grids is developed. The model uses chance constraints to compensate for forecast errors of wind and solar power with hydropower, and introduces maximum daily power regulation times and stair-like power curve constraints of HVDC tie lines to avoid frequent HVDC power change and ensure power grid safety. The case studies in Yunnan province, which has large scale hydro, wind and solar power sources and delivers power to multiple regional power grids via HVDC transmission lines, shows the proposed model can shave peaks from multiple power grids effectively, hydropower can compensate for wind and solar forecast error and obtain satisfying results for multiple power grids, and that HVDC constraints can avoid their frequent power change and ensure the power grid safety.

关键词： Hydro-wind-solar peak shaving operation mixed-integer linear programming HVDC

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Variable Selection for Kernel Two-Sample Tests

arXiv

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arXiv 2023年

作者： Wang, Jie Dey, Santanu S. Xie, Yao School of Industrial and Systems Engineering Georgia Institute of Technology AtlantaGA30332 United States

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a subset of variables with a pre-specified size that maximizes the variance-regularized kernel MMD statistic. We focus on three commonly used types of kernels: linear, quadratic, and Gaussian. From a computational perspective, we derive mixed-integer programming formulations and propose exact and approximation algorithms with performance guarantees to solve these formulations. From a statistical viewpoint, we derive the rate of testing power of our framework under appropriate conditions. These results show that the sample size requirements for the three kernels depend crucially on the number of selected variables, rather than the data dimension. Experimental results on synthetic and real datasets demonstrate the superior performance of our method, compared to other variable selection frameworks, particularly in high-dimensional settings. Copyright © 2023, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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integer programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

arXiv

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arXiv 2023年

作者： Zhang, Yiling Industrial and Systems Engineering University of Minnesota United States

We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. The introduction of adjustable risks, unfortunately, leads to NP-hard optimization problems. We develop integer programming approaches for individual chance constraints with uncertainty either on the right-hand side or on the left-hand side. In particular, we derive mixed integer programming reformulations for the two types of uncertainty to determine the optimal risk tolerance for the chance constraint. Valid inequalities are derived to strengthen the formulations. We test diverse instances of diverse sizes. © 2023, CC BY-NC-ND.

关键词： mixed-integer linear programming

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Decomposition of the vehicle routing problem with time windows on the time dimension

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Transportation Research Procedia 2022年 62卷 131-138页

作者： Christian Truden Kerstin Maier Philipp Armbrust Lakeside Labs GmbH 9020-Klagenfurt Austria Department of Mathematics Alpen-Adria-Universität Klagenfurt 9020-Klagenfurt Austria

The Vehicle Routing Problem with Time Windows (VRPTW) asks for the optimal set of routes to be performed by a fleet of vehicles to serve a set of customers within their assigned time windows. In this work, we propose a matheuristic for the VRPTW which utilizes the sub-problem constituted by optimizing only a selected time window of the VRPTW whereas the tours outside of this time window are regarded as fixed. We call this problem the Single Time Window Vehicle Routing Problem (STWVRP). For applying the STWVRP, we must assume that several customers are assigned to the same time window, i.e., the number of time windows is much smaller than the number of customers. An exact problem description of the STWVRP is given in the form of a mixed-integer linear programming formulation. We apply this exact formulation within a matheuristic for the VRPTW. The paper concludes with extensive computational experiments.

关键词： vehicle routing problem with time windows mixed-integer linear programming matheuristic

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New strategy for providing the existence of spanning trees without small degree stems

arXiv

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arXiv 2023年

作者： Furuya, Michitaka Tsuchiya, Shoichi College of Liberal Arts and Sciences Kitasato University 1-15-1 Kitasato Minami-ku Kanagawa Sagamihara252-0373 Japan

For an integer k ≥ 2, a spanning tree of a graph without vertices of degree from 2 to k is called a [2, k]-ST of the graph. The concept of [2, k]-STs is a natural extension of a homeomorphically irreducible spanning tree (or HIST), which is a well-studied graph structure. In this paper, we give a new strategy for finding [2, k]-STs. By using the strategy, we refine or extend a known degree-sum condition for the existence of a HIST. Furthermore, we also investigate a degree-product condition for the existence of a [2, k]-*** Codes 05C05, 05C07 © 2023, CC BY.

关键词： mixed-integer linear programming

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A Clustering Approach for the Optimal Siting of Recharging Stations in the Electric Vehicle Routing Problem with Time Windows

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ENERGIES 2022年第7期15卷 2372页

作者： Sanchez, Danny Garcia Tabares, Alejandra Faria, Lucas Teles Rivera, Juan Carlos Franco, John Fredy Sao Paulo State Univ UNESP Dept Elect Engn BR-15385000 Ilha Solteira SP Brazil Los Andes Univ Dept Ind Engn Bogota 111711 Colombia Sao Paulo State Univ UNESP Dept Energy Engn BR-19274000 Rosana SP Brazil EAFIT Univ Dept Math Sci Medellin 050022 Colombia

Transportation has been incorporating electric vehicles (EVs) progressively. EVs do not produce air or noise pollution, and they have high energy efficiency and low maintenance costs. In this context, the development of efficient techniques to overcome the vehicle routing problem becomes crucial with the proliferation of EVs. The vehicle routing problem concerns the freight capacity and battery autonomy limitations in different delivery-service scenarios, and the challenge of best locating recharging stations. This work proposes a mixed-integer linear programming model to solve the electric location routing problem with time windows (E-LRPTW) considering the state of charge, freight and battery capacities, and customer time windows in the decision model. A clustering strategy based on the k-means algorithm is proposed to divide the set of vertices (EVs) into small areas and define potential sites for recharging stations, while reducing the number of binary variables. The proposed model for E-LRPTW was implemented in Python and solved using mathematical modeling language AMPL together with CPLEX. Performed tests on instances with 5 and 10 clients showed a large reduction in the time required to find the solution (by about 60 times in one instance). It is concluded that the strategy of dividing customers by sectors has the potential to be applied and generate solutions for larger geographical areas and numbers of recharging stations, and determine recharging station locations as part of planning decisions in more realistic scenarios.

关键词： charging stations electric vehicles k-means algorithm location routing problem with time windows mixed-integer linear programming vehicle routing

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Power system resilience to floods: Modeling, impact assessment, and mid-term mitigation strategies

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2022年 135卷 107545-107545页

作者： Souto, Laiz Yip, Joshua Wu, Wen-Ying Austgen, Brent Kutanoglu, Erhan Hasenbein, John Yang, Zong-Liang King, Carey W. Santoso, Surya Univ Bristol Elect Energy Management Grp Bristol BS8 1UB Avon England Univ Texas Austin Dept Elect & Comp Engn Austin TX 78712 USA Univ Texas Austin Cockrell Sch Engn Operat Res & Ind Engn Grad Program Austin TX 78712 USA Univ Texas Austin Dept Geol Sci Austin TX 78712 USA Univ Texas Austin Energy Inst Austin TX 78712 USA

This article presents a methodology aimed at improving mid-term power system resilience at transmission substations in areas potentially affected by floods, combining hardening strategies and quantitative metrics. It takes into account flood forecasts from a hydrological model and the location of electrical equipment to perform impact assessment "as is"and with resilience planning strategies. Thus, the impact of floods on the grid is evaluated over a range of realistic flood scenarios, based on the accumulated cost and load energy unserved as metrics together with future transmission system expansion capacity projections. The mixed-integer linear programming formulation is aimed at minimizing accumulated cost and load energy unserved with optimal hardening of substations, assuming that any non-hardened substation disabled by flooding must be repaired. Furthermore, the methodology is demonstrated in the coastal area of Texas with simulations of floods based on the rainfall of Hurricane Harvey in 2017. Ultimately, the choice of the most appropriate mitigation strategies shall optimize resilience metrics and/or cost indicators with robustness over a range of scenarios.

关键词： Critical infrastructure Extreme weather Flood mixed-integer linear programming Optimization Power system planning Power transmission system Resilience Resiliency Substation

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mixed-integer programming for unrelated parallel machines scheduling problem considering electricity cost and makespan penalty cost

Mixed-integer programming for unrelated parallel machines sc...

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International Conference on Industrial Engineering and Systems Management (IESM)

作者： Cheng, Junheng Wu, Peng Chu, Feng Fujian Normal Univ Sch Econ Fuzhou Peoples R China Fujian Normal Univ Sch Econ & Management Fuzhou Peoples R China Univ Paris Saclay Univ Evry Val dEssonne Paris France

ISBN: (纸本)9781728115665

A recent study proposed an interesting unrelated parallel machines scheduling problem under time-varying electricity cost, which assumes significant importance for industrial enterprises competitiveness improvement and sustainable economic development. The existing solution method is a hybrid genetic algorithm, which cannot ensure the optimality of the solutions. In this work, we provide a mixed-integer linear programming model to exactly solve the problem. The computational results show that the proposed model can obtain optimal solutions efficiently.

关键词： mixed-integer linear programming parallel machines scheduling electricity cost makespan time-of-use tariffs

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Continuous-time scheduling of production, distribution and sales in photovoltaic supply chains with declining prices

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FLEXIBLE SERVICES AND MANUFACTURING JOURNAL 2020年第3期32卷 629-667页

作者： Albrecht, Wolfgang Steinruecke, Martin Ernst Moritz Arndt Univ Greifswald Fac Law & Econ Friedrich Loeffler Str 70 D-17489 Greifswald Germany

Supply chain networks in the photovoltaic sector were faced with a rapid decline in prices during the past few years, which is predicted to go on in the following years. These circumstances force related companies to coordinate production, distribution and transportation planning of all their network sites thoroughly. Moreover, continuous-time scheduling of processes is required to determine times of sales exactly within a multi-day planning horizon. Applying this type of scheduling is possible due to assessable price trends and existing framework agreements with wholesalers, and even necessary due to its impact on the realized sales prices, and thus, the network profit. For this reason, we develop a mixed-integer linear programming model that meets the requirements of fully-integrated photovoltaic supply chains that cover processing of raw materials, manufacturing of intermediate and finished products in two alternative methods, and selling them on international markets. The multi-product approach enables to connect supply chain stages with different product maturities. The modeling is motivated by a real-life case of a global photovoltaic group headquartered in Germany. As it was not possible to optimize this problem with high-performance software and hardware within 3 months, we tested several relax-and-fix decomposition methods. By selecting those algorithms that were able to generate high-quality solutions within acceptable computation times of less than half a day, a satisfying solution was found. The appropriateness of the selected algorithms is additionally demonstrated by analyzing randomly generated scenarios in a numerical study.

关键词： Supply chain management Sales and operations planning Continuous-time scheduling mixed-integer linear programming

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mixed-integer nonseparable piecewise linear models for the hydropower production function in the Unit Commitment problem

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ELECTRIC POWER SYSTEMS RESEARCH 2020年第0期182卷 106234-000页

作者： Brito, B. H. Finardi, E. C. Takigawa, F. Y. K. Fed Inst Tocantins BR-77020450 Palmas Brazil Univ Fed Santa Catarina INESC P&D Brazil BR-88040900 Florianopolis SC Brazil Fed Inst Santa Catarina BR-88020300 Florianopolis SC Brazil

The hydro unit commitment (HUC) problem seeks to determine, for a short-term horizon with (semi)hourly discretization, the status (on/off) and generation level of each generating unit (GU) to meet plant and GUs constraints. In the HUC problem, the nonlinearities and non-convexities of the hydro production function (HPF), and the presence of binary variables that identify which GUs must be dispatched at each time step make the search for a solution challenging. Due to the recent developments in commercial mixed-integer linear programming (MILP) solvers, it is possible to approximate the nonlinear and nonconvex HPF through piecewise-linear (PWL) models with reasonable accuracy. Throughout this paper we emphasize the potential advantages of seven MILP formulations that can be categorized as parametric and non-parametric methods. Given the complexities of state-of-the-art solvers, it is hard to predict which formulation performs better. Although some guidelines can be found in literature, the formulation that performs best can be strongly dependent on the specific problem structure or data. In this context, we develop and compare seven multidimensional nonseparable PWL models for representing the HPF in the HUC problem. To assess the performance of each PWL model, we present results using a 6-GU hydro plant of two different types.

关键词： Hydro unit commitment Piecewise-linear models Hydro production function mixed-integer linear programming

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