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Cooperative trading in smart-grid networks 智能电网中的协同交易
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-09-10 DOI: 10.1016/j.segan.2025.101965
Pragya Shrivastava , Neminath Hubballi , Sameer G. Kulkarni
Continuous Double Auction (CDA) methods provide an efficient mechanism for price matching between buyers and sellers. Hence, these techniques have been adopted in smart-grid and micro-grid scenarios for Peer-to-Peer (P2P) energy trading. However, existing CDA methods either violate the natural ordering of P2P trading or introduce considerable overhead or make unrealistic assumptions about the underlying communication setup. In this paper, we introduce a CDA method involving trading agents that are coordinated with token allocation system for participation in the smart-grid market. Our proposed trading mechanism minimizes the natural order violations in the trading, and can recover from issues like token loss arising due to node or network connectivity issues. We provide algorithms for different operations of the CDA such as token request, token allocation, trading, etc. The proposed CDA mechanism has been evaluated with publicly available energy demand data and compared with another CDA method to show that it reduces natural ordering violations. Subsequently, we describe a variant of the CDA method where bids/asks from different participants are queued up for potential future price matches, thereby elaborating the scope for P2P trade. Both CDA variants can scale to large number of participants and can also work with heterogeneous bidding strategies adopted by clients.
连续双拍卖(CDA)方法为买家和卖家之间的价格匹配提供了有效的机制。因此,这些技术已被用于智能电网和微电网场景中的点对点(P2P)能源交易。然而,现有的CDA方法要么违反了P2P交易的自然顺序,要么引入了相当大的开销,要么对底层通信设置做出了不切实际的假设。在本文中,我们引入了一种涉及交易代理的CDA方法,这些交易代理与代币分配系统相协调,以参与智能电网市场。我们提出的交易机制最大限度地减少了交易中的自然秩序违规,并可以从由于节点或网络连接问题而导致的令牌丢失等问题中恢复过来。我们为CDA的不同操作提供算法,如令牌请求、令牌分配、交易等。利用公开可用的能源需求数据对提出的CDA机制进行了评估,并与另一种CDA方法进行了比较,表明它减少了自然顺序的违反。随后,我们描述了CDA方法的一种变体,其中来自不同参与者的出价/要价排队等待潜在的未来价格匹配,从而详细说明了P2P交易的范围。这两种CDA变体都可以扩展到大量参与者,并且还可以与客户采用的异构投标策略一起工作。
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引用次数: 0
A hybrid model predictive control-deep reinforcement learning algorithm with application to plug-in electric vehicles smart charging 混合模型预测控制-深度强化学习算法在插电式电动汽车智能充电中的应用
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-09-09 DOI: 10.1016/j.segan.2025.101963
Francesco Liberati, Mohab M.H. Atanasious, Emanuele De Santis, Alessandro Di Giorgio
This paper focuses on a novel use of deep reinforcement learning (RL) to optimally tune in real-time a model predictive control (MPC) smart charging algorithm for plug-in electric vehicles (PEVs). The coefficients of the terminal cost function of the MPC algorithm are updated online by a neural network, which is trained offline to maximize the control performance (linked to the satisfaction of the users’ charging preferences and the tracking of a power reference profile, at PEV fleet level). This approach is different and more flexible compared to most of the other approaches in the literature, which instead use deep RL to fix offline the MPC parametrization. The proposed method allows one to select a shorter MPC control window (compared to standard MPC) and/or a shorter sampling time, while improving the control performance. Simulations are presented to validate the approach: the proposed MPC-RL controller improves control performance by an average of 4.3 % compared to classic MPC, while having a lower computing time.
本文重点研究了深度强化学习(RL)的一种新应用,以优化实时调整插电式电动汽车(pev)的模型预测控制(MPC)智能充电算法。MPC算法的终端成本函数系数由神经网络在线更新,该神经网络离线训练以最大限度地提高控制性能(与用户充电偏好的满意度和对PEV车队功率参考剖面的跟踪有关)。与文献中使用深度强化学习离线修复MPC参数化的大多数其他方法相比,这种方法不同且更灵活。所提出的方法允许人们选择更短的MPC控制窗口(与标准MPC相比)和/或更短的采样时间,同时提高控制性能。通过仿真验证了该方法的有效性:与传统MPC相比,所提出的MPC- rl控制器的控制性能平均提高了4.3%,同时计算时间更短。
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引用次数: 0
Multi-uncertainty risk analysis framework for hydropower-wind-photovoltaic hybrid systems 水电-风-光伏混合系统多不确定性风险分析框架
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-10-16 DOI: 10.1016/j.segan.2025.102016
Zhiyuan Wu , Guohua Fang , Jian Ye , Xianfeng Huang , Min Yan
The stability and economic efficiency of hydropower-wind-photovoltaic hybrid systems are significantly influenced by various uncertainties and risks. However, existing research lacks a systematic framework to evaluate the synergistic effects of these uncertainties, identify adverse conditions that trigger risk events, and assess the role of forecasting accuracy in risk evaluation. To address these gaps, this study proposes a multi-uncertainty risk analysis framework designed to systematically quantify the impact of uncertainties on system risks. The framework evaluates system risk distribution and employs clustering and correlation analysis to identify adverse conditions, which provide critical inputs for refining scheduling strategies. Additionally, the framework conducts an ablation study to quantify the synergistic effects of multiple uncertainties and clarify their influence on system risks. It further examines the relationship between forecasting accuracy and system risk levels. The effectiveness of the framework was validated through an annual operation case study of a hydropower-wind-photovoltaic hybrid system in the Yalong River Basin. The framework systematically evaluated power shortage and over-generation risks across subsystems under multiple uncertainties using an ablation study, risk event extraction, and correlation analysis. Based on these analyses, an improvement strategy was formulated to mitigate system risks.
水电-风-光伏混合发电系统的稳定性和经济性受到各种不确定性和风险的显著影响。然而,现有的研究缺乏一个系统的框架来评估这些不确定性的协同效应,识别触发风险事件的不利条件,以及评估预测准确性在风险评估中的作用。为了解决这些差距,本研究提出了一个多不确定性风险分析框架,旨在系统地量化不确定性对系统风险的影响。该框架评估系统风险分布,并采用聚类和相关分析来识别不利条件,为优化调度策略提供关键输入。此外,该框架还进行了消融研究,以量化多个不确定性的协同效应,并阐明它们对系统风险的影响。进一步探讨了预测精度与系统风险水平之间的关系。通过雅砻江流域水电-风电-光伏混合发电系统的年度运行案例研究,验证了该框架的有效性。该框架通过消融研究、风险事件提取和相关性分析,系统地评估了多个不确定因素下子系统的电力短缺和发电过剩风险。基于这些分析,制定了改进策略以降低系统风险。
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引用次数: 0
User-centered decentralized P2P energy trading model for managing line congestion in energy communities 以用户为中心的分布式P2P能源交易模型,用于管理能源社区的线路拥堵
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-08-23 DOI: 10.1016/j.segan.2025.101931
Sebastián San Martín , Fernando García-Muñoz , Franco Quezada , Sebastián Dávila
This paper presents a user-centered, fully decentralized framework to allow an energy community (EC) to self-manage line congestion issues through peer-to-peer (P2P) energy trading and a flexibility market using the users’ distributed energy resources (DERs) assets to take an energy seller (buyer) role when they have a surplus (deficit). A three-stage optimization-based model is introduced to consider the users’ preferences and identify line congestion issues using the Distflow model to evaluate the distribution network (DN) limitations. In this regard, users maximize their benefits in the first optimization stage by optimizing their DER operation. In the second stage, the distribution system operator (DSO) solves an optimal power flow model to identify potential congestion given the users’ preferences. If congestion occurs, the third stage activates a P2P energy and flexibility market designed to resolve the issue by minimizing deviations from the users’ initial preferences. To achieve full decentralization, a two-step alternating direction method of multipliers (ADMM) algorithm is employed: the first step addresses optimal power flow, while the second manages the P2P and flexibility market. Tests were conducted on a 33-bus DN for different DER penetration levels, showing that the methodology efficiently meets energy requirements while respecting the network’s physical constraints and improving information security.
本文提出了一个以用户为中心的、完全去中心化的框架,允许能源社区(EC)通过点对点(P2P)能源交易和灵活的市场来自我管理线路拥堵问题,使用用户的分布式能源资源(DERs)资产在有盈余(赤字)时扮演能源卖方(买方)的角色。引入了一个基于三阶段优化的模型来考虑用户的偏好,并使用Distflow模型来评估配电网络(DN)的局限性,从而识别线路拥塞问题。在这方面,用户在第一个优化阶段通过优化他们的DER操作来最大化他们的利益。第二阶段,配电网运营商根据用户的偏好,求解最优潮流模型来识别潜在的拥塞。如果出现拥塞,第三阶段启动P2P能源和灵活性市场,旨在通过最小化与用户初始偏好的偏差来解决问题。为了实现完全的去中心化,采用了两步交替方向乘数法(ADMM)算法:第一步解决最优潮流问题,第二步管理P2P和灵活性市场。在33总线DN上进行了不同DER渗透水平的测试,表明该方法有效地满足了能源需求,同时尊重了网络的物理限制并提高了信息安全性。
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引用次数: 0
Restoring structural controllability of interdependent multi-layered heterogenous cyber-physical-social networks via optimal network reconfiguration 通过优化网络重构恢复相互依赖的多层异质网络-物理-社会网络的结构可控性
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-09-01 DOI: 10.1016/j.segan.2025.101954
Zahra Azimi , Ahmad Afshar
This paper addresses the critical challenge of restoring structural controllability in cyber-physical-social systems (CPSS) compromised by cyber-attacks. Unlike existing studies that focus on homogenous networks or neglect the role of interlayer couplings and intralayer topologies, this work introduces a novel approach to enhance cyber resilience in interdependent multi-layered heterogenous CPSS. We establish new necessary and sufficient conditions for achieving post-attack structural controllability and propose an optimal network reconfiguration algorithm that restores controllability with minimal intervention. This novel algorithm identifies the minimum set of edges required to reconfigure this network, ensuring structural controllability in a polynomial time. Our approach is validated through simulations on various CPSS, including IEEE 14-bus and IEEE 118-bus power networks, as well as scale-free, clustered scale-free, small-world, and random networks subjected to various attack strategies. Additionally, the approach is applied to real-world large-scale datasets, demonstrating its scalability and practical applicability. The results reveal that, among intralayer topologies, scale-free networks are highly vulnerable to structural uncontrollability. Furthermore, sparse interlayer coupling significantly reduces the resilience of the CPSS compared to mesh and peer-to-peer (P2P) coupling configurations. Notably, targeted attacks based on betweenness require about 53 % more edge additions to restore controllability compared to random attacks.
本文解决了在受网络攻击损害的网络-物理-社会系统(CPSS)中恢复结构可控性的关键挑战。与现有研究关注同质网络或忽视层间耦合和层内拓扑的作用不同,这项工作引入了一种新的方法来增强相互依赖的多层异质CPSS的网络弹性。我们建立了实现攻击后结构可控性的新充分必要条件,并提出了一种以最小干预恢复可控性的网络重构算法。该算法确定了重新配置该网络所需的最小边集,确保了在多项式时间内的结构可控性。我们的方法通过各种CPSS的仿真得到验证,包括IEEE 14总线和IEEE 118总线电源网络,以及遭受各种攻击策略的无标度、聚类无标度、小世界和随机网络。此外,将该方法应用于现实世界的大规模数据集,证明了该方法的可扩展性和实用性。结果表明,在层内拓扑中,无标度网络极易受到结构不可控性的影响。此外,与网格和点对点(P2P)耦合配置相比,稀疏层间耦合显着降低了CPSS的弹性。值得注意的是,与随机攻击相比,基于中间性的目标攻击需要大约53 %的边缘添加来恢复可控性。
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引用次数: 0
Incentive-oriented strategy for optimizing microgrid-enabled distribution network voltage regulation based on SQDDPG algorithm 基于SQDDPG算法的微网配电网电压优化激励策略
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-10-14 DOI: 10.1016/j.segan.2025.102000
Xianglong Qi, Jian Chen, Wen Zhang, Keyu Zhang, Xianzhuo Sun
The continuous popularization of distributed energy and the increasing energy demand have led to more severe voltage violation problems in distribution networks. To address this challenge, grid-connected microgrids with sufficient flexible voltage regulation resources can be utilized to provide effective voltage support for the distribution network. However, microgrids typically operate as independent entities, and there are barriers to collaboration between distribution networks and microgrids. Consequently, this paper proposes a strategy based on incentivizing microgrids to regulate the voltage for the distribution network. First, the willingness for microgrids to participate in voltage regulation is enhanced by establishing an incentive-based voltage regulation scheme, which includes the cost savings of voltage regulation in the distribution network, the distributed generator disconnection risk in the distribution network, and the cost of voltage-dependent loads in the microgrids. The microgrids provide voltage support for the distribution network by adjusting the operation plan and obtaining the corresponding voltage regulation incentive. Second, to optimize the operation strategy of multi-microgrids while considering voltage regulation incentives, the Shapley Q-value deep deterministic policy gradient (SQDDPG) algorithm is proposed. The Shapley Q value is incorporated into the traditional multi-agent deep deterministic policy gradient (MADDPG) algorithm for distributing the global reward to measure the contribution of different microgrids in the voltage regulation process, which allows the algorithm to converge to higher cumulative rewards. Finally, the simulation results for a modified IEEE 33-bus system show that the rate of the voltage violations of the distribution network is reduced by 51.52 %, and the operational economy of microgrids has been improved by 9.12 %. The efficiency of cooperation between distribution network and microgrids has been effectively improved.
随着分布式能源的不断普及和能源需求的不断增长,配电网中的电压违例问题日益严重。为了应对这一挑战,可以利用具有足够灵活电压调节资源的并网微电网为配电网提供有效的电压支持。然而,微电网通常作为独立实体运行,配电网和微电网之间的合作存在障碍。因此,本文提出了一种基于激励微电网调节配电网电压的策略。首先,通过建立基于激励的电压调节方案,提高微电网参与电压调节的意愿,该方案包括配电网电压调节的成本节约、配电网分布式发电机的断网风险以及微电网电压相关负载的成本。微电网通过调整运行计划,获得相应的调压激励,为配电网提供电压支持。其次,为了在考虑电压调节激励的情况下优化多微电网的运行策略,提出了Shapley q值深度确定性策略梯度(SQDDPG)算法。将Shapley Q值引入传统的多智能体深度确定性策略梯度(MADDPG)算法中进行全局奖励分配,以衡量不同微电网在电压调节过程中的贡献,使算法收敛到更高的累积奖励。最后,对改进后的IEEE 33总线系统的仿真结果表明,配电网的电压违例率降低了51.52 %,微电网的运行经济性提高了9.12 %。配电网与微电网的合作效率得到有效提高。
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引用次数: 0
Framework for enhancing fairness and security in active distribution networks via transactive control signals 通过交互控制信号增强有源配电网公平性和安全性的框架
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-09-19 DOI: 10.1016/j.segan.2025.101968
Hajar Abdolahinia , Morteza Aryani , Moein Moeini-Aghtaie , Mohammad Heidarizadeh , Inoccent Kamwa
With the development of peer-to-peer (P2P) energy trading, transactive energy markets (TEMs) face challenges such as ensuring fair access for market participants to the upstream grid and addressing limitations of distribution networks. To tackle these challenges, the distribution system operator (DSO) should incentivize market participants to contribute to their mitigation. To this end, this paper proposes a bi-level framework in which the DSO designs transactive control signals (TCSs) to influence the behavior of market participants. In this framework, fairness, security, and peak shaving signals are introduced at the upper level, while P2P energy trading is implemented at the lower level. The TCSs are calculated based on sensitivity analyses related to fair allocation and secure network operation constraints. As the results demonstrate, the goals of fairness and network security are achieved simultaneously. Moreover, while market participants effectively contribute to meeting technical objectives, their privacy is preserved.
随着点对点(P2P)能源交易的发展,交易型能源市场(tem)面临着确保市场参与者公平接入上游电网和解决配电网限制等挑战。为了应对这些挑战,配电系统运营商(DSO)应该激励市场参与者为缓解这些挑战做出贡献。为此,本文提出了一个双层框架,其中DSO设计交互控制信号(TCSs)来影响市场参与者的行为。在该框架中,公平性、安全性和调峰信号在上层被引入,P2P能源交易在下层被实现。tcs的计算基于公平分配和安全网络运行约束的敏感性分析。结果表明,公平和网络安全的目标是同时实现的。此外,虽然市场参与者有效地为实现技术目标做出了贡献,但他们的隐私得到了保护。
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引用次数: 0
Pricing mechanism for EV fast charging stations considering distributed energy resources 考虑分布式能源的电动汽车快速充电站定价机制
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-08-26 DOI: 10.1016/j.segan.2025.101943
Shakti Vashisth , Praveen Kumar Agrawal , Nikhil Gupta , Vipin Chandra Pandey , K.R. Niazi , Anil Swarnkar
The growing demand for electric vehicles (EVs) requires large-scale deployment of fast charging stations (FCS). These FCS owners are usually private investors and focus on the growth of their businesses. This enforces FCS to design a suitable pricing mechanism to achieve their financial goals, build customer relationships, and maintain competitiveness in the market while considering distributed energy resources (DERs). Therefore, there is a need to develop a holistic approach to keep the interests of all stakeholders in mind while deciding the pricing for EV charging at FCS. Hence, this paper proposes pricing mechanisms, flat and dynamic pricing for EVs charging at FCS considering DERs against dynamic market prices. The proposed pricing mechanisms are designed to keep profit margin of FCS remains same relative to no DERs considering EVs users’ convenience, satisfaction and waiting time. Price-cum-convenience responsive models are proposed for price elasticity of demand and EV users’ satisfaction. The study reveals that both pricing mechanisms under DERs are equally promising as they produce more competitive price signals which are around 11 % lower, up to 61.81 % reduction in grid energy demand during overload periods, and up to 6 % increment in mean satisfaction of EV users while keeping the profit margin intact for FCS owners.
对电动汽车日益增长的需求要求大规模部署快速充电站(FCS)。这些FCS所有者通常是私人投资者,专注于业务的增长。这迫使FCS设计一个合适的定价机制,以实现其财务目标,建立客户关系,并在考虑分布式能源(DERs)的同时保持市场竞争力。因此,在决定电动汽车在FCS充电的定价时,有必要制定一种全面的方法,以考虑所有利益相关者的利益。在此基础上,本文提出了基于动态市场价格的电动汽车在FCS充电的定价机制、扁平定价和动态定价。考虑到电动汽车用户的便利性、满意度和等待时间,建议的定价机制旨在保持FCS相对于无DERs的利润率不变。针对需求的价格弹性和电动汽车用户满意度,提出了价格-便利响应模型。研究表明,DERs下的两种定价机制同样有希望,因为它们产生了更具竞争力的价格信号,在保持FCS所有者的利润率不变的情况下,这些价格信号降低了11. %左右,在过载期间,电网能源需求减少了61.81 %,电动汽车用户的平均满意度增加了6. %。
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引用次数: 0
EV charging strategies for office parking lots to relieve local grids 办公停车场电动汽车充电策略缓解地方电网压力
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-09-03 DOI: 10.1016/j.segan.2025.101942
Hitesh Kumar Verma, Nikhil Gupta, Praveen Kumar Agrawal, K.R. Niazi, Anil Swarnkar
High penetration of electric cars in urban areas may lead to concentrated and uncoordinated heavy EV charging demand in residential areas of the distribution systems. This demand may coincide with the peak demand of the system and consequently poses issues pertaining to reliability, power quality, security, and the difficult operation of stressed distribution systems. Office Parking Lots (OPLs) equipped with adequate EV charging facilities have been seen as one of the tangible solutions to cope with such irresistible situations if found financially viable.
This work proposes two charging strategies, uncoordinated EV charging (UEVC) and coordinated EV charging (CEVC), for OPLs to minimize the impact of EV charging demand on local grids by placing suitable capacity of distributed energy resources (DERs) such as solar photovoltaic (SPVs) and battery energy storage systems (BESS). The proposed CEVC strategy schedules EVs considering mean generation from the grid-connected rooftop SPV system and the state-of-charge of BESS and aligns EV charging demand with SPV generation. Further, the proposed model is tested on an 83-bus real distribution system to investigate the impact of OPL integration on the system’s technical parameters, such as peak demand, total energy losses, peak power loss, and node voltage deviation. Moreover, the techno-economic benefits of both strategies are compared, and EV parking charges are calculated while considering the profit for OPL owners. Simulation results show that the proposed CEVC strategy reduces the OPL’s annual grid energy import, OPL’s annual peak demand, total system energy losses, and parking charge by 85 %, 65 %, 20 %, and 11 %, respectively, when compared with UEVC without DERs. Moreover, despite heavy investment in DERs’ placement at OPL, the proposed charging strategies preserve the benefit of the utility and OPL owners, yet offer more competitive EV parking charges.
电动汽车在城市地区的高渗透率可能导致配电系统中居民区电动汽车重充电需求集中且不协调。这种需求可能与系统的高峰需求相吻合,因此带来了与可靠性、电能质量、安全性和高压配电系统的困难运行有关的问题。如果在经济上可行,配备电动汽车充电设施的办公室停车场(opl)被视为应对这种不可抗拒的情况的切实可行的解决方案之一。本文提出了两种充电策略,即不协调电动汽车充电(UEVC)和协调电动汽车充电(CEVC),通过部署适当容量的分布式能源(DERs),如太阳能光伏(spv)和电池储能系统(BESS),最大限度地减少电动汽车充电需求对当地电网的影响。提出的CEVC策略考虑并网屋顶SPV系统的平均发电量和BESS的充电状态来调度电动汽车,并使电动汽车充电需求与SPV发电量保持一致。最后,在83总线的实际配电系统上对该模型进行了测试,研究了OPL集成对系统峰值需求、总能量损耗、峰值功率损耗和节点电压偏差等技术参数的影响。比较了两种策略的技术经济效益,并在考虑OPL车主利益的情况下计算了电动汽车停车收费。仿真结果表明,与无DERs的UEVC相比,CEVC策略使OPL年电网能源进口、OPL年峰值需求、系统总能量损失和停车费用分别降低了85%、65%、20%和11%。此外,尽管在OPL投入了大量资金,但拟议的充电策略保留了公用事业公司和OPL车主的利益,同时提供了更具竞争力的电动汽车停车费用。
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引用次数: 0
Effects of line dynamics on the stability margin to Hopf bifurcation in grid-forming inverters 线动力学对成网逆变器Hopf分叉稳定裕度的影响
IF 5.6 2区 工程技术 Q2 ENERGY & FUELS Pub Date : 2025-12-01 Epub Date: 2025-08-26 DOI: 10.1016/j.segan.2025.101947
Sushobhan Chatterjee, Sijia Geng
This paper studies oscillatory instability in grid-forming inverters through Hopf bifurcation analysis. An analytical expression for the parameter sensitivity of the stability margin is derived based on the normal vector to the bifurcation hypersurface. Through comprehensive analysis, we identify the most effective control parameters in counteracting the destabilizing effect due to parameter variations. In particular, the impacts of dynamic line modeling on the stability margin are investigated. It is observed that including line dynamics introduces a generally significant reduction in the stability margin across parameters. Additionally, dynamic line models introduce new bifurcations not present in the static model case. This suggests that adopting static line models may lead to overly optimistic stability assessment results.
本文通过Hopf分岔分析研究了并网逆变器的振荡不稳定性。基于分岔超曲面的法向量,导出了稳定裕度参数灵敏度的解析表达式。通过综合分析,确定了最有效的控制参数,以抵消参数变化引起的不稳定效应。特别研究了动态线建模对稳定裕度的影响。可以观察到,包括线动力学引入了跨参数稳定裕度的一般显著减小。此外,动态线模型引入了静态模型中不存在的新分支。这说明采用静线模型可能导致稳定性评估结果过于乐观。
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引用次数: 0
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