IEEE Open Journal of Industry Applications最新文献

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Design and Optimization Strategy to Size Resilient Stand-Alone Hybrid Microgrids in Various Climatic Conditions 不同气候条件下弹性独立混合微电网的设计与优化策略
IEEE Open Journal of Industry Applications Pub Date : 2022-08-23 DOI: 10.1109/OJIA.2022.3201161
Norma Anglani;Giovanna Oriti;Ruth Fish;Douglas L. Van Bossuyt
{"title":"Design and Optimization Strategy to Size Resilient Stand-Alone Hybrid Microgrids in Various Climatic Conditions","authors":"Norma Anglani;Giovanna Oriti;Ruth Fish;Douglas L. Van Bossuyt","doi":"10.1109/OJIA.2022.3201161","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3201161","url":null,"abstract":"This paper presents an original two-steps methodology to size DERs (Distributed Energy Resources) in stand-alone microgrids, to be installed in different areas, featuring different meteorological conditions, but same kind of loads. Design examples are simulated to analyze how an increased level of resilience, considered in terms of number of days of autonomy after an initial incident, affects the sizing of a PV field and its storage. A practical tool to support strategic choices is methodologically illustrated and applied to two case studies to find the best configuration, which is identified by a trade-off among fuel consumption, sizes of PV arrays and resilience. Key design parameters help in designing the best system according to the location, by focusing on the newly identified key performance indicator \u0000<inline-formula><tex-math>$NPV^{s}$</tex-math></inline-formula>\u0000, the simplified net present value of specific scenarios of interest, where a penalty is introduced to account for less than the ideal target of autonomy. The model-based design used to create the microgrid simulations is validated by experimental measurements on a test-bed hybrid microgrid.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"237-246"},"PeriodicalIF":0.0,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09865121.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50323990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Impact of Power Converters and Battery Lifetime on Economic Profitability of Residential Photovoltaic Systems 功率转换器和电池寿命对住宅光伏系统经济效益的影响
IEEE Open Journal of Industry Applications Pub Date : 2022-08-15 DOI: 10.1109/OJIA.2022.3198366
Monika Sandelic;Ariya Sangwongwanich;Frede Blaabjerg
{"title":"Impact of Power Converters and Battery Lifetime on Economic Profitability of Residential Photovoltaic Systems","authors":"Monika Sandelic;Ariya Sangwongwanich;Frede Blaabjerg","doi":"10.1109/OJIA.2022.3198366","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3198366","url":null,"abstract":"The installations of the residential photovoltaic (PV) systems with integrated battery energy storage are strongly dependent on their economic profitability. The Net Present Value (NPV), which is a metric to evaluate the cost-effectiveness of PV-battery systems, can be strongly influenced by the replacement cost. Thus, the lifetime of the reliability-critical components such as power converters and battery plays an important role and needs to be considered during the economic evaluation. In this paper, an impact of power converters and battery lifetime on the economic profitability of the PV-battery system for different installation sites is analyzed. A comprehensive model, consisting of system performance, lifetime, and economic profitability aspects as well as their interconnections is developed in this paper. A case study reveals that the NPV can be significantly over-estimated if the power converters and battery need to be replaced several times during the entire lifespan of the PV-battery system. Hence, the lifetime analysis should be included in the economic assessment and reflected with a more realistic component replacement cost during the planning stage of the residential PV-battery projects.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"224-236"},"PeriodicalIF":0.0,"publicationDate":"2022-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09855838.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50323991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Power Relay Based Multiple Device Cryogenic Characterization Method and Results 基于功率继电器的多器件低温表征方法及结果
IEEE Open Journal of Industry Applications Pub Date : 2022-08-01 DOI: 10.1109/OJIA.2022.3195278
Yuqi Wei;Maksudul Hossain;Dereje Woldegiorgis;Xia Du;H. Alan Mantooth
{"title":"Power Relay Based Multiple Device Cryogenic Characterization Method and Results","authors":"Yuqi Wei;Maksudul Hossain;Dereje Woldegiorgis;Xia Du;H. Alan Mantooth","doi":"10.1109/OJIA.2022.3195278","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3195278","url":null,"abstract":"Cryogenic power electronics is a promising technology due to their high efficiency and high power density characteristics. As the key element of power electronic systems, semiconductor performance should be evaluated under cryogenic temperatures. Liquid nitrogen or liquid helium are usually adopted to achieve cryogenic temperatures. Traditionally, only one semiconductor can be evaluated at one time under different temperatures, which is time-consuming and not energy-friendly. To enable multiple-device characterization at one time under different temperatures, a novel power relay based characterization circuit and corresponding control strategy are described. With the aid of the proposed circuit, multiple devices can be characterized by controlling the power relays. The introduced parasitics by the power relays are minimized through paralleling, which has negligible influence on the device under test (DUT). Cryogenic characterization results of the gate driver, power relay, and semiconductors are presented. Both silicon (Si) metal–oxide–semiconductor field-effect transistor (MOSFET) and silicon carbide (SiC) MOSFETs are characterized and their performances are discussed.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"211-223"},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09847049.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50323992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Very Low-Frequency Oscillation Source Localization on Ireland's Power System 爱尔兰电力系统的极低频振荡源定位
IEEE Open Journal of Industry Applications Pub Date : 2022-07-27 DOI: 10.1109/OJIA.2022.3194140
Connor Duggan;Xueqin Liu;Paul Brogan;Robert Best;D John Morrow
{"title":"Very Low-Frequency Oscillation Source Localization on Ireland's Power System","authors":"Connor Duggan;Xueqin Liu;Paul Brogan;Robert Best;D John Morrow","doi":"10.1109/OJIA.2022.3194140","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3194140","url":null,"abstract":"This paper presents an approach for studying Very Low-Frequency Oscillations (VLFOs) between 0.03 and 0.08 Hz that have been observed on Irelands All-Island transmission system. Previous work by Ireland's TSO has found that the occurrence of the VLFO is linked to the generation dispatch of synchronous machines with governor control. This study verifies previous research by Ireland's TSO and analyses sensitivities such as inertia, system frequency and online generator status that causes an increase in VLF mode magnitude. This paper's results are based on 1-second resolution system frequency, metered generation and power system metric data from 1/1/2018 to 1/10/2020. This analysis demonstrates that the VLF oscillatory mode's stability is highly correlated if governors that consistently provide positive damping torque to the VLF mode are not synchronized. The findings from the study are demonstrated on several events on the Irish system using PMU data. The governor-based dissipating energy flow method is used to validate the relationships found from the generator status and system frequency case study.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"192-201"},"PeriodicalIF":0.0,"publicationDate":"2022-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09842289.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50325621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A Control Concept for Battery Emulators Using a Reference Governor With a Variable PT1-Element for Constraint Handling 一种电池模拟器的控制概念,使用具有可变PT1元件的参考调速器进行约束处理
IEEE Open Journal of Industry Applications Pub Date : 2022-07-26 DOI: 10.1109/OJIA.2022.3194083
Michael Zauner;Christoph Hametner;Oliver König;Stefan Jakubek
{"title":"A Control Concept for Battery Emulators Using a Reference Governor With a Variable PT1-Element for Constraint Handling","authors":"Michael Zauner;Christoph Hametner;Oliver König;Stefan Jakubek","doi":"10.1109/OJIA.2022.3194083","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3194083","url":null,"abstract":"This paper presents a method for highly dynamic nonlinear control of DC-DC converters with constraints used in battery emulators. Controlling this system is particularly challenging as the connected units-under-test often behave like constant power loads (CPLs), which introduce unstable system dynamics and render the system nonlinear. In order to achieve fast output dynamics with the DC-DC converters over a large operating range, a special control architecture is proposed where feedback equivalence is established between a nonlinear system description and a linear description. The nonlinear system dynamics can then be transformed into linear ones for controller synthesis by exploiting the flatness property of the system. Additionally, constraints have to be met at any time during operation to prevent damage to components. In order to satisfy the constraints, a reference governor (RG) is added to the loop. This novel RG concept uses a low-pass filter in the shape of a PT1-element to modify the voltage reference. By changing the time constant of the PT1-element, the RG is able to generate smooth constraints-aware trajectories for setpoint changes. Finally, the capabilities of the control concept are demonstrated and discussed based on high-fidelity simulations.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"202-210"},"PeriodicalIF":0.0,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09840906.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50323993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
In-Situ Measurement and Investigation of Winding Loss in High-Frequency Cored Transformers Under Large-Signal Condition 大信号条件下高频铁心变压器绕组损耗的现场测量与研究
IEEE Open Journal of Industry Applications Pub Date : 2022-07-25 DOI: 10.1109/OJIA.2022.3193584
Navid Rasekh;Jun Wang;Xibo Yuan
{"title":"In-Situ Measurement and Investigation of Winding Loss in High-Frequency Cored Transformers Under Large-Signal Condition","authors":"Navid Rasekh;Jun Wang;Xibo Yuan","doi":"10.1109/OJIA.2022.3193584","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3193584","url":null,"abstract":"This paper presents an in-situ measurement method to accurately characterize the winding loss in high-frequency (HF) transformers, which is challenging to quantify in power electronics applications. This approach adapts the reactive voltage cancellation concept to measure the complete winding loss in HF transformers with the presence of the magnetic core and the load on the secondary side, while this concept was originally brought up for core loss measurement. As an in-situ method, the proposed testing method can factor in the non-linear winding loss elements impacted by the magnetic field interaction between the windings and the core under the large-signal operation, which are not properly assessed in existing approaches. The presented method significantly reduces the sensitivity of the measurement errors linked to the probe phase discrepancy, since the resistive winding loss is well separated out from the core loss. The acquired experimental results are compared and verified with other common empirical measurement methods and three-dimensional (3D) finite element analysis (FEA). As the finding, the measured winding AC resistance is found to be correlated with the load level. Furthermore, treating the complex winding loss and core loss as a black-box problem, this paper proposes a “total loss map” as an engineering solution to practically distribute the measured loss data of magnetic components to the end-users to enable quick and accurate loss estimation/modelling.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"164-177"},"PeriodicalIF":0.0,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09839507.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50325631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Minimum Energy Adaptive Load Sharing of Parallel Operated Compressors 并联压缩机的最小能量自适应负载分配
IEEE Open Journal of Industry Applications Pub Date : 2022-07-20 DOI: 10.1109/OJIA.2022.3192565
Ayman Al Zawaideh;Khalifa Al Hosani;Igor Boiko;Mohammad Luai Hammadih
{"title":"Minimum Energy Adaptive Load Sharing of Parallel Operated Compressors","authors":"Ayman Al Zawaideh;Khalifa Al Hosani;Igor Boiko;Mohammad Luai Hammadih","doi":"10.1109/OJIA.2022.3192565","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3192565","url":null,"abstract":"Compressors operating in parallel are widely used in compressor stations on natural gas pipelines to address the required flow demands. This paper presents a design of a new control structure and a load sharing optimal adaptive controller for multiple compressors connected in parallel and equipped with variable speed drives. The load sharing optimization (LSO) controller computes the split factor to distribute the flow among the compressors which depends on the current operating conditions, with the optimization's objective being to minimize the total energy consumption. In addition, the compressor maps are continuously updated to account for any changes due to external and untraceable factors resulting in an enhancement of the LSO. The presented control structure includes a common single controller for parallel compressors, which eliminates the need for loop-decoupling. Thus, ensuring a better stability and a faster dynamics with respect to the flow or pressure process variable. The proposed control structure and the adaptive LSO performance is evaluated through simulations and a lab hardware setup. The results show an improvement of more than 4% in the total energy consumption compared to an equal load sharing scheme and more than 2.5% compared to the equal distance to surge industrial scheme. This efficiency improvement leads to significant energy cost saving over large periods of time.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"178-191"},"PeriodicalIF":0.0,"publicationDate":"2022-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09834116.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50325622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytical Investigation and Heuristic Optimization of Surface Mounted Permanent Magnet Machines With Hybrid Magnetic Structure 混合磁结构表面安装永磁电机的分析研究与启发式优化
IEEE Open Journal of Industry Applications Pub Date : 2022-07-19 DOI: 10.1109/OJIA.2022.3192313
Bikrant Poudel;Ebrahim Amiri;Parviz Rastgoufard
{"title":"Analytical Investigation and Heuristic Optimization of Surface Mounted Permanent Magnet Machines With Hybrid Magnetic Structure","authors":"Bikrant Poudel;Ebrahim Amiri;Parviz Rastgoufard","doi":"10.1109/OJIA.2022.3192313","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3192313","url":null,"abstract":"Cogging torque causes major operational setbacks for Permanent Magnet (PM) machine operation, particularly in applications where a quiet performance is desired. This paper presents a heuristic optimization framework to optimize the cogging torque in Surface Mounted Permanent Magnet (SPM) machines consisting of a hybrid magnetic structure (i.e., rare-earth and ferrite magnets). To avoid excessive computational time and volume associated with Finite Element (FE)-based optimization solutions, analytical approach is paired up with the optimization algorithm to determine the optimal design while FE is utilized for verification and validation purposes. First, analytical expressions are established for individual objective functions (i.e., airgap PM flux distribution, and cogging torque), and their corresponding spatial harmonics are identified using the air-gap field modulation theory. Next, the presented analytical model is utilized to optimize the system (i.e., minimize the cogging torque) to the desired target level via two different solutions (i.e., Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)), and their respective performance are compared. To determine the efficacy of the presented solutions, the optimal hybrid machine response is compared against the baseline structure.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"152-163"},"PeriodicalIF":0.0,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09833259.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50325632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Torque Ripple Minimization Control Strategy in Synchronous Reluctance Machines 同步磁阻电机转矩脉动最小化控制策略
IEEE Open Journal of Industry Applications Pub Date : 2022-07-14 DOI: 10.1109/OJIA.2022.3190905
Anant K Singh;Ramakrishnan Raja;Tomy Sebastian;Kaushik Rajashekara
{"title":"Torque Ripple Minimization Control Strategy in Synchronous Reluctance Machines","authors":"Anant K Singh;Ramakrishnan Raja;Tomy Sebastian;Kaushik Rajashekara","doi":"10.1109/OJIA.2022.3190905","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3190905","url":null,"abstract":"Torque smoothness is an essential requirement for high-performance motor drive applications. Synchronous reluctance machines (SyRM) have high torque ripple due to non-linear magnetic circuit and saturation. Typically, in Permanent magnet machines the active torque ripple compensation is achieved by injecting a compensating ripple current in the \u0000<italic>q-axis</i>\u0000. For SyRM, the current injection method for active torque ripple cancellation can be used in both the \u0000<italic>d-axis</i>\u0000 and \u0000<italic>q-axis</i>\u0000. However, the saturation of the motor parameters with the changing current can result in varied performance between the two methods. This paper evaluates the effectiveness of both of these methods for torque ripple cancellation. For evaluation, the impact of parameter saturation with ripple current injection on the \u0000<italic>d-axis</i>\u0000 and the \u0000<italic>q-axis</i>\u0000 is studied. The mathematical conclusions obtained are evaluated by both the simulation and the experimental results performed on a 4 pole 1200W Synchronous reluctance machine.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"141-151"},"PeriodicalIF":0.0,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09829907.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50325633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Online Auto-Tuning Method in Field-Orientation-Controlled Induction Motor Driving Inertial Load 磁场定向控制异步电机驱动惯性负载的在线自动调谐方法
IEEE Open Journal of Industry Applications Pub Date : 2022-07-08 DOI: 10.1109/OJIA.2022.3189343
Masaki Nagataki;Keiichiro Kondo;Osamu Yamazaki;Kazuaki Yuki;Yosuke Nakazawa
{"title":"Online Auto-Tuning Method in Field-Orientation-Controlled Induction Motor Driving Inertial Load","authors":"Masaki Nagataki;Keiichiro Kondo;Osamu Yamazaki;Kazuaki Yuki;Yosuke Nakazawa","doi":"10.1109/OJIA.2022.3189343","DOIUrl":"https://doi.org/10.1109/OJIA.2022.3189343","url":null,"abstract":"Feed-forward current control, which employs a single-pulse mode of inverters over a wide speed range, is applied in inertial load drive applications such as electric vehicles and electric railway vehicles. It is necessary to identify both primary and secondary motor parameters to realize sophisticated torque control in the feed-forward current control region, wherein the current controller cannot compensate for motor parameter errors. An online auto-tuning method that is based on the fundamental components of motor voltages during acceleration with an inertial load is proposed in this study. The convergence of the proposed auto-tuning is discussed, and a calculation method for correction gains is proposed to compensate for the motor parameters. The proposed method is verified via numerical simulation and experiments with a 750 W induction motor and an inertial load.","PeriodicalId":100629,"journal":{"name":"IEEE Open Journal of Industry Applications","volume":"3 ","pages":"125-140"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8782707/9666452/09823410.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50325634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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