Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846054
Hung-Liang Cheng, Yong-Nong Chang, H. Yen, C. Hua, Peng-Yu Su
This paper presents a novel interleaved dc-to-dc converter that is mainly composed of two flyback converters. Prior to turning on the active switch of one flyback converter, its parasitic capacitance is discharged to nearly zero voltage by the induced current in the secondary winding of the coupled inductor of the other flyback one. By this mean, both active switches can achieve zero-voltage switching on (ZVS) without needing to use any active-clamping circuit or snubber circuit. In spite of improving the overall circuit efficiency, ZVS operation can eliminate the current spike in the active switch, leading to increase the circuit reliability. The steady-state analyses at different operation modes and the mathematical equations are provided. Finally, a 200-W prototype circuit was built and tested to verify the analytical predictions. Satisfactory performances are obtained from the experimental results.
{"title":"A novel interleaved flyback-typed converter with ZVS operation","authors":"Hung-Liang Cheng, Yong-Nong Chang, H. Yen, C. Hua, Peng-Yu Su","doi":"10.1109/SPEC.2016.7846054","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846054","url":null,"abstract":"This paper presents a novel interleaved dc-to-dc converter that is mainly composed of two flyback converters. Prior to turning on the active switch of one flyback converter, its parasitic capacitance is discharged to nearly zero voltage by the induced current in the secondary winding of the coupled inductor of the other flyback one. By this mean, both active switches can achieve zero-voltage switching on (ZVS) without needing to use any active-clamping circuit or snubber circuit. In spite of improving the overall circuit efficiency, ZVS operation can eliminate the current spike in the active switch, leading to increase the circuit reliability. The steady-state analyses at different operation modes and the mathematical equations are provided. Finally, a 200-W prototype circuit was built and tested to verify the analytical predictions. Satisfactory performances are obtained from the experimental results.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122035645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846198
Hyun-Jun Choi, Young-pyo Cho, Jeehoon Jung
In order to improve the reliability and the stability of DC microgrids (MG) and performance of DC bus voltage regulator, at the same time, a new concept of DC bus control signal (DBCS) algorithm based on pulse frequency variation is proposed. In conventional power management algorithms such as centralized control, power line signaling (PLS), and DC bus signaling (DBS), the reliability of DC MGs could be degraded. In this paper, the switching ripple carried on the dc-bus voltage is presented as the operating information for communication between interfaced converters in DC MG. By varying the switching frequency of a grid-connected DC-DC converter according to the load conditions, all DC MG components connected to the DC bus can be aware of the operating status. Experimental results verify the practical feasibility and the effectiveness of the proposed strategy through the 3.3 kW prototype dual active bridge converter.
{"title":"A novel DC bus control signal using pulse frequency modulation for DC microgrids","authors":"Hyun-Jun Choi, Young-pyo Cho, Jeehoon Jung","doi":"10.1109/SPEC.2016.7846198","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846198","url":null,"abstract":"In order to improve the reliability and the stability of DC microgrids (MG) and performance of DC bus voltage regulator, at the same time, a new concept of DC bus control signal (DBCS) algorithm based on pulse frequency variation is proposed. In conventional power management algorithms such as centralized control, power line signaling (PLS), and DC bus signaling (DBS), the reliability of DC MGs could be degraded. In this paper, the switching ripple carried on the dc-bus voltage is presented as the operating information for communication between interfaced converters in DC MG. By varying the switching frequency of a grid-connected DC-DC converter according to the load conditions, all DC MG components connected to the DC bus can be aware of the operating status. Experimental results verify the practical feasibility and the effectiveness of the proposed strategy through the 3.3 kW prototype dual active bridge converter.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122126233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846036
Maciej Grabarek, R. Strzelecki
Paper raises a point of power surges and theirs adverse effects in the marine power plants. The article explains a source of surges appearance, and presents measurements carried out on a modern ship. It discusses effects of dynamic power transients on the ship's energy safety. Finally it proposes, a novel approach for power surge elimination, based on medium voltage active conditioner. As well as it propose the topology and control strategy of such conditioning system, together with preliminary experimental result.
{"title":"A novel approach to energy safety improvement in the marine power plants with active power surge compensator","authors":"Maciej Grabarek, R. Strzelecki","doi":"10.1109/SPEC.2016.7846036","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846036","url":null,"abstract":"Paper raises a point of power surges and theirs adverse effects in the marine power plants. The article explains a source of surges appearance, and presents measurements carried out on a modern ship. It discusses effects of dynamic power transients on the ship's energy safety. Finally it proposes, a novel approach for power surge elimination, based on medium voltage active conditioner. As well as it propose the topology and control strategy of such conditioning system, together with preliminary experimental result.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124410143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846110
Hae-jun Choi, Kwan-Yuhl Cho, Hag-Wone Kim, Se-Kyo Chung
For the sensorless control of a PM synchronous motor without using rotor position sensors, the information on the actual voltages and actual currents of the motor are required. In the model based rotor position estimator of a PM synchronous motor, the reference voltages, which are the output of the current controller, are commonly used. The reference voltages in over modulation regions for high speed operation are different from the actual voltages applied to the motor so that the estimated rotor position and rotor speed may fail to track the real rotor position and real rotor speed. In this paper, the sensorless control for a PM synchronous motor in over modulation regions for high speed operation is proposed. Three phase voltages applied to the motor are measured by using additional voltage detection circuits, and the rotor position estimator based on the measured three phase voltages is validated through experiment.
{"title":"Sensorless control of a PM synchronous motor in over modulation regions for high speed operation","authors":"Hae-jun Choi, Kwan-Yuhl Cho, Hag-Wone Kim, Se-Kyo Chung","doi":"10.1109/SPEC.2016.7846110","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846110","url":null,"abstract":"For the sensorless control of a PM synchronous motor without using rotor position sensors, the information on the actual voltages and actual currents of the motor are required. In the model based rotor position estimator of a PM synchronous motor, the reference voltages, which are the output of the current controller, are commonly used. The reference voltages in over modulation regions for high speed operation are different from the actual voltages applied to the motor so that the estimated rotor position and rotor speed may fail to track the real rotor position and real rotor speed. In this paper, the sensorless control for a PM synchronous motor in over modulation regions for high speed operation is proposed. Three phase voltages applied to the motor are measured by using additional voltage detection circuits, and the rotor position estimator based on the measured three phase voltages is validated through experiment.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125750413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846211
F. Lin, G. Covic, J. Boys
Coupling factor is a important design parameter in inductive power transfer (IPT) systems as it determines the amount of VA effort required from the primary pad to deliver the necessary VA to the secondary pad. As IPT systems involve more complex magnetic systems such as multi-coil primary pads (whose currents can have an amplitude and phase difference), the effective coupling factor becomes more difficult to describe and validate. Typically, an equivalent T-model is used for two coupled single coil pads; however, this is insufficient for multi-coil primaries such as a bi-polar pad (BPP). As such, this paper introduces an equation which is able to describe the effective coupling factor of an IPT system with a multi-coil primary and a single coil secondary while considering the reflected impedances between the coils.
{"title":"Differentiating coupling factor and VA transfer of IPT systems using bipolar pad primaries","authors":"F. Lin, G. Covic, J. Boys","doi":"10.1109/SPEC.2016.7846211","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846211","url":null,"abstract":"Coupling factor is a important design parameter in inductive power transfer (IPT) systems as it determines the amount of VA effort required from the primary pad to deliver the necessary VA to the secondary pad. As IPT systems involve more complex magnetic systems such as multi-coil primary pads (whose currents can have an amplitude and phase difference), the effective coupling factor becomes more difficult to describe and validate. Typically, an equivalent T-model is used for two coupled single coil pads; however, this is insufficient for multi-coil primaries such as a bi-polar pad (BPP). As such, this paper introduces an equation which is able to describe the effective coupling factor of an IPT system with a multi-coil primary and a single coil secondary while considering the reflected impedances between the coils.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125820130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846066
Ming‐Fa Tsai, C. Tseng, Chun-Han Chen, Yung-Jen Cheng, Chunbao Yang
This paper presents the phase-variable modeling of a SynRM motor in PSIM simulation tool. Just like a real motor, the three-phase input is modeled by means of resistor, inductor, and dependent voltage source circuit elements. The dependent voltage source is used to replace the variable inductance of the stator equivalent circuit by using the voltage source absorption theorem. There are two features of the constructed model block. One is that the three-phase input is circuit-based, so it can be directly connected to the inverter for integrated system simulation. The other one is that the load torque input is equation-based, so the load torque can be given by a mathematical function. Simulation test demonstrates the correctness of the constructed SynRM model.
{"title":"Phase-variable modeling of a synchronous reluctance motor using PSIM","authors":"Ming‐Fa Tsai, C. Tseng, Chun-Han Chen, Yung-Jen Cheng, Chunbao Yang","doi":"10.1109/SPEC.2016.7846066","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846066","url":null,"abstract":"This paper presents the phase-variable modeling of a SynRM motor in PSIM simulation tool. Just like a real motor, the three-phase input is modeled by means of resistor, inductor, and dependent voltage source circuit elements. The dependent voltage source is used to replace the variable inductance of the stator equivalent circuit by using the voltage source absorption theorem. There are two features of the constructed model block. One is that the three-phase input is circuit-based, so it can be directly connected to the inverter for integrated system simulation. The other one is that the load torque input is equation-based, so the load torque can be given by a mathematical function. Simulation test demonstrates the correctness of the constructed SynRM model.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128744012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846196
D. Guan, M. X. Bui, D. Xiao, M. F. Rahman
The Fundamental PWM Excitation (FPE) is a recent sensorless motor control method in the electrical drive system which uses the current derivative measurement to estimate the rotor position. However, parasitic effects arising from the IGBT switches cause high frequency oscillation in current, so the current derivative estimation cannot be made until these high frequency oscillations die down. In this case, the voltage vector needs to be extended to the minimal pulse width in order to have accurate current derivative estimation. The voltage vector extension however leads to current distortion and reduces the performance of machine, which are compensated by inserting opposite voltage vectors. This paper will describe the FPE method briefly and then focus on the evaluation of current derivative based position estimation in the FPE method which uses a high-bandwidth current sensor and a Least Square curve fitting algorithm in an FPGA. Position estimation accuracy is checked experimentally via a mechanical position sensor.
{"title":"Evaluation of an FPGA current derivative measurement system for the fundamental PWM excitation sensorless method for IPMSM","authors":"D. Guan, M. X. Bui, D. Xiao, M. F. Rahman","doi":"10.1109/SPEC.2016.7846196","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846196","url":null,"abstract":"The Fundamental PWM Excitation (FPE) is a recent sensorless motor control method in the electrical drive system which uses the current derivative measurement to estimate the rotor position. However, parasitic effects arising from the IGBT switches cause high frequency oscillation in current, so the current derivative estimation cannot be made until these high frequency oscillations die down. In this case, the voltage vector needs to be extended to the minimal pulse width in order to have accurate current derivative estimation. The voltage vector extension however leads to current distortion and reduces the performance of machine, which are compensated by inserting opposite voltage vectors. This paper will describe the FPE method briefly and then focus on the evaluation of current derivative based position estimation in the FPE method which uses a high-bandwidth current sensor and a Least Square curve fitting algorithm in an FPGA. Position estimation accuracy is checked experimentally via a mechanical position sensor.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128215264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Power Electronic Transformer(PET) is a promising component in the future power system. The modular PET is the most attractive due to its high voltage level and flexible function. Unfortunately, when the modular PET is driving multiple loads, there would be overmodulation issue in the AC-DC stage caused by the unbalanced load power. This paper proposed a reactive component injection control strategy to prevent overmodulation for a three-module PET under unbalanced load. Two specific algorithms are proposed. The effectiveness of the proposed control strategy and the two algorithms are verified by simulation results.
{"title":"Reactive component injection control of the modular multi-output power electronic transformer","authors":"Shaodi Ouyang, Jinjun Liu, Shuguang Song, Xingxing Chen","doi":"10.1109/SPEC.2016.7846187","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846187","url":null,"abstract":"Power Electronic Transformer(PET) is a promising component in the future power system. The modular PET is the most attractive due to its high voltage level and flexible function. Unfortunately, when the modular PET is driving multiple loads, there would be overmodulation issue in the AC-DC stage caused by the unbalanced load power. This paper proposed a reactive component injection control strategy to prevent overmodulation for a three-module PET under unbalanced load. Two specific algorithms are proposed. The effectiveness of the proposed control strategy and the two algorithms are verified by simulation results.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129658313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846210
N. Fernando, S. Jayasinghe, Alireza Tashakori Abkenar
Fault tolerance is an essential feature in marine and naval electric propulsion drives. Therefore, there is a growing research interest in developing fault tolerant technologies for marine applications. This paper investigates the control and operation of an inverter fed PM propulsion motor under a specific power electronic failure case. Compared to the technologies reported in literature, this paper formulates a special control strategy for the motor operation during the situation where only one high side switch and one low side switch in two different phases are operational in a standard three-phase six-switch inverter. The proposed control strategy assumes that the remaining switches are failed in open circuit while the corresponding anti-parallel diodes are functional. The mathematical background of the two quadrant control strategy is formulated. The operation is analyzed in the context of marine propulsion power/speed requirements. Simulations for a 50 kW three-phase fault tolerant motor is presented for the operation with the proposed dual switch control strategy. Controllability of motor torque for speeds up to 45% rated speed corresponding to approximately 9% rated propulsion power output is achieved without overrating the device current ratings.
{"title":"Marine propulsion PM motor control under inverter partial fault","authors":"N. Fernando, S. Jayasinghe, Alireza Tashakori Abkenar","doi":"10.1109/SPEC.2016.7846210","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846210","url":null,"abstract":"Fault tolerance is an essential feature in marine and naval electric propulsion drives. Therefore, there is a growing research interest in developing fault tolerant technologies for marine applications. This paper investigates the control and operation of an inverter fed PM propulsion motor under a specific power electronic failure case. Compared to the technologies reported in literature, this paper formulates a special control strategy for the motor operation during the situation where only one high side switch and one low side switch in two different phases are operational in a standard three-phase six-switch inverter. The proposed control strategy assumes that the remaining switches are failed in open circuit while the corresponding anti-parallel diodes are functional. The mathematical background of the two quadrant control strategy is formulated. The operation is analyzed in the context of marine propulsion power/speed requirements. Simulations for a 50 kW three-phase fault tolerant motor is presented for the operation with the proposed dual switch control strategy. Controllability of motor torque for speeds up to 45% rated speed corresponding to approximately 9% rated propulsion power output is achieved without overrating the device current ratings.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127437981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-12-01DOI: 10.1109/SPEC.2016.7846174
D. Sgro, S. A. S. Tibúrcio, R. Leão, R. F. Sampaio, F. Antunes
This paper presents a new approach that provides scaling the LCL-filter inductances based on the harmonic analysis of the filter output current. The approach considers the filter design together with the inverter control, both together, improving the system stability and the dynamic response. The model and general guidelines for selecting the filter parameters, taking into account the variation of the grid equivalent inductor and the use of non-linear inductances, are presented. The proposed control system makes use of feed-forward control in order to increase performances of the feedback control and eliminates the need of synchronization procedure. Simulation tests with a 15 kW three-phase VSI with a LCL filter have proved the effectiveness of the proposed approach.
{"title":"New control strategy for grid-connected inverter using LCL filter","authors":"D. Sgro, S. A. S. Tibúrcio, R. Leão, R. F. Sampaio, F. Antunes","doi":"10.1109/SPEC.2016.7846174","DOIUrl":"https://doi.org/10.1109/SPEC.2016.7846174","url":null,"abstract":"This paper presents a new approach that provides scaling the LCL-filter inductances based on the harmonic analysis of the filter output current. The approach considers the filter design together with the inverter control, both together, improving the system stability and the dynamic response. The model and general guidelines for selecting the filter parameters, taking into account the variation of the grid equivalent inductor and the use of non-linear inductances, are presented. The proposed control system makes use of feed-forward control in order to increase performances of the feedback control and eliminates the need of synchronization procedure. Simulation tests with a 15 kW three-phase VSI with a LCL filter have proved the effectiveness of the proposed approach.","PeriodicalId":403316,"journal":{"name":"2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128931984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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