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Distributionally robust optimization for green hydrogen plant planning considering extreme scenarios

INTERNATIONAL JOURNAL OF HYDROGEN ENERGY 2025年 133卷 112-123页

作者： Oroya, Luis A. Cortez, Juan Carlos Terada, Lucas Zenichi Silva, Jessica A. A. Rider, Marcos J. Univ Estadual Campinas UNICAMP Sch Elect & Comp Engn FEEC BR-13083852 Campinas SP Brazil

As efforts to reduce carbon emissions increase, green hydrogen from sources like wind (WD) and photovoltaic (PV) power is a promising solution for industrial decarbonization. However, the variability of renewable energy sources (RES) challenges the planning and operation of green hydrogen plants. To address these challenges, this paper proposes a novel two-stage extreme distributionally robust optimization (X-DRO) model for sizing distributed energy resources efficiently for green hydrogen production and selling. The proposed model minimizes the total capital (CAPEX) and operating expenditures (OPEX) while ensuring the robustness of performance under an uncertain renewable energy supply. The methodology includes selecting representative and extreme scenarios to input into the model, representing the variability of RES. In the first stage, capacity planning decisions, including the sizing of PV and WD units, battery energy storage systems (BESS), hydrogen storage tanks (HSTs), and electrolyzers (ELs), are considered. The second stage addresses the operating decisions concerning power exchange with the grid, hydrogen production, and storage under worst-case scenario probabilities of RES generation. The column-and-constraint generation (C&CG) algorithm is applied to solve the X-DRO model. Simulations show that the proposed model balances economic efficiency and robustness compared to robust optimization (RO) and stochastic optimization (SO) models. A comparison between the X-DRO and DRO models highlights the importance of considering extreme cases for resilient planning.

关键词： column-and-constraint generation algorithm Distributionally robust optimization Extreme scenario Green hydrogen plant planning

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Facility location and capacity planning for sampling and testing processes under demand uncertainty

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COMPUTERS & INDUSTRIAL ENGINEERING 2025年 204卷

作者： Zhou, Zhongbao Sun, Wenting Ren, Tiantian Zeng, Ximei Hunan Univ Sch Business Adm Changsha 410082 Peoples R China Hunan Univ Hunan Key Lab Emergency Management Intelligent Dec Changsha 410082 Peoples R China Xiangtan Univ Business Sch Xiangtan 411105 Peoples R China Changsha Univ Sci & Technol Sch Econ & Management Changsha 410076 Peoples R China

During an outbreak, nucleic acid testing is essential for early infection detection and virus transmission control. In this study, we aim to location and capacity planning of testing facilities, balancing minimal costs with maximum population coverage during public health emergencies. We propose a novel two-stage robust optimization model that addresses uncertainties in sampling demand during an epidemic, with distinct phases for sampling and testing. Applying this model to medium and high-risk areas in Beijing during COVID-19, we use the column-and-constraint generation (C&CG) algorithm and compare its performance with three meta-heuristic algorithms: Differential Evolution (DE), Genetic algorithm (GA), and Simulated Annealing (SA). Our findings reveal that the C&CG algorithm reduces sampling costs by 31.10% compared to DE, 26.77% to GA, and 21.17% to SA. It also lowers testing costs by 7.48%, 79.79%, and 60.63%, respectively, and achieves a higher completion rate for sampling and testing volumes, ranging from 93.12% to 100%. In addition, C&CG outperforms the other algorithms in handling large sample sizes by 43.98% to 61.84%. Despite its longer computational time, C&CG is more efficient in cost reduction and demand satisfaction. Furthermore, we analyze the impact of uncertainty set parameters, including a unified value of the demand risk parameter, and assess different cases. The corresponding location and capacity solutions can offer decision support for emergency agencies managing public health crises.

关键词： Facility location Capacity planning Demand uncertainty Two-stage robust optimization column-and-constraint generation algorithm

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Optimizing expressway battery electric vehicle charging and mobile storage energy truck scheduling: A two-stage approach to improve photovoltaic generation utilization

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ENERGY 2025年 320卷

作者： Wang, Dawei Guo, Jingwei Zhang, Yongxiang Zhong, Qingwei Xu, Hongke Changan Univ Sch Elect & Control Engn Xian 710064 Peoples R China City Univ Macau Fac Business Taipa 999078 Macao Peoples R China Southwest Jiaotong Univ Sch Transportat & Logist Natl United Engn Lab Integrated & Intelligent Tran Natl Engn Lab Integrated Transportat Big Data Appl Chengdu 610031 Peoples R China Civil Aviat Flight Univ China Coll Air Traff Management Guanghan 618307 Peoples R China

Promoting the utilization of photovoltaic generation along expressways is crucial for advancing green transportation. The long-distance distribution of photovoltaic devices on expressways results in underutilized photovoltaic generation. An effective solution to this issue is to direct the charging of battery electric vehicles in an orderly manner. Nowadays, research on charging battery electric vehicles using mobile energy storage trucks has emerged as a significant area of interest. Therefore, this paper proposes a two-stage approach for optimizing the coupled relationship between battery electric vehicle charging and mobile energy storage truck scheduling along expressways for efficient photovoltaic generation resource allocation. The proposed model employs spatial-temporal network concepts for battery electric vehicles and mobile energy storage trucks to depict the interplay between transportation and energy. In the first stage, a two-layer optimization model is developed to determine the charging plans of battery electric vehicles, balancing the profits of expressway managers with the expenses incurred by battery electric vehicle drivers. The upper-layer model focuses on maximizing the net earnings of the expressway manager, whereas the lower-layer model aims to minimize the charging and parking costs for battery electric vehicle drivers. The two-layer optimization model is solved with a column-and-constraint generation algorithm. The second stage optimizes the discharge/charge power and paths for mobile energy storage trucks to effectively distribute photovoltaic generation according to grid-supplied charging loads. The case study demonstrates that the proposed method significantly boosts photovoltaic generation utilization to 81.7% and reduces main grid purchase costs to 2122.0 RMB, fostering a mutually beneficial environment and economy for expressway managers.

关键词： Battery electric vehicle charging Two-stage optimization column-and-constraint generation algorithm Mobile energy storage truck scheduling Spatial-temporal network model

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Robust Optimization Model Based on a Static Rebalancing Design for Bike- Sharing Systems Affected by Demand Uncertainty

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IEEE ACCESS 2024年 12卷 73936-73949页

作者： Yu, Lijun Xu, Yaogeng Shi, Haochen Zhang, Zhimin South China Univ Technol Sch Civil Engn & Transportat Guangzhou 510640 Peoples R China South China Univ Technol Sch Architecture State Key Lab Subtrop Bldg & Urban Sci Guangzhou Peoples R China

Demand uncertainty and variations in user rental-return behavior can lead to an uneven spatial distribution of bicycles, which forces bike-sharing operators to rebalance the bike-sharing system by relocating bicycles from overstocked to understocked stations. In addition, this may lead to increased costs for bike-sharing operators. This paper proposed a two-stage robust model based on spatio-temporal networks to solve the static rebalancing problem in a bike-sharing system affected by demand uncertainty. The model designed a static rebalancing scheme for bike-sharing at a strategic level. To solve the problem, the paper used a customized column-and-constraint generation algorithm. Finally, the effectiveness of the proposed model and algorithm was confirmed using real data from Shanghai, China, providing strategic decision support for the static rebalancing problem in actual bike-sharing systems.

关键词： Uncertainty Bicycles Costs Transportation Stochastic processes Heuristic algorithms Computational modeling Bike-sharing system static rebalancing problem robust optimization column-and-constraint generation algorithm

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A two-stage robust low-carbon operation strategy for interconnected distributed energy systems considering source-load uncertainty

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APPLIED ENERGY 2024年 368卷

作者： Zhang, Sen Hu, Weihao Cao, Xilin Du, Jialin Zhao, Yincheng Bai, Chunguang Liu, Wen Tang, Ming Zhan, Wei Chen, Zhe Univ Elect Sci & Technol China Sch Mech & Elect Engn Sichuan Prov Key Lab Power Syst Wide Area Measurem 2006 Xiyuan Ave Chengdu 611731 Peoples R China Beijing Inst Technol Sch Management & Econ Beijing 100081 Peoples R China Univ Elect Sci & Technol China Inst Econ & Management 2006 Xiyuan Ave Chengdu 611731 Peoples R China Univ Utrecht Copernicus Inst Sustainable Dev Princetonlaan 8a NL-3584 CB Utrecht Netherlands SPIC Sichuan Elect Power Co LTD Chengdu 610041 Peoples R China SPIC Southwest Energy Res Inst Chengdu 610218 Peoples R China Aalborg Univ Dept Energy Technol Pontoppidanstr 111 Aalborg Denmark

Interconnected distributed energy systems (DESs) can facilitate multi-energy consumption, improve energy efficiency, and advance decarbonization goals. In this context, this study proposes an energy sharing framework that considers multiple uncertainties to optimize the low-carbon robust economic operation of interconnected DESs. First, a low-carbon dispatch model for DESs that includes electricity and heat sharing, integrated demand response (IDR), and low-carbon policies is constructed. Then, a two-stage robust optimization model is developed considering the source-load uncertainty, and the Karush-Kuhn-Tucker (KKT) condition is introduced to transform the max-min problem in the second stage into a single-layer issue. In addition, an approach combining the alternating direction multiplier method (ADMM) with the column-and-constraint generation algorithm (CCG) is proposed for a distributed and hierarchical solving of the two-stage energy sharing problem. Finally, to address the issue of transactional payments for energy sharing, a profit allocation model based on multi-factor contributions is developed to ensure that the benefits generated by the sharing system are fairly distributed. Based on actual data simulation, the effectiveness of the two-stage robust sharing scheme presented in this study is demonstrated for economy and carbon reduction.

关键词： Distributed energy systems Energy sharing Source-load uncertainty Alternating direction multiplier method column-and-constraint generation algorithm Low-carbon operation

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Resilience-oriented planning of integrated electricity and heat systems: A stochastic distributionally robust optimization approach

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APPLIED ENERGY 2024年第PartA期353卷

作者： Zhou, Yizhou Li, Xiang Han, Haiteng Wei, Zhinong Zang, Haixiang Sun, Guoqiang Chen, Sheng Hohai Univ Coll Energy & Elect Engn Nanjing 210098 Peoples R China

The resilience management of energy and power systems is of utmost importance in mitigating the impact of extreme events, which have resulted in devastating disasters and substantial economic losses. We present a novel stochastic distributionally robust optimization approach for the resilience-oriented planning of integrated electricity and heat systems (IEHSs). Firstly, A resilience-oriented planning model is developed for the IEHS, which incorporates the hardening of both electricity and heat networks, while also considering the deployment of both electric and thermal energy storages to enhance the resilience of the IEHS as a whole. Then, the stage-by-stage uncertainties associated with extreme weather events faced by the IEHS are accounted for by a stochastic distributionally robust optimization approach, where the uncertainty in the intensity of contingent extreme events is addressed via a stochastic optimization approach, while the uncertainty in the occurrence of outages resulting from a specific extreme event is addressed by a distributionally robust optimization approach. Finally, the stochastic distributionally robust optimization model is transformed into an equivalent three-level model, which is solved using a customized column-and-constraint generation algorithm. The effectiveness and superiority of the proposed approach according to the enhanced resilience and reduced costs are demonstrated by numerical simulations.

关键词： Resilience Integrated energy systems Stochastic optimization Distributionally robust optimization column-and-constraint generation algorithm

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Reliable multiple allocation hub location problem under disruptions

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FLEXIBLE SERVICES AND MANUFACTURING JOURNAL 2023年第4期36卷 1503-1529页

作者： Li, Tingting Xu, Wangtu Ningbo Univ Fac Maritime & Transportat Ningbo 315211 Peoples R China Xiamen Univ Dept Urban Planning Xiamen 361005 Peoples R China

Hubs play an important role in the network of many distribution systems. However, hubs can be disrupted due to various reasons, and such disruptions can lead to a substantial transportation cost increase. In this study, we investigate the reliable multiple allocation hub location problem with fixed cost considering multiple hub disruptions. We use multiple uncertainty sets to model the uncertainty of hub disruptions and propose a model based on the two-stage robust optimization approach. To solve the two-stage robust model, we develop an efficient exact solution method based on the column-and-constraint generation algorithm. Numerical examples from the CAB dataset confirm the effectiveness and efficiency of the proposed model and the solution algorithm.

关键词： Reliable hub location problem Hub disruption Two-stage robust optimization column-and-constraint generation algorithm

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Optimal Energy Management of Internet Data Center With Distributed Energy Resources

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IEEE TRANSACTIONS ON CLOUD COMPUTING 2023年第3期11卷 2285-2295页

作者： Zhou, Kaile Fei, Zhineng Lu, Xinhui Hefei Univ Technol Sch Management Minist Educ Key Lab Proc Optimizat & Intelligent Decis Making Hefei 230009 Anhui Peoples R China

Currently, an increasing number of Internet data centers (IDCs) are trying to apply distributed energy resources (DERs), such as renewable energy, battery energy storage systems (BESS), and conventional generators (CG). However, uncertain renewable energy presents significant challenges to the safe and stable operation of IDCs. A two-stage optimal operation model based on distributionally robust optimization (DRO) is proposed for an IDC with DERs to lower the total cost of the IDC, including operating cost, carbon emission cost, and re-dispatch cost under the worst-case probability distribution of renewable energy. An ambiguity set is formed by combining norm-1 and norm-inf under the given confidence level to capture the possible probability distributions of uncertain renewable energy. The proposed model can be turned into a tractable mixed-integer linear programming problem and efficiently solved by the column-and-constraint generation algorithm. Experimental results show the benefits of DERs integration and workload dispatch. Comparative analysis further demonstrates the superiority and scalability of the proposed model.

关键词： Internet data centers distributed energy resources distributionally robust optimization column-and-constraint generation algorithm

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Distributionally Robust Optimal Strategy for Resilience Enhancement of Power Distribution Networks under Uncertain Earthquake Failures 2

Distributionally Robust Optimal Strategy for Resilience Enha...

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IEEE 2nd International Conference on Power Science and Technology (ICPST)

作者： Zou, Changjie Deng, Chuang Xue, Zhihang Zhang, Xiaoling Univ Elect Sci & Technol China Sch Mech & Elect Engn Chengdu Sichuan Peoples R China State Grid Sichuan Elect Power Co Elect Power Emergency Management Ctr Chengdu Sichuan Peoples R China State Grid Sichuan Elect Power Co Elect Power Res Inst Chengdu Sichuan Peoples R China

ISBN: (纸本)9798350349047;9798350349030

Earthquakes have posed a significant threat to the power system, and it is imperative to enhance the earthquake resilience of power distribution networks (PDN). However, the uncertainty of line failure due to earthquakes presents a formidable challenge in decision-making. In this article, the strategies for resilience enhancement are carried out from the perspectives of pre-earthquake and post-earthquake. In the pre-earthquake stage, three kinds of strategies are considered: line hardening, distributed generator (DG) configuration, and line setting;in the post-earthquake stage, emergency teams are dispatched to repair failed lines, the distributed generators are started, and the contact lines are switched, according to the strategy taken before the disaster and the post-earthquake failure scenario. The moment-based ambiguity set of line failure is established, and a two-stage distributionally robust optimization model is put forth to find the optimal decision. The column-and-constraint generation algorithm is used to solve the two-stage problem. The results show that it is essential to install the tie line with a line switch to enhance the resilience of PDNs.

关键词： resilience power distribution network restoration column-and-constraint generation algorithm

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Emergency reserve constrained optimal allocation of energy storage in a novel honeycomb-like microgrid cluster with volatile renewable energy resources

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IET generation TRANSMISSION & DISTRIBUTION 2022年第2期16卷 305-318页

作者： Zhu, Naixuan Hu, Pengfei Liu, Siqi Jiang, Daozhuo Liang, Yiqiao Li, Zhiyi Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China Zhejiang Univ City Coll Sch Informat & Elect Engn Hangzhou Zhejiang Peoples R China

With the increasing penetration of large-scale distributed renewable energies, the electricity distribution network is growing more complex with challenges brought by the intermittency and uncertainty of renewable energies. Microgrid (MG), one of feasible solutions to integrating renewable energies, has shortages because of limited capacity. Therefore, MG cluster (MGC) was proposed as an improved solution. To efficiently and friendly integrate renewable energies, a novel honeycomb-like MG cluster (H-MGC) is proposed in this paper. Considering the uncertainty of renewable energies, a robust optimisation method of the siting and sizing of energy storage system (ESS) constrained by emergency reserve is proposed. Combining the column-and-constraint generation algorithm and big-M method, the proposed optimisation model is decomposed into mixed integer second-order cone programming master problem and sub-problems, which are alternately solved. Based on the optimal results of study case, the siting and sizing results of ESS are analysed, as well as the operating characteristics of H-MGC. Compared to existing MGC system, the proposed H-MGC has a more flexible operation mode. The related costs of ESS are reduced, and the operational life is relatively extended, under the condition that the emergency reserve of system is satisfied.

关键词： mixed integer second-order cone programming master problem distributed power generation honeycomb-like MG cluster renewable energy sources electricity distribution network integrating renewable energies honeycomb structures emergency reserve constrained optimal allocation column-and-constraint generation algorithm integer programming volatile renewable energy resources MG cluster energy storage large-scale distributed renewable energies microgrid honeycomb-like microgrid cluster energy storage system big-M method H-MGC power distribution reliability

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