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PMUs data based detection of oscillatory events and identification of their associated variable: Estimation of information measures approach 基于 PMU 数据的振荡事件检测及其相关变量的识别:信息量估算方法
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-27 DOI: 10.1016/j.segan.2024.101457
Sanjay Singh Negi , Nand Kishor , A.K. Singh

Information theory can be a useful tool for quantifying the perturbations in the associated state variables at the time of disturbance occurrence. The study introduces a framework for the spectral decomposition of multivariate information measures to detect initiation of low frequency oscillations (LFOs), caused due to physical events in the power grid. A frequency-specific quantification of the information is shared between a target variable and two source variables from their time series data. Initially, the approach is applied on different synthetic test signals having different oscillatory frequency modes and decay time constant. Then, approach is extended on PMUs signals. The combination of cross-spectral and information-theoretic approaches is applied for the multi-variable analysis of PMUs signals from the same bus. The interdependence among the frequency, voltage angle and voltage magnitude, corresponding to specific oscillations, manifested due to cause-effect relationships obtained in terms of statistics is estimated. The dynamics in terms of unique (interaction), redundant and synergetic information is determined with the contribution from two of these three signals as source variables to target variable (frequency/voltage angle). This provides a direct coupling to identify driver-response relationships between source variables and target variable to indicate the onset of LFOs, following physical events in power network. The extension of approach among the variables from different buses aids to identify the responsible area of event occurrence.

信息论是量化干扰发生时相关状态变量扰动的有用工具。本研究介绍了一种多变量信息测量的频谱分解框架,用于检测电网物理事件引起的低频振荡(LFO)。一个目标变量和两个源变量从其时间序列数据中共享特定频率的量化信息。起初,该方法应用于具有不同振荡频率模式和衰减时间常数的不同合成测试信号。然后,将该方法扩展到 PMU 信号上。跨谱法和信息理论法相结合,用于对来自同一总线的 PMU 信号进行多变量分析。对频率、电压角和电压幅值之间的相互依存关系进行了估算,这些相互依存关系与特定的振荡相对应,并通过统计得到的因果关系表现出来。通过将这三个信号中的两个信号作为目标变量(频率/电压角)的源变量,确定了独特(交互)、冗余和协同信息方面的动态。这就提供了一种直接耦合,以确定源变量和目标变量之间的驱动-响应关系,从而在电网发生物理事件后指示 LFO 的发生。在不同总线的变量之间扩展方法有助于确定事件发生的责任区域。
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引用次数: 0
Hierarchical transactive home energy management system groups coordination through multi-level consensus sharing-based distributed ADMM 通过基于多级共识共享的分布式 ADMM 实现分层交互式家庭能源管理系统组协调
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-27 DOI: 10.1016/j.segan.2024.101460
Farshad Etedadi , Sousso Kelouwani , Kodjo Agbossou , Nilson Henao , François Laurencelle , Sayed Saeed Hosseini

Coordinating residential building groups requires a hierarchical structure in which aggregate objectives and coupled constraints are incorporated into decision-making processes at different layers of the electric distribution system. Failure to handle these matters can raise issues, such as rebound peaks and contingencies. This paper proposes a Hierarchical Transactive Coordination Mechanism (HTCM) capable of dealing with residential consumers’ objectives/constraints and local and grid coordinators’ shared objectives/coupled constraints under a bottom-up strategy. Particularly, the proposed multi-level framework distributes local and grid coordinators’ shared objectives among consumers to flatten the aggregate consumption profile and minimize the aggregate energy cost at each level. The suggested scheme is enhanced by developing two additional operations. A gain-sharing technique is designed to fairly divide the total gain acquired by the grid coordinator across the hierarchy from higher to lower levels, successively. Besides, a coupled constraint-sharing method is devised to link these levels and fulfill the coupled constraints by revising consumers’ decisions. The proposed approach is applied to a society of buildings comprising Home Energy Management System (HEMS) groups with demand response-enabled electric Baseboard Heaters (BHs), and its effectiveness is investigated through different case studies. The results demonstrate that the recommended HTCM is able to improve the society’s aggregate power profile load factor by 89%, from 0.45 up to 0.85, and decreases its overall electricity cost by 6.2%.

协调住宅建筑群需要一个分层结构,将总体目标和耦合约束纳入配电系统不同层级的决策过程。如果不处理这些问题,就会引发反弹峰值和突发事件等问题。本文提出了一种分层交互协调机制 (HTCM),能够在自下而上的策略下处理居民消费者的目标/约束以及本地和电网协调者的共同目标/耦合约束。特别是,建议的多级框架将地方和电网协调者的共享目标分配给消费者,以扁平化总消费曲线,并最大限度地降低每个级别的总能源成本。建议的方案通过开发两个附加操作得到了增强。设计了一种收益分享技术,以公平分配电网协调器在整个层次结构中从较高层次到较低层次连续获得的总收益。此外,还设计了一种耦合约束共享方法,通过修改消费者的决策来连接这些层级并实现耦合约束。建议的方法被应用于由家庭能源管理系统(HEMS)组和需求响应电热板(BHs)组成的建筑群,并通过不同的案例研究考察了其有效性。结果表明,推荐的 HTCM 能够将社会的总功率曲线负荷率提高 89%,从 0.45 提高到 0.85,并将其总体电力成本降低 6.2%。
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引用次数: 0
Mapping the charging demand for electric vehicles in 2050 from mobility habits 从出行习惯看 2050 年的电动汽车充电需求
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-27 DOI: 10.1016/j.segan.2024.101468
Noémie Jeannin, Alejandro Pena-Bello, Christophe Ballif, Nicolas Wyrsch

This paper proposes a method to spatially model and compare charging needs on the European scale, considering local disparities in population density, distance to city centres, car ownership and mobility habits. Mobility habits are modelled across Europe in terms of distance and time frame to elaborate scenarios of charging behaviour. The first step of the method is to calculate the density of electric vehicles with a resolution of 1 km2, according to the progressive electrification of the fleet each year between 2020 and 2050. The second step is to quantify the mobility of commuters using their driving distance to work areas and mobility statistics. The model is then applied in a case study in Switzerland to plan the public charging infrastructure required to satisfy the charging needs of the local population. Despite lower motorization rates and driving distances, the results show a stronger need for charging in cities. With 50% of commuters charging at work and 20% at home during the workday, the demand in the evening can be reduced by 50% in the suburban areas compared to the baseline scenario in which all commuters are charging at home in the evening. This model can be used to quantify the energy needs of commuters, plan the deployment of the charging infrastructure, or simulate the effect of policies.

本文提出了一种在欧洲范围内对充电需求进行空间建模和比较的方法,其中考虑到了各地在人口密度、与市中心的距离、汽车拥有量和移动习惯等方面的差异。从距离和时间框架的角度对整个欧洲的移动习惯进行建模,以制定充电行为方案。该方法的第一步是根据 2020 年至 2050 年期间每年逐步电气化的车队,以 1 平方公里的分辨率计算电动汽车的密度。第二步是利用通勤者到工作区域的驾驶距离和流动性统计数据,量化通勤者的流动性。然后将该模型应用于瑞士的一项案例研究,规划满足当地居民充电需求所需的公共充电基础设施。尽管机动化率和驾驶距离较低,但结果显示城市对充电的需求更为强烈。在工作日,50% 的通勤者在工作时充电,20% 的通勤者在家中充电,与所有通勤者晚上都在家中充电的基准情景相比,郊区晚上的需求可减少 50%。该模型可用于量化通勤者的能源需求、规划充电基础设施的部署或模拟政策效果。
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引用次数: 0
Charging scheduling in a workplace parking lot: Bi-objective optimization approaches through predictive analytics of electric vehicle users' charging behavior 工作场所停车场的充电调度:通过预测分析电动汽车用户充电行为的双目标优化方法
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-26 DOI: 10.1016/j.segan.2024.101463

Decarbonization of the transportation sector relies on the widespread adoption of Electric Vehicles (EVs) and appropriate charging strategies. However, uncoordinated EV charging can adversely affect the power grid, and effective scheduling schemes are necessary to mitigate adverse effects. This study aims to develop bi-objective optimization models for EV charging scheduling at a workplace charging station, addressing the EV users’ preferences in terms of economic and Quality-of-Service (QoS) dimensions, by minimizing the charging cost considering the participation in Vehicle-to-Grid (V2G) schemes and minimizing the deviation from the desired State-of-Charge (SoC). To address this deviation, two perspectives are considered: minimizing the sum of deviations, embodying a compensatory criterion, and minimizing the worst deviation, a fairness criterion based on a min-max approach. To obtain a representation of the non-dominated solution set corresponding to the scheduling plan for each EV, the Epsilon-constraint method is used. Furthermore, machine learning techniques are employed to predict the charging behavior of EV users, including the desired SoC and charging budget. A sensitivity analysis is also conducted to explore the influence of energy selling prices in V2G mode to accommodate EV users’ preferences. The findings indicate that as the difference between the energy buying and selling prices increases, it becomes more challenging to satisfy the desired SoC based on the defined charging budget. Additionally, the model that aims to minimize the charging cost and the worst-case deviation to the desired SoC is more sensitive to changes in energy selling prices, highlighting the impact of price variations in scheduling plans.

交通部门的去碳化有赖于电动汽车(EV)的广泛应用和适当的充电策略。然而,不协调的电动汽车充电会对电网产生不利影响,因此需要有效的调度方案来减轻不利影响。本研究旨在为工作场所充电站的电动汽车充电调度开发双目标优化模型,解决电动汽车用户在经济和服务质量(QoS)方面的偏好问题,即考虑到参与车辆到电网(V2G)计划而使充电成本最小化,以及使与理想充电状态(SoC)的偏差最小化。为解决这一偏差问题,我们从两个角度进行了考虑:最小化偏差总和(体现补偿标准)和最小化最差偏差(基于最小-最大方法的公平标准)。为了获得与每辆电动汽车的调度计划相对应的非主导解集的表示方法,使用了 Epsilon 约束方法。此外,还采用了机器学习技术来预测电动汽车用户的充电行为,包括所需的 SoC 和充电预算。还进行了敏感性分析,以探讨 V2G 模式下能源销售价格对满足电动汽车用户偏好的影响。研究结果表明,随着能源购买价格和销售价格之间的差额增大,要在规定的充电预算基础上满足所需的 SoC 就变得更具挑战性。此外,旨在最小化充电成本和最坏情况下偏离期望 SoC 的模型对能源销售价格的变化更加敏感,突出了价格变化对调度计划的影响。
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引用次数: 0
Temporal assessment of operational resilience of transmission network and adaptation measures for a high-impact long duration cyclonic windstorm 输电网络运行恢复能力的时间评估以及针对高影响、持续时间长的气旋风暴的适应措施
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-26 DOI: 10.1016/j.segan.2024.101465
Abhishek Kumar Gupta, Kusum Verma

The exposure to High-Impact Low-Probability (HILP) events can have significant impact on the performance of transmission networks. Under such conditions, the power system components must be resilient and robust to meet the uninterrupted load demand. This paper proposes a quantitative framework for temporal assessment of operational resilience of transmission network and suggests suitable adaptation measures when the system is subjected to high impact cyclonic windstorm lasting for a long duration. The fragility curves of transmission lines are correlated with wind profiles during cyclone and failure probability each transmission line is determined using the Monte Carlo Simulation (MCS) The operational resilience of transmission networks is quantified by computing Total Transfer Capability (TTC), Available Transfer Capability (ATC), Existing Transmission Uses (ETU), Total Reliability Margin (TRM) and unserved load. To improve the operational resilience, adaptation measures with modifications in the robustness of the structural strength is proposed and investigated on standard IEEE 57 bus system and IEEE 118 bus system. Sensitivity analysis is performed to understand how changes in the percentage increase of robustness affect the overall system performance. The findings give valuable insights for evaluating the operational resilience of transmission line infrastructure during such extreme weather events.

高影响低概率(HILP)事件会对输电网络的性能产生重大影响。在这种情况下,电力系统组件必须具有弹性和稳健性,以满足不间断的负荷需求。本文提出了一个定量框架,用于对输电网络的运行恢复能力进行时间评估,并建议在系统遭受持续时间较长的高影响气旋风暴时采取适当的适应措施。通过计算总传输能力 (TTC)、可用传输能力 (ATC)、现有传输用途 (ETU)、总可靠性边际 (TRM) 和未服务负荷,对输电网络的运行恢复能力进行量化。为提高运行恢复能力,提出了修改结构强度的适应措施,并在标准 IEEE 57 总线系统和 IEEE 118 总线系统上进行了研究。进行了灵敏度分析,以了解鲁棒性百分比增加的变化对整个系统性能的影响。研究结果为评估输电线路基础设施在此类极端天气事件中的运行恢复能力提供了有价值的见解。
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引用次数: 0
Distributed power system coordination via parametric optimization and ADMM 通过参数优化和 ADMM 实现分布式电力系统协调
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-21 DOI: 10.1016/j.segan.2024.101456
Branimir Novoselnik, Mato Baotić

In this paper we present an efficient model predictive control algorithm for distributed coordination of an electrical power system comprising many spatially distributed controllable units. The coordination problem is formulated using parametric solutions of local optimization problems corresponding to individual subsystems leading to favorable problem structure which can be split across all subsystems and nodes in the network. The structure of the obtained coordination problem is exploited to develop a very efficient solution algorithm based on an ADMM technique. The key features of the overall approach are: (i) private data of individual subsystems are protected, (ii) simple and efficient on-line computations, (iii) parallelization of computation across all subsystems and all nodes in the network. Efficiency of the proposed control strategy is demonstrated on a number of numerical case studies of varying size.

本文提出了一种高效的模型预测控制算法,用于由多个空间分布式可控单元组成的电力系统的分布式协调。协调问题是利用与单个子系统相对应的局部优化问题的参数化解决方案来解决的,从而形成了可在网络中的所有子系统和节点之间拆分的有利问题结构。利用所获得的协调问题结构,开发了一种基于 ADMM 技术的高效求解算法。整个方法的主要特点是(i) 单个子系统的私人数据受到保护,(ii) 简单高效的在线计算,(iii) 所有子系统和网络中所有节点的并行计算。我们通过大量不同规模的数值案例研究证明了拟议控制策略的效率。
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引用次数: 0
A stochastic-MILP dispatch optimization model for concentrated solar thermal under uncertainty 不确定条件下聚光太阳能热发电的随机-MILP 调度优化模型
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-20 DOI: 10.1016/j.segan.2024.101458
Navid Mohammadzadeh , Huy Truong-Ba , Michael E. Cholette , Theodore A. Steinberg , Giampaolo Manzolini

Concentrated Solar Thermal (CST) offers a promising solution for large-scale solar energy utilization as Thermal Energy Storage (TES) enables electricity generation independent of daily solar fluctuations, shifting to high-priced electricity intervals. The development of dispatch planning tools is mandatory to account for uncertainties associated with weather and electricity price forecasts. A Stochastic Mixed-Integer Linear Program (SMILP) is proposed to maximize Sample Average Approximation (SAA) of expected profit within a specified scenario space. The SMILP exhibits robust performance, yet its computational time poses a challenge. Three heuristic solutions are developed which run a set of deterministic optimizations on different historical weather profiles to generate candidate Dispatch Plans (DPs). Subsequently, the DP with the best average performance on all profiles is selected. The new methods are applied to a hypothetical 115 MW CST plant in South Australia. When the historical database has a limited set of historical weather profiles, the SMILP achieves 6–9 % higher profit than the closest heuristic when the DPs are applied to novel weather conditions. With a large historical weather dataset, the performance of the SMILP and closet heuristic becomes nearly identical since the SMILP can only utilize a limited number of trajectories for optimization without becoming computationally infeasible. In this case, the heuristic emerges a practical alternative, providing similar average profit in a reasonable time. Taken together, the results illustrate the importance of considering uncertainty in DP optimization and indicate that straightforward heuristics on a large database are a practical method for addressing uncertainty.

聚光太阳能热发电(CST)为大规模太阳能利用提供了一种前景广阔的解决方案,因为热能存储(TES)可使发电不受每日太阳能波动的影响,从而转移到高价电力区间。为了考虑与天气和电价预测相关的不确定性,必须开发调度规划工具。我们提出了一种随机混合整数线性规划(SMILP),以在指定的情景空间内最大化预期利润的样本平均近似值(SAA)。SMILP 具有稳健的性能,但其计算时间也是一个挑战。我们开发了三种启发式解决方案,在不同的历史天气曲线上运行一组确定性优化,生成候选调度计划(DP)。随后,选出在所有剖面图上平均性能最佳的 DP。新方法被应用于南澳大利亚的一个假设的 115 兆瓦 CST 发电厂。当历史数据库中只有有限的一组历史天气曲线时,SMILP 的利润比最接近的启发式方法高 6-9%,而当 DP 应用于新的天气条件时,SMILP 的利润比最接近的启发式方法高 6-9%。当历史天气数据集较大时,SMILP 和最接近启发式的性能几乎相同,因为 SMILP 只能利用有限数量的轨迹进行优化,而不会在计算上变得不可行。在这种情况下,启发式成为一种实用的替代方案,能在合理的时间内提供相似的平均利润。综上所述,这些结果说明了在 DP 优化中考虑不确定性的重要性,并表明在大型数据库中采用直接启发式方法是解决不确定性的一种实用方法。
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引用次数: 0
Evaluation of possible network states in the future German hydrogen network 2025 and 2030 评估 2025 年和 2030 年德国未来氢网络的可能网络状态
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-20 DOI: 10.1016/j.segan.2024.101455

This study provides insights into possible future gas network states in the initial German hydrogen network by 2025 and 2030, as per the German transmission system operators Network Development Plan Gas 2020. Not only is the overall transport feasibility assessed, but also possible operating conditions in terms of pressures, flows and velocities. To that end, two data sets for the network topology by 2025 and 2030 were created. A heuristic, semi-random nomination generation is employed to generate 100 consistent steady-state source–sink nominations for both years, based on collected production/consumption bounds. The authors employ a so-called nomination-validation model (MILP-formulation) for the solution of the resulting transport problem(s). For the evaluation of pipeline flow velocities, the authors combine those solutions with a hypothesis on limiting flow speeds suggested in a German technical journal. The analysis exhibits feasibility among all generated nominations with respect to flows and admissible velocities.

根据德国输电系统运营商网络发展计划《天然气 2020》,本研究对 2025 年和 2030 年德国初始氢气网络中可能出现的未来天然气网络状态进行了深入分析。不仅对整体运输可行性进行了评估,还对压力、流量和速度方面可能的运行条件进行了评估。为此,为 2025 年和 2030 年的网络拓扑结构创建了两个数据集。根据收集到的生产/消费界限,采用启发式半随机提名生成方法,为这两年生成 100 个一致的稳态源-汇提名。作者采用所谓的提名-验证模型(MILP-公式)来解决由此产生的运输问题。在评估管道流速时,作者将这些解决方案与德国技术期刊上提出的极限流速假设相结合。分析表明,在流量和允许流速方面,所有生成的提名都是可行的。
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引用次数: 0
Safe reinforcement learning based optimal low-carbon scheduling strategy for multi-energy system 基于强化学习的多能源系统安全低碳优化调度策略
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-20 DOI: 10.1016/j.segan.2024.101454
Fu Jiang , Jie Chen , Jieqi Rong , Weirong Liu , Heng Li , Hui Peng

Multi-energy system with distributed energy resources has become the inevitable trend in recent years due to their potential for creating the efficient and sustainable energy infrastructure, with a strong ability on carbon emission reduction. To accommodate the uncertainties of renewable energy generation and energy demand, model-free deep reinforcement learning methods are emerging for energy management in multi-energy system. However, traditional reinforcement learning methods still have operation safety issue of violating the physical constraints of multi-energy system. To address the challenges, a low-carbon scheduling strategy based on safe soft actor-critic algorithm is proposed in this paper. Firstly, an electricity-thermal-carbon joint scheduling framework is constructed, where carbon trading mechanism is incorporated to further motivate carbon emission reductions. Secondly, the energy cost and carbon trading cost are simultaneously integrated in the objective function, and the dynamic optimization problem of multi-energy system is modeled as a constrained Markov decision process by taking into account the diverse uncertainties. Then, a novel safe soft actor-critic method is proposed to achieve the benefits of economic and carbon emissions, where the security networks and Lagrangian relaxation are introduced to deal with operation constraints. The case study validates that the proposed scheduling strategy can reduce the energy cost and carbon trading cost by up to 26.24% and 33.73% within constraints, compared with existing methods.

近年来,分布式能源资源的多能源系统已成为必然趋势,因为它们具有创建高效和可持续能源基础设施的潜力,并具有很强的碳减排能力。为了适应可再生能源发电和能源需求的不确定性,无模型深度强化学习方法在多能源系统的能源管理中逐渐兴起。然而,传统的强化学习方法仍然存在违反多能源系统物理约束的运行安全问题。为解决这一难题,本文提出了一种基于安全软行为批判算法的低碳调度策略。首先,构建了电-热-碳联合调度框架,并在此框架中加入了碳交易机制,以进一步激励碳减排。其次,将能源成本和碳交易成本同时纳入目标函数,并考虑到多种不确定性,将多能源系统的动态优化问题建模为一个有约束的马尔可夫决策过程。然后,引入安全网络和拉格朗日松弛来处理运行约束,提出了一种新型的安全软行为批判方法,以实现经济效益和碳排放效益。案例研究证实,与现有方法相比,所提出的调度策略可在约束条件下将能源成本和碳交易成本分别降低 26.24% 和 33.73%。
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引用次数: 0
Optimal operation of an electricity-hydrogen DC microgrid with integrated demand response 具有综合需求响应功能的电力-氢气直流微电网的优化运行
IF 4.8 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2024-06-20 DOI: 10.1016/j.segan.2024.101451
Abhishek Singh, Alok Kumar, K.A. Chinmaya, Avirup Maulik

Uncertainties introduced by the high penetration of renewable sources, plug-in-hybrid-electric vehicle load demand, and limited capacity of firm generation available in a DC microgrid make the energy scheduling task rather challenging. This paper proposes a decentralized energy management scheme with a real-time pricing-based demand response implementation for a DC microgrid, considering the sectoral coupling between electricity and hydrogen energy. The objectives of the scheduling strategy are to maximize the profit of the DC microgrid operator and reduce the cost of energy use by the consumers, considering the interaction and interdependence of the electrical and hydrogen systems with a detailed DC microgrid network model and associated network constraints. The DC microgrid operator schedules flexible resources under its control (power procurement from the upstream grid, microturbines, battery energy storage, hydrogen storage, electrolyzer and fuel cell) and sets real-time prices. The consumers set their consumption patterns according to the real-time price. The DC microgrid operator side flexibilities are coordinated with the consumer side flexibilities (thermostatically controlled load like air-conditioner and plug-in-hybrid electric vehicle) using the decentralized “Alternating Direction Method of Multipliers” approach. The probabilistic Copula theory models correlated input uncertainties. Simulation results on a six-bus DC microgrid test system reveal that the operating cost of the DC microgrid operator reduces by 11.06% while the energy use cost of consumers reduces by 4.80% using the proposed approach for the system under study.

可再生能源的高渗透率、插电式混合动力电动汽车的负载需求以及直流微电网中有限的稳定发电能力所带来的不确定性,使得能源调度任务变得相当具有挑战性。考虑到电力和氢能之间的部门耦合,本文为直流微电网提出了一种基于实时定价需求响应的分散式能源管理方案。调度策略的目标是通过详细的直流微电网网络模型和相关网络约束条件,考虑电力和氢能系统的相互作用和相互依存关系,最大限度地提高直流微电网运营商的利润,降低消费者的能源使用成本。直流微电网运营商调度其控制下的灵活资源(从上游电网采购电力、微型涡轮机、电池储能、氢储能、电解槽和燃料电池),并设定实时价格。消费者根据实时价格设定其消费模式。直流微电网运营商侧的灵活性与消费者侧的灵活性(恒温控制负载,如空调和插电式混合动力电动汽车)采用分散的 "交替方向乘法 "方法进行协调。概率 Copula 理论对相关输入不确定性进行建模。对一个六总线直流微电网测试系统的仿真结果表明,在所研究的系统中,使用建议的方法,直流微电网运营商的运营成本降低了 11.06%,而消费者的能源使用成本降低了 4.80%。
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