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DER-Inverter Based Reactive Power Ancillary Service for Supporting Peer-to-Peer Transactive Energy Trading in Distribution Networks

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IEEE TRANSACTIONS ON POWER SYSTEMS 2025年第1期40卷 753-764页

作者： Zou, Yunyang Xu, Yan Nanyang Technol Univ Ctr Power Engn CPE Sch Elect & Elect Engn Singapore 639798 Singapore

Fast proliferation of distributed energy resources (DERs) and emergence of peer-to-peer (P2P) energy trading are introducing significant operation challenges to distribution networks. This paper designs a multi-timescale reactive power ancillary service trading framework in this context. The framework consists of a contract-based day-ahead Var reserve service trading stage and an hourly-ahead Var support service trading stage. At the day-ahead stage, the distribution system operator (DSO) signs a robust Var reserve contract with inverter-interfaced DERs which have sufficient Var capacity, and the problem is formulated as a two-stage robust optimization model considering uncertain nodal loads and hourly-ahead market behaviors. As an important advantage, the robust Var reserve contract eliminates the potential market power that the DERs may gain due to system configuration deficiency and market structure flaws at the later hourly-ahead trading stage. After uncertainty realization, at the hourly-ahead stage, DERs further provide the DSO with paid hourly-ahead Var supports using their spare Var capacity. The bilateral hourly-ahead Var trading between the DSO and DERs is modelled as a non-cooperative game. To attain a generalized Nash equilibrium (GNE) of the non-cooperative game, a distributed algorithm is developed by building the connection between the GNE and the primal-dual solution of a related social cost minimization problem. The proposed framework and methods are tested on three distribution systems of different scales.

关键词： Reactive power Distributed power generation Costs Peer-to-peer computing Inverters Contracts Distribution networks Reactive power ancillary service DER inverter auction two-stage robust optimization non-cooperative game distributed algorithm

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Multi-timescale optimization scheduling of integrated energy systems oriented towards generalized energy storage services

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SCIENTIFIC REPORTS 2025年第1期15卷 1-20页

作者： Mao, Yunshou Cai, Zhihong Jiao, Xianan Long, Dafeng Huizhou Univ Sch Elect Informat & Elect Engn Huizhou 516007 Guangdong Peoples R China Huizhou Univ Guangdong Prov Key Lab Elect Funct Mat & Devices Huizhou 516007 Guangdong Peoples R China EHV Power Transmiss Co Elect Power Res Inst CSG Guangzhou 510663 Guangdong Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China

This paper addresses the limitations of existing research that focuses on single-sided resources and two-timescale optimization, overlooking the coordinated response of various energy storage resources across different timescales in comprehensive energy systems. To tackle these shortcomings, the study integrates flexible demand-side resources, such as electric vehicles (EVs), hydrogen storage, and air conditioning clusters, as generalized energy storage. It explores their impact on the operation cost of the comprehensive energy system across three stages: day-ahead, intraday, and real-time. The paper establishes an optimization scheduling model for mobile energy storage, hydrogen storage, and virtual energy storage of air conditioning clusters, considering the physical and temporal constraints of different storage devices, aiming to minimize the operational cost. The day-ahead stage employs C&CG to address the uncertainty of wind and photovoltaic power generations, while the intraday stage synergizes hydrogen storage, gas turbines, and demand-side substitutable and transferable loads to mitigate renewable energy fluctuations. The real-time stage leverages the virtual energy storage model of air conditioning clusters for rapid response to renewable energy deviations. Case studies validate the effectiveness of the model, demonstrating that multi-timescale optimization of generalized energy storage in comprehensive energy systems can significantly reduce operational costs and enhance system reliability.

关键词： Generalized energy storage two-stage robust optimization Column-and-constraint generation Integrated energy system Air conditioning virtual energy storage

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two-stage robust planning-operation co-optimization of energy hub considering precise energy storage economic model

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APPLIED ENERGY 2019年 252卷 113372-000页

作者： Chen, Cong Sun, Hongbin Shen, Xinwei Guo, Ye Guo, Qinglai Xia, Tian Tsinghua Univ Tsinghua Berkeley Shenzhen Inst Shenzhen Guangdong Peoples R China Tsinghua Univ Dept Elect Engn Beijing Peoples R China

The increasing penetration of renewable energy resources in integrated energy system makes it necessary to consider uncertainty, appropriate investment and scientific operation for energy storage systems, including battery energy storage systems and thermal energy storage systems. In this paper, we propose a two-stage robust planning-operation co-optimization method for Energy Hub considering uncertainties from renewable energy resources as well as multi-load demands, the sizing problem and precise economic model of energy storage systems, in which lifetime loss cost of battery energy storage systems and static loss of thermal energy storage systems are mainly included. Integer variables exist in both stages, thus in the proposed method, dual norms are used to transform uncertain constraints into robust counterparts with which the worst cases are calculated directly, then the problem is merged into a single stage mixed integer linear program. In case studies, optimal planning strategies including multiple storages in Energy Hub are explored under the consideration of sizing problem and uncertainties, and it's found that simultaneously constructing multiple energy storages can have mutually beneficial relationships and propose more economic planning/operation strategies. Then it's validated that precise energy storage model can better improve economics and flexibility of Energy Hub both in longer term and short term planning optimization. Meanwhile, convergence speed of the model and solution algorithm in this paper is acceptable for practical planning problem.

关键词： Energy hubs Energy storage systems two-stage robust optimization Lifetime of batteries Dual norm

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Adjustable robust optimization Reformulations of two-stage Worst-Case Regret Minimization Problems

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OPERATIONS RESEARCH 2021年第5期70卷 2906页

作者： Poursoltani, Mehran Delage, Erick HEC Montreal GERAD Montreal PQ H3T 2A7 Canada HEC Montreal Dept Decis Sci Montreal PQ H3T 2A7 Canada

This paper explores the idea that two-stage worst-case regret minimization problems with either objective or right-hand side uncertainty can be reformulated as two-stage robust optimization problems and can therefore benefit from the solution schemes and theoretical knowledge that have been developed in the last decade for this class of problems. In particular, we identify conditions under which a first-stage decision can be obtained either exactly using popular adjustable robust optimization decomposition schemes or approximately by conservatively using affine decision rules. Furthermore, we provide both numerical and theoretical evidence that, in practice, the first-stage decision obtained using affine decision rules is of high quality. Initially, this is done by establishing mild conditions under which these decisions can be proven exact, which effectively extends the space of regret minimization problems known to be solvable in polynomial time. We further evaluate both the sub-optimality and computational efficiency of this tractable approximation scheme in a multi-item newsvendor problem and a production transportation problem.

关键词： two-stage robust optimization regret minimlzation affline decision rules

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robust optimization of regional integrated energy systems considering thermal comfort and uncertainty in heat networks

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Applied Thermal Engineering 2025年 275卷

作者： Lyu, Zhilin Huang, Mingyou Liu, Bin Liu, Yudong School of Electrical Engineering Guangxi University Nanning 530000 China

Under the background of the increasing multi-energy coupling of Integrated Energy System, the coupling effect of multi-dimensional uncertainty factors will affect the user's energy use experience. Therefore, in the environment of multiple uncertainties, this paper focuses on the uncertainty of the heat network side, and constructs a robust optimization model of the electric-heat-gas integrated energy system considering thermal comfort. Firstly, multiple uncertainty sets are constructed for multiple uncertainties such as renewable energy, heat load, district heating pipeline parameters, environmental temperature and temperature gain, and uncertain budget values are introduced to adjust the conservative degree of scheduling decisions. Secondly, the factors affecting the user's thermal comfort are developed, and the thermal comfort control strategy is proposed to ensure the user's thermal experience under uncertain environment. Finally, a two-stage robust optimization model of regional integrated energy system under various uncertainties is established by modeling and analyzing the electrical, thermal and gas networks and coupling models. The model is solved based on duality theory and the Column and Constraint Generation algorithm. The integrated energy system of 39-node power system, 20-node gas supply system and 6-node heating system is taken as a simulation example. The results show that the model and solving algorithm can effectively realize the coordinated optimization of various heterogeneous energy flows under multi-dimensional uncertain environment, while taking into account the robustness and economy, and ensure the thermal comfort of users. © 2025 Elsevier Ltd

关键词： Regional integrated energy systems Thermal comfort control two-stage robust optimization Uncertainty in heat networks

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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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Γ-robust optimization of project scheduling problems

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COMPUTERS & OPERATIONS RESEARCH 2024年 161卷

作者： Koster, Arie M. C. A. Segschneider, Jenny Ventsch, Nicole Rhein Westfal TH Aachen Res Area Discrete Optimizat Pontdriesch 10-12 D-52056 Aachen Germany

In this paper, we investigate the problem of finding a robust baseline schedule for the project scheduling problem under uncertain process times. We assume that the probability distribution for the duration is unknown, but an estimate is given along with an interval in which this time can vary. At most Gamma of the tasks will deviate from the estimated time. We present two approaches to solving this problem. The first approach treats the problem of determining the earliest guaranteed finish times and can be solved in polynomial time by an extension of the critical path method. The second is a two-stage approach that determines the baseline schedule in the first stage and an adaptation to the scenario in the second stage. We show strong NP-hardness of the second stage problem and introduce a novel formulation. From this formulation we derive an exact algorithm and three heuristics. A computational study on benchmark instances shows that the heuristics perform well on larger instances.

关键词： robust project scheduling Budgeted uncertainty two-stage robust optimization Heuristics Mixed-integer programming

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An interval-prediction based robust optimization approach for energy-hub operation scheduling considering flexible ramping products

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ENERGY 2020年第0期194卷 116821-000页

作者： Zhu, Xi Zeng, Bo Dong, Houqi Liu, Jiaomin North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China

The energy-hub (EH) technique provides a new-type conceptual framework for the interaction, coupling, conversion of different forms of energies to achieve the improvement of energy usage efficiency. In this paper, an optimal economic dispatching model for a residential-level EH in the energy market considering the flexible ramping product (FRP) is proposed. As distinct from existing studies, in this work, we assume that the EH not only involves bidding in the energy market but may also get profits by providing the FRP to the grid. The discussed problem is formulated as a two-stage robust optimization (RO) model, wherein the first-stage is dedicated to minimizing the operation cost of the EH by optimizing its bidding strategy (energy and flexible ramping trading quantities) in the DA market, while the second-stage aims to determine the optimal re-dispatch/corrective schedule of the EH (including adjusted output of EH components, bidding and flexible ramping amount) in the RT market to achieve the energy balancing with the least cost, considering the worst-case realization of uncertainties. In practice, since the selection of uncertainty interval has an important impact on the efficacy of the RO solution, we propose an interval prediction-based approach combining the long short-term memory (LSTM) recurrent neural network and bootstrapping technique to determine the uncertainty interval used in our RO formulation. Compared with the conventional empirical-based interval-setting, the proposed prediction-based technique is useful to reduce the conservative level of RO solutions by deep learning the value of historical data and reflecting the real error distribution of point forecast results in its estimation. The effectiveness of the proposed methodology is examined based on a residential EH case, and the obtained results confirm the validity of the proposed approach in actual implementations. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Energy hub two-stage robust optimization Interval prediction Machine learning Uncertainty

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Adjustable robust optimization with objective uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期312卷 373-384页

作者： Detienne, Boris Lefebvre, Henri Malaguti, Enrico Monaci, Michele Univ Bordeaux IMB UMR CNRS 5251 Inria Bordeaux Sud Ouest 200 Ave Vieille Tour F-33405 Talence France Univ Bologna Dipartimento Ingn Energia Elettr & Informaz Guglie Viale Risorgimento 2 I-40136 Bologna Italy

In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and involve mixed-integer variables, thus extending the existing literature to a much wider class of problems. We show how these problems can be reformulated using Fenchel duality, allowing to derive an enumerative exact algorithm, for which we prove asymptotic convergence in the general case, and finite convergence for cases where the first-stage variables are all integer. An implementation of the resulting algorithm, embedding a column generation scheme, is then computationally evaluated on a variant of the Capacitated Facility Location Problem with uncertain transportation costs, using instances that are derived from the existing literature. To the best of our knowledge, this is the first approach providing results on the practical solution of this class of problems. & COPY;2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )

关键词： Uncertainty modelling two-stage robust optimization Reformulation Fenchel duality Branch-and-price Computational experiments

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Interval-Partitioned and Correlated Uncertainty Set Based robust optimization of Microgrid

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IEEE SYSTEMS JOURNAL 2024年第3期18卷 1516-1527页

作者： Zheng, Zuqing Chen, Guo Shen, Zixiang Cent South Univ Sch Automat Changsha 410083 Peoples R China

The dramatic increase in renewable energy sources has created significant uncertainties in the operation of power systems. This article investigates a day-ahead economic dispatch problem for a typical microgrid, considering the uncertainties of renewable energy sources and load demand. An interval-partitioned and temporal-correlated uncertainty set based robust optimization model is proposed, which allows a more accurate characterization of the distribution of uncertainties. The proposed robust optimization model can reduce the conservativeness of the optimal solution by avoiding scenarios that are low-probability or even impossible in reality. The model is then decomposed into a master problem and a nonlinear bi-level subproblem and solved by the C&CG method and Big-M method. However, this method requires the introduction of a large number of auxiliary variables and related constraints, significantly increasing the computation burden. To tackle this problem, an efficient solution method, Improved-C&CG, is developed by integrating an outer approximation method into the C&CG method. Finally, case studies verify the effectiveness of the proposed model, uncertainty set, and solution methods.

关键词： Uncertainty Microgrids Renewable energy sources optimization Load modeling Costs Dispatching C&CG interval-partitioned outer approximation temporal-correlated two-stage robust optimization

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