多元主体博弈下的用户侧综合能源优化理论与方法研究

项目来源

国家自然科学基金(NSFC)

项目主持人

贾宏杰

项目受资助机构

天津大学

项目编号

U1766210

立项年度

2017

立项时间

未公开

项目级别

国家级

研究期限

未知 / 未知

受资助金额

292.00万元

学科

工程与材料科学-电气科学与工程

学科代码

E-E07

基金类别

联合基金项目-重点支持项目-智能电网联合基金

关键词

用户侧综合能源 ; 多主体博弈 ; 可信调控容量 ; 综合能源优化 ; 联合优化 ; Multi-energy optimization ; integrated energy system in the customer side ; multiple game roles ; combined optimization ; credible regulative capacity

参与者

穆云飞;侯恺;安青松;蒲天骄;陈乃仕;何剑;邓卫;屈慧;叶华

参与机构

中国电力科学研究院有限公司;中国科学院电工研究所

项目标书摘要:构建新一代综合能源系统是实现人类社会能源绿色和可持续供应的关键,而用户侧是电/气/冷/热各类能源消费、转化、使用和获取的主要场所,因此是实施社会综合能源优化的关键。用户侧综合能源系统具有的多元主体博弈特征和大量不确定因素,与各类能源的复杂时空特性交织耦合,使得用户侧综合能源优化面临诸多挑战。本项目将针对用户侧综合能源优化的基础理论、分析方法和相关技术开展研究,重点解决如下五个关键科学问题:1多主体博弈环境下的用户侧多能源时空耦合机理揭示;2用户侧源/储/荷/转环节各调控手段的可信调控容量估算方法;3多主体博弈下的多能源联合优化及综合调控理论与方法;4用户侧综合能源系统多主体博弈的市场互动机制与决策理论;5用户侧综合能源优化仿真用例构建理论与方法。通过本项目研究,希望突破制约用户侧综合能源优化应用的关键理论与技术瓶颈,为我国实施用户侧综合能源优化提供理论支持和技术储备。

Application Abstract: Integrated energy system is regarded as a new generation of energy supply system,which can realize the green and sustainable energy supply to the whole society.Most of the energy conversion,consumption,utilization,storage and access take place in the Customer Side of the Integrated Energy System(CSoIES).There are various game bodies,a lot of uncertainties and various coupled points of multiple energies such as electricity,heating,cooling,and natural gas in CSoIES.All these factors interacting with each other makes the CSoIES as the key point of the whole integrated energy system,and brings a lot of challenges in the this area.This project mainly focuses on the basic theoretic studies of CSoIES’s modelling,mechanism analysis,optimization,control,etc.And five scientific issues faced by CSoIES will be deeply analyzed:1)Research on the spatial-temporal coupling mechanism of CSoIES with multiple game roles;2)Research on the evaluation method of credible regulative capacity in various components in the CSoIES;3)Research on the combined optimization and regulation method to the multi-energy in the CSoIES with multiple game roles;4)Research on the business model and its analysis theory for the CSoIES with multiple game roles;5)Research on the method to build the testbed of CSoIES with multiple game roles.Through this research project,effective solutions to the key challenges faced by CSoIES will be provided,and the research outputs of this project will provide the theoretical support and technical reserve to the further development of CSoIES.

项目受资助省

天津市

项目结题报告(全文)

本项目重点围绕用户侧综合能源系统的多能源耦合机理、可信调控容量估算、多能源联合优化及综合调控、商业及服务模式、仿真用例构建等方面,开展了深入研究。项目构建了多类型分布式电源、电/热/气/氢用能设备及耦合单元、储能单元、负荷侧楼宇与电动汽车等负荷单元的通用模型,形成了基于动态能量集线器的统一建模框架和仿真方法;提出了综合能源系统综合效用多属性评价方法,多能源耦合机理分析模型等实用化分析手段,建立了源—网—荷灵活资源的可调控潜力量化计算模型;提出了随机环境下多能流联合优化调控方法体系,包括多能源联合预测、状态感知与运行优化、多时间尺度运行调控以及安全防控策略;建立了多主体博弈运行与决策机制;形成了具有通用性、可扩展性的仿真用例系统。本项目先后培养博士研究生5人,硕士研究生20人;发表高水平学术论文77篇;申请发明专利31项,授权8项。研究团队与我国多个电力和能源企业开展了深入合作,成果已在我国数百个实际工程中获成功应用,促进了企业在综合能源系统规划运行,风险防控等领域的技术进步和工程应用水平。合作成果先后获9项省部级等各类科技奖励,创造了显著的社会与经济效益。研究团队与国外知名科研机构及高校,开展了深入交流与合作,共同创办了国际学术期刊IET Energy Systems Integration,已成功被EI和SCI收录;在综合能源领域,合作组织了10余个的期刊专辑和多个国际会议,扩大了我国在该领域的国际影响力。项目研究团队成员中,多人入选国家百千万人才工程、政府特殊津贴、国家优青基金等人才奖励计划,研究团队入选了2个省部级创新人才团队,2人晋升教授,项目研究有力地促进了综合能源系统领域的人才培养和队伍建设;此外,项目在科技创新、学生培养、队伍建设、基地建设、国际合作等方面,促进了天津大学电气工程学科的学科建设和学科水平的提升。综上,尽管受到突如其来的新冠疫情的影响,本项目仍按预期研究计划开展了研究工作,取得了预期成效,达到了预期目标。

  • 排序方式:
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  • 1.Entropy state calculation model for integrated energy systems

    • 关键词:
    • Energy development;Energy efficiency;Calculation models;Energy;Energy degradation;Energy quality;Entropy increase;Entropy increase flow;Entropy state;Exergy loss;Integrated energy systems;Uncertainty
    • Li, Yizhe;Wang, Dan;Li, Jiaxi;Jia, Hongjie;Zhou, Tianshuo;Liu, Jiawei;Cheng, Hao
    • 《Applied Energy》
    • 2025年
    • 394卷
    • 期刊

    The integration of renewable energy sources and multi-energy networks in integrated energy systems (IES) introduces significant challenges related to energy degradation, driven by exergy losses during energy conversion/transmission and uncertainty-induced usability reduction. To address these issues, this study proposes a novel entropy state calculation model and analytical framework for assessing energy quality degradation within IES. By unifying thermodynamic entropy (quantifying physical exergy loss) and information entropy (capturing uncertainty-driven energy mismatch), the model integrates physical and information systems into a cohesive entropy state framework. The methodology is validated through a case study on a real-world IES in Tianjin, China (TJBC), demonstrating its capability to reveal entropy state distributions across subsystems under varying network structures and operational modes. Results highlight the dominance of energy conversion processes (e.g., combined heat and power units) in system-wide entropy increase and the critical role of renewable uncertainty in local energy quality degradation. The proposed framework provides a unified metric for optimizing energy efficiency, guiding infrastructure planning, and mitigating energy degradation in high-renewable-penetration IES, contributing to sustainable and high-quality energy system development. © 2025 The Authors

    ...
  • 2.A three-layer planning framework for regional integrated energy systems based on the quasi-quantum theory

    • 关键词:
    • Behavioral research;Chaotic systems;Control theory;Decision making;Economic and social effects;Errors;Function evaluation;Model predictive control;Stochastic control systems;Stochastic models ;Stochastic systems;Uncertainty analysis;Wave functions;Information gap decision theory;Information-gap;Integrated energy systems;Model-predictive control;Multiple uncertainty;Quantum models;Quasi quantum model;Regional integrated energy system rolling stochastic planning;Stochastic planning;Uncertainty
    • Lei, Yang;Wang, Dan;Cheng, Hao;Jia, Hongjie;Li, Ya;Ding, Shichuan;Guo, Xiaoxuan
    • 《International Journal of Electrical Power and Energy Systems》
    • 2024年
    • 155卷
    • 期刊

    With the rapid development in social informatization, more and more factors, such as regional economy, technological development, and people's living needs, will affect the supply–demand relationship of regional integrated energy systems (RIES), which involve multiple energy forms. These factors turn the supply–demand relationship of an energy system into a nonlinear and time-varying chaotic system. This makes it difficult to predict and balance these relationships, which poses a huge challenge to the prediction, planning, operation, etc. Existing conventional methods attempt to quantify the prediction bias caused by various external environmental factors of energy systems and to weaken the uncertainty caused by multiple energy loads through random programming. However, uncertainty factors increase with the development of an energy system, thereby inreasing the requirements of such uncertainty quantification methods. Furthermore, in conventional methods, the prediction or planning decisions are often made by an observer while neglecting the impact of the observer's decision-making behavior on prediction and planning. Therefore, this paper proposes a three-layer planning framework for to solve the above problems. This architecture includes quasi-quantum uncertainty periodic evaluation, stochastic planning based on information gap decision theory, and rolling planning based on model predictive control. First, we establish a quasi-quantum model of multi-energy system prediction error based on the quasi-quantum wave function model to qualitatively analyze prediction errors affected by uncertainty before and after planning. Simultaneously, combined with the evaluation model of the quasi-quantum potential energy function, a quasi-quantum uncertainty period evaluation model is proposed. Based on the minimum equivalent planning entropy, the planning cycle of multistage rolling planning is divided to minimize uncertainty. Second, the information gap decision theory is used to quantify the influence range of source and load uncertainty in the planning process and the multistage planning cycle is randomly planned. Then, the model predictive control method is used to control the actual error, and the planning strategy is changed in time to reduce the planning deviation caused by the prediction error. Finally, adopting a Beichen demonstration area in Tianjin, China, as a case study, the effectiveness of the proposed method in uncertainty analysis and long-term planning improvement is verified. The three-layer planning framework can improve the adaptability of the regional integrated energy system in the long-term planning process, and can timely adjust the planning scheme to cope with the impact of unpredictable uncertainties in the planning process. © 2017 Elsevier Inc. All rights reserved. © 2023

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  • 3.Electricity-Heat-Based Integrated Demand Response Considering Double Auction Energy Market with Multi-Energy Storage for Interconnected Areas

    • 关键词:
    • Resistance heating; Cogeneration; Energy storage; Demand response;Costs; Supply and demand; Load modeling; Double auction; energy market;integrated energy system; interconnected energy stations; multi-energystorage;POWER-SYSTEMS; NETWORK; OPTIMIZATION; MODEL
    • Wang, Dan;Huang, Deyu;Hu, Qing'e;Jia, Hongjie;Liu, Bo;Lei, Yang
    • 《CSEE JOURNAL OF POWER AND ENERGY SYSTEMS》
    • 2024年
    • 10卷
    • 4期
    • 期刊

    With development of integrated energy systems and energy markets, transactive energy has received increasing attention from society and academia, and realization of energy distribution and integrated demand response through market transactions has become a current research hotspot. Research on optimized operation of a distributed energy station as a regional energy supply center is of great significance for improving flexibility and reliability of the system. Based on retail-side energy trading market, this study first establishes a framework of combined electric and heating energy markets and analyses a double auction market mechanism model of interconnected distributed energy stations. This study establishes a mechanism model of energy market participants, and establishes the electric heating combined market-clearing model to maximize global surplus considering multi-energy storage. Finally, in the case study, a typical user energy consumption scenario in winter is selected, showing market-clearing results and demand response effects on a typical day. Impact of transmission line constraints, energy supply equipment capacity, and other factors on clearing results and global surplus are compared and analyzed, verifying the effects of the proposed method on improving global surplus, enhancing interests of market participants and realizing coordination and optimal allocation of both supply and demand resources through energy complementarity between regions.

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  • 4.考虑交通行为的电动汽车快充站协同规划与时空引导策略

    • 关键词:
    • 交通行为 充电负荷预测 协同规划 多目标规划 充电引导 基金资助:国家自然科学基金项目U1766210、513111017和51307115; 国家电网公司总部科技项目SGTYHT/17-JS-199; 天津市科技计划项目18YFZCGX00570; 专辑:工程科技Ⅱ辑 专题:公路与水路运输 电力工业 DOI:10.27356/d.cnki.gtjdu.2019.002185 分类号:U491.8TM910.6 导师:贾宏杰 穆云飞 余晓丹 手机阅读
    • 期刊

    本文以电动汽车(Electric Vehicle,EV)为研究对象,以高速和城市区域为典型场景,围绕EV充电负荷预测、EV快充站协同规划和时空引导策略开展研究,主要工作如下:1)EV充电负荷预测研究:首先考虑EV特有的电池特性和交通行为,提出了基于起讫点(Origin-Destination,OD)分析的充电负荷时空预测(Spatial and Temporal Forecast,STF)模型;进一步,在信息交互框架和STF模型的基础上,提出了信息协调下的EV充电负荷预测方法;最后,利用所提模型及方法,与无信息交互的充电负荷预测结果相比,由于用户可以充分获取快充站的分布和运行信息,改变其充电选择,进而改变充电负荷分布,使其在空间上分布更加合理。2)EV快充站协同规划研究:基于前述STF模型,首先提出了基于交通行为的EV快充站规划方法。基于STF模型,利用共享邻居聚类方法构建选址模型以满足充电需求;其次,基于选址方案、充电需求和排队论,构建定容模型以满足用户的等待时间约束,从而确定规划方案;进一步,提出了考虑配电网潮流约束的EV快充站协同规划方法。该方法构建考虑配电网潮流约束的规划方案校正模型,通过调整规划方案使其满足配电网潮流约束,延缓配电网投资同时满足EV充电需求和用户的等待时间约束。3)EV快充站多目标规划研究:基于前述STF模型,提出了考虑充电需求不确定性的EV快充站多目标规划方法。首先,利用集合覆盖方法和排队论,构建候选方案生成模型得到满足用户充电需求和等待时间约束的规划方案;然后,构建以快充站期望年投资及运行成本最小,配电网期望年网损最小和用户充电需求到相应快充站的期望总距离最小为目标的多目标规划模型,并将配电网相关约束以罚函数的形式引入到多目标规划模型中。利用NSGA-II(Non-dominant Sorting Genetic Algorithm II)算法求解该模型。4)时空引导策略研究:提出了面向配电网电压品质提升的EV快充站充电价格定价策略。首先,考虑城市区域用户多次出行特点、存在慢充设施、路网约束、交通路况等因素,构建基于出行链的交通仿真模型以得到快充需求分布;其次,在快充站收入不变的前提下,以配电网电压幅值总偏移最小为目标,构建双层定价优化模型确定快充站的充电价格;最后以某个城市为算例场景,验证了通过制定快充网络中不同充电价格,可引导快充负荷重新分布,进而可改善配电网运行,提升配电网电压品质。

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  • 5.集成智能楼宇的微网系统多时间尺度模型预测调度方法

    • 关键词:
    • 智能楼宇 微网(微电网) 虚拟储能 多时间尺度优化调度 模型预测控制 基金资助:国家自然科学基金委员会-国家电网公司智能电网联合基金资助项目(U1766210); 国家自然科学基金资助项目(51625702); 国家电网公司科技项目(SGTJJY00GHJS1800123)~~; 专辑:工程科技Ⅱ辑 信息科技 专题:建筑科学与工程 自动化技术 分类号:TU855 手机阅读
    • 靳小龙;穆云飞;贾宏杰;余晓丹;徐科;徐晶
    • 期刊

    针对含多智能楼宇的微网系统,提出一种基于模型预测的多时间尺度调度方法。首先,为有效利用建筑围护结构蓄热特性所带来的灵活性,构建了虚拟储能系统数学模型,并将其集成到智能楼宇微网多时间尺度调度方法中。随后,提出了基于模型预测的日内滚动修正方法,通过每个控制时域内的滚动优化,实现日内微网系统运行方案的精确修正。最后,以夏季制冷场景为例,利用含智能楼宇的微网系统验证了所提方法的有效性。结果表明,该方法可在保证楼宇室内温度舒适度的前提下,在日前经济优化调度阶段降低运行成本;在日内滚动修正阶段平抑由日前预测误差导致的微网联络线功率波动。

    ...
  • 6.集成智能楼宇的电/气/热区域综合能源系统建模及运行优化研究

    • 关键词:
    • 区域综合能源系统 智能楼宇 系统建模 特性分析 优化调度 多时间尺度 模型预测 基金资助:国家自然科学基金(51625702,U1766210); 专辑:工程科技Ⅱ辑 信息科技 专题:建筑科学与工程 动力工程 电力工业 自动化技术 DOI:10.27356/d.cnki.gtjdu.2018.000157 分类号:TU855TM73TK01 导师:贾宏杰 穆云飞 手机阅读
    • 期刊

    可再生能源技术,分布式发电供能技术,综合能源利用技术以及能源监视、控制和管理等技术的快速发展,为城市提升用能品质和降低能源消耗提供了重要支撑手段。区域综合能源系统(Integrated Community Energy Systems,ICES)和终端楼宇综合能源系统(简称为智能楼宇),作为未来智慧型城市发展的重要基础受到越来越多的关注。本文以集成智能楼宇的ICES为研究对象,通过模型构建、特性分析、运行优化和协调控制等研究,以期挖掘ICES内部不同能源间的互补替代潜力,实现ICES系统中多种能源的协调优化,降低运行成本和提高能源利用效率,并最大限度地实现可再生能源安全消纳。本文主要工作如下:(1)针对终端楼宇综合能源系统:经优化协调后的终端楼宇综合能源系统,可视为ICES中的一种调控源。本文深入分析了楼宇围护结构的热动态特性,在此基础上构建了终端楼宇虚拟储能系统模型,以充分挖掘智能楼宇建筑围护结构的蓄热能力;进一步,采用模型预测及多时间尺度调度等方法,提出了融合虚拟储能的单体智能楼宇及智能楼宇集群优化调度方法,在保持用户用能舒适性前提下对楼宇室温进行优化调节,实现对虚拟储能环节的充放电管理,在降低楼宇能耗的同时提高了ICES的能源利用效率。(2)针对区域综合能源系统:首先,为对ICES中的多能源耦合设备进行协调优化,基于能源集线器理论,给出了能量转换环节的建模方法。进而,为实现ICES的灵活调度,构建了考虑多能源网络复杂约束的最优潮流数学模型,其优化结果能有效反映ICES中不同能源网络经协调优化后所带来的系统运行灵活性的提升。最后,构建了ICES系统的“源-网”优化调度模型,实现对不同供用能单元及多能源网络的优化调度。算例表明,所提模型可有效降低ICES的运行成本和提高系统的综合用能效率。(3)针对集成智能楼宇的区域综合能源系统:为实现ICES和智能楼宇系统的协调配合和优化调度,构建了考虑“源-网-荷”全环节的ICES多阶段优化调度模型;进一步,基于二阶锥规划方法给出了适用的求解算法;算例表明,所提方法可有效挖掘ICES各环节之间的互补优化能力,实现综合能源利用效率的提升和降低系统运行成本。(4)针对区域综合能源系统的运行灵活性:提出了一种基于ICES灵活运行能力的输电线路过载控制策略,在输电网发生线路过载时,通过灵活调整ICES的运行方式和对“源-网-荷”各环节的优化调控,帮助电网从紧急状态过渡到正常运行状态,通过提升系统的灵活性来提高其运行安全性。

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  • 7.Day-ahead optimal scheduling of building energy microgrids based on time-varying virtual energy storage

    • 关键词:
    • Cost reduction;Heat transfer;Scheduling;Solar buildings;Thermal comfort;Building energy;Building envelopes;Day-ahead;Electricity costs;Microgrid;Optimal scheduling strategies;Scheduling flexibility;Storage capability;Time varying;Time varying parameter
    • Mu Y;
    • 《IET Renewable Power Generation》
    • 2022年
    • 17卷
    • 2期
    • 期刊

    The thermal inertia of a building envelope endows a building with a heat storage capability, introducing scheduling flexibility to a building energy microgrid (BEM). The flexibility is usually modelled as virtual energy storage (VES) and used to optimize the operation of BEMs to reduce electricity costs. However, the VES capacity is impacted by and varies with variations in indoor/outdoor temperature. If only the building envelope's effect on heat transfer is considered, without proper quantification of scheduling flexibility provided by the building envelope, the scheduling scheme (especially VES charging/discharging schemes) will deviate from the actual VES operating conditions, which may affect the thermal comfort of individuals in buildings or bring high electricity costs. In this paper, a time-varying building VES model (TVES) with three time-varying parameters (virtual electric capacity (VEC), state of charge (SOC), and charge and discharge power) is proposed to quantify the electricity storage capability of the VES at different time periods for participating in operation of the BEM. Based on the TVES, a day-ahead optimal scheduling strategy is developed for the BEM to simultaneously reduce the electricity cost and guarantee the user's thermal comfort, where the proposed time-varying parameters of TVES are taken as constraints in the optimization. Numerical studies verify the effectiveness of the proposed TVES and optimal scheduling strategy.
    © 2022 The Authors. IET Renewable Power Generation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.

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  • 8.Operation optimization of electric power - hot water - steam integrated energy system

    • 关键词:
    • Electric load flow;Energy utilization;Genetic algorithms;Iterative methods;Water;Electric power;Hot water;Hot water network;Integrated energy systems;Operations optimization;Optimal operation;Power flow calculations;Power-flow solution;Steam networks;Water steam
    • Ma, Wenxiang;Deng, Wei;Pei, Wei;Yang, Hailin;Wang, Yuhui;Wang, Lihui;Li, Qiang;Zhang, Ling;Wan, Lei;Liang, Zengyao
    • 《Energy Reports》
    • 2022年
    • 8卷
    • 期刊

    The distributed integrated energy system can optimize the energy structure of the user side by using natural gas and realize the cascade utilization and low energy consumption of energy. This paper takes the integrated energy system as the research object, establishes the electric power "source-network-load" model, the combined hydrothermal model and the steam network model, and proposes alternate iterative power flow solution method. On the basis of power flow solution, the integrated energy system optimization model is established with economy and system energy efficiency as the objective function, and the genetic algorithm toolbox is used to optimize the solution. The results show that the proposed operation optimization method is effective and feasible, which can effectively improve the integrated energy efficiency and realize the optimized operation of the integrated energy system.
    © 2022 The Authors

    ...
  • 9.Efficient Smart Grid Load Balancing via Fog and Cloud Computing

    • 关键词:
    • VIRTUAL MACHINE PLACEMENT; MIGRATION; ALGORITHM
    • Yu, Dongmin;Ma, Zimeng;Wang, Rijun
    • 《MATHEMATICAL PROBLEMS IN ENGINEERING》
    • 2022年
    • 2022卷
    • 期刊

    As the cloud data centers size increases, the number of virtual machines (VMs) grows speedily. Application requests are served by VMs be located in the physical machine (PM). The rapid growth of Internet services has created an imbalance of network resources. Some hosts have high bandwidth usage and can cause network congestion. Network congestion affects overall network performance. Cloud computing load balancing is an important feature that needs to be optimized. Therefore, this research proposes a 3-tier architecture, which consists of Cloud layer, Fog layer, and Consumer layer. The Cloud serves the world, and Fog analyzes the services at the local edge of network. Fog stores data temporarily, and the data is transmitted to the cloud. The world is classified into 6 regions on the basis of 6 continents in consumer layer. Consider Area 0 as North America, for which two fogs and two cluster buildings are considered. Microgrids (MG) are used to supply energy to consumers. In this research, a real-time VM migration algorithm for balancing fog load has been proposed. Load balancing algorithms focus on effective resource utilization, maximum throughput, and optimal response time. Compared to the closest data center (CDC), the real-time VM migration algorithm achieves 18% better cost results and optimized response time (ORT). Realtime VM migration and ORT increase response time by 11% compared to dynamic reconFigure with load (DRL) with load. Realtime VM migration always seeks the best solution to minimize cost and increase processing time.

    ...
  • 10.Optimal performance of hybrid energy system in the presence of electrical and heat storage systems under uncertainties using stochastic p-robust optimization technique

    • 关键词:
    • Hybrid energy system; Stochastic p-robust optimization technique;Maximum relative regret; Regret-based operation; Renewable energyresources;OPERATION; BATTERY
    • Yu, Dongmin;Wu, Juntao;Wang, Weidong;Gu, Bing
    • 《SUSTAINABLE CITIES AND SOCIETY》
    • 2022年
    • 83卷
    • 期刊

    A hybrid energy system (HES) is a recommended solution to simultaneously electricity and heat loads supply with minimum power purchasing from the external grid. Due to the existence of different energy resources loads in the HES, uncertainty is an undeniable challenge in the optimal operation of these systems. Besides, the financial risk imposed by the uncertainties is a big concern for the HES operators. Therefore, in this paper, by a combination of the stochastic optimization (SO) and robust optimization (RO) approaches, a new regret analysis method called the stochastic p-robust optimization (SPRO) technique is proposed to take advantage of SO and RO methods simultaneously. The proposed approach results are regret-based, which is a risk measure. Based on the obtained results, the system expected cost in the SO is $ 39.70, which is increased to $ 39.92 by applying the robust-based approach to SO. Besides, applying the proposed approach to SO reduces the maximum relative regret from 1.32% to 0.74%. According to the reported numerical results, it can be concluded that the HES operation cost is increased by 0.56%, while the maximum relative regret of the system operator is reduced by 44%.

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