Pub Date : 2012-06-25DOI: 10.1109/PEDG.2012.6253975
H. S. Che, W. Hew, N. Rahim, E. Levi, M. Jones, M. Durán
The paper presents a study of a six-phase wind energy conversion system (WECS) with series-connected dc-links. The structure of the generation system requires the dc-link voltages to be balanced at the generator's side. To achieve this, it is shown that a dc-link voltage balancing controller can be realised by exploiting the extra degrees of freedom provided by the xy plane of the six-phase machine. To facilitate the controller's implementation, an alternative modified transformation matrix is also suggested. The feasibility of the studied system, including the operation of the dc-link voltage balancing controller, is verified using Matlab/Simulink simulations.
{"title":"A six-phase wind energy induction generator system with series-connected DC-links","authors":"H. S. Che, W. Hew, N. Rahim, E. Levi, M. Jones, M. Durán","doi":"10.1109/PEDG.2012.6253975","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6253975","url":null,"abstract":"The paper presents a study of a six-phase wind energy conversion system (WECS) with series-connected dc-links. The structure of the generation system requires the dc-link voltages to be balanced at the generator's side. To achieve this, it is shown that a dc-link voltage balancing controller can be realised by exploiting the extra degrees of freedom provided by the xy plane of the six-phase machine. To facilitate the controller's implementation, an alternative modified transformation matrix is also suggested. The feasibility of the studied system, including the operation of the dc-link voltage balancing controller, is verified using Matlab/Simulink simulations.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128606824","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6253987
S. Saridakis, E. Koutroulis, F. Blaabjerg
Targeting at a cost-effective deployment of grid-connected PhotoVoltaic (PV) systems, this paper presents a new methodology for the optimal design of transformerless PV inverters, which are based on the Neutral Point Clamped (NPC) and the Active-Neutral Point Clamped (ANPC) topologies. The design optimization results demonstrate that a different set of optimal values of the PV inverter switching frequency and output filter components are derived for the NPC and ANPC topologies, respectively, as well as for each of the PV inverter installation sites under study. The NPC and ANPC PV inverter structures, which are derived using the proposed design optimization methodology exhibit lower Levelized Cost Of generated Electricity (LCOE) and manufacturing cost and they are simultaneously capable to inject more energy into the electric grid than the corresponding non-optimized PV inverters. Thus, the proposed optimal design methodology enables to maximize the economic benefit obtained during the lifetime period of the installed PV system.
{"title":"Optimal design of NPC and Active-NPC transformerless PV inverters","authors":"S. Saridakis, E. Koutroulis, F. Blaabjerg","doi":"10.1109/PEDG.2012.6253987","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6253987","url":null,"abstract":"Targeting at a cost-effective deployment of grid-connected PhotoVoltaic (PV) systems, this paper presents a new methodology for the optimal design of transformerless PV inverters, which are based on the Neutral Point Clamped (NPC) and the Active-Neutral Point Clamped (ANPC) topologies. The design optimization results demonstrate that a different set of optimal values of the PV inverter switching frequency and output filter components are derived for the NPC and ANPC topologies, respectively, as well as for each of the PV inverter installation sites under study. The NPC and ANPC PV inverter structures, which are derived using the proposed design optimization methodology exhibit lower Levelized Cost Of generated Electricity (LCOE) and manufacturing cost and they are simultaneously capable to inject more energy into the electric grid than the corresponding non-optimized PV inverters. Thus, the proposed optimal design methodology enables to maximize the economic benefit obtained during the lifetime period of the installed PV system.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127128226","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6254060
T. Jalakas, I. Roasto, D. Vinnikov, H. Agabus
This paper describes a novel power conditioning system for residential fuel cell power plants, consisting of a step-up DC/DC converter and a single or a multiphase inverter. To increase the efficiency of the whole system a quasi Z-source inverter along with a step-up isolation transformer and a voltage doubler rectifier can be used. Due the continuous input current and low current ripple, the service life of a fuel cell is significantly increased. Further reduction in the output current ripple of a fuel cell is achieved by implementing an interleaved converter design with shifted switching and active ripple cancellation. Interleaved converter design also enables variations in the operating cell count to increase the overall efficiency of a power conditioning system.
{"title":"Novel power conditioning system for residential fuel cell power plants","authors":"T. Jalakas, I. Roasto, D. Vinnikov, H. Agabus","doi":"10.1109/PEDG.2012.6254060","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6254060","url":null,"abstract":"This paper describes a novel power conditioning system for residential fuel cell power plants, consisting of a step-up DC/DC converter and a single or a multiphase inverter. To increase the efficiency of the whole system a quasi Z-source inverter along with a step-up isolation transformer and a voltage doubler rectifier can be used. Due the continuous input current and low current ripple, the service life of a fuel cell is significantly increased. Further reduction in the output current ripple of a fuel cell is achieved by implementing an interleaved converter design with shifted switching and active ripple cancellation. Interleaved converter design also enables variations in the operating cell count to increase the overall efficiency of a power conditioning system.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127883782","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6254079
M. Pahlevaninezhad, S. Eren, A. Bakhshai, P. Jain
This paper presents a novel digital control scheme for a power factor correction boost converter based on a discrete energy function. It is shown in this paper that the dynamics of the power factor correction AC/DC boost converter can be significantly improved by implementing a very simple yet novel optimal control scheme, which is superior to the conventional controller for the AC/DC power factor correction boost converters used in plug-in electric vehicles. In the proposed control scheme, first an energy function is introduced, which represents the discrete energy of the error signals, then the control law is designed based on the discrete energy function. In order to verify the performance of the proposed controller, it is examined on a digitally controlled 3KW boost PFC operating at 100 kHz switching frequency. Experimental results show that the proposed controller results in low current harmonics and significantly faster output voltage transient responses as compared to the one for conventional control schemes.
{"title":"An optimal control strategy based on a discrete energy function, for single-phase AC/DC converters used in plug-in electric vehicles","authors":"M. Pahlevaninezhad, S. Eren, A. Bakhshai, P. Jain","doi":"10.1109/PEDG.2012.6254079","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6254079","url":null,"abstract":"This paper presents a novel digital control scheme for a power factor correction boost converter based on a discrete energy function. It is shown in this paper that the dynamics of the power factor correction AC/DC boost converter can be significantly improved by implementing a very simple yet novel optimal control scheme, which is superior to the conventional controller for the AC/DC power factor correction boost converters used in plug-in electric vehicles. In the proposed control scheme, first an energy function is introduced, which represents the discrete energy of the error signals, then the control law is designed based on the discrete energy function. In order to verify the performance of the proposed controller, it is examined on a digitally controlled 3KW boost PFC operating at 100 kHz switching frequency. Experimental results show that the proposed controller results in low current harmonics and significantly faster output voltage transient responses as compared to the one for conventional control schemes.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131671300","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6254091
A. Hasmasan, C. Busca, R. Teodorescu, L. Helle
In this paper, a FEM (finite element method) based mechanical model for PP (press-pack) IGBTs (insulated gate bipolar transistors) is presented, which can be used to calculate the clamping force distribution among chips under various clamping conditions. The clamping force is an important parameter for the chip, because it influences contact electrical resistance, contact thermal resistance and power cycling capability. Ideally, the clamping force should be equally distributed among chips, in order to maximize the reliability of the PP IGBT. The model is built around a hypothetical PP IGBT with 9 chips, and it has numerous simplifications in order to reduce the simulation time as much as possible. The developed model is used to analyze the clamping force distribution among chips, in various study cases, where uniform and non-uniform clamping pressures are applied on the studied PP IGBT.
{"title":"Modelling the clamping force distribution among chips in press-pack IGBTs using the finite element method","authors":"A. Hasmasan, C. Busca, R. Teodorescu, L. Helle","doi":"10.1109/PEDG.2012.6254091","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6254091","url":null,"abstract":"In this paper, a FEM (finite element method) based mechanical model for PP (press-pack) IGBTs (insulated gate bipolar transistors) is presented, which can be used to calculate the clamping force distribution among chips under various clamping conditions. The clamping force is an important parameter for the chip, because it influences contact electrical resistance, contact thermal resistance and power cycling capability. Ideally, the clamping force should be equally distributed among chips, in order to maximize the reliability of the PP IGBT. The model is built around a hypothetical PP IGBT with 9 chips, and it has numerous simplifications in order to reduce the simulation time as much as possible. The developed model is used to analyze the clamping force distribution among chips, in various study cases, where uniform and non-uniform clamping pressures are applied on the studied PP IGBT.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125402888","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6254062
G. Konstantinou, S. R. Pulikanti, M. Ciobotaru, V. Agelidis, K. Muttaqi
The installed capacity of grid connected PV plants has increased significantly over the past few years and is expected to continue its growth over the next decade due to the continuous demand for renewable energy and distributed generation systems. This paper presents a seven-level flying capacitor (FC) based active neutral point clamped (ANPC) converter for the connection of utility-scale PV system to the electricity grid. The multilevel voltage output of the topology provides high quality waveforms while maintaining the operational characteristics of NPC based converters for PV systems. The converter topology together with a method to regulate the FC voltages to their reference values and an optimal third harmonic injection for utilization of the DC-link voltage are presented. Simulation results for the operation of the grid connected converter under steady state and transient operation are provided in order to demonstrate the operation and performance of the topology in grid connected applications.
{"title":"The seven-level flying capacitor based ANPC converter for grid intergration of utility-scale PV systems","authors":"G. Konstantinou, S. R. Pulikanti, M. Ciobotaru, V. Agelidis, K. Muttaqi","doi":"10.1109/PEDG.2012.6254062","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6254062","url":null,"abstract":"The installed capacity of grid connected PV plants has increased significantly over the past few years and is expected to continue its growth over the next decade due to the continuous demand for renewable energy and distributed generation systems. This paper presents a seven-level flying capacitor (FC) based active neutral point clamped (ANPC) converter for the connection of utility-scale PV system to the electricity grid. The multilevel voltage output of the topology provides high quality waveforms while maintaining the operational characteristics of NPC based converters for PV systems. The converter topology together with a method to regulate the FC voltages to their reference values and an optimal third harmonic injection for utilization of the DC-link voltage are presented. Simulation results for the operation of the grid connected converter under steady state and transient operation are provided in order to demonstrate the operation and performance of the topology in grid connected applications.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125581689","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6253988
H. Chen, C. Liu, Z. Chen
This paper firstly describes the research background of the wind turbine imitation system, indicating the needs for the wind turbine imitation in laboratories. The current development status and the significance of the wind turbine imitation based on the switched reluctance (SR) motor are introduced. Then the model of the wind turbine and SR motor is expounded, from which the control theory and methods of the imitation system are derived. The control model got simplified and the corresponding compensation is added considering the actual operating environment. Finally, an experimental platform is built. Experimental results are consistent with the designed theoretical results and met the system design requirements.
{"title":"Simulation and implementation of wind turbine based on switched reluctance motor drive","authors":"H. Chen, C. Liu, Z. Chen","doi":"10.1109/PEDG.2012.6253988","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6253988","url":null,"abstract":"This paper firstly describes the research background of the wind turbine imitation system, indicating the needs for the wind turbine imitation in laboratories. The current development status and the significance of the wind turbine imitation based on the switched reluctance (SR) motor are introduced. Then the model of the wind turbine and SR motor is expounded, from which the control theory and methods of the imitation system are derived. The control model got simplified and the corresponding compensation is added considering the actual operating environment. Finally, an experimental platform is built. Experimental results are consistent with the designed theoretical results and met the system design requirements.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126645601","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6254067
Mingxia Xu, Dehong Xu, Ping-Yi Lin, Min Chen, Jianxun Ni, Tao Zhang
The relationship between resonant control and repetitive control is investigated in this paper. Resonant control and repetitive control are compared by using them to an active power filter (APF). The stability and design of parameter with the two control methods in APF system are analyzed, and the steady-state error and transient response are also analyzed for them. The theory is verified by experiment.
{"title":"Understanding repetitive control and resonant control","authors":"Mingxia Xu, Dehong Xu, Ping-Yi Lin, Min Chen, Jianxun Ni, Tao Zhang","doi":"10.1109/PEDG.2012.6254067","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6254067","url":null,"abstract":"The relationship between resonant control and repetitive control is investigated in this paper. Resonant control and repetitive control are compared by using them to an active power filter (APF). The stability and design of parameter with the two control methods in APF system are analyzed, and the steady-state error and transient response are also analyzed for them. The theory is verified by experiment.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126902171","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6253982
D. Schwartz
The thermoelectric generator (TEG) is the predominant compact, solid-state heat engine. Effective utilization of a heat resource using a TEG requires maximizing its power output by interposing a regulated power converter between the source and load. In this work, a maximum-power-point-tracking system architecture is introduced that is compatible with efficient pulse-width modulated converter topologies. The control system, based on input voltage sampling, does not require a microcontroller or analog-to-digital converter and can be built with available discrete components. Measurement results of a demonstration SEPIC converter are presented, validating the concept.
{"title":"A maximum-power-point-tracking control system for thermoelectric generators","authors":"D. Schwartz","doi":"10.1109/PEDG.2012.6253982","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6253982","url":null,"abstract":"The thermoelectric generator (TEG) is the predominant compact, solid-state heat engine. Effective utilization of a heat resource using a TEG requires maximizing its power output by interposing a regulated power converter between the source and load. In this work, a maximum-power-point-tracking system architecture is introduced that is compatible with efficient pulse-width modulated converter topologies. The control system, based on input voltage sampling, does not require a microcontroller or analog-to-digital converter and can be built with available discrete components. Measurement results of a demonstration SEPIC converter are presented, validating the concept.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116058297","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 : 2012-06-25DOI: 10.1109/PEDG.2012.6254093
Hyun-Chil Choi, Wei Zhao, M. Ciobotaru, V. Agelidis
The large-scale photovoltaic (PV) systems have already been reached 200 MW power level and they will continue to grow in size in the upcoming years. This trend will challenge the existing PV system architectures by requiring power converters with a higher power rating and a higher voltage level at the point of common coupling (PCC). The cascaded H-bridge (CHB) multilevel converter is one of the solutions which could deal with the aforementioned challenges. However, the topology based on the CHB converter faces the issue of leakage current that flows through the solar panel parasitic capacitance to ground which could damage the PV panels and pose safety problems. This paper proposes a multiphase isolated DC/DC converter for the CHB topology for a large-scale PV system which eliminates the leakage current issue. At the same time, the multiphase structure of the DC/DC converter helps to increase the power rating of the converter and to reduce the PV voltage and current ripples. A 0.54 MW rated seven-level CHB converter using multiphase isolated DC/DC converters has been modeled and simulated using MATLAB/Simulink and PLECS Blockset. Simulation results of different case studies are presented to evaluate the performance of the proposed PV system configuration.
{"title":"Large-scale PV system based on the multiphase isolated DC/DC converter","authors":"Hyun-Chil Choi, Wei Zhao, M. Ciobotaru, V. Agelidis","doi":"10.1109/PEDG.2012.6254093","DOIUrl":"https://doi.org/10.1109/PEDG.2012.6254093","url":null,"abstract":"The large-scale photovoltaic (PV) systems have already been reached 200 MW power level and they will continue to grow in size in the upcoming years. This trend will challenge the existing PV system architectures by requiring power converters with a higher power rating and a higher voltage level at the point of common coupling (PCC). The cascaded H-bridge (CHB) multilevel converter is one of the solutions which could deal with the aforementioned challenges. However, the topology based on the CHB converter faces the issue of leakage current that flows through the solar panel parasitic capacitance to ground which could damage the PV panels and pose safety problems. This paper proposes a multiphase isolated DC/DC converter for the CHB topology for a large-scale PV system which eliminates the leakage current issue. At the same time, the multiphase structure of the DC/DC converter helps to increase the power rating of the converter and to reduce the PV voltage and current ripples. A 0.54 MW rated seven-level CHB converter using multiphase isolated DC/DC converters has been modeled and simulated using MATLAB/Simulink and PLECS Blockset. Simulation results of different case studies are presented to evaluate the performance of the proposed PV system configuration.","PeriodicalId":146438,"journal":{"name":"2012 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG)","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123796524","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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