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Data-Driven two-stage robust optimization Allocation and Loading for Salt Lake Chemical Enterprise Products Under Demand Uncertainty

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IEEE-CAA JOURNAL OF AUTOMATICA SINICA 2025年第5期12卷 989-1003页

作者： Tang, Yiyin Wang, Yalin Liu, Chenliang Sui, Qingkai Liu, Yishun Huang, Keke Gui, Weihua Cent South Univ Sch Automat Changsha 410083 Peoples R China

Most enterprises rely on railway transportation to deliver their products to customers, particularly in the salt lake chemical industry. Notably, allocating products to freight spaces and their assembly on transport vehicles are critical pre-transportation processes. However, due to demand fluctuations from changing product orders and unforeseen railway scheduling delays, manually adjusted allocation and loading may lead to excessive loading and unloading distances and times, ultimately increasing transportation costs for enterprises. To address these issues, this paper proposes a data-driven two-stage robust optimization (TSRO) framework embedding with the gated stacked temporal autoencoder clustering based on the attention mechanism (GSTAC-AM), which aims to overcome demand uncertainty and enhance the efficiency of freight allocation and loading. Specifically, GSTAC-AM is developed to help predict the deviation level of demand uncertainty and mitigate the impact of potential outliers. Then, a robust counterpart model is formulated to ensure computational tractability. In addition, a multi-stage hybrid heuristic algorithm is designed to handle the large scale and complexity inherent in the freight space allocation and loading processes. Finally, the effectiveness and applicability of the proposed framework are validated through a real case study conducted in a large salt lake chemical enterprise.

关键词： Salt Uncertainty Costs Loading Transportation Rail transportation robustness Resource management optimization Chemicals Data-driven modeling demand uncertainty product resource allocation and loading salt lake chemical enterprise two-stage robust optimization

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Optimal Design of Distributed Energy Resource Systems under Uncertainties Based on two-stage robust optimization

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Journal of Thermal Science 2021年第1期30卷 51-63页

作者： LI Da ZHANG Shijie Key Laboratory of Advanced Energy and Power Institute of Engineering ThermophysicsChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China Research Center for Clean Energy and Power Chinese Academy of SciencesLianyungang 222069China

Distributed energy resource(DER)systems are widely used owing to their excellent economic and environmental ***,uncertainties in the system generate difficulties in the optimal design of DER *** practice,the distribution of uncertain parameters is generally *** this work,a two-stage robust optimization(RO)model was proposed for the optimal design of DER systems considering uncertainties in renewable energy intensity,energy prices,and load *** uncertainty sets(i.e.,the box,ellipsoid,and convex-hull uncertainty sets)were adopted to describe the distribution of uncertain parameters,and the proposed two-stage RO problem was solved using affine decision rules.A typical hospital in Lianyungang,Jiangsu Province,China,was selected as the case study object,and the effectiveness of the model was *** case study results showed that uncertainties in energy prices and load demands have a significant impact on system configuration and economic performance,and mainly affect the installed capacities of gas boilers,absorption chillers,and *** set will affect the optimization results and an appropriate uncertainty set should be adopted to describe uncertainties precisely and increase accuracy of results.

关键词： distributed energy resource optimal design two-stage robust optimization uncertainty uncertainty set

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A Feasibility Pump Based Solution Algorithm for two-stage robust optimization With Integer Recourses of Energy Storage Systems

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2021年第3期12卷 1834-1837页

作者： Zhang, Cuo Dong, ZhaoYang Yang, Linfeng Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Guangxi Univ Sch Comp Elect & Informat Nanning 530004 Peoples R China

To address uncertainties, two-stage robust optimization (TSRO) methods have been widely used for power system operation and planning problems. However, solving TSRO problems with integer recourses of energy storage systems (ESSs) is challenging. This article proposes a feasibility pump based column and constraint generation (FP-CCG) solution algorithm to solve these TSRO problems. In this article, firstly, a TSRO problem of ESS operation with state-of-charge management is formulated. Then, the FP-CCG algorithm is proposed and applied to solve this TSRO problem. Simulation results indicate full solution robustness and high computation efficiency of the proposed FP-CCG solution algorithm.

关键词： Uncertainty Energy storage Microgrids optimization Mathematical model Load modeling Upper bound Column and constraint generation energy storage system feasibility pump integer recourse mixed integer linear programming two-stage robust optimization

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Exploiting the Structure of two-stage robust optimization Models with Exponential Scenarios

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INFORMS JOURNAL ON COMPUTING 2021年第1期33卷 143-162页

作者： Doulabi, Hossein Hashemi Jaillet, Patrick Pesant, Gilles Rousseau, Louis-Martin Concordia Univ Dept Mech Ind & Aerosp Engn Montreal PQ H3G 1M8 Canada Univ Montreal Interuniv Res Ctr Enterprise Networks Logist & Tr Montreal PQ H3C 3J7 Canada MIT Dept Elect Engn & Comp Sci Lab Informat & Decis Syst Operat Res Ctr Cambridge MA 02139 USA Polytech Montreal Dept Comp & Software Engn Montreal PQ H3T 1J4 Canada Polytech Montreal Dept Math & Ind Engn Montreal PQ H3T 1J4 Canada

This paper addresses a class of two-stage robust optimization models with an exponential number of scenarios given implicitly. We apply Dantzig-Wolfe decomposition to exploit the structure of these models and show that the original problem reduces to a single-stage robust problem. We propose a Benders algorithm for the reformulated single-stage problem. We also develop a heuristic algorithm that dualizes the linear programming relaxation of the inner maximization problem in the reformulated model and iteratively generates cuts to shape the convex hull of the uncertainty set. We combine this heuristic with the Benders algorithm to create a more effective hybrid Benders algorithm. Because the master problem and subproblem in the Benders algorithm are mixed-integer programs, it is computationally demanding to solve them optimally at each iteration of the algorithm. Therefore, we develop novel stopping conditions for these mixed-integer programs and provide the relevant convergence proofs. Extensive computational experiments on a nurse planning problem and a two-echelon supply chain problem are performed to evaluate the efficiency of the proposed algorithms.

关键词： integer programming Dantzig-Wolfe decomposition two-stage robust optimization

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Economic dispatch of generation load aggregators based on two-stage robust optimization

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FRONTIERS IN ENERGY RESEARCH 2023年 11卷

作者： Zhang, Haonan Tian, Youwen Zhao, Yi Liu, Qingyu Zhang, Nannan Shenyang Agr Univ Sch Informat & Elect Engn Shenyang Liaoning Peoples R China Shenyang Inst Engn Coll Elect Power Shenyang Liaoning Peoples R China

Introduction: In recent years, with the rapid development of renewable energy generation, the stability of the power grid has been greatly reduced. In response to this problem, integrating the user side transferable load into the power market has become the key to the development of future power grid. At present, large transferable loads have entered the electricity market in some pilot areas of China, but the relevant research on small and medium-sized transferable users entering the electricity market is still ***: This paper proposes the concept of generation load aggregators. A two-stage generation load aggregator robust optimization model is developed to obtain the scheduling scheme with the lowest operating cost under the worst scenario. The model consists of distributed renewable power, transferable load, self-provided power, energy storage, etc. Uncertainties of renewable energy and load are introduced in the model. By using the column constraint generation algorithm and strong pairwise theory, the original problem is decomposed into the main problem and sub-problems to be solved alternately, so as to obtain the scheduling scheme with the lowest operating cost in the worst scenario under different ***: The solved results are compared with those without the generation load aggregator, illustrating the role of the generation load aggregator in relieving peak and valley pressure on the grid from the load side, reducing the cost of electricity for loads, and promoting the consumption of renewable energy. The comparison with the deterministic optimization algorithm shows a significant decrease in the total cost and validates the performance of the selected solution algorithm. The boundary conditions for the use of energy storage by generation load aggregators for peak and valley reduction under the time-sharing tariff mechanism are also ***: This study can provide reference for the investors of generation load aggregators w

关键词： generation load aggregator two-stage robust optimization uncertainty optimization economic dispatch column constraint generation algorithm

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A two-stage robust optimization model for a virtual power plant considering responsiveness-based electric vehicle aggregation

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JOURNAL OF CLEANER PRODUCTION 2023年 405卷

作者： Chen, Yue Niu, Yuguang Du, Ming Wang, Jiahui North China Elect Power Univ Sch Control & Comp Engn State Key Lab Alternate Elect Power Syst Renewable Beijing 102206 Peoples R China

With the goal of pursuing carbon neutrality, this study is aimed to investigate effectively managing distributed renewable energy. Considering the uncertainty of wind power (WP), photovoltaic power (PV), and load, a two-stage robust optimization model for virtual power plant (VPP) is proposed, with a focus on calculating the available capacity of electric vehicle (EV) aggregated virtual energy storage (VES). Time-space distribution characteristics of EVs and the responsiveness of EV users are analyzed and the available capacity calculation model is constructed. In the first stage, the bidding strategy and unit combination of the VPP are determined based on the predicted values of WP, PV, and load. Combining with the pre-decided decision from the first stage, the output of each unit is determined by considering an uncertainty set in the second stage, for achieving the best operational benefit under worst-case scenarios. robust control parameters are introduced into the model and used to adjust conservativeness. The model is solved by applying the C&CG algorithm. Additionally, a carbon trading mechanism is leveraged to balance the system economy and environmental friendliness. The results show that the optimal scheduling solution helps to reduce fluctuations caused by uncertainties, balancing the economic benefits and operational risks of the VPP. Besides, guidance is provided for VPP operators to formulate reasonable incentives for EV users and the construction of energy storage systems. When the carbon trading price of the VPP proposed in the paper is set at 160 yen /ton, economic and environmental sustainability can be effectively balanced.

关键词： Virtual power plant Electric vehicle virtual energy storage Available capacity two-stage robust optimization Carbon trading mechanism

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two-stage robust co-optimization of energy and reserve scheduling for resilient distribution systems considering line reinforcement

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ENERGY 2025年 316卷

作者： Han, Haiteng Yu, Lichengzi Zhou, Yizhou Zang, Haixiang Cao, Yang Chen, Sheng Sun, Guoqiang Wei, Zhinong Hohai Univ Sch Elect & Power Engn Nanjing 211100 Peoples R China

In recent years, the resilience of distribution systems has faced challenges due to the increasing frequency of extreme weather events and the intensifying global effects of climate change. To mitigate the adverse effects of these weather occurrences, we propose a day-ahead energy scheduling and line reinforcement strategy designed to address day-ahead spare capacity scheduling during extreme weather conditions, while also accommodating the unpredictability associated with such events. Initially, we integrate a rapid power regulation model for photovoltaic (PV) power plants to enhance the swift regulation of new energy sources. Subsequently, we develop a two-stage robust planning approach aimed at minimizing both load shedding and dispatch costs amidst extreme weather uncertainties. It enhances the system resilience, lowering load shedding by 7.8 %. Finally, the proposed model is decomposed into master and subproblems and solved iteratively through the application of nested column-and-constraint generation (NC&CG) algorithm. Numerical results demonstrate that the proposed approach improves economic efficiency by reducing the total investment by 3.8 % and the day-ahead cost by 3.05 %, as well as enhancing the system resilience by mitigating potential load shedding under extreme conditions.

关键词： two-stage robust optimization Day-ahead dispatch Distribution systems Extreme weather events Nested column-and-constraint generation algorithm

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LP-based approximations for disjoint bilinear and two-stage adjustable robust optimization

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MATHEMATICAL PROGRAMMING 2024年第1-2期206卷 239-281页

作者： El Housni, Omar Foussoul, Ayoub Goyal, Vineet Cornell Univ Operat Res & Informat Engn New York NY USA Columbia Univ Ind Engn & Operat Res New York NY 10027 USA

We consider the class of disjoint bilinear programs max {x(T) y | x is an element of X, y is an element of Y} where X and Y are packing polytopes. We present an O( log logm1 /logm1 log logm2/ logm2)-approximation algorithm for this problem where m1 and m2 are the number of packing constraints in X and Y respectively. In particular, we show that there exists a near-optimal solution ( (x) over tilde, (y) over tilde) such that (x) over tilde and (y) over tilde are "near-integral". We give an LP relaxation of the problem from which we obtain the near-optimal near-integral solution via randomized rounding. We show that our relaxation is tightly related to the widely used reformulation linearization technique. As an application of our techniques, we present a tight approximation for the two-stage adjustable robust optimization problem with covering constraints and right-hand side uncertainty where the separation problem is a bilinear optimization problem. In particular, based on the ideas above, we give an LP restriction of the two-stage problem that is an O( log n /log log n log L/ log log L)-approximation where L is the number of constraints in the uncertainty set. This significantly improves over state-of-the-art approximation bounds known for this problem. Furthermore, we show that our LP restriction gives a feasible affine policy for the two-stage robust problem with the same (or better) objective value. As a consequence, affine policies give an O( log n log log n/ log L log log L)-approximation of the two-stage problem, significantly generalizing the previously known bounds on their performance.

关键词： Disjoint bilinear programming two-stage robust optimization Approximation algorithms RLT Affine policies

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two-stage robust transaction optimization model and benefit allocation strategy for new energy power stations with shared energy storage considering green certificate and virtual energy storage mode

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APPLIED ENERGY 2024年 362卷

作者： Ju, Liwei Bai, Xiping Li, Gen Gan, Wei Qi, Xin Ye, Fan North China Elect Power Univ Sch Econ & Management Changping 102206 Beijing Peoples R China North China Elect Power Univ Beijing Key Lab New Energy & Low Carbon Dev Beijing 102206 Peoples R China Tech Univ Denmark DTU Dept Engn Technol & Didact DK-2750 Ballerup Denmark Cardiff Univ Sch Engn Cardiff CF24 3AA Wales State Grid Jiangxi Extra High Voltage Co Nanchang 330096 Peoples R China

In the context of the large-scale participation of renewable energy in market trading, this paper designs a cooperation mode of new energy power stations (NEPSs) and shared energy storage (SES) to participate in the power-green certificate market, which divides SES into physical energy storage and virtual energy storage. Secondly, combining the advantages of scenario generation and robust optimization (RO), a two-stage RO model with improved uncertainty interval is proposed to determine the optimal trading strategy. Then, to better align the distribution results of cooperative benefits with the actual contributions of NEPSs and SES, an entropy weight modified Shapley value benefit allocation strategy is constructed. Finally, the new energy base in Qinghai Province, China is chosen for simulation. The results show: (1) Adding energy storage and using two-stage RO are able to effectively improve the ability of NEPSs to resist uncertainty, which increases the revenue of the alliance by 22.8%. (2) The application of SES has better economic benefits than each member equipped with energy storage separately. Compared with the latter, the deviation penalty cost of the former is reduced by 66.4%, and the revenue is increased by 3.4%. (3) The proposed entropy weight modified Shapley value method embodies the important auxiliary role of SES more obviously. Based on this method, the overall satisfaction of the alliance increases by 12.6%. Generally speaking, the optimization model and benefit allocation strategy proposed in this paper can provide guidance for NEPSs and SES participating in power trading, and promote the low -carbon transformation of the power sector.

关键词： Variable renewable energy Shared energy storage two-stage robust optimization Benefit allocation

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two-stage robust QUADRATIC optimization WITH EQUALITIES AND ITS APPLICATION TO OPTIMAL POWER FLOW

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SIAM JOURNAL ON optimization 2023年第4期33卷 2830-2857页

作者： Kuryatnikova, Olga Ghaddar, Bissan Molzahn, Daniel K. Erasmus Univ Econometr Inst NL-3062 PA Rotterdam Netherlands Western Univ Ivey Business Sch London ON NG6 0N1 Canada Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30313 USA

In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the uncertainty is revealed, and the rest of the optimization variables (state variables) are set up as a solution to a known system of possibly nonlinear equations. This type of problem occurs, for instance, in optimization for dynamical systems, such as electric power systems as well as gas and water networks. We propose a convergent iterative algorithm to build a sequence of approximately robustly feasible solutions with an improving objective value. At each iteration, the algorithm optimizes over a subset of the feasible set and uses affine approximations of the second-stage equations while preserving the nonlinearity of other constraints. We implement our approach and demonstrate its performance on Matpower instances of AC optimal power flow. Although this paper focuses on quadratic problems, the approach is suitable for more general setups.

关键词： nonconvex quadratic optimization two-stage robust optimization AC optimal power flow uncertainty in energy systems

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