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A Systematic Small-signal Analysis Procedure for Improving Synchronization Stability of Grid-forming Virtual Synchronous Generators 提高并网虚拟同步发电机同步稳定性的系统小信号分析方法
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-27 DOI: 10.35833/MPCE.2024.000316
Francisco Jesús Matas-Díaz;Manuel Barragán-Villarejo;José María Maza-Ortega
The integration of converter-interfaced generators (CIGs) into power systems is rapidly replacing traditional synchronous machines. To ensure the security of power supply, modern power systems require the application of grid-forming technologies. This study presents a systematic small-signal analysis procedure to assess the synchronization stability of gridforming virtual synchronous generators (VSGs) considering the power system characteristics. Specifically, this procedure offers guidance in tuning controller gains to enhance stability. It is applied to six different grid-forming VSGs and experimentally tested to validate the theoretical analysis. This study concludes with key findings and a discussion on the suitability of the analyzed grid-forming VSGs based on the power system characteristics.
变流器内置发电机(CIG)与电力系统的整合正在迅速取代传统的同步电机。为确保供电安全,现代电力系统需要应用电网成形技术。本研究提出了一种系统的小信号分析程序,用于评估电网形成虚拟同步发电机(VSG)的同步稳定性,并考虑了电力系统的特性。具体而言,该程序为调整控制器增益以提高稳定性提供了指导。该方法适用于六种不同的并网型虚拟同步发电机,并通过实验测试验证了理论分析。本研究最后根据电力系统特性,对所分析的并网型 VSG 的适用性进行了总结和讨论。
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引用次数: 0
Operational Reliability Evaluation and Risk Mitigation of Asynchronous Grids Coupled Through Flexible HVDC Systems 柔性高压直流系统耦合异步电网的运行可靠性评估与风险缓解
IF 6.1 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-23 DOI: 10.35833/MPCE.2024.000677
Qing Sun;Junjie Tang;Sui Peng;Weijie Zhong;Liu Zhu;Yuan Zhao;Wenyuan Li
This paper constructs a synthetic framework for the operational reliability evaluation and risk mitigation of asynchronous grids coupled through flexible high-voltage DC (HVDC) systems (AGs-FDCSs). First of all, an analytical model for the unavailability of DC units is reformulated to refine and facilitate the reliability modeling of such flexible HVDC systems considering their time-dependent features as well as the impacts of converter station configurations. Subsequently, the operational risk associated with the redispatch procedure is extended to the reliability evaluation of composite power system, and the risk is mitigated through an optimal power flow (OPF) based short-term state assessment model. In addition, some new reliability indices like expected DC transmission power (EDCTP) and DC terminal outage probability (DCTOP) are defined to quantify the impact of the reliability of flexible HVDC systems on the entire grid. The effectiveness of the proposed framework on a modified IEEE RTS-79 system is validated with the elabo-rate discussions on the time-dependent reliability of AGs-FDC-Ss as well as the impacts of the converter station configurations.
本文构建了一个基于柔性高压直流系统(ags - fdcs)耦合的异步电网运行可靠性评估与风险缓解的综合框架。首先,重新建立了直流单元不可用的分析模型,以完善和促进这种灵活的高压直流系统的可靠性建模,考虑其时间依赖性以及换流站配置的影响。随后,将再调度过程的运行风险扩展到复合电力系统的可靠性评估中,并通过基于最优潮流(OPF)的短期状态评估模型来降低风险。此外,还定义了一些新的可靠性指标,如期望直流传输功率(EDCTP)和直流终端中断概率(DCTOP),以量化柔性直流系统可靠性对整个电网的影响。通过详细讨论ags - fdc - s的时变可靠性以及换流站配置的影响,验证了该框架在改进的IEEE RTS-79系统上的有效性。
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引用次数: 0
Robust Distribution System State Estimation Considering Anomalous Real-Time Measurements and Topology Change 考虑异常实时测量和拓扑变化的配电系统鲁棒状态估计
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-23 DOI: 10.35833/MPCE.2024.000683
Jiaxiang Hu;Weihao Hu;Di Cao;Jianjun Chen;Sayed Abulanwar;Mohammed K. Hassan;Zhe Chen;Frede Blaabjerg
This paper develops a physics-guided graph network to enhance the robustness of distribution system state estimation (DSSE) against anomalous real-time measurements, as well as a deep auto-encoder (DAE)-based detector and a Gaussian process-aided residual learning (GARL) to deal with challenges arising from topology changes. A global-scanning jumping knowledge network (GSJKN) is first designed to establish the regression rule between the measurement data and state variables. The structural information of distribution system (DS) and a global-scanning module are incorporated to guide the propagation of scarce measurements in the graph topology, contributing to valid estimation precision in sparsely measured DSs. To monitor the topology changes of the network, a DAE network is employed to learn an efficient representation of the measurements of the system under a certain topology, which can achieve online monitoring of the network structure by observing the variation tendency of the reconstruction error. When the topology change occurs, a Gaussian process with a composite kernel is applied to the modeling of the pretrained GSJKN residual to adapt to the new topology. The embedding of the physical structural knowledge enables the proposed GSJKN method to restore the missing/noisy values utilizing the adjacent measurements, which enhances the robustness to typical data acquisition errors. The adopted DAE network and special GARL-based transfer method further allow the DSSE method to rapidly detect and adapt to the topology change, as well as achieve effective quantification of the estimation uncertainties. Comparative tests on balanced and unbalanced systems demonstrate the accuracy, robustness, and adaptability of the proposed DSSE method.
本文开发了一种物理引导图网络来增强配电系统状态估计(DSSE)对异常实时测量的鲁棒性,以及基于深度自编码器(DAE)的检测器和高斯过程辅助残差学习(GARL)来处理拓扑变化带来的挑战。首先设计了全局扫描跳跃知识网络(GSJKN),建立了测量数据与状态变量之间的回归规则。该方法利用配电系统的结构信息和全局扫描模块来指导稀疏测量在图拓扑中的传播,提高了稀疏测量配电系统的估计精度。为了监测网络的拓扑变化,采用DAE网络学习系统在一定拓扑下的测量值的有效表示,通过观察重构误差的变化趋势,实现对网络结构的在线监测。当拓扑发生变化时,采用复合核高斯过程对预训练的GSJKN残差进行建模,以适应新的拓扑结构。物理结构知识的嵌入使GSJKN方法能够利用相邻测量值恢复缺失/噪声值,增强了对典型数据采集误差的鲁棒性。采用DAE网络和特殊的基于garl的传输方法,进一步使DSSE方法能够快速检测和适应拓扑变化,并实现对估计不确定性的有效量化。平衡系统和不平衡系统的对比实验证明了该方法的准确性、鲁棒性和适应性。
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引用次数: 0
Multi-Stage Robust Unit Commitment with Discrete Load Shedding Based on Partially Affine Policy and Two-Stage Reformulation 基于部分仿射策略和两阶段重构的离散减载多阶段鲁棒机组承诺
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-23 DOI: 10.35833/MPCE.2024.000202
Zhongjie Guo;Jiayu Bai;Wei Wei;Haifeng Qiu;Weihao Hu
This paper studies the problem of multi-stage robust unit commitment with discrete load shedding. In the day-ahead phase, the on-off status of thermal units is scheduled. During each period of real-time dispatch, the output of thermal units and the action of load shedding are determined, and the discrete choice of load shedding corresponds to the practice of tripping substation outlets. The entire decision-making process is formulated as a multi-stage adaptive robust optimization problem with mixed-integer recourse, whose solution takes three steps. First, we propose and apply partially affine policy, which is optimized ahead of the day and restricts intertemporal dispatch variables as affine functions of previous uncertainty realizations, leaving remaining continuous and binary dispatch variables to be optimized in real time. Second, we demonstrate that the resulting model with partially affine policy can be reformulated as a two-stage robust optimization problem with mixed-integer recourse. Third, we modify the standard nested column-and-constraint generation algorithm to accelerate the inner loops by warm start. The modified algorithm solves the two-stage problem more efficiently. Case studies on the IEEE 118-bus system verify that the proposed partially affine policy outperforms conventional affine policy in terms of optimality and robustness; the modified nested column-and-constraint generation algorithm significantly reduces the total computation time; and the proposed method balances well optimality and efficiency compared with state-of-the-art methods.
研究了具有离散减载的多阶段鲁棒机组承诺问题。在前一天阶段,热机组的开关状态是预定的。在实时调度的各个时段,确定了热力机组的出力和减载动作,减载方式的离散选择对应于变电站插座跳闸的做法。将整个决策过程描述为一个混合整数资源的多阶段自适应鲁棒优化问题,求解过程分为三步。首先,我们提出并应用了部分仿射策略,该策略提前优化,并将跨期调度变量限制为先前不确定性实现的仿射函数,留下剩余的连续和二进制调度变量进行实时优化。其次,我们证明了具有部分仿射策略的模型可以重新表述为具有混合整数资源的两阶段鲁棒优化问题。第三,我们修改了标准的嵌套列约束生成算法,通过热启动加速内循环。改进后的算法更有效地解决了两阶段问题。在IEEE 118总线系统上的实例研究验证了所提出的部分仿射策略在最优性和鲁棒性方面优于传统的仿射策略;改进的嵌套列约束生成算法显著减少了总计算时间;与现有方法相比,该方法兼顾了优化性和效率。
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引用次数: 0
Robust Scheduling of Integrated Electricity-Heat-Hydrogen System Considering Bidirectional Heat Exchange Between Alkaline Electrolyzers and District Heating Networks 考虑碱性电解槽与区域供热网络双向换热的电-热-氢一体化系统鲁棒调度
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-23 DOI: 10.35833/MPCE.2024.000810
Pengfei Han;Xiaoyuan Xu;Zheng Yan;Mohammad Shahidehpour;Zhenfei Tan;Han Wang;Gang Li
The integrated electricity-heat-hydrogen system (IEHHS) facilitates the efficient utilization of multiple energy sources, while the operational flexibility of IEHHS is hindered by the high heat inertia of alkaline electrolyzers (AELs) and the variations of renewable energy. In this paper, we propose a robust scheduling of IEHHS considering the bidirectional heat exchange (BHE) between AELs and district heating networks (DHNs). First, we propose an IEHHS model to coordinate the operations of AELs, active distribution networks (ADNs), and DHNs. In particular, we propose a BHE that not only enables the waste heat recovery for district heating but also accelerates the thermal dynamics in AELs. Then, we formulate a two-stage robust optimization (RO) problem for the IEHHS operation to consider the variability of renewable energy in ADNs. We propose a new solution method, i. e., multi-affine decision rule (MADR), to solve the two-stage RO problem with less conservatism. The simulation results show that the operational flexibility of IEHHS with BHE is remarkably improved compared with that only with unidirectional heat exchange (UHE). Compared with the traditional affine decision rule (ADR), the MADR effectively reduces the IEHHS operating costs while guaranteeing the reliability of scheduling strategies.
电-热-氢一体化系统(IEHHS)有利于多种能源的高效利用,但碱性电解槽(ael)的高热惯性和可再生能源的变化阻碍了IEHHS的运行灵活性。在本文中,我们提出了一种考虑AELs和区域供热网络之间双向热交换(BHE)的IEHHS鲁棒调度方法。首先,我们提出了一个IEHHS模型来协调AELs、active distribution networks (adn)和dhn的运作。我们特别提出了一种BHE,它不仅可以实现区域供热的废热回收,而且可以加速AELs的热动力学。然后,考虑ADNs中可再生能源的可变性,提出了IEHHS运行的两阶段鲁棒优化(RO)问题。针对保守性较差的两阶段RO问题,提出了一种新的求解方法——多仿射决策规则(MADR)。仿真结果表明,与单向换热(UHE)相比,采用BHE的IEHHS的运行灵活性得到了显著提高。与传统的仿射决策规则(ADR)相比,MADR在保证调度策略可靠性的同时,有效降低了IEHHS的运行成本。
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引用次数: 0
Defense Strategy Against Cyber Attacks on Substations Considering Attack Resource Uncertainty 考虑攻击资源不确定性的变电站网络攻击防御策略
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-20 DOI: 10.35833/MPCE.2024.000375
Tianlei Zang;Yujian Xiao;Yunfei Liu;Shijun Wang;Zi'an Wang;Yi Zhou
With the rapid integration of communication and information technology into substations, the risk of cyber attacks has significantly increased. Attackers may infiltrate sub-station networks, manipulate switches, and disrupt power lines, potentially causing severe damage to the power system. To minimize such risks, this paper proposes a three-layer defender-attacker-defender (DAD) model for optimally allocating limited defensive resources to substations. To model the uncertainty surrounding the knowledge of defender of potential attacks in real-world scenarios, we employ a fuzzy analytic hierarchy process combined with the decision-making trial and evaluation laboratory (FAHP-DEMATEL). This method accounts for the attack resource uncertainty by utilizing intelligence data on factors potentially influenced by attackers, which serves as an evaluation metric to simulate the likelihood of various attack scenarios. These uncertainty probabilities are then incorporated into the substation DAD model consisting three layers of agents: the decision-maker., the attacker, and the operator. The decision-maker devises a defense strategy before the attack, while the attacker aims to identify the strategy that causes the maximum load loss. Meanwhile, the operator seeks to minimize the load loss through optimal power flow scheduling. To solve the model, the original problem is transformed into a two-layer subproblem and a single-layer master problem, which are solved iteratively using a column-and-constraint generation algorithm. Case studies conducted on the IEEE RTS-96 system and the IEEE 118-node system demonstrate the effectiveness and practicality of the proposed model. Comparative experiments further highlight the advantages of the proposed model.
随着通信和信息技术迅速融入变电站,网络攻击的风险显著增加。攻击者可能渗透到变电站网络,操纵交换机,破坏电力线路,对电力系统造成潜在的严重破坏。为了最大限度地降低这种风险,本文提出了一个三层防御者-攻击者-防御者(DAD)模型,以优化分配有限的防御资源给变电站。为了对现实世界中潜在攻击防御者知识的不确定性进行建模,我们采用了模糊层次分析法结合决策试验和评估实验室(FAHP-DEMATEL)。该方法利用攻击者潜在影响因素的情报数据来考虑攻击资源的不确定性,作为模拟各种攻击场景可能性的评估指标。然后将这些不确定性概率合并到变电站DAD模型中,该模型由三层代理组成:决策者。攻击者和操作者。决策者在攻击前设计了防御策略,而攻击者的目标是识别导致最大负载损失的策略。同时,通过优化潮流调度,使负荷损失最小化。为了求解该模型,将原问题转化为两层子问题和单层主问题,采用列约束生成算法迭代求解。以IEEE RTS-96系统和IEEE 118节点系统为例,验证了该模型的有效性和实用性。对比实验进一步突出了该模型的优越性。
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引用次数: 0
Bi-Level Supply Restoration Method for Active Distribution Networks Considering Multi-Resource Coordination 考虑多资源协调的主动式配电网双层供应恢复方法
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-20 DOI: 10.35833/MPCE.2024.000616
Guanyu Song;Chiyuan Ma;Haoran Ji;Hany M. Hasanien;Jiancheng Yu;Jinli Zhao;Hao Yu;Peng Li
The volatility of increasing distributed generators (DGs) poses a severe challenge to the supply restoration of active distribution networks (ADNs). The integration of power electronic devices represented by soft open points (SOPs) and mobile energy storages (MESs) provides a promising opportunity for rapid supply restoration with high DG penetration. Oriented for the post-event rapid restoration of ADNs, a bi-level supply restoration method is proposed considering the multi-resource co-ordination of switches, SOPs, and MESs. At the upper level (long-timescale), a multi-stage supply restoration model is developed for multiple resources under uncertainties of DGs and loads. At the lower level (short-timescale), a rolling correction restoration strategy is proposed to adapt to the DG and load fluctuations on short timescales. Finally, the effectiveness of the proposed method is verified based on a modified practical distribution network and IEEE 123-node distribution network. Re-sults show that the proposed method can fully utilize the coordination potential of multiple resources to improve load restoration ratio for ADNs with DG uncertainties.
日益增加的分布式发电机组的波动性对有功配电网的供电恢复提出了严峻的挑战。以软开点(SOPs)和移动储能(MESs)为代表的电力电子器件的集成为高DG渗透率的快速供电恢复提供了一个有希望的机会。针对ADNs的事后快速恢复问题,提出了一种考虑交换机、sop和MESs多资源协调的双级供电恢复方法。在上层(长时间尺度),建立了考虑dg和负荷不确定性的多资源多阶段供电恢复模型。在较低的时间尺度上,提出了一种滚动修正恢复策略,以适应DG和负荷在短时间尺度上的波动。最后,基于改进的实际配电网和IEEE 123节点配电网验证了所提方法的有效性。结果表明,该方法可以充分利用多种资源的协调潜力,提高具有DG不确定性的ADNs的负荷恢复率。
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引用次数: 0
Co-Design of Power Dispatch with Dynamic Power Regulation and Communication Transmission Optimization for Frequency Control in VPPs 动态功率调节与vpp频率控制通信传输优化协同设计
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-20 DOI: 10.35833/MPCE.2024.000604
Jinrui Guo;Chunxia Dou;Dong Yue;Zhijun Zhang;Zhanqiang Zhang;Bo Zhang
The increasing integration of intermittent renewable energy sources into distribution networks has exerted significant pressure on the frequency regulation of power systems. Meanwhile, integrating small-capacity battery energy storage systems into distribution network is a growing trend in the construction of virtual power plants (VPPs), which offer great potential advantages in improving the system frequency regulation capabilities. However, the process of power dispatch for VPPs may be hindered by imperfections in the communication network, which affects their frequency control performance. Simultaneously, the economic benefits associated with their frequency control services are often overlooked. As such, we propose a co-design method of power dispatch with dynamic power regulation and communication transmission optimization for frequency control in VPPs. First, a joint design scheme of power dispatch and routing optimization under cloud-edge collaborations is proposed. This scheme encompasses a power dispatch method considering the influences of communication network and a routing optimization policy based on graph convolutional neural networks, both of which are designed to ensure the accurate and real-time frequency control service. Further, we propose a dynamic power regulation strategy under edge-edge collaborations. Specifically, according to the established correction control objective, an adaptive distributed auction algorithm (ADAA) based dynamic power regulation control method is designed to determine the optimal regulation power of VPPs, thereby improving the economic benefits of frequency control service. Finally, the simulation results validate the feasibility and superiority of the proposed co-design method for frequency control.
间断性可再生能源日益融入配电网,给电力系统的频率调节带来了巨大压力。同时,将小容量电池储能系统并入配电网是虚拟电厂建设的发展趋势,在提高系统调频能力方面具有巨大的潜在优势。然而,由于通信网络的不完善,vpp的电力调度过程可能会受到阻碍,从而影响其频率控制性能。同时,与他们的频率控制服务相关的经济效益往往被忽视。因此,我们提出了一种基于动态功率调节和通信传输优化的vpp频率控制功率调度协同设计方法。首先,提出了云边缘协同下电力调度与路由优化的联合设计方案。该方案包括考虑通信网络影响的电力调度方法和基于图卷积神经网络的路由优化策略,以确保频率控制服务的准确性和实时性。此外,我们还提出了一种基于边缘协作的动态功率调节策略。具体而言,根据所建立的校正控制目标,设计了一种基于自适应分布式拍卖算法(ADAA)的动态功率调节控制方法,确定vpp的最优调节功率,从而提高变频业务的经济效益。最后,仿真结果验证了所提出的频率控制协同设计方法的可行性和优越性。
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引用次数: 0
Transfer-Learning-Based BiLSTM-WGAN Approach for Synthetic Data Generation of Sub-Synchronous Oscillations in Wind Farms 基于迁移学习的风电场次同步振荡综合数据生成的BiLSTM-WGAN方法
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-20 DOI: 10.35833/MPCE.2024.000550
Shuang Feng;Zhirui Zhang;Yuhang Zheng;Jiaxing Lei;Yi Tang
The phenomenon of sub-synchronous oscillation (SSO) poses significant threats to the stability of power systems. The advent of artificial intelligence (AI) has revolutionized SSO research through data-driven methodologies, which necessitates a substantial collection of data for effective training, a requirement frequently unfulfilled in practical power systems due to limited data availability. To address the critical issue of data scarcity in training AI models, this paper proposes a novel transfer-learning-based (TL-based) Wasserstein generative adversarial network (WGAN) approach for synthetic data generation of SSO in wind farms. To improve the capability of WGAN to capture the bidirectional temporal features inherent in oscillation data, a bidirectional long short-term memory (BiLSTM) layer is introduced. Additionally, to address the training instability caused by few-shot learning scenarios, the discriminator is augmented with mini-batch discrimination (MBD) layers and gradient penalty (GP) terms. Finally, TL is leveraged to fine-tune the model, effectively bridging the gap between the training data and real-world system data. To evaluate the quality of the synthetic data, two indexes are proposed based on dynamic time warping (DTW) and frequency domain analysis, followed by a classification task. Case studies demonstrate the effectiveness of the proposed approach in swiftly generating a large volume of synthetic SSO data, thereby significantly mitigating the issue of data scarcity prevalent in SSO research.
次同步振荡现象严重威胁着电力系统的稳定运行。人工智能(AI)的出现通过数据驱动的方法彻底改变了SSO研究,这需要大量的数据收集来进行有效的训练,由于数据可用性有限,在实际电力系统中经常无法满足这一要求。为了解决训练人工智能模型中数据稀缺的关键问题,本文提出了一种新的基于迁移学习(TL-based)的Wasserstein生成对抗网络(WGAN)方法,用于风电场SSO的合成数据生成。为了提高WGAN捕获振荡数据中固有的双向时间特征的能力,引入了双向长短期记忆(BiLSTM)层。此外,为了解决由少量学习场景引起的训练不稳定性,该鉴别器被增强为小批量鉴别(MBD)层和梯度惩罚(GP)项。最后,利用TL对模型进行微调,有效地弥合了训练数据和真实系统数据之间的差距。为了评价合成数据的质量,提出了基于动态时间规整(DTW)和频域分析的两个指标,然后进行分类任务。案例研究证明了该方法在快速生成大量合成单点登录数据方面的有效性,从而显著缓解了单点登录研究中普遍存在的数据稀缺问题。
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引用次数: 0
Reduced-Order Bus Frequency Response Model for Bulk Power Systems 大容量电力系统的降阶母线频率响应模型
IF 5.7 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-01-20 DOI: 10.35833/MPCE.2024.000737
Xiangxu Wang;Weidong Li;Jiakai Shen;Qili Ding
Bulk power systems show increasingly significant frequency spatial distribution characteristics (FSDCs), leading to a huge difference in the frequency response between regions. Existing uniform-frequency models based on analytical methods are no longer applicable. This paper develops a reduced-order bus frequency response (BFR) model to preserve the FSDC and describe the frequency response of all buses. Its mathematical equation is proved to be isomorphic to the forced vibration of a mass-spring-damper system, and the closed-form solution (CFS) of the BFR model is derived by the modal analysis method and forced decoupling method in vibration mechanics. The correlation between its mathematical equation and the state equation for small-signal stability analysis is discussed, and related parameters in the CFS are defined by the eigen-analysis method without any additional devices or tools. Case studies show that the proposed reduced-order BFR model and its CFS can improve the solution accuracy while keeping the solution speed within milliseconds, which can preserve the significant FSDC of bulk power systems and represent a normalized mathematical description of distinct-frequency models.
大容量电力系统呈现出越来越显著的频率空间分布特征(FSDCs),导致区域间频率响应差异巨大。现有的基于解析方法的等频模型已不再适用。本文建立了一个降低阶母线频率响应(BFR)模型,以保持FSDC并描述所有母线的频率响应。证明了其数学方程与质量-弹簧-阻尼系统的强迫振动是同构的,并利用振动力学中的模态分析方法和强迫解耦方法推导了BFR模型的封闭解。讨论了其数学方程与小信号稳定性分析的状态方程之间的关系,并在不附加任何设备或工具的情况下,采用本征分析方法定义了CFS中的相关参数。实例研究表明,所提出的降阶BFR模型及其CFS在保证求解速度在毫秒级的前提下,提高了求解精度,既保持了大容量电力系统的显著FSDC,又代表了不同频率模型的规范化数学描述。
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引用次数: 0
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