International Journal of Circuit Theory and Applications最新文献

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Analysis and comparison of the coupled coil structures in dual-load magnetic coupled resonance wireless power transfer systems 双负载磁耦合共振无线电力传输系统中耦合线圈结构的分析与比较
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-08 DOI: 10.1002/cta.4193
Jun Cai, Ying Yan, Adrian David Cheok, Xin Zhang
{"title":"Analysis and comparison of the coupled coil structures in dual-load magnetic coupled resonance wireless power transfer systems","authors":"Jun Cai,&nbsp;Ying Yan,&nbsp;Adrian David Cheok,&nbsp;Xin Zhang","doi":"10.1002/cta.4193","DOIUrl":"10.1002/cta.4193","url":null,"abstract":"<p>The dual-load magnetic coupled resonance wireless power transfer (WPT) technology has the advantages of integrated conversion function, higher power density, and higher energy utilization rate. Reasonable coil structure selection and design is a challenge in the dual load WPT system. This article conducts electromagnetic analysis on three types of coil structures: circular–circular, rectangular–circular, and rectangular–rectangular, and uses Ansys Maxwell software to analyze and compare the magnetic field distribution intensity and transmission characteristics of each structure when the coil is offset. The analysis results showed that the rectangular–rectangular coils have stronger offset characteristics. Therefore, the double-load MCR-WPT system ultimately adopts the rectangular–rectangular coil structure. The transmitting and receiving coils of the WPT system were wound and tested, and the dual-load WPT system with rectangular–rectangular coupling coil structures are constructed for experimental verification.</p>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"1892-1908"},"PeriodicalIF":1.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141928706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Implementation of digital MemComputing using standard electronic components 使用标准电子元件实现数字 MemComputing
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-08 DOI: 10.1002/cta.4220
Yuan-Hang Zhang, Massimiliano Di Ventra
{"title":"Implementation of digital MemComputing using standard electronic components","authors":"Yuan-Hang Zhang,&nbsp;Massimiliano Di Ventra","doi":"10.1002/cta.4220","DOIUrl":"10.1002/cta.4220","url":null,"abstract":"<div>\u0000 \u0000 <p>Digital MemComputing machines (DMMs), which employ nonlinear dynamical systems with memory (time non-locality), have proven to be a robust and scalable unconventional computing approach for solving a wide variety of combinatorial optimization problems. However, most of the research so far has focused on the numerical simulations of the equations of motion of DMMs. This inevitably subjects time to discretization, which brings its own (numerical) issues that would be otherwise absent in actual physical systems operating in continuous time. Although hardware realizations of DMMs have been previously suggested, their implementation would require materials and devices that are not so easy to integrate with traditional electronics. Addressing this, our study introduces a novel hardware design for DMMs, utilizing readily available electronic components. This approach not only significantly boosts computational speed compared to current models but also exhibits remarkable robustness against additive noise. Crucially, it circumvents the limitations imposed by numerical noise, ensuring enhanced stability and reliability during extended operations. This paves a new path for tackling increasingly complex problems, leveraging the inherent advantages of DMMs in a more practical and accessible framework.</p>\u0000 </div>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"2447-2465"},"PeriodicalIF":1.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An improved derivative-based phase-locked loop for single-phase grid synchronization under abnormal grid conditions 基于导数的改进型锁相环,用于异常电网条件下的单相电网同步
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-07 DOI: 10.1002/cta.4211
Faridul Hassan, Alok Kumar Dubey, Amritesh Kumar, Avadh Pati
{"title":"An improved derivative-based phase-locked loop for single-phase grid synchronization under abnormal grid conditions","authors":"Faridul Hassan,&nbsp;Alok Kumar Dubey,&nbsp;Amritesh Kumar,&nbsp;Avadh Pati","doi":"10.1002/cta.4211","DOIUrl":"10.1002/cta.4211","url":null,"abstract":"<div>\u0000 \u0000 <p>Generating a quadrature signal in a single-phase system using a second-order generalized integrator (SOGI) requires accurate frequency information. The standard SOGI phase-locked loop (PLL) includes frequency feedback to the SOGI. However, during grid abnormalities such as voltage sag/swell and phase angle jumps, the SOGI-PLL faces frequency disturbances that propagate to the phase detector (PD) and affects the quadrature signal generator (QSG). Furthermore, the SOGI-PLL having two loops dependent on each other creates loop coupling phenomena; either a change in phase or frequency affects each other. SOGI-PLL is tuning sensitive, as the SOGI block has a gain that needs to be adjusted, increases the complexity, and affects the performance of the system. There is a trade-off between SOGI gain and PLL parameters that needs to be considered for adequate parameter design to provide accurate grid synchronization while maintaining the stability of the system. To attain better performance, researchers have proposed derivative-based PLL (DPLL). The conventional DPLL faces challenges to noise and harmonics amplification. This paper presents an improved DPLL for single-phase grid synchronization under adverse grid conditions. The improved derivative-based PLL (IDPLL) comprises two improved derivative-based quadrature signal generator (IDQSG) blocks to extract the phase-error information for accurately estimating phase and frequency. The detailed mathematical modeling and bode plot for the IDQSG and IDPLL are presented. The proposed IDQSG eliminates the requirement of gain tuning, hence reducing complexity. Moreover, there is no interdependent loop in the IDPLL, which significantly improves the dynamic performance. A hardware setup is developed to evaluate the performance of the system in real-time. The experimental results are obtained using an field programmable gate array (FPGA)-based controller.</p>\u0000 </div>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"2059-2074"},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Noncirculating current series resonant converter with pulse frequency modulation 具有脉冲频率调制功能的非环流串联谐振变换器
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-07 DOI: 10.1002/cta.4206
Guangfu Ning, Litao Du, Ben Dai, Mei Su, Wenjing Xiong, Jingtao Xu, Guo Xu
{"title":"Noncirculating current series resonant converter with pulse frequency modulation","authors":"Guangfu Ning,&nbsp;Litao Du,&nbsp;Ben Dai,&nbsp;Mei Su,&nbsp;Wenjing Xiong,&nbsp;Jingtao Xu,&nbsp;Guo Xu","doi":"10.1002/cta.4206","DOIUrl":"10.1002/cta.4206","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, an asymmetric pulse frequency modulation (APFM) is applied to the full-bridge series resonant converter with a secondary LC resonant tank. Different from the traditional PFM, the upper and lower switches have complementary gate drivers and the lower switches have constant on time of half-resonant period in this paper. Thanks to the resonant tank moved to the secondary side with the adopted APFM, the maximum magnetic flux density <i>B</i><sub><i>m</i></sub> of a high-frequency transformer (HFT) is only concerned with the fixed resonant frequency rather than the variable switching frequency. Hence, the switching frequency can be widely regulated, as well as the voltage gain. Furthermore, the circulating current flowing back to the input voltage source in the traditional LC series resonant converter can be eliminated by the APFM, leading to a low resonant current peak value. The operation principles and characteristics of the adopted method are analyzed in detail. Finally, a 500 W/70–120 V to 300 V/21–180 kHz prototype is built, and the experimental results verified the theoretical analysis well.</p>\u0000 </div>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"2075-2088"},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 novel compact and shadow resistance-to-frequency and resistance-to-time converter 新型紧凑型阴影电阻频率转换器和电阻时间转换器
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-07 DOI: 10.1002/cta.4225
Muneer A. Al-Absi, Abdulaziz Alkhulaifi
{"title":"A novel compact and shadow resistance-to-frequency and resistance-to-time converter","authors":"Muneer A. Al-Absi,&nbsp;Abdulaziz Alkhulaifi","doi":"10.1002/cta.4225","DOIUrl":"10.1002/cta.4225","url":null,"abstract":"<p>This paper presents a novel compact and shadow resistance-to-frequency converter and resistance-to-time converter. The design incorporates three current feedback operational amplifiers (CFOA) and can be implemented in CMOS technology. The design's functionality has been proven through simulation and experimental verification. The simulation and experimental findings show that the proposed design works well with small deviation between simulation and experimental results.</p>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 2","pages":"1151-1158"},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Macroscopic state-based reactive voltage control of virtual synchronous generator in AC microgrid 交流微电网中基于宏观状态的虚拟同步发电机无功电压控制
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-07 DOI: 10.1002/cta.4197
Fangyuan Li, Yan Liu, Yanhong Liu
{"title":"Macroscopic state-based reactive voltage control of virtual synchronous generator in AC microgrid","authors":"Fangyuan Li,&nbsp;Yan Liu,&nbsp;Yanhong Liu","doi":"10.1002/cta.4197","DOIUrl":"10.1002/cta.4197","url":null,"abstract":"<p>In building a smarter and more flexible low-carbon smart grid system, alternating current (AC) microgrids using virtual synchronous generator (VSG) technology are viewed as a key link in integrating distributed renewable energy access into the main grid. Given that renewable energy sources (such as solar, hydroenergy, and wind) do not have sufficient capacity for reactive power when not available, AC microgrids face challenges in maintaining stable operation. In order to overcome this difficulty, it is hoped that digging deeper and applying more system information can significantly improve the overall performance of the microgrid. This paper proposes a novel method based on macroscopic state dynamic modeling. This method expands the understanding of the inherent rational control mechanism within the microgrid, enabling the overall control objective of the microgrid to be expressed in a more abstract and direct manner. Additionally, by implementing additional convergence constraint conditions on the macroscopic state dynamics, such as based on some optimality criteria, a set of macroscopic state controllers can be obtained to meet specific performance indicators. Theoretical analysis combined with simulation validation demonstrate the effectiveness of this macroscopic state based control strategy. It proves that when meeting the predefined design requirements, the designed controller can enhance the transient response of microgrids in practical applications, thus supporting higher rate of renewable energy access and promoting the development of the smart grid.</p>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"2214-2226"},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Analysis and design of a three-coil IPT system with independent dual output ports 分析和设计具有独立双输出端口的三线圈 IPT 系统
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-07 DOI: 10.1002/cta.4224
Xuebin Zhou, Kangshuai Dong, Jiabin Wang, Lin Yang
{"title":"Analysis and design of a three-coil IPT system with independent dual output ports","authors":"Xuebin Zhou,&nbsp;Kangshuai Dong,&nbsp;Jiabin Wang,&nbsp;Lin Yang","doi":"10.1002/cta.4224","DOIUrl":"10.1002/cta.4224","url":null,"abstract":"<p>Industrial applications tend to involve a substantial assemblage of electronic devices, and it is imperative to consider diverse charging requirements while charging these devices. This paper proposes a three-coil single-input-and-dual-output (SIDO) inductive power transfer (IPT) system to meet the charging requirements of different devices. The system includes two independent output ports, providing constant voltage (CV) output and constant current (CC) output for different loads, respectively. In addition, the zero-phase angle (ZPA) operation can be achieved, thus avoiding injection of reactive power and improving energy transfer efficiency. Unlike previous related studies, the receiver of the proposed SIDO IPT system only includes one receiving coil to pick up energy, eliminating unnecessary cross-coupling and complex decoupling circuits in traditional IPT systems with multiple outputs. This study first analyzes the CC/CV output theory of the proposed SIDO IPT system in detail, and designs and optimizes the parameters by establishing an equivalent model. Then, the conditions for achieving zero-voltage switching (ZVS) operation of the inverter are obtained by analyzing the sensitivity of CC/CV performance to the variation of the compensation capacitors. Finally, a verification experimental prototype with 2.5A CC output and 72 V CV output is established to verify the effectiveness of the proposed IPT system.</p>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"1879-1891"},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Comparative analysis of control strategies impact on power losses in IGBT power modules with a multiphysics-circuit coupling method 利用多物理场-电路耦合方法比较分析控制策略对 IGBT 功率模块功率损耗的影响
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-07 DOI: 10.1002/cta.4219
Zhifeng Dou, Changai Zhang, Ye Tian, Falong Lu, Qian Wang
{"title":"Comparative analysis of control strategies impact on power losses in IGBT power modules with a multiphysics-circuit coupling method","authors":"Zhifeng Dou,&nbsp;Changai Zhang,&nbsp;Ye Tian,&nbsp;Falong Lu,&nbsp;Qian Wang","doi":"10.1002/cta.4219","DOIUrl":"10.1002/cta.4219","url":null,"abstract":"<p>Power losses in semiconductor devices present a significant impediment to advancing power electronics systems for achieving higher frequencies, improved efficiency, and greater integration. A major challenge lies in directly coupling power losses with various control strategies, considering the variations in manufacturers, packaging, and process structures within the power electronics field. This paper introduces a field-circuit coupling simulation methodology of the insulated gate bipolar transistor (IGBT) within the Simulink/COMSOL environment, using a conventional three-phase six-switch voltage source inverter (VSI) IGBT module as a case study. A composite transfer function interconnects the electrical and thermal aspects, enabling bidirectional coupling between IGBT temperature and losses. This study aims to comprehensively compare the effects of various control strategies, namely, single-vector, dual-vector, and three-vector current model predictive control (CMPC) and space vector pulse width modulation (SVPWM), on the losses and temperature of IGBT power modules. The findings emphasize that losses are significantly influenced by the selection of weighting factor coefficients and power factor settings under the same CMPC control strategy with a fixed switching frequency. Additionally, the selection of control strategies, such as CMPC and SVPWM, substantially impacts power losses in power electronic devices.</p>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"2089-2108"},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Double-order negative group delay filtering function: A brilliant capability of the bilinear double-order transfer function 双阶负群延迟滤波函数双线性双阶传递函数的卓越能力
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-07 DOI: 10.1002/cta.4213
Rawid Banchuin
{"title":"Double-order negative group delay filtering function: A brilliant capability of the bilinear double-order transfer function","authors":"Rawid Banchuin","doi":"10.1002/cta.4213","DOIUrl":"10.1002/cta.4213","url":null,"abstract":"<p>In this work, the capability to generate the negative group delay (NGD) phenomenon at those frequencies higher than a certain value, that is, the NGD high-pass (HP) filtering function, of the bilinear double-order transfer function has been demonstrated. Based on the Type-I bilinear double-order filter circuit, our theory has been verified by strong agreements between the formulae and their proof-of-concept (POC) circuit-based simulation results. Both formula-based and POC circuit-based simulations give the minimum group delay of −5 ms yet the cut-off frequency of 10 and 9 rad/s, respectively. Such slight deviation is caused by the approximation error of the bilinear double-order impedance. By employing two orders, the bilinear double-order transfer function has been found to be the basis transfer function for the NGD filtering function with the highest degree of freedom. Based on our design equation for the NGD filtering function, it can be seen that the distances between zero and pole and the characteristic frequency of the bilinear double-order transfer function are governed by such characteristic frequency itself, the cut-off frequency of the NGD filtering function, and the fractional order of the Laplacian operator. In addition, the effects of the fractional order of the Laplacian operator, the fractional order of the transfer function, and the ratio of the abovementioned distances to the characteristics of the newly found double-order NGD filtering function have been studied in detail.</p>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 5","pages":"3157-3169"},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Single-stage single-phase multiport DC–AC inverter suitable for standalone applications due to its notable performance in different operation modes 单级单相多端口直流-交流逆变器在不同运行模式下性能卓越,适合独立应用
IF 1.8 3区 工程技术
International Journal of Circuit Theory and Applications Pub Date : 2024-08-06 DOI: 10.1002/cta.4201
Sina Ahmadian, Vahid Abbasi, Siroos Hemmati
{"title":"Single-stage single-phase multiport DC–AC inverter suitable for standalone applications due to its notable performance in different operation modes","authors":"Sina Ahmadian,&nbsp;Vahid Abbasi,&nbsp;Siroos Hemmati","doi":"10.1002/cta.4201","DOIUrl":"10.1002/cta.4201","url":null,"abstract":"<p>A new multiport DC–AC converter is proposed for standalone and off-grid tied applications. The configuration converts power from DC to AC form in a single stage with suitable voltage gain. To increase the certainty of supporting power, the converter is designed to operate in four modes, including battery-alone mode. The other advantage of the presented work is supplying the output power during unbalanced voltage conditions of the input ports. The advanced features of the converter for being used in standalone applications are related to the suitable placement and structure of the bidirectional port. In addition, the configuration is designed in a way to contain appropriate structural properties such as the existence of a common ground between the DC section and inverter, continuity of input currents, configured by an acceptable number of components, and low-voltage stress on the DC–DC section's switches. Furthermore, it has an impedance network to protect the inverter's switches in a shoot-through state. To confirm the converter advantages from the mentioned points of view, it has been compared with similar configurations. A prototype rated at 110 V is prepared to demonstrate the advantages of the converter performance per different conditions. The results of the steady-state and transient experiments validate the suitability of the presented converter.</p>","PeriodicalId":13874,"journal":{"name":"International Journal of Circuit Theory and Applications","volume":"53 4","pages":"2275-2291"},"PeriodicalIF":1.8,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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