IEEE Transactions on Power Delivery最新文献

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Enhancing Security in Microgrids via Grid-Forming Converter Control by Contingency Mitigation, Overload Protection, and Voltage Balancing 基于事故缓解、过载保护和电压平衡的成网变流器控制提高微电网安全性
IF 4.4 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2025-01-07 DOI: 10.1109/tpwrd.2025.3526726
Stefan Häselbarth, Kai Strunz
{"title":"Enhancing Security in Microgrids via Grid-Forming Converter Control by Contingency Mitigation, Overload Protection, and Voltage Balancing","authors":"Stefan Häselbarth, Kai Strunz","doi":"10.1109/tpwrd.2025.3526726","DOIUrl":"https://doi.org/10.1109/tpwrd.2025.3526726","url":null,"abstract":"","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"30 1","pages":""},"PeriodicalIF":4.4,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simulation Study on the Suppression Effect on Secondary Arcs Based on Online Injection Power Compensation 基于在线喷射功率补偿的二次电弧抑制效果仿真研究
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2025-01-07 DOI: 10.1109/TPWRD.2025.3526639
Haoxi Cong;Yuxuan Wang;Xuefeng Hu;Xuan Zhang;Wenjing Su;Qingmin Li
{"title":"Simulation Study on the Suppression Effect on Secondary Arcs Based on Online Injection Power Compensation","authors":"Haoxi Cong;Yuxuan Wang;Xuefeng Hu;Xuan Zhang;Wenjing Su;Qingmin Li","doi":"10.1109/TPWRD.2025.3526639","DOIUrl":"10.1109/TPWRD.2025.3526639","url":null,"abstract":"The issue of secondary arc in ultra-high voltage transmission lines poses a significant threat to power system stability. This paper proposes a novel approach to mitigate the perniciousness of secondary arc by employing injection power compensation. The method integrates an evolution model that encompasses arc dynamics and an injection power compensation model. Through rigorous validation, the effectiveness of this method has been demonstrated. Furthermore, the impact of key factors, namely, initial recovery voltage gradient, fault location, line length, and injection power compensation delay time on the suppression effect has been analyzed. The results reveal that the injection power compensation-based method reduces the recovery voltage by 24.7% and shortens the average arc duration along the transmission line under 600 km by 22% compared to two groups utilizing high-speed grounding switches. Notably, fault location demonstrates a trend where the effect is superior at both ends of the line. The enhancement of other factors diminishes the suppression effect. Although the proposed method shows promise, further practical research is warranted to fully validate its feasibility.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"878-888"},"PeriodicalIF":3.8,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142936200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Review on DFIG Supplementary SSI Damping Controllers: Design, Development, and Directions DFIG补充SSI阻尼控制器综述:设计、发展和方向
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2025-01-03 DOI: 10.1109/TPWRD.2025.3525551
Tao Xue;Ulas Karaagac;Mohsen Ghafouri;Ilhan Kocar
{"title":"Review on DFIG Supplementary SSI Damping Controllers: Design, Development, and Directions","authors":"Tao Xue;Ulas Karaagac;Mohsen Ghafouri;Ilhan Kocar","doi":"10.1109/TPWRD.2025.3525551","DOIUrl":"10.1109/TPWRD.2025.3525551","url":null,"abstract":"This paper presents a comprehensive review of the supplementary damping controllers (SDCs) proposed for the mitigation of sub-synchronous interaction (SSI) between doubly-fed induction generator-based wind parks (DFIG-WPs) and series capacitor compensated grids. First, the terms sub-synchronous control interaction (SSCI) and induction generator effect (IGE) are clarified by delineating their occurrence conditions and instability mechanisms in series compensated DFIG-WPs. Then, a generic design and testing framework of SDCs is proposed as a basis including the selection and adjustment of key aspects, and tests of mitigation performance, transient response and practical implementation. SDCs in the existing literature are classified into four main types considering the control structures. Their strengths and limitations are thoroughly discussed. Finally, the future directions are indicated to develop adaptive SDCs with high efficacy and robustness considering data-driven techniques.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"797-809"},"PeriodicalIF":3.8,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142924712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamic TOU Tariff for the Hierarchical Coordination of PEV Charging 面向电动汽车分级收费协调的动态分时电价
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2025-01-01 DOI: 10.1109/TPWRD.2024.3523744
Angel M. Sanchez;Andrés A. Romero
{"title":"Dynamic TOU Tariff for the Hierarchical Coordination of PEV Charging","authors":"Angel M. Sanchez;Andrés A. Romero","doi":"10.1109/TPWRD.2024.3523744","DOIUrl":"10.1109/TPWRD.2024.3523744","url":null,"abstract":"This paper presents a three-stage methodology for the charging coordination of Plug-in Electric Vehicles (PEVs), incorporating the calculation of Time-of-Use (TOU) daily rates to mitigate the increase of energy cost of the aggregators caused by the coordination. Our previous work has been taken as a basis, where a PEV coordination methodology is proposed to minimize the Loss of Life (LOL) of Primary Distribution Transformers (PDTs) in the network supplying the charging of a set of PEVs. In the first stage, the charging power profiles of PEV aggregators, which are favorable for the Distribution System Operator (DSO), are calculated. Then, in the second stage, time-bands of TOU tariffs are computed for each aggregator to incentivize PEV charging in accordance with the result of the first stage. Such time-bands mitigate the increase in aggregator energy costs due to PEV charging coordination. Finally, in the third stage, the obtained TOU tariffs are applied to the PEV coordination methodology. The proposed methodology has been applied to a case study involving 32 aggregators. Results indicate that the increase in aggregator costs due to PDT power limitation is relatively small, while the reduction in LOL of PDT is significant.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"822-830"},"PeriodicalIF":3.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142912178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Evaluation and Analysis of Gassing Material Performance Used in Low-Voltage Circuit Breakers 低压断路器用气体材料性能评价与分析
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2025-01-01 DOI: 10.1109/TPWRD.2024.3516725
Weidong Cao;Chaojie Luo;Qian Wang;Tao Zhuang;Yanfeng Zhang;Xingwen Li
{"title":"Evaluation and Analysis of Gassing Material Performance Used in Low-Voltage Circuit Breakers","authors":"Weidong Cao;Chaojie Luo;Qian Wang;Tao Zhuang;Yanfeng Zhang;Xingwen Li","doi":"10.1109/TPWRD.2024.3516725","DOIUrl":"10.1109/TPWRD.2024.3516725","url":null,"abstract":"This paper introduces an evaluation method for gassing materials used in low-voltage circuit breakers and identifies key factors affecting arc characteristics. Firstly, sixteen types of gassing materials were prepared using PA6 and PA66 as matrices, with various flame retardants and reinforcements as additives. Breaking experiments were conducted in both low-frequency and direct-current circuits to assess these materials in terms of arcing and post-arc phenomena. Material characterization techniques were then employed to analyze the optical absorption and pyrolysis properties of the selected gassing materials. Finally, based on the physical mechanisms of interaction between arcs and gassing materials, a detailed mechanistic analysis and theoretical explanation were provided, integrating material characterization and microscopic modeling. The results suggest that the proposed evaluation method effectively identifies one or two materials with optimal overall performance from the 16 types tested. Superior materials are characterized by organic molecular fillers and high radiation absorption, which enhance arc energy absorption and increase ablation gas generation. Hydrogen-containing gases (e.g., H<sub>2</sub>, CH<sub>4</sub>, H<sub>2</sub>O) and gases with high dissociation energy (e.g., CO<sub>2</sub>, N<sub>2</sub>) are crucial for arc extinction. This paper also highlights two major challenges facing current gassing materials, suggesting areas for further research.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"728-738"},"PeriodicalIF":3.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142912179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Improved Dielectric Strength of GIL Insulator by Multi-Dimensional Functionally Graded Materials Under Polarity Reversal Voltage 极性反转电压下多层功能梯度材料提高GIL绝缘子介电强度
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2024-12-30 DOI: 10.1109/TPWRD.2024.3523902
Jianan Dong;Boxue Du;Hucheng Liang;Hang Yao
{"title":"Improved Dielectric Strength of GIL Insulator by Multi-Dimensional Functionally Graded Materials Under Polarity Reversal Voltage","authors":"Jianan Dong;Boxue Du;Hucheng Liang;Hang Yao","doi":"10.1109/TPWRD.2024.3523902","DOIUrl":"10.1109/TPWRD.2024.3523902","url":null,"abstract":"In direct current gas-insulated transmission lines (DC-GILs), insulators often operate under temperature gradients and may experience polarity reversal voltages. To reduce flashover faults of DC-GIL insulators, this paper introduces a novel multi-dimensional functionally graded material (MFGM) insulator, which integrates a surface coating made of nonlinear conductivity material (SNCM) with a bulk constructed from permittivity functionally graded material (<italic>ϵ</i>-FGM). Simulation and experimental studies were conducted under polarity reversal conditions and across different temperature gradients. Results show that the SNCM insulators can uniform the electric field (E-field) distributions before polarity reversal under various temperature gradients, but enhance the E-field distortion after polarity reversal at <italic>T</i><sub>HV</sub> of 25 and 50 °C. The MFGM insulator can effectively regulate the E-field distributions across all temperature gradients both before and after polarity reversal, leading to flashover voltage improvements of 6.5%, 9.8%, and 21.9% at <italic>T</i><sub>HV</sub> of 25, 50, and 70 °C, respectively. Moreover, flashover voltages of all insulators under the negative-to-positive condition are notably higher than those under the positive-to-negative condition, exhibiting a pronounced polarity effect. Results suggest that the MFGM insulator holds promise for applications in DC-GIL projects.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"843-851"},"PeriodicalIF":3.8,"publicationDate":"2024-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142905558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Lightweight Method Integrating Keypoint Detection and Perspective Geometry for Substation Safety Distance Monitoring 一种集成关键点检测和透视几何的变电站安全距离监测轻量化方法
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2024-12-25 DOI: 10.1109/TPWRD.2024.3522808
Hanbo Zheng;Shiqi Xu;Jinheng Li;Fang Gao;Zhimei Cui
{"title":"A Lightweight Method Integrating Keypoint Detection and Perspective Geometry for Substation Safety Distance Monitoring","authors":"Hanbo Zheng;Shiqi Xu;Jinheng Li;Fang Gao;Zhimei Cui","doi":"10.1109/TPWRD.2024.3522808","DOIUrl":"10.1109/TPWRD.2024.3522808","url":null,"abstract":"In the high-voltage environment of substations, due to the lack of effective monitoring methods, personnel may fail to maintain a safe distance from the equipment due to subjective factors, leading to electric shock accidents. To more effectively reduce the occurrence of such accidents, this paper proposes a monocular vision-based method for monitoring the safety distance between personnel and live equipment. Firstly, this paper makes lightweight improvements to the YOLOv8 (You Only Look Once) keypoint detection model by introducing the proposed dense feature fusion (DFF) module and adaptive channel cross (ACC) module into the backbone and neck, respectively, and replacing the network's original path aggregation network (PAN) structure with the bi-directional feature pyramid network (BiFPN) structure. Subsequently, based on the principles of camera imaging and perspective geometry, this paper calculates the mapping relationship between two-dimensional pixel coordinates and three-dimensional world coordinates. Finally, based on the detected keypoints and the obtained mapping relationship, the distance between personnel and live equipment is monitored. Experiments conducted in a substation scenario show that the improved keypoint detection model increases AP from 0.718 to 0.771, reduces parameters from 3.09M to 2.10M, and lowers FLOPs from 8.48G to 7.01G, and the maximum distance measurement error is only 3.778%.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"810-821"},"PeriodicalIF":3.8,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flexible Impedance Calculation of Inverter-Based Resources via Descriptor State Space Models 基于广义状态空间模型的逆变器资源柔性阻抗计算
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2024-12-23 DOI: 10.1109/TPWRD.2024.3521291
Andrés Argüello;Ricardo Torquato;Tiago Barbosa;Walmir Freitas;Maurício B. C. Salles
{"title":"Flexible Impedance Calculation of Inverter-Based Resources via Descriptor State Space Models","authors":"Andrés Argüello;Ricardo Torquato;Tiago Barbosa;Walmir Freitas;Maurício B. C. Salles","doi":"10.1109/TPWRD.2024.3521291","DOIUrl":"10.1109/TPWRD.2024.3521291","url":null,"abstract":"Impedance-based models of inverter-based resources (IBR) such as wind/photovoltaic generators are widely used to study control to grid interactions. Existing methods for obtaining detailed analytic expressions of the impedance equivalents are time consuming and reliant on extensive algebraic manipulation of numerous equations. In this context, this paper presents a method for calculating impedance profiles numerically, by using a descriptor state-space (DSS) representation of the IBRs which considers all IBR control blocks modularly, so that they can be added, removed, or modified without extensive algebraic manipulations. The method is based on DSS models, which are more transparent than traditional state-space models as algebraic expressions are modeled explicitly. This modular approach speeds up the investigation of the impact of different control designs and tunings on the risk of instabilities, while preserving a high level of detail of IBR behavior and mitigating potential human error. The proposed calculation methodology is validated with detailed electromagnetic transient simulations, for single-phase and three-phase IBRs. Applications of the proposed approach are presented to illustrate its ability to assist on the efficient investigation of characteristics of different control designs, and to help identify simplified models tailored for studying specific types of instabilities at different frequency ranges.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"764-775"},"PeriodicalIF":3.8,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142879703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Multi-Stage Under Frequency Load Shedding Scheme Considering Virtual Inertial Response of Wind Turbines 考虑风力涡轮机虚拟惯性响应的多阶段欠频甩负荷优化方案
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2024-12-20 DOI: 10.1109/TPWRD.2024.3521287
Saleh Irandoust;Turaj Amraee;Mohammadreza Toulabi;Alireza Ashouri-Zadeh
{"title":"Optimal Multi-Stage Under Frequency Load Shedding Scheme Considering Virtual Inertial Response of Wind Turbines","authors":"Saleh Irandoust;Turaj Amraee;Mohammadreza Toulabi;Alireza Ashouri-Zadeh","doi":"10.1109/TPWRD.2024.3521287","DOIUrl":"10.1109/TPWRD.2024.3521287","url":null,"abstract":"Insufficient primary frequency control during severe disturbances requires the implementation of effective under frequency load shedding (UFLS) measures to prevent system collapse. The integration of non-dispatchable renewable energy sources like wind and solar, which are known for their variability, poses challenges to frequency management due to decreased system inertia. Consequently, there is a need for a comprehensive UFLS relay scheme tailored to renewable energy-integrated systems, aiming to enhance reliability and stability while minimizing unnecessary load shedding during under frequency events caused by unpredictable renewable sources. In this research paper, we present an optimal and robust multi-stage UFLS scheme designed for two operating points: base-load and peak-load. The suggested scheme considers different levels of wind power penetration and incorporates various contingency scenarios. The proposed UFLS scheme assumes that wind turbines are equipped with auxiliary controllers to actively participate in the power system frequency control task. To optimize the scheme, a genetic algorithm (GA) is employed, and the performance is evaluated through simulations using MATLAB and DIgSILENT/PowerFactory link. The results of the study demonstrate that the involvement of wind turbines in the frequency response significantly improves the performance of the UFLS scheme and reduces the total amount of load shedding required. This research provides valuable insights into addressing the challenges posed by renewable energy integration and offers a potential solution to enhance the reliability and stability of power systems in the presence of renewable sources.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"681-692"},"PeriodicalIF":3.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Centralized Post-Transient Derivatives Based Protection Scheme for LVDC Distribution Networks 一种基于LVDC配电网暂态后导数的集中式保护方案
IF 3.8 2区 工程技术
IEEE Transactions on Power Delivery Pub Date : 2024-12-19 DOI: 10.1109/TPWRD.2024.3520244
Dong Wang;Pengfei Hu;Yu Cao;Mazheruddin Syed
{"title":"A Centralized Post-Transient Derivatives Based Protection Scheme for LVDC Distribution Networks","authors":"Dong Wang;Pengfei Hu;Yu Cao;Mazheruddin Syed","doi":"10.1109/TPWRD.2024.3520244","DOIUrl":"10.1109/TPWRD.2024.3520244","url":null,"abstract":"With the growing integration of renewable energy sources, Low Voltage (LV) distribution networks are experiencing increased demands to accommodate a diverse range of renewables. As a potential solution to alleviate the strain on existing distribution networks, the adoption of Low Voltage Direct Current (LVDC) distribution networks is under consideration. However, establishing reliable and selective protection techniques remains a significant challenge. Several protection algorithms focus on significant fault currents, fixed threshold settings, and high sampling frequencies for effective coordination, which often face limitations in low fault current scenarios or require costly data acquisition techniques. Therefore, this paper presents a novel centralized Post-Transient Derivatives (PTD) based protection scheme, which Leverages only the sign of Post-Transient Voltage Derivative (PTVD) and Post-Transient Current Derivative (PTCD). This approach addresses the selectivity constraints of existing voltage and current based solutions, particularly when lower sampling frequencies are applied. The proposed scheme is validated against various fault scenarios on an LVDC test network simulated in PSCAD/EMTDC and verified using an RT-Box based hardware test bed.","PeriodicalId":13498,"journal":{"name":"IEEE Transactions on Power Delivery","volume":"40 2","pages":"705-717"},"PeriodicalIF":3.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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