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two-stage robust optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage hybrid energy system

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FRONTIERS IN ENERGY RESEARCH 2023年 11卷

作者： Zhou, Hong Lu, Liang Shen, Li Zhang, Peng Wen, Yiyu Jiang, Hongyu Yang, Shiyou Southwest Branch SGCC Dev Planning Dept Chengdu Peoples R China Zhejiang Univ Coll Elect Engn Hangzhou Peoples R China

The hybrid energy system of hydro-powers, pumped storages and renewable energies has become a new topic direction in modern power system developments. Consequently, it is essential to realize a rational and efficient allocation of different energy source capacities. Nevertheless, there is still a gap between the available studies and the requirement for further hybrid energy system development. This paper focuses on the optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage power system. In this direction, a bi-level programming model for the optimal capacity configuration of wind, photovoltaic, hydropower, pumped storage power system is derived. To model the operating mode of a pumped storage power station, two 0-1 variables are introduced. To handle the nonlinear and nonconvex lower level programing problem caused by the two 0-1 variables, it is proposed that the 0-1 variables are treated as some uncertain parameters. Also, by treating the 0-1 variables as some uncertain parameters, a two-stage robust optimization problem to decompose the original bi-level programing one into a master problem and a subproblem is finally introduced. The Karush-Kuhn-Tucker (KKT) conditions are then applied to simplify and linearize the min-max problem and nonlinear terms in the master problem. This results in both the master problem and the subproblem being formulated as mixed integer linear programming (MILP) problems. By utilizing the powerful Column-and-Constraint Generation (C&CG) algorithm, the two-stage robust optimization model is decomposed into an iterative procedure of solving the master problem and the subproblem sequentially. This approach eliminates the need for intricate optimization algorithms as commonly used in existing bi-level planning problems in hybrid energy systems. Finally, the effectiveness and advantages of the proposed model is verified by the numerical results on a case study.

关键词： hybrid energy system two-stage robust optimization C&CG algorithm capacity configuration pumped storage station

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A robust planning model for offshore microgrid considering tidal power and desalination

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APPLIED ENERGY 2023年第1期350卷

作者： Wang, Zhimeng Xuan, Ang Shen, Xinwei Du, Yunfei Sun, Hongbin Tsinghua Univ Tsinghua Shenzhen Int Grad Sch SIGS Shenzhen 518055 Peoples R China Taiyuan Univ Technol Taiyuan 030002 Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

Increasing attention has been paid to resources on islands, thus microgrids on islands need to be invested. Different from onshore microgrids, offshore microgrids (OM) are usually abundant in ocean renewable energy (ORE), such as offshore wind, tidal power generation (TPG), etc. Moreover, some special loads such as seawater desalination unit (SDU) should be included. In this sense, this paper proposes a planning method for OM to minimize the investment cost while the ORE's fluctuation could be accommodated with robustness. First, a deterministic planning model (DPM) is formulated for the OM with TPG and SDU. A robust planning model (RPM) is then developed considering the uncertainties from both TPG and load demand. The Column-and constraint generation (C&CG) algorithm is then employed to solve the RPM, producing planning results for the OM that is robust against the worst scenario. Results of the case studies show that the investment and operation decisions of the proposed model are robust, and TPG shows good complementarity with the other RESs.

关键词： Offshore microgrid planning Column-and-constraint generation algorithm two-stage robust optimization Tidal power Seawater desalination

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Distributed robust operation of integrated energy system considering gas inertia and biogas-wind renewables

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2023年第1期151卷

作者： Chen, Feixiong Chen, Yuchao Deng, Hongjie Lin, Weihui Shao, Zhenguo Fuzhou Univ Coll Elect Engn & Automat Fujian Smart Elect Engn Technol Res Ctr Fuzhou 350108 Peoples R China Guangzhou Power Supply Bur Co Ltd Guangzhou 510620 Peoples R China

Multiple uncertainties caused by renewable energy and loads bring challenges to the secure operation of integrated energy system (IES). Concurrently, the centralized control methods based on global information of IES cannot preserve the data privacy of each individual subsystem. To deal with these issues, this paper proposes a distributed two-stage robust optimization (TRO) scheduling strategy for IES considering gas inertia and biogas-wind renewables. To address the uncertainties of wind turbines output and electricity loads in IES, a TRO model is first established, and the column and constraint generation (C&CG) algorithm is employed to handle the min-max-min problem of TRO model. On this basis, a distributed cooperative scheduling framework based on the consensus-based alternating direction method of multipliers (C-ADMM) for IES is developed, which requires no overall system information but only local information. Additionally, natural gas pipelines that consider gas inertia are used as gas storage facilities, which provides IES with additional scheduling resources and flexibility. Furthermore, an adaptive step-size strategy is proposed to adjust the step-size of ADMM in real time, which reduces the dependence of ADMM performance on the initial parameters selection and improves its convergence performance. The simulation results in a three-subsystem joint IES are presented to demonstrate the effectiveness of the proposed distributed TRO scheduling strategy.

关键词： Integrated energy system Biogas-wind renewable Natural gas inertia Distributed scheduling method two-stage robust optimization

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robustly Coordinated Distributed Voltage Control Through Residential Demand Response Under Multiple Uncertainties

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2021年第4期57卷 4042-4058页

作者： Sharma, Sumedha Verma, Ashu Panigrahi, B. K. Indian Inst Technol Delhi Ctr Energy Studies New Delhi 110016 India Indian Inst Technol Delhi Dept Elect Engn New Delhi 110016 India

This article proposes a multilevel coordinated voltage control (CVC) strategy for facilitating distributed residential demand response for network voltage optimization. The proposed CVC scheme coordinates multiple home energy management systems (HEMS) connected on a low-voltage radial distribution network through a sensitivity-based approach to minimize voltage deviations in multiple timescales owing to high photovoltaic (PV) penetrations and load variability. In order to mitigate the effects of uncertain PV output and load during actual system operation, a day-ahead two-stage robust optimization (TSRO) model has been developed, which optimizes network operation in the longer timescale, for worst-case realization of uncertainties in shorter timescales. This is sequentially followed by fully distributed hour-ahead CVC which is decomposed into network optimization and energy management subproblems through alternating direction method of multipliers. In order to counteract the effects of real-time uncertainties, local adjustments are performed by redispatching HEMS at individual households to locally adapt to unforeseen variations, thereby minimizing real-time voltage deviations. Extensive simulations are performed on the modified Dutch LV network. Simulation results demonstrate effectiveness of the proposed multilevel CVC approach to robustly handle uncertainties while ensuring reliable operation and maximum user-comfort.

关键词： Voltage control optimization Uncertainty Real-time systems Inverters Load modeling Load management Alternating direction method of multipliers demand response home energy management sensitivity analysis two-stage robust optimization voltage control

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An adjustable Predictive&Prescriptive method for the RO-based optimal power flow problem

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HELIYON 2023年第10期9卷 e20290页

作者： Zheng, Liqin Bai, Xiaoqing Shi, Xiaoqing Li, Yunyi Xie, Dongmei Wei, Chun Guangxi Univ Coll Elect Engn Guangxi Key Lab Power Syst Optimizat & Energy Tech Nanning 530004 Peoples R China State Grid Xiamen Elect Power Supply Co Xiamen 361004 Peoples R China Zhejiang Univ Technol Zhejiang 310014 Peoples R China

Traditionally before solving the optimal power flow considering uncertainty (OPF-U) problem, the predicted value of uncertainty parameters, such as wind power, e.g., is derived from data using a statistics approach or machine learning. Based on the predicted uncertainty parameters, the solution to the OPF-U problem can be obtained by the prescriptive analytics technique, such as robust optimization (RO). However, it is unclarified how the prediction error in predictive analytics affects solving the OPF-U problem in prescriptive analytics. We propose an adjustable framework method combining machine learning and RO for the OPF-U problem. The k-nearest neighbor is applied to obtain k samples around the predicted value from sufficient historical data. And the optimization results from a minimum volume ellipsoid set containing the k samples are applied to construct KMV set. Then a robust fluctuation region with an adjustable budget level is gained from the KMV set by a two-term exponential formula, which can be embedded into a twostage RO model. Computational experiments under test cases of different uncertainty scales show the robustness and adjustability of the proposed fluctuation region are better than the state-ofthe-art box and ellipsoidal sets. The solution of the proposed two-stage RO model is more economical than the state-of-the-art RO model. The out-of-sample simulation also demonstrates the proposed adjustable Predictive&Prescriptive method can reduce the computational burden as the scale of the system increases when predictive and prescriptive analytics are separated.

关键词： Machine learning two-stage robust optimization Uncertain fluctuation region Optimal power flow

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Data-driven robust optimization for energy and reserve scheduling considering multi-uncertainty

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International Journal of Electrical Power & Energy Systems 2025年 169卷

作者： Zuqing Zheng Guo Chen Zixiang Shen Zhaoyang Dong School of Automation Central South University Changsha 410083 China School of Electrical Engineering and Telecommunications The University of New South Wales Sydney NSW 2052 Australia Department of Electrical Engineering City University of Hong Kong Kowloon Hong Kong

The intermittency of renewable energy sources and unscheduled outages threaten power system security, increasing the need for operational flexibility. This paper addresses the energy and reserve scheduling problem under photovoltaic power output uncertainty and N-k transmission line security criteria by proposing a data-driven two-stage robust optimization model. The first stage involves day-ahead scheduling for energy and reserve, while the second stage minimizes re-scheduling cost under the worst-case scenario. The model is decomposed into a master problem and a subproblem, using the column-and-constraint generation method for alternating solutions. A data-driven method constructs an interval-partitioned uncertainty set, effectively capturing the characteristics of photovoltaic power output uncertainty while balancing robustness and economy. The model also integrates generator, energy storage and both price-based and incentive-based demand response strategies to enhance reserve capacity, improving risk mitigation. Simulation results confirm the model’s feasibility and effectiveness for reliable and economical operation.

关键词： Data-driven method Energy and reserve scheduling two-stage robust optimization Photovoltaic power uncertainty N-k security criteria

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robustly Coordinated Distributed Voltage Control Through Residential Demand Response Under Multiple Uncertainties

Robustly Coordinated Distributed Voltage Control Through Res...

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19th IEEE International Conference on Environment and Electrical Engineering (EEEIC) / 3rd IEEE Industrial and Commercial Power Systems Europe Conference (I and CPS Europe)

作者： Sharma, Sumedha Verma, Ashu Panigrahi, B. K. Indian Inst Technol Delhi Ctr Energy Studies New Delhi 110016 India Indian Inst Technol Delhi Dept Elect Engn New Delhi 110016 India

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A robust optimization approach for the winner determination problem with uncertainty on shipment volumes and carriers' capacity

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2019年第May期123卷 127-148页

作者： Remli, Nabila Amrouss, Amine El Hallaoui, Issmail Rekik, Monia HEC Montreal Grp Res Decis Anal GERAD 3000 Ch Cote St Catherine Montreal PQ H3T 2A7 Canada Polytech Montreal Dept Appl Math & Ind Engn CP 6079Succ Ctr Ville Montreal PQ H3C 3A7 Canada Laval Univ Dept Operat & Decis Syst 2325 Rue Terrasse Laval PQ G1V 0A6 Canada Interuniv Res Ctr Enterprise Networks Logist & Tr Montreal PQ Canada

This paper addresses the winner determination problem (WDP) for TL transportation procurement auctions under uncertain shipment volumes and uncertain carriers' capacity. It extends an existing two-stage robust formulation proposed for the WDP with uncertain shipment volumes. The paper identifies and theoretically validates a number of accelerating strategies to speed up the convergence of a basic constraint generation algorithm proposed in the literature. Experimental results prove the high computational performance of the proposed new algorithm and the relevance of considering uncertainty on the carriers' capacity when solving the WDP. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Winner determination problem TL services Combinatorial auctions Uncertain shipment volumes Uncertain carriers' capacity two-stage robust optimization Constraint generation

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Optimal coordination of zero carbon building energy systems

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National Science Open 2024年第3期3卷 13-28页

作者： Wangyi Guo Zhanbo Xu Jinhui Liu Yaping Liu Jiang Wu Kun Liu Xiaohong Guan School of Future Technology Xi'an Jiaotong UniversityXi'an 710049China Ministry of Education Key Lab for Intelligent Networks and Network Security School of Automation Science and EngineeringXi'an Jiaotong UniversityXi'an 710049China Center for Intelligent and Networked Systems Department of AutomationTNLISTTsinghua UniversityBeijing 100084China

Optimal scheduling of renewable energy sources and building energy systems serves as a pivotal strategy for achieving zero carbon ***,the coordination of zero carbon building energy systems(ZCBS)is still challenging due to the complicated interactions among multi-energy hybrid storage and the complex coordination between seasonal and daily ***,this study develops a coordination scheduling approach for *** operation model and a seasonal-daily scheduling approach are developed to optimize the operation of hydrogen,geothermal,and water storage *** performance of the developed method is demonstrated using numerical case *** results show that the ZCBS can be achieved by using renewable energy sources with the system flexibility provided by hydrogen,geothermal,and water storage *** is also found that the developed scheduling approach reduces operation costs by more than 43.4%under the same device capacity,compared with existing scheduling approaches.

关键词： zero carbon building energy systems seasonal-daily scheduling multi-energy storage two-stage robust optimization

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two-stage robust Economic Dispatch of Regional Integrated Energy System Considering Source-Load Uncertainty Based on Carbon Neutral Vision

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ENERGIES 2022年第4期15卷 1596页

作者： Gao, Jianwei Yang, Yu Gao, Fangjie Wu, Haoyu North China Elect Power Univ Sch Econ & Management Beijing 102206 Peoples R China North China Elect Power Univ Beijing Key Lab New Energy & Low Carbon Dev Beijing 102206 Peoples R China

A regional integrated energy system is an important carrier of the energy Internet. It is a major challenge for the operation of a regional integrated energy system to deal with the uncertainty of distributed energy and multiple loads by using the coupling characteristics of equipment in a regional integrated energy system. In this paper, a two-stage robust economic dispatch model of a regional integrated energy system is proposed considering the source-load uncertainty. Firstly, the basic architecture of the regional integrated energy system is introduced. Based on the extreme scenario of uncertain power supply and load, the uncertainty set was established, the two-stage robust optimization model of regional integrated energy system was constructed and the column-and-constraint generation algorithm was used to solve the model. The effectiveness of the two-stage robust optimization model in improving the economy and robustness of the system was analyzed.

关键词： regional integrated energy system two-stage robust optimization column-and-constraint generation economic dispatch source-load uncertainty

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