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Arbitrage strategy of virtual power plants in energy, spinning reserve and reactive power markets

IET GENERATION TRANSMISSION & DISTRIBUTION 2016年第3期10卷 750-763页

作者： Nezamabadi, Hossein Nazar, Mehrdad Setayesh Shahid Beheshti Univ Fac Elect Engn AC Tehran Iran

Virtual power plant (VPP) concept was developed to integrate distributed energy resources (DERs) into the grid in order that they are seen as a single power plant by the market and power system operator. Therefore, VPPs are faced with optimal bidding, and identifying arbitrage opportunities in a market environment. In this study, the authors present an arbitrage strategy for VPPs by participating in energy and ancillary service (i.e. spinning reserve and reactive power services) markets. On the basis of a security-constrained price-based unit commitment, their proposed model maximises VPP's profit (revenue minus costs) considering arbitrage opportunities. The supply-demand balancing, transmission network topology and security constraints are considered to ensure reliable operation of VPP. The mathematical model is a mixed-integer non-linear optimisation problem with inter-temporal constraints, and solved by mixed-integer non-linear programming. The result is a single optimal bidding profile and a schedule for managing active and reactive power under participating in the markets. These profile and schedule consider the DERs and network constraints simultaneously, and explore arbitrage opportunities of VPP. Results pertaining to an illustrative example and a case study are discussed.

关键词： distributed power generation power distribution economics power transmission economics power markets power system management power system security integer programming nonlinear programming power generation scheduling reactive power management active power management mixed-integer nonlinear programming intertemporal constraints mixed-integer nonlinear optimisation problem mathematical model transmission network security constraint transmission network topology constraint supply-demand balancing security-constrained price-based unit commitment VPP profit maximization ancillary service market energy service market single optimal bidding profile power system operator distributed energy resource integration reactive power markets spinning reserve virtual power plants arbitrage strategy

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Multi-product unrelated parallel machines scheduling problem with rework processes

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SCIENTIA IRANICA 2012年第6期19卷 1887-1893页

作者： Ramezanian, R. Saidi-Mehrabad, M. Iran Univ Sci & Technol Dept Ind Engn Tehran Iran

In this paper, we addressed a multi-product unrelated parallel machines scheduling problem with the possibility of producing imperfect jobs. Rework processes in the problem are studied and a mixed-integer nonlinear programming (MINLP) model to formulate this problem is proposed. Rework activities are used to upgrade imperfect jobs to a preset standard quality level. It is assumed that the defective production probability for each job on machines can be estimated through historical data acquisition. Since the problem is strongly NP-hard, exact algorithms are inefficient for medium and large-sized problems. Thus, some heuristic methods focusing on the rework processes are developed based on dispatching rules. In order to evaluate the efficiency of the presented algorithms, makespan is used as the objective function. Computational experiments show the efficacy of the modified shortest processing time (MSPT) heuristic, in terms of computational time and objective value for randomly generated test problems. (C) 2012 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.

关键词： Parallel machines scheduling Imperfect job Rework process mixed-integer nonlinear programming Heuristic algorithms

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An exact projection-based algorithm for bilevel mixed-integer problems with nonlinearities

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JOURNAL OF GLOBAL OPTIMIZATION 2022年第3期84卷 607-650页

作者： Merkert, Maximilian Orlinskaya, Galina Weninger, Dieter Otto von Guericke Univ Dept Math Univ Pl 2 D-39106 Magdeburg Germany Tech Univ Carolo Wilhelmina Braunschweig Univ Pl 2 D-38106 Braunschweig Germany Friedrich Alexander Univ Erlangen Nurnberg Dept Math Cauerstr 11 D-91058 Erlangen Germany

We propose an exact global solution method for bilevel mixed-integer optimization problems with lower-level integer variables and including nonlinear terms such as, e.g., products of upper-level and lower-level variables. Problems of this type are extremely challenging as a single-level reformulation suitable for off-the-shelf solvers is not available in general. In order to solve these problems to global optimality, we enhance an approximative projection-based algorithm for mixed-integer linear bilevel programming problems from the literature to become exact under one additional assumption. This assumption still allows for discrete and continuous leader and follower variables on both levels, but forbids continuous upper-level variables to appear in lower-level constraints and thus ensures that a bilevel optimum is attained. In addition, we extend our exact algorithm to make it applicable to a wider problem class. This setting allows nonlinear constraints and objective functions on both levels under certain assumptions, but still requires that the lower-level problem is convex in its continuous variables. We also discuss computational experiments on modified library instances.

关键词： Bilevel optimization mixed-integer nonlinear programming Strong duality Projection Global optimization

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The Steiner travelling salesman problem with correlated costs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第1期245卷 62-69页

作者： Letchford, Adam N. Nasiri, Saeideh D. Univ Lancaster Dept Management Sci Lancaster LA1 4YX England Univ Lancaster Dept Math & Stat Lancaster LA1 4YX England

The Steiner Travelling Salesman Problem (STSP) is a variant of the TSP that is suitable for instances defined on road networks. We consider an extension of the STSP in which the road traversal costs are both stochastic and correlated. This happens, for example, when vehicles are prone to delays due to rush hours, road Works or accidents. Following the work of Markowitz on portfolio selection, we model this problem as a bi-objettive mean-variance problem. Then, we show how to approximate the efficient frontier via integer programming. We also show how to exploit certain special structures in the correlation matrices. Computational results indicate that our approach is viable for instances with up to 100 nodes. It turns out that minimum variance tours can look rather different from minimum expected cost tours. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Travelling salesman problem Mean-variance optimisation mixed-integer nonlinear programming

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MIP RELAXATIONS IN FACTORABLE programming

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SIAM JOURNAL ON OPTIMIZATION 2024年第3期34卷 2856-2882页

作者： He, Taotao Tawarmalani, Mohit Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai 200030 Peoples R China Purdue Univ Mitchell E Daniels Jr Sch Business W Lafayette IN 47907 USA

In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxations to develop mixed-integer programming relaxations. Our relaxations rely on ideal formulations of convex hulls of outer-functions over a combinatorial structure that captures local inner-function structure. The resulting relaxations often require fewer variables and are tighter than currently prevalent ones. Finally, we provide computational evidence to demonstrate that our relaxations close approximately 60\%--70\% of the gap relative to McCormick relaxations and significantly improve the relaxations used in a state-of-the-art solver on various instances involving polynomial functions.

关键词： mixed-integer nonlinear programming mixed-integer programming relaxation convexification incremental formulation relaxation propagation

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Quantifying polymer structural component evolution using X-ray scattering and mixed-integer network component analysis

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COMPUTERS & CHEMICAL ENGINEERING 2011年第11期35卷 2564-2578页

作者： Tolle, Ian Martin, Lealon L. Univ Texas Austin Dept Chem Engn Cockrell Sch Engn Austin TX 78712 USA Rensselaer Polytech Inst Dept Chem & Biol Engn Troy NY 12180 USA Rensselaer Polytech Inst Dept Decis Sci & Engn Syst Troy NY 12180 USA

In this work we present a novel computational approach for the extraction of underlying polymer structural component signatures and corresponding structural evolution through decomposition of multivariate X-ray scattering (SAXS/WAXS) datasets. Without assumptions based on structural geometry, this mixed-integer network component analysis (NCA) methodology generates a reduced set of component scattering signatures and component fraction evolution. Structural models are then assigned to each component based on a generalized expression for scattering from multi-phase materials. The methodology is applied systematically to the study of ethylene/alpha-olefin copolymer isothermal crystallization. The decomposition generates component signatures defining structures of varying extent within the sample but with constant average local structure. For WAXS datasets, these components can be correlated to crystalline and amorphous regions, while for SAXS datasets they can be correlated to ordered and disordered crystalline lamellae. These model choices agree with structures observed in the literature and are confirmed by comparison to reference crystallinity data. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Network component analysis mixed-integer nonlinear programming Chemometrics X-ray scattering Ethylene/alpha-olefin copolymers Crystallization

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Optimization of multi-echelon supply chain networks with uncertain sales prices

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JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 2004年第7期37卷 822-834页

作者： Chen, CL Lee, WC Natl Taiwan Univ Dept Chem Engn Taipei 10617 Taiwan

A multi-product, multi-stage, and multi-period production and distribution planning model is proposed in this paper to tackle the compromised sales prices and the total profit problem of a multi-echelon supply chain network with uncertain sales prices. This model is constructed as a mixed-integer nonlinear programming problem to achieve a maximum total profit of the whole network and to guarantee the maximum satisfactory levels of sellers' and buyers' preference on sales prices. For the purpose that a compensatory solution among all participants of the supply chain can be achieved, a fuzzy decision-making method is proposed and, by means of applying it to a numerical example, proved effective in providing a compromised solution in a multi-echelon supply chain network.

关键词： process systems engineering supply chain management uncertainty mixed-integer nonlinear programming fuzzy optimization

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Optimizing vehicle fleet and assignment for concentrating solar power plant heliostat washing

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IISE TRANSACTIONS 2022年第6期54卷 550-562页

作者： Wales, Jesse G. Zolan, Alexander J. Newman, Alexandra M. Wagner, Michael J. Colorado Sch Mines Dept Mech Engn Golden CO 80401 USA Natl Renewable Energy Lab Thermal Energy Syst Grp Golden CO USA Univ Wisconsin Dept Mech Engn Madison WI 53706 USA

Concentrating solar power central-receiver plants use thousands of sun-tracking mirrors, i.e., heliostats, to reflect sunlight to a central receiver, which collects and uses the heat to generate electricity. Over time, soiling reduces the reflectivity of the heliostats and, therefore, the efficiency of the system. Current industry practice sends vehicles to wash heliostats in an ad hoc fashion. We present a mixed-integer nonlinear program that determines wash vehicle fleet size, mix, and assignment of wash crews to heliostats to minimize the sum of (i) the revenues lost due to heliostat soiling, (ii) the costs of hiring wash crews and operating the vehicles, and (iii) the costs of purchasing wash vehicles. We establish conditions for convexity of the objective function, and then propose a decomposition method that enables near-optimal solutions to the wash vehicle fleet sizing and assignment problem on the order of a couple of minutes. These solutions yield hundreds of thousands of dollars in savings per year over current industry practices.

关键词： Fleet sizing vehicle assignment concentrating solar power operations and maintenance optimization mixed-integer nonlinear programming decomposition

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Optimal price and quantity determination for retail electric power contracts

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IEEE TRANSACTIONS ON POWER SYSTEMS 2006年第1期21卷 180-187页

作者： Gabriel, SA Conejo, AJ Plazas, MA Balakrishnan, S Univ Maryland Dept Civil & Environm Engn College Pk MD 20742 USA Univ Castilla La Mancha Dept Elect Engn E-13071 Ciudad Real Spain ANB Enterprises Inc Sugar Land TX 77479 USA

Considering the viewpoint of a retailer, this paper analyzes the problem of setting up contracts on both the supplier and end-user sides to maximize profits while maintaining an acceptable level of settlement risk. The proposed stochastic optimization model can assist retailers with these efforts and guide them in their contractual arrangements. A realistic example illustrates the capabilities of the methodology proposed.

关键词： contract design electricity market mixed-integer nonlinear programming retailer viewpoint stochastic optimization

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A column generation algorithm for solving energy system planning problems

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OPTIMIZATION AND ENGINEERING 2023年第1期24卷 317-351页

作者： Muts, Pavlo Bruche, Stefan Nowak, Ivo Wu, Ouyang Hendrix, Eligius M. T. Tsatsaronis, George Hamburg Univ Appl Sci Hamburg Germany Tech Univ Berlin Berlin Germany Univ Malaga Malaga Spain

Energy system optimization models are typically large models which combine sub-models which range from linear to very nonlinear. Column generation (CG) is a classical tool to generate feasible solutions of sub-models, defining columns of global master problems, which are used to steer the search for a global solution. In this paper, we present a new inner approximation method for solving energy system MINLP models. The approach is based on combining CG and the Frank Wolfe algorithm for generating an inner approximation of a convex relaxation and a primal heuristic for computing solution candidates. The features of this approach are: (i) no global branch-and-bound tree is used, (ii) sub-problems can be solved in parallel to generate columns, which do not have to be optimal, nor become available at the same time to synchronize the solution, (iii) an arbitrary solver can be used to solve sub-models, (iv) the approach (and the implementation) is generic and can be used to solve other nonconvex MINLP models. We perform experiments with decentralized energy supply system models with more than 3000 variables. The numerical results show that the new decomposition method is able to compute high-quality solutions and has the potential to outperform state-of-the-art MINLP solvers.

关键词： Decomposition method Parallel computing Column generation Nonconvex optimization Global optimization mixed-integer nonlinear programming

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