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two-stage robust optimization of a virtual power plant considering a refined demand response

ENERGY 2025年 322卷

作者： Liu, Jinpeng Peng, Jinchun Liu, Hushihan Deng, Jiaming Song, Xiaohua North China Elect Power Univ Sch Econ & Management Beijing 102206 Peoples R China

A reasonable demand response strategy and flexible resource planning technology are the key methods for constructing new power systems. Based on this, a virtual power plant economic optimization model considering a refined demand response strategy is proposed. First, considering the regulatory characteristics of flexible loads and the satisfaction degree of residents, flexible loads are finely classified, and a demand response model is constructed. Second, considering the power uncertainty of wind turbines and photovoltaics in virtual power plants, a two-stage robust optimization model with a min-max-min structure is constructed;then, a transformation method of fuzzy sets and subproblems is proposed to improve the solution efficiency. Finally, the total operating cost of virtual power plants under the deviation of power forecasts and fluctuations in intraday electricity prices is analysed. The simulation results reveal that refined load classification can reduce the system day-ahead operating cost by 7.12 %;the proposed two-stage robust optimization model reduces the total real time operating cost by 0.81-6.39 % compared to the deterministic optimization model.

关键词： Virtual power plants Demand response two-stage robust optimization Economic scheduling

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two-stage robust optimization of hydrogen microgrid in plateau tourist cities -taking Yunnan Lijiang as an example

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CARBON NEUTRALITY 2025年第1期4卷 1-21页

作者： Xu, Ran Hong, Zhanghua Wang, Guohua Zhu, Tao Li, Dongfang Li, Zhishan Zhang, Liang Zhu, Xing Kunming Univ Sci & Technol Fac Met & Energy Engn Kunming 650093 Peoples R China China Three Gorges Corp Yunnan Energy Investment C Kunming 650051 Peoples R China

Hydrogen energy, as a vital supplement to renewable energy, contributes significantly to the system's energy storage benefits. In this work, we build and optimize a hydrogen energy microgrid for the plateau tourist city of Lijiang, taking into account the city's unique geographic and climatic circumstances, with the goal of investigating the potential role of hydrogen energy in the regional energy structure and its economics. The study uses a two-stage robust optimization method to change the microgrid's configuration and operation strategy. The system uses a set of alkaline (ALK) electrolyzers, prioritizes wind turbine (WT) and photovoltaic (PV) production, as well as considers three hydrogen use pathways: hydrogen peaking, hydrogen transportation (HEV), hydrogen sales. The oxygen produced by the P2G technology can be used to refill portable oxygen cylinders, which will provide additional cash for highland attractions. The performance of this microgrid system was experimentally evaluated under different operating scenarios through simulation. The results show that the system is able to meet the daily power demand of about 920 residents in the ancient city area, supply 16 hydrogen-energy buses in a single day, and provide 694 kg oxygen. Furthermore, the single-day operational cost analysis reveals that using hydrogen energy saves the microgrid 25.72% in running expenses compared to a traditional microgrid. The use of data-driven uncertainty sets reduces operating costs by 20.82% compared to standard microgrids. This paper presents an innovative hydrogen microgrid design strategy for highland tourist communities, proving the benefits of hydrogen energy in facilitating a regional low-carbon transition.

关键词： Microgrid Hydrogen Flexibility Data-driven two-stage robust optimization

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two-stage robust optimization of unified power quality conditioner (UPQC) siting and sizing in active distribution networks considering uncertainty of loads and renewable generators

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RENEWABLE ENERGY 2024年 224卷

作者： Zhu, Xiaoguang Guo, Yubo Li, Ao Li, Shurong Zhang, Juning Gu, Borui Deng, Junbo Xi An Jiao Tong Univ Sch Elect Engn State Key Lab Elect Insulat & Power Equipment Xian 710049 Peoples R China Tsinghua Univ Sichuan Energy Internet Res Inst Chengdu 610299 Peoples R China

This paper proposes a robust optimization siting and sizing strategy for the unified power quality conditioner (UPQC) in the active distribution network (ADN) integrated with renewable energy generators. The optimization objectives including investment cost, line loss, and voltage deviation are integrated into an overall cost for both the planning and operating stages. A novel UPQC equivalent power injection model is proposed based on the auxiliary branch method. A set of linear and second-order conic (SOC) constraints are employed to accurately describe the steady -state operation of UPQC. An improved branch current flow model is developed to incorporate radial distribution networks with UPQCs. The UPQC siting and sizing planning is formulated as a mixed integer second-order conic programming (MISOCP) problem. Accounting for the uncertainty in loads and distributed generators, a two-stage robust optimization model is established to address worst-case operational scenarios. A solving strategy is developed based on the strong duality theory and the column-and-constraint generation (C&CG) algorithm, and then commercial solvers can solve the problem accurately and efficiently. Case studies on an IEEE 33 -node distribution network demonstrate this strategy's robustness in dealing with loads and renewable energy uncertainties, making it applicable across different UPQC topologies and operation modes. The proposed method has superior performance over the representative meta-heuristic approaches in terms of global optimality as well as an over 7.5 times faster computation speed. This work has significance in enhancing the quality and efficiency of modern power systems highly integrated with renewable energy.

关键词： Unified power quality conditioner (UPQC) Renewable energy Siting and sizing allocation two-stage robust optimization Mixed integer second-order conic programming

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two-stage robust optimization Model for Capacity Configuration of Biogas-Solar-Wind Integrated Energy System

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2023年第1期59卷 662-675页

作者： Li, Xiaoqing Zhang, Lizhi Wang, Ruiqi Sun, Bo Xie, Weijian Shandong Univ Sch Control Sci & Engn Jinan 250061 Peoples R China State Grid Tianjin Elect Power Co Chengxi Power Supply Branch Tianjin 300190 Peoples R China State Grid Shandong Integrated Energy Serv CO LTD Jinan 250001 Peoples R China

Biogas-solar-wind integrated energy systems are effective for optimizing rural energy consumption and improving agricultural production. The performance of an integrated energy system generally depends on its capacity configuration. However, the uncertainties of renewable energy sources and loads deepen the coupling relationship between the capacity configuration and energy dispatching of integrated energy systems, which makes optimizing the capacity difficult. We propose a two-stage robust optimization model for the capacity configuration of a biogas-solar-wind integrated energy system that is applicable to rural areas. First, a framework of the biogas-solar-wind integrated energy system was designed and diverse evaluation indices were introduced. Then, the integrated energy system model was transformed into a two-stage robust optimization problem, where the column-and-constraint generation algorithm is used to solve the installed capacity problem of the system equipment in the first stage, and the nested column-and-constraint generation algorithm is used to optimize the energy dispatching schedule in the second stage. Finally, the proposed model was applied to a rural area in China to confirm the rationality and effectiveness of the optimization results.

关键词： Resistance heating Uncertainty Wind turbines Heat recovery optimization Costs Load modeling Capacity configuration integrated energy system nested column-and-constraint generation algorithm two-stage robust optimization

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two-stage robust optimization Method for Joint System Considering Uncertainty of Electric Vehicles 8

Two-Stage Robust Optimization Method for Joint System Consid...

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8th International Conference on Power Energy Systems and Applications, ICoPESA 2024

作者： Ma, Ying Chen, Yu Liao, Xiaozhong Liu, Bin Liu, Ruyi Li, Zhen School of Automation Beijing Institute of Technology Beijing China Beijing China School of Mathematics and Statistics University of Sydney Sydney Australia

ISBN: (纸本)9798350351668

To conduct the green and low-carbon development, renewable energy needs to play more vigorous role in power generation. Through the cooperative regulation and participation in the spot market, renewable energy, energy storage and electric vehicles (EVs) jointly participate in the regulation so as to improve energy efficiency and increase the penetration of renewable energy. In this paper, a two-stage robust optimization model is established considering the uncertainty of EVs' number. The first and second stages determine the bidding plans of such joint system in the day-ahead and real-time markets respectively, so as to minimize the cost. The associated optimization can provide the robust and economical results. Importantly, the modeling in perspective of uncertainty is applied to EVs participating in spot markets in an aggregated manner. To solve this model, an improved column-and-constraint generation (C&CG) algorithm is proposed, which is solved by combination of genetic algorithm and solver. The test results verify the effectiveness of the model and method proposed in this paper. © 2024 IEEE.

关键词： electric vehicles energy storage renewable energy two-stage robust optimization uncertainty

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An Extended C&CG Algorithm for Solving two-stage robust optimization of Economic and Feasible Scheduling

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JOURNAL OF optimization THEORY AND APPLICATIONS 2025年第2期205卷 1-29页

作者： Chen, Ruibin Bao, Zhejing Lu, Lingxia Yu, Miao Zhejiang Univ Hangzhou Peoples R China

The extensively researched column-and-constraint-generation (C&CG) algorithm, which utilizes the KKT (Karush-Kuhn-Tucker) condition or duality theory to reformulate the subproblem, encounters challenges when solving two-stage robust optimization (TSRO) problems with extreme parameters that could adversely affect the feasibility of the second-stage decision. After the analysis of the original C&CG algorithm, an extended C&CG algorithm with multiple subproblems is proposed to overcome the challenges, which decompose a TSRO model into the master problem and several subproblems searching for the worst-case scenarios. A simple linear case is given to show the shortcoming of the traditional C&CG algorithm and the advantage of the extended C&CG algorithm. Then, a TSRO model for the scheduling optimization of electricity system considering the optimal power flow (OPF) is proposed, in order to explore the effectiveness of the extended C&CG algorithm in handling the general optimization problem while considering the feasibility. Finally, the proposed solving method is validated by case studies.

关键词： Column and constraint generation two-stage robust optimization Feasibility check epsilon-Constraint method

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Optimizing flexibility and low-carbon emissions in integrated energy systems: A two-stage robust optimization model incorporating hydrogen and carbon trading

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ENERGY REPORTS 2025年 13卷 1620-1631页

作者： Wang, Limeng Dong, Wenkai Wang, Shuo Shen, Haonan Zhao, Zhenhao Wang, Jinyue Northeast Elect Power Univ Key Lab Modern Power Syst Simulat & Control & Rene Minist Educ Jilin 132012 Peoples R China

Source-load output uncertainty poses significant risks to the stable operation of Integrated Energy Systems (IESs). To ensure safe and stable system operation while optimizing the balance among robustness, economic viability, and low-carbon emissions, this paper presents a two-stage robust optimal scheduling model for IESs. This model is supported by hydrogen-containing electric dual-energy conversion characteristics under source-load uncertainty. Additionally, to promote the low-carbon characteristics of the system, a ladder carbon trading mechanism is introduced on the source side of the carbon source equipment. Furthermore, the integration of hydrogen energy enhances the clean characteristics of source-side multi-energy coupling. The proposed utilization mode, Power-to-Hydrogen, Hydrogen-to-Power, Hydrogen Energy Storage, and Hydrogen Load (P2H-H2P-HES-HL), allows for bidirectional conversion, thereby increasing the flexibility and responsiveness of overall system scheduling. Finally, to ensure that the model closely reflects actual operational and scheduling conditions, a twophase robust approach is employed to address source-load uncertainties. This approach is solved iteratively using the linear transformation of the Karush-Kuhn-Tucker (KKT) conditions and the Column-and-Constraint Generation (C&CG) algorithm. The results demonstrate that the proposed model significantly enhances the scheduling capability of the system in coping with uncertainty, thereby effectively ensuring its flexibility and security.

关键词： Uncertainty two-stage robust optimization Integrated energy system Hydrogen utilization Carbon trading mechanism

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Multi-objective two-stage robust optimization of wind/PV/thermal power system based on meta multi-agent reinforcement learning

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 162卷

作者： Li, Dengao Zhang, Zhuokai Feng, Ding Zhou, Yu Yu Bai, Xiaodong Zhao, Jumin Shanxi Energy Internet Res Inst Taiyuan 030000 Shanxi Peoples R China Taiyuan Univ Technol Coll Comp Sci & Technol Taiyuan 030024 Shanxi Peoples R China Taiyuan Univ Technol Coll Data Sci Taiyuan 030024 Shanxi Peoples R China Key Lab Big Data Fus Anal & Applicat Shanxi Prov Taiyuan 030024 Shanxi Peoples R China Taiyuan Normal Univ Coll Comp Sci & Technol Taiyuan 030619 Shanxi Peoples R China

The integration of renewable energy into the power grid poses significant challenges for optimization and scheduling of the power system. In recent years, methods based on deep reinforcement learning have surpassed traditional methods on the high complexity and long-term decision-making of power system optimization and scheduling. However, faced with the inherent uncertainty of renewable energy generation and the different optimization objectives in power system, the deep reinforcement learning methods are unable to effectively address them. This paper proposes a method that combines meta reinforcement learning with multi-agent reinforcement learning to solve the multi-objective two-stage robust optimization of wind/PV/thermal power system. We conducts optimization and scheduling experiments on the IEEE39 bus system. The results indicate that our method not only enhances the robustness of the scheduling strategy, but also outperforms baseline methods in terms of convergence, diversity, and uniformity of the Pareto frontier.

关键词： Renewable energy Multi-objective optimization two-stage robust optimization Meta reinforcement learning Multi-agent reinforcement learning

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Uncertain parameters adjustable two-stage robust optimization of a rural housing integrated energy system considering biomass on-site utilization

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ENERGY 2024年 296卷

作者： Han, Fengwu Zhao, Yunlong Zeng, Jianfeng Zhang, Shengnan Wu, Tianyu North China Elect Power Univ Dept Econ & Management Baoding 071003 Hebei Province Peoples R China

Rural areas will be an important component to achieve carbon neutrality. However, there are currently issues such as an unreasonable energy consumption structure and low efficiency in renewable energy utilization. It is urgent to propose an energy optimization solution to address these problems. Therefore, considering the advantages of renewable energy in rural areas and the diversified and decentralized energy consumption patterns of rural households, a rural housing integrated energy system (RHIES) is proposed, which includes photovoltaics and a biomass utilization chain through self -production and local consumption. Subsequently, considering the economic and low -carbon aspects of the system ' s operational process, an uncertain parameters adjustable twostage robust optimization model (UPATSRO) is developed to achieve a balance between robustness and economic efficiency during the scheduling optimization process. The results of case study indicate that the proposed RHIES reduces costs and carbon emissions by 28.15% and 93.83%, respectively, compared to conventional approaches. The biomass utilization mode satisfies 52.31% of the gas load and 39.71% of the thermal load for households. Additionally, it is shown that the proposed UPATSRO optimization model can achieve a flexible adjustment of scheduling schemes during the scheduling optimization process.

关键词： Rural housing integrated energy system Biomass on-site utilization mode Carbon emissions two-stage robust optimization Uncertainty parameters adjustment

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A two-stage robust optimization model for emergency service facilities location-allocation problem under demand uncertainty and sustainable development

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SCIENTIFIC REPORTS 2025年第1期15卷 1-18页

作者： Li, Hongyan Yu, Dongmei Zhang, Yiming Yuan, Yifei Liaoning Tech Univ Ordos Inst Ordos 017004 Peoples R China Liaoning Tech Univ Sch Business Adm Huludao 125105 Peoples R China Liaoning Tech Univ Inst Optimizat & Decis Analyt Fuxin 123000 Peoples R China

Under the backdrop of frequent emergencies, the rational layout of emergency service facilities (ESF) and the effective allocation of emergency supplies have emerged as crucial in determining the timeliness of post-disaster response. By adequately accounting for potential uncertainties and carrying out comprehensive pre-planning, the robustness of location-allocation decisions can be significantly improved. This paper delves into the ESF network design problem under demand uncertainty and formulates this problem as a two-stage robust optimization model. The presented model defines a generalized budget uncertainty set to capture victims' uncertain demand and minimizes the sum of the costs involved in the two stages. The objective function integrates the input cost in the preparedness phase, the deprivation cost from the victims' perspective and the environmental impact cost responding to sustainable development in the response phase, which respectively correspond to the comprehensive optimization of the deployment of ESF, the distribution of emergency supplies and the implementation of sustainable measures. Subsequently, we employ the column and constraint generation (C&CG) algorithm to solve the proposed model and take the COVID-19 epidemic in Wuhan as a case to verify the effectiveness of the model and algorithm. Finally, we examine the influence of demand uncertainty and environmental impact cost on the optimal solution, yielding valuable managerial insights.

关键词： Emergency service facilities Location-allocation two-stage robust optimization Demand uncertainty Sustainable development

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