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Data-Driven interval robust optimization method of VPP Bidding strategy in spot market under multiple uncertainties

APPLIED ENERGY 2025年 384卷

作者： Ma, Ying Li, Zhen Liu, Ruyi Liu, Bin Yu, Samson S. Liao, Xiaozhong Shi, Peng Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Beijing Inst Technol Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Hong Kong Polytech Univ Dept Appl Math Hung Hom Kowloon Hong Kong Peoples R China China Univ Petr Coll Informat Sci & Engn Beijing 102249 Peoples R China Deakin Univ Sch Engn Waurn Ponds Vic 3216 Australia Univ Adelaide Sch Elect & Elect Engn Adelaide SA 5005 Australia Obuda Univ Res & Innovat Ctr H-1034 Budapest Hungary

The participation of Virtual Power Plants (VPPs) in the spot market enhances the flexibility of modern power systems as renewable energy penetration increases. However, multiple uncertainties on the market, load, and generation sides can significantly affect the bidding strategies and operational efficiency of VPPs. This paper employs interval numbers generated by a data-driven model to capture the uncertainty and correlation of electricity prices in the spot market. Additionally, uncertainty sets are utilized to represent the variability in the number of electric vehicles (EVs) and photovoltaic (PV) power generation. A two-stage interval robust optimization model considering arbitrage opportunity is established to optimize the bidding strategies of a VPP that includes gas turbines, energy storage, PV systems, and EVs. An improved column-and-constraint generation (C&CG) algorithm is developed to solve this model. The results demonstrate that the interval numbers of electricity prices produced by the proposed data- driven model can reduce VPP cost fluctuations by 9.3%. The two-stage interval robust optimization model reduces costs by 2.5% compared to a single-stage robust method and 52.0% compared to robust method ignoring arbitrage opportunities. As parameters change, the advantages of the proposed model become more significant. The improved C&CG algorithm shows superior convergence and accuracy. Unlike stochastic optimization methods that generate n scenarios, the computational time for the interval optimization method can be reduced to 1/n. This study offers a feasible solution for the bidding strategies of VPPs considering multiple uncertainties in the spot market.

关键词： Energy arbitrage Interval optimization Spot market two-stage robust optimization Uncertainties Virtual power plant (VPP)

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Γ-robust optimization of project scheduling problems

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COMPUTERS & OPERATIONS RESEARCH 2024年 161卷

作者： Koster, Arie M. C. A. Segschneider, Jenny Ventsch, Nicole Rhein Westfal TH Aachen Res Area Discrete Optimizat Pontdriesch 10-12 D-52056 Aachen Germany

In this paper, we investigate the problem of finding a robust baseline schedule for the project scheduling problem under uncertain process times. We assume that the probability distribution for the duration is unknown, but an estimate is given along with an interval in which this time can vary. At most Gamma of the tasks will deviate from the estimated time. We present two approaches to solving this problem. The first approach treats the problem of determining the earliest guaranteed finish times and can be solved in polynomial time by an extension of the critical path method. The second is a two-stage approach that determines the baseline schedule in the first stage and an adaptation to the scenario in the second stage. We show strong NP-hardness of the second stage problem and introduce a novel formulation. From this formulation we derive an exact algorithm and three heuristics. A computational study on benchmark instances shows that the heuristics perform well on larger instances.

关键词： robust project scheduling Budgeted uncertainty two-stage robust optimization Heuristics Mixed-integer programming

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Adjustable robust optimization with objective uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期312卷 373-384页

作者： Detienne, Boris Lefebvre, Henri Malaguti, Enrico Monaci, Michele Univ Bordeaux IMB UMR CNRS 5251 Inria Bordeaux Sud Ouest 200 Ave Vieille Tour F-33405 Talence France Univ Bologna Dipartimento Ingn Energia Elettr & Informaz Guglie Viale Risorgimento 2 I-40136 Bologna Italy

In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and involve mixed-integer variables, thus extending the existing literature to a much wider class of problems. We show how these problems can be reformulated using Fenchel duality, allowing to derive an enumerative exact algorithm, for which we prove asymptotic convergence in the general case, and finite convergence for cases where the first-stage variables are all integer. An implementation of the resulting algorithm, embedding a column generation scheme, is then computationally evaluated on a variant of the Capacitated Facility Location Problem with uncertain transportation costs, using instances that are derived from the existing literature. To the best of our knowledge, this is the first approach providing results on the practical solution of this class of problems. & COPY;2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： Uncertainty modelling two-stage robust optimization Reformulation Fenchel duality Branch-and-price Computational experiments

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Interval-Partitioned and Correlated Uncertainty Set Based robust optimization of Microgrid

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IEEE SYSTEMS JOURNAL 2024年第3期18卷 1516-1527页

作者： Zheng, Zuqing Chen, Guo Shen, Zixiang Cent South Univ Sch Automat Changsha 410083 Peoples R China

The dramatic increase in renewable energy sources has created significant uncertainties in the operation of power systems. This article investigates a day-ahead economic dispatch problem for a typical microgrid, considering the uncertainties of renewable energy sources and load demand. An interval-partitioned and temporal-correlated uncertainty set based robust optimization model is proposed, which allows a more accurate characterization of the distribution of uncertainties. The proposed robust optimization model can reduce the conservativeness of the optimal solution by avoiding scenarios that are low-probability or even impossible in reality. The model is then decomposed into a master problem and a nonlinear bi-level subproblem and solved by the C&CG method and Big-M method. However, this method requires the introduction of a large number of auxiliary variables and related constraints, significantly increasing the computation burden. To tackle this problem, an efficient solution method, Improved-C&CG, is developed by integrating an outer approximation method into the C&CG method. Finally, case studies verify the effectiveness of the proposed model, uncertainty set, and solution methods.

关键词： Uncertainty Microgrids Renewable energy sources optimization Load modeling Costs Dispatching C&CG interval-partitioned outer approximation temporal-correlated two-stage robust optimization

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A robust optimization framework for two-echelon vehicle and UAV routing for post-disaster humanitarian logistics operations

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NEtwoRKS 2024年第2期84卷 200-219页

作者： Faiz, Tasnim Ibn Vogiatzis, Chrysafis Liu, Jiongbai Noor-E-Alam, Md. Northeastern Univ Dept Mech & Ind Engn Boston MA 02115 USA Univ Illinois Urbana & Champaign Ind & Enterprise Syst Engn Urbana IL USA

Providing first aid and other supplies (e.g., epi-pens, medical supplies, dry food, water) during and after a disaster is always challenging. The complexity of these operations increases when the transportation, power, and communications networks fail, leaving people stranded and unable to communicate their locations and needs. The advent of emerging technologies like uncrewed autonomous vehicles can help humanitarian logistics providers reach otherwise stranded populations after transportation network failures. However, due to the failures in telecommunication infrastructure, demand for emergency aid can become uncertain. To address the challenges of delivering emergency aid to trapped populations with failing infrastructure networks, we propose a novel robust computational framework for a two-echelon vehicle routing problem that uses uncrewed autonomous vehicles (UAVs), or drones, for the deliveries. We formulate the problem as a two-stage robust optimization model to handle demand uncertainty. Then, we propose a column-and-constraint generation approach for worst-case demand scenario generation for a given set of truck and UAV routes. Moreover, we develop a decomposition scheme inspired by the column generation approach to generate UAV routes for a set of demand scenarios heuristically. Finally, we combine the decomposition scheme within the column-and-constraint generation approach to determine robust routes for both trucks (first echelon vehicles) and UAVs (second echelon vehicles), the time that affected communities are served, and the quantities of aid materials delivered. To validate our proposed algorithms, we use a simulated dataset that aims to recreate emergency aid requests in different areas of Puerto Rico after Hurricane Maria in 2017.

关键词： column generation column-and-constraint generation disaster management humanitarian logistics two-echelon vehicle and UAV routing two-stage robust optimization

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A robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets

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FRONTIERS IN ENERGY RESEARCH 2024年 12卷

作者： Ye, Yuming Wang, Jungang Pan, Dingcai Zhang, Jingsong Li, Fan Yin, Xueli Elect Power Res Inst Guizhou Power Grid Co Ltd Guiyang Guizhou Peoples R China China Southern Power Grid Energy Dev Res Inst Guangzhou Guangdong Peoples R China China Southern Power Grid Digital Power Grid Grp C Guangzhou Guangdong Peoples R China

In order to better describe the uncertainty of renewable energy output, this paper proposed a novel robust optimization method for new distribution systems based on adaptive data-driven polyhedral sets. First, an ellipsoidal uncertainty set was established using historical data on renewable energy output, and a data-driven convex hull polyhedral set was established by connecting high-dimensional ellipsoidal vertices;on this basis, an adaptive data-driven polyhedral set model was established to address the problem of high conservatism in the scaling process of convex hull polyhedral sets. Furthermore, a novel adaptive data-driven robust scheduling model for new distribution systems was established, and a column-and-constraint generation (C&CG) algorithm was used to solve the robust scheduling model. Finally, the improved IEEE-33 bus system simulation verification shows that the robust scheduling model for new distribution systems based on adaptive data-driven polyhedral sets can reduce conservatism and improve the robustness of optimization results.

关键词： two-stage robust optimization convex hull polyhedral set hyperplane polyhedral set economic dispatch C&CG algorithm

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robust optimization for Microgrid Management With Compensator, EV, Storage, Demand Response, and Renewable Integration

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IEEE ACCESS 2024年 12卷 73413-73425页

作者： Hematian, Hamid Askari, Mohamad Tolou Ahmadi, Meysam Amir Sameemoqadam, Mahmood Nik, Majid Babaei Islamic Azad Univ Dept Elect Engn Semnan Branch Semnan *** Iran Islamic Azad Univ Dept Elect Engn Shahrood Branch Shahrood *** Iran

Navigating the complex terrain of microgrid energy management is challenging due to the uncertainties linked with abundant renewable resources, fluctuating demand, and a wide range of devices including batteries, distributed energy sources, electric vehicles, and compensatory devices. This paper presents an advanced two-stage robust day-ahead optimization model designed specifically for MG operations. The model primarily addresses challenges arising from the integration of power electronics-based generation units, the unpredictable nature of demand in microgrids, and the integration of small-scale renewable energy sources. The proposed model includes detailed formulations for MG energy management, covering optimal battery usage, efficient EV energy management, compensator usage, and strategic dispatching of DG resources. The multi-objective function aims to minimize various costs related to energy losses, power purchases, load curtailment, DG operation, and battery/EV expenses over a 24-hour period. To efficiently solve this optimization problem, the C&CG algorithm is utilized. Numerical simulations on a test system validate the effectiveness of the proposed model and solution algorithm, showing a significant reduction in the operating costs of the microgrid. This approach offers a robust framework to enhance the resilience and efficiency of microgrid energy management. The results conclusively demonstrate that the proposed approach surpasses comparable methods by at least 5%, highlighting its effectiveness in improving key indicators within the microgrid system.

关键词： Batteries Costs Renewable energy sources Electric vehicles Energy management optimization Demand response Uncertainty Microgrid two-stage robust optimization demand response storage electric vehicle uncertainty

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Adjustable robust optimization Reformulations of two-stage Worst-Case Regret Minimization Problems

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OPERATIONS RESEARCH 2021年第5期70卷 2906页

作者： Poursoltani, Mehran Delage, Erick HEC Montreal GERAD Montreal PQ H3T 2A7 Canada HEC Montreal Dept Decis Sci Montreal PQ H3T 2A7 Canada

This paper explores the idea that two-stage worst-case regret minimization problems with either objective or right-hand side uncertainty can be reformulated as two-stage robust optimization problems and can therefore benefit from the solution schemes and theoretical knowledge that have been developed in the last decade for this class of problems. In particular, we identify conditions under which a first-stage decision can be obtained either exactly using popular adjustable robust optimization decomposition schemes or approximately by conservatively using affine decision rules. Furthermore, we provide both numerical and theoretical evidence that, in practice, the first-stage decision obtained using affine decision rules is of high quality. Initially, this is done by establishing mild conditions under which these decisions can be proven exact, which effectively extends the space of regret minimization problems known to be solvable in polynomial time. We further evaluate both the sub-optimality and computational efficiency of this tractable approximation scheme in a multi-item newsvendor problem and a production transportation problem.

关键词： two-stage robust optimization regret minimlzation affline decision rules

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A robust optimization approach to steel grade design problem subject to uncertain yield and demand

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第15期61卷 5176-5192页

作者： Zhang, Qi Liu, Shixin Zhou, MengChu Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China New Jersey Inst Technol Dept Elect & Comp Engn Newark NJ 07102 USA

This work formulates and investigates a steel grade design problem (SGDP) arising from a production process of steelmaking continuous casting. For the first time, we consider uncertain yield and demand in SGDP and construct a two-stage robust optimisation model accordingly. Then, we propose an enhanced column-and-constraint generation algorithm to obtain high-quality solutions. By exploiting the problem characteristics, we first use a Lagrangian relaxation method to decompose SGDP into multiple subproblems and then apply a standard column-and-constraint generation algorithm to solve the latter. At last, we test the proposed algorithm by extensive instances constructed based on actual production rules of a steelmaking shop. Numerical results show that it can effectively solve large-scale SGDPs. The obtained plan is better than those obtained by a commonly-used and standard column-and-constraint generation algorithm.

关键词： Steel grade design steelmaking continuous casting two-stage robust optimization Lagrangian relaxation column-and-constraint generation

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Solving two-stage robust optimization problems using a column-and-constraint generation method

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OPERATIONS RESEARCH LETTERS 2013年第5期41卷 457-461页

作者： Zeng, Bo Zhao, Long Univ S Florida Dept Ind & Management Syst Engn Tampa FL 33620 USA

In this paper, we present a column-and-constraint generation algorithm to solve two-stage robust optimization problems. Compared with existing Benders-style cutting plane methods, the column-and-constraint generation algorithm is a general procedure with a unified approach to deal with optimality and feasibility. A computational study on a two-stage robust location-transportation problem shows that it performs an order of magnitude faster. (c) 2013 Elsevier B.V. All rights reserved.

关键词： two-stage robust optimization Cutting plane algorithm Location-and-transportation

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