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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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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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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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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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two-stage robust optimization for Resilient Operation of Microgrids Considering Hierarchical Frequency Control Structure

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2020年第11期67卷 9439-9449页

作者： Mohiti, Maryam Monsef, Hassan Anvari-Moghaddam, Amjad Lesani, Hamid Univ Tehran Dept Elect & Comp Engn Tehran *** Iran Aalborg Univ Dept Energy Technol DK-9100 Aalborg Denmark

Following a major outage in the main grid due to natural disasters, microgrids (MGs) have the ability to disconnect from the main grid and provide electricity to their consumers. However, integration of power electronic-based generation units and small-scale energy resources into MGs reduces the system inertia. Therefore, frequency deviations arising from the loss of grid power or fluctuations of renewable energy resources and loads should be managed. In this article, a two-stage robust day-ahead optimization model for resilient operation of MGs is proposed in which the hierarchical frequency control structure of the MG is precisely formulated. Based on this model, the operation cost of MG is minimized while sufficient primary and secondary reserves are scheduled to restrict frequency deviations and avoid load shedding under the worst-case realization of islanding events. A column-and-constraint generation algorithm is utilized to efficiently solve the problem. Numerical cases on a test system show the effectiveness of the proposed model and the solution algorithm. The obtained results verify that by applying the proposed model, the operating cost of MG is minimized while the frequency deviation and load shedding can be successfully managed during islanding events.

关键词： Frequency control Resilience robustness Load modeling Voltage control optimization Microgrids Frequency control microgrid (MG) optimal operation resilient microgrid two-stage robust optimization uncertainty

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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 for expansion planning of active distribution systems coupled with urban transportation networks

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APPLIED ENERGY 2020年第0期261卷 114412-000页

作者： Xie, Shiwei Hu, Zhijian Wang, Jueying Wuhan Univ Sch Elect Engn & Automat Wuhan Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore

Widespread utilization of electric vehicles has incurred more uncertainties and led to profound inter-dependencies across the power grid and transportation network. This creates an urgent demand for uncertainty modelling tools. Under this context, this paper proposes a two-stage robust optimization model for expansion planning of coupled active distribution and transportation. This model identifies the best type, location and capacity for roads, distribution lines, distributed generations, static VAR compensators, on-load tap changers, energy storage systems and charging facilities. From a system-level perspective, the steady-state pattern of the traffic flow in a transportation network is characterized by the Wardrop user equilibrium. In the active distribution system, the conic relaxation-based branch flow equations are employed, and the operating status of related devices are formulated by the linearized convex constraints. Considering the interdependency between two coupled systems, a deterministic expansion planning model is first established. Furthermore, with multiple uncertainties considered, a two-stage robust optimization model is proposed to optimize the investment and operation strategies coordinately, and thus a robust optimal solution is achieved. A two-level algorithm based on a combination of the column-and-constraint generation and outer approximation technique is developed for solving the two-stage model. The results demonstrate that the robust approach can effectively reduce the operation cost of coupled systems under the worst-case scenarios. Moreover, a comparative analysis indicates that operation costs in both systems increase linearly as the uncertainty level of traffic demand increases, while increasing that of the power load does not show an obvious change in the traffic operation cost.

关键词： Active distribution system Transportation network two-stage robust optimization Uncertain renewable energies Electric vehicle

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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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