超级电容电动公交客车高效直流驱动系统的研究
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摘要
超级电容作为高功率密度储能电源,其充放电速度快,适合于起制动频繁、运行线路固定的城市电动公交客车,但超级电容供电电压变化范围宽,能量密度低。如何提高有限能源利用率,实现驱动系统高效的电驱动和能量回馈制动,是促进超级电容电动公交客车(UCEB)实际应用和技术进步的关键。因此,本论文对UCEB高效率直流驱动系统进行了研究,通过降低超级电容、驱动系统变换器、电增磁永磁直流电机等系统环节的损耗,并有效回收制动能量,以期最大限度提高有限车载能源的利用率。
驱动系统变换器的特性决定了UCEB整车性能。针对UCEB车载能源更加有限的瓶颈问题,从效率、可靠性、成本等因素对基本双向直流变换拓扑进行对比分析,选择了电流双象限变换器作为UCEB驱动电路拓扑。根据电容电压宽范围变化特点,提出了兼具降压驱动、升压制动能量回馈和车载充电功能的电增磁永磁直流电机驱动系统方案。针对大功率变换器开关损耗较大的问题,基于电感耦合馈能的方法,设计了馈能缓冲式软开关电路,实现了开关管零电流开通、零电压关断以及开通缓冲能量的转移存储,从而改善了开关管工作环境,降低了变换器开关损耗;兼顾车辆运行的动力性和舒适性要求,采用占空比展开过程的限幅跟随调节方法,有效抑制了驱动电流超调;根据超级电容的充电特性,利用线路切换使驱动变换器兼具恒流-恒压车载充电电源功能,降低了充电站设备的复杂程度,有利于节省UCEB公交系统成本。
在保证车辆制动安全性的前提下,基于增磁直流电机的电励磁可控特性,为优化UCEB制动能量回馈性能,分析了在电枢电流和转速稳定等条件下,励磁电流对电机发电效率和制动能量回馈功率的影响规律,提出了机电组合制动优化控制策略:车辆中轻度制动模式下,根据电机发电效率最大化条件,设计了效率优化控制策略,获得了电制动单独作用时电机回馈制动能量的最大效率;机电复合制动时,为增大电制动回馈车辆动能的比例,设计了能量优化控制策略,获得了电机回馈制动能量功率的最大值。同时,分析了电励磁对电机电动运行时效率和能量损耗的影响规律,根据电枢电流闭环控制时电机效率最大化条件,或输出转矩闭环控制时能量损耗最小化条件,分别设计了电机电动运行的效率和能量优化控制策略,实现了电机驱动时能量转换性能的优化。通过台架实验模拟UCEB工况运行,验证了上述驱动系统变换器和增磁直流电机的典型特性,为整车性能及其改进方案的进一步研究提供了必要条件。
根据台架实验结果,为进一步提高各系统环节的电能转换效率,针对车辆轻载工况时驱动系统变换器效率偏低,以及高频斩波脉冲电流放电对超级电容寿命和内阻热耗的不利影响等问题,提出了采用多重化直流变换的改进方案。轻载工况时,为提高驱动系统变换器中小功率区间的效率,根据变换器输出功率或电流调节工作单元数目,设计了多重化电路的降重工作模式,保证了各单元电路工作在优化效率区域,拓宽了变换器高效功率区间;车辆重载工况运行时,多个单元电路同时工作,减小了流过超级电容高频脉冲电流变化幅度,从而降低了超级电容等效内阻损耗,改善了超级电容的工作环境;同时,输出电流纹波变化幅度的降低以及纹波频率的提高,改善了UCEB驱动系统增磁直流电机的动态性能。
仿真分析表明,常规多重化变换器的软开关电路实现困难,据此提出了错相PWM控制并联交错电路方案。交错单元内部以滤波电感耦合的方式,实现了开关管零电流开通,并降低了续流二极管的反向恢复损耗,改善了功率器件的运行环境;交错单元间的并联降低了大功率应用场合对功率器件电流应力要求;错相PWM控制提高了并联交错变换器的等效开关频率,并保留了多重化的优点。运用理论分析、仿真和实验相结合的方法,对交错单元内部开关管间的均流特性进行了研究,得出交错单元内部可实现自动均流。基于数据手册估算和多项式拟合相结合的方法,对主要功率器件损耗进行定量分析,结果表明:在开关频率或等效开关频率相同的条件下,并联交错电路主要功率器件损耗低于同等功率条件下的单重电流双象限电路,从功耗角度验证了并联交错方案应用于UCEB的可行性,为促进UCEB驱动系统性能提升提供了技术储备。
As the energy storage equipment, ultra-capacitor with the outstanding performance of high power density is suitable for city bus with the characteristics of frequent start-stop and fixed line. It is the key problem of promoting ultra-capacitor electric bus (UCEB) development that how to improve the utilization rate of the limited on-vehicle energy by driving the vehicle and recovering the braking energy efficiently. Hereby, the high efficient DC drive system of UCEB is studied in this dissertation by decreasing the loss of ultra-capacitor, converter, enhanced magnetism DC motor for the UCEB drive system and recycling the braking energy efficiently.
The characteristics of the drive system converter play a decisive role in the vehicle performance. The on-vehicle energy of UCEB is very limited, so, a current two-quadrant converter is chosen by analyzing and comparing the efficiency, reliability and cost of basic bi-directional DC converters; and then the drive system scheme with the functions of buck chopping driving, boost chopping braking energy regeneration and on-vehicle charging is proposed. Based on the method of feedback energy by coupled inductors, a snubber circuit that transfers the turning-on snubber energy to the ultra-capacitor is designed to achieve ZCS, ZVS of switches and reduce the switching loss of high-power converter. Considering the demands of dynamic and comfort performance, a control circuit suppressing current overshoot is designed to regulate the duty cycle by following the given reference and limiting the amplitude real-timely. The aforementioned converter is also used as the ultra-capacitor on-vehicle charging power by changing the circuit connection, which is helpful to simplify the charging station devices and save the cost of the UCEB system.
In order to optimize the performance of braking energy regeneration, the influence laws that how excitation current affects the efficiency and power of recycling braking energy for the enhanced magnetism DC generator are analyzed. Then, the optimal braking control strategy combining the electric braking with mechanical braking is put forward under the conditions of stable motor speed and armature current. According to the condition of getting the maximum generation efficiency, the efficiency optimal control strategy of recycling braking energy or the enhanced magnetism DC generator is designed when electric braking works independently. Then, in order to obtain the maximum power of recycling braking energy under vehicle composite braking, the energy optimal control strategy is designed to recycle much more braking energy during once braking process. Homoplastically, the optimal driving control strategy is designed to improve the performance of energy transformation for the enhanced magnetism DC motor. The experimental results verify the above-mentioned typical characteristics of the drive system converter and enhanced magnetism DC motor, which provides necessary conditions for the further study about the vehicle performance and its improvement scheme.
The platform experimental results indicate that the efficiency of drive system converter is low under light load condition and the high frequency chopping pulse current causes the unfavorable influence to the ultra-capacitor service life and internal resistance power loss. Specifically, in order to improve the conversion efficiency of limited on-vehicle energy for the UCEB drive system, the multiple DC conversion scheme is proposed. According to the different output power and current of the drive system converter, the regulation scheme of working unit number for multiple converter is employed to increase the converter efficiency under low power transmission, which widens the power range of high efficiency for the drive system converter. Then, the variation amplitude of the high frequency pulse current following through the ultra-capacitor is decreased when multiple circuit units work together under heavy load road condition, which reduces the power loss and improves the work environment for the ultra-capacitor. Furthermore, the decreasing of current ripple amplitude and the increasing of current ripple frequency improve the dynamic performance of the enhanced magnetism DC motor for the UCEB.
The simulation results show that it is difficult to realize the soft-switching for the conventional multiple converter. Hereby, the parallel interleaved converter under phase staggers PWM control is proposed. The switches of interleaved unit internal realize ZCS and the reverse recovery loss of freewheeling diode is reduced by coupled filter inductors. The parallel connection of interleaved units decreases the current capacity demand for the high power converter. The phase staggers PWM control increases the equivalent switch frequency and retains advantages of multiple converter for the parallel interleaved converter. The current sharing characteristic of interleaved unit internal is presented with combination of theory analysis, simulation and experimental study. Based on the datasheet estimation combined with polynomial fitting method, quantitative analysis about power loss indicates that the main power device loss of parallel interleaved converter is lower than that of the current two-quadrant converter under the same power grade, which verifies it is feasible that parallel interleaved converter is applied to UCEB from the power loss perspective. It provides technical reserve for improving the performance of the UCEB drive system.
驱动系统变换器的特性决定了UCEB整车性能。针对UCEB车载能源更加有限的瓶颈问题,从效率、可靠性、成本等因素对基本双向直流变换拓扑进行对比分析,选择了电流双象限变换器作为UCEB驱动电路拓扑。根据电容电压宽范围变化特点,提出了兼具降压驱动、升压制动能量回馈和车载充电功能的电增磁永磁直流电机驱动系统方案。针对大功率变换器开关损耗较大的问题,基于电感耦合馈能的方法,设计了馈能缓冲式软开关电路,实现了开关管零电流开通、零电压关断以及开通缓冲能量的转移存储,从而改善了开关管工作环境,降低了变换器开关损耗;兼顾车辆运行的动力性和舒适性要求,采用占空比展开过程的限幅跟随调节方法,有效抑制了驱动电流超调;根据超级电容的充电特性,利用线路切换使驱动变换器兼具恒流-恒压车载充电电源功能,降低了充电站设备的复杂程度,有利于节省UCEB公交系统成本。
在保证车辆制动安全性的前提下,基于增磁直流电机的电励磁可控特性,为优化UCEB制动能量回馈性能,分析了在电枢电流和转速稳定等条件下,励磁电流对电机发电效率和制动能量回馈功率的影响规律,提出了机电组合制动优化控制策略:车辆中轻度制动模式下,根据电机发电效率最大化条件,设计了效率优化控制策略,获得了电制动单独作用时电机回馈制动能量的最大效率;机电复合制动时,为增大电制动回馈车辆动能的比例,设计了能量优化控制策略,获得了电机回馈制动能量功率的最大值。同时,分析了电励磁对电机电动运行时效率和能量损耗的影响规律,根据电枢电流闭环控制时电机效率最大化条件,或输出转矩闭环控制时能量损耗最小化条件,分别设计了电机电动运行的效率和能量优化控制策略,实现了电机驱动时能量转换性能的优化。通过台架实验模拟UCEB工况运行,验证了上述驱动系统变换器和增磁直流电机的典型特性,为整车性能及其改进方案的进一步研究提供了必要条件。
根据台架实验结果,为进一步提高各系统环节的电能转换效率,针对车辆轻载工况时驱动系统变换器效率偏低,以及高频斩波脉冲电流放电对超级电容寿命和内阻热耗的不利影响等问题,提出了采用多重化直流变换的改进方案。轻载工况时,为提高驱动系统变换器中小功率区间的效率,根据变换器输出功率或电流调节工作单元数目,设计了多重化电路的降重工作模式,保证了各单元电路工作在优化效率区域,拓宽了变换器高效功率区间;车辆重载工况运行时,多个单元电路同时工作,减小了流过超级电容高频脉冲电流变化幅度,从而降低了超级电容等效内阻损耗,改善了超级电容的工作环境;同时,输出电流纹波变化幅度的降低以及纹波频率的提高,改善了UCEB驱动系统增磁直流电机的动态性能。
仿真分析表明,常规多重化变换器的软开关电路实现困难,据此提出了错相PWM控制并联交错电路方案。交错单元内部以滤波电感耦合的方式,实现了开关管零电流开通,并降低了续流二极管的反向恢复损耗,改善了功率器件的运行环境;交错单元间的并联降低了大功率应用场合对功率器件电流应力要求;错相PWM控制提高了并联交错变换器的等效开关频率,并保留了多重化的优点。运用理论分析、仿真和实验相结合的方法,对交错单元内部开关管间的均流特性进行了研究,得出交错单元内部可实现自动均流。基于数据手册估算和多项式拟合相结合的方法,对主要功率器件损耗进行定量分析,结果表明:在开关频率或等效开关频率相同的条件下,并联交错电路主要功率器件损耗低于同等功率条件下的单重电流双象限电路,从功耗角度验证了并联交错方案应用于UCEB的可行性,为促进UCEB驱动系统性能提升提供了技术储备。
As the energy storage equipment, ultra-capacitor with the outstanding performance of high power density is suitable for city bus with the characteristics of frequent start-stop and fixed line. It is the key problem of promoting ultra-capacitor electric bus (UCEB) development that how to improve the utilization rate of the limited on-vehicle energy by driving the vehicle and recovering the braking energy efficiently. Hereby, the high efficient DC drive system of UCEB is studied in this dissertation by decreasing the loss of ultra-capacitor, converter, enhanced magnetism DC motor for the UCEB drive system and recycling the braking energy efficiently.
The characteristics of the drive system converter play a decisive role in the vehicle performance. The on-vehicle energy of UCEB is very limited, so, a current two-quadrant converter is chosen by analyzing and comparing the efficiency, reliability and cost of basic bi-directional DC converters; and then the drive system scheme with the functions of buck chopping driving, boost chopping braking energy regeneration and on-vehicle charging is proposed. Based on the method of feedback energy by coupled inductors, a snubber circuit that transfers the turning-on snubber energy to the ultra-capacitor is designed to achieve ZCS, ZVS of switches and reduce the switching loss of high-power converter. Considering the demands of dynamic and comfort performance, a control circuit suppressing current overshoot is designed to regulate the duty cycle by following the given reference and limiting the amplitude real-timely. The aforementioned converter is also used as the ultra-capacitor on-vehicle charging power by changing the circuit connection, which is helpful to simplify the charging station devices and save the cost of the UCEB system.
In order to optimize the performance of braking energy regeneration, the influence laws that how excitation current affects the efficiency and power of recycling braking energy for the enhanced magnetism DC generator are analyzed. Then, the optimal braking control strategy combining the electric braking with mechanical braking is put forward under the conditions of stable motor speed and armature current. According to the condition of getting the maximum generation efficiency, the efficiency optimal control strategy of recycling braking energy or the enhanced magnetism DC generator is designed when electric braking works independently. Then, in order to obtain the maximum power of recycling braking energy under vehicle composite braking, the energy optimal control strategy is designed to recycle much more braking energy during once braking process. Homoplastically, the optimal driving control strategy is designed to improve the performance of energy transformation for the enhanced magnetism DC motor. The experimental results verify the above-mentioned typical characteristics of the drive system converter and enhanced magnetism DC motor, which provides necessary conditions for the further study about the vehicle performance and its improvement scheme.
The platform experimental results indicate that the efficiency of drive system converter is low under light load condition and the high frequency chopping pulse current causes the unfavorable influence to the ultra-capacitor service life and internal resistance power loss. Specifically, in order to improve the conversion efficiency of limited on-vehicle energy for the UCEB drive system, the multiple DC conversion scheme is proposed. According to the different output power and current of the drive system converter, the regulation scheme of working unit number for multiple converter is employed to increase the converter efficiency under low power transmission, which widens the power range of high efficiency for the drive system converter. Then, the variation amplitude of the high frequency pulse current following through the ultra-capacitor is decreased when multiple circuit units work together under heavy load road condition, which reduces the power loss and improves the work environment for the ultra-capacitor. Furthermore, the decreasing of current ripple amplitude and the increasing of current ripple frequency improve the dynamic performance of the enhanced magnetism DC motor for the UCEB.
The simulation results show that it is difficult to realize the soft-switching for the conventional multiple converter. Hereby, the parallel interleaved converter under phase staggers PWM control is proposed. The switches of interleaved unit internal realize ZCS and the reverse recovery loss of freewheeling diode is reduced by coupled filter inductors. The parallel connection of interleaved units decreases the current capacity demand for the high power converter. The phase staggers PWM control increases the equivalent switch frequency and retains advantages of multiple converter for the parallel interleaved converter. The current sharing characteristic of interleaved unit internal is presented with combination of theory analysis, simulation and experimental study. Based on the datasheet estimation combined with polynomial fitting method, quantitative analysis about power loss indicates that the main power device loss of parallel interleaved converter is lower than that of the current two-quadrant converter under the same power grade, which verifies it is feasible that parallel interleaved converter is applied to UCEB from the power loss perspective. It provides technical reserve for improving the performance of the UCEB drive system.
引文
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35范健文.电动汽车电气驱动系统.广西工学院学报. 2003, 14(2):51~55
36夏云.电动汽车动力驱动系统的研究现状和应用前景(2).微电机, 2003, 36(4):47~50
37范健文,马小强,吴彤峰.电动汽车电驱动系统控制技术.广西工学院学报. 2003, 14(3):25~28
38马宪民.电动汽车的电气驱动系统.西安公路交通大学学报. 2001, 21(3):83~86
39闫大伟,陈世元.电动汽车驱动电机性能比较.汽车电器. 2004, (2):4~6
40刑伟.电动汽车用永磁同步电动机及传动控制系统研究.沈阳工业大学硕士学位论文. 2004:2~5
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42张承宁,谭建,孙逢春,等.电动公交大客车驱动系统控制特性分析.电工技术学报. 2004, 19(1):69~74
43张毅,杨林,朱建新,等.电动汽车能量回馈的整车控制.汽车工程. 2005, 27(1):24~27
44王子杰,黄妙华,邓亚东. EV再生制动系统的建模与仿真.武汉理工大学学报. 2001, 23(4):102~105
45 S. R. Cikanek. Electric Vehicle Braking Systems. 14th International Electric Vehicle Symposium. EVS14, Orlando, Fla., USA, 1997
46 K. E. Balley. Dynamic Model and Coordinated Control System for a Hybrid Electric Vehicle. 14th International Electric Vehicle Symposium. EVS14, Orlando, Fla., USA, 1997
47 F. Caricchi, F. Crescimbini, F. G. Capponi, et al. Study of bi-directional buck-boost converter topologies for application in electrical vehicle motor drives. Proc. of APEC'98, 1998:287~293
48 F. Caricchi, F. Crescimbini, A. Di Napoli. 20 kW water-cooled prototype of a buck-boost bidirectional DC-DC converter topology for electrical vehicle motor drives. Proc. of APEC'95, 1995:887~892
49 N. P. Filho, V. J. Farias, L. C. de Freitas. A novel family of DC-DC self-resonant PWM converter. Proc. of IECON'94, 1994:268~274
50林渭勋.现代电力电子电路.浙江大学出版社, 2002:316~327
51 E. S. Kim, K. Y. Joe, M. H. Kye, et al. An Improved Soft Switching PWM FB DC/DC Converter for Reducing Conduction Losses. Power Electronics, IEEE Transactions on. 1999, 14(2):258~264
52 H. L. Chan, K. W. E. Cheng, D. Sutanto. Bidirectional phase-shifted DC-DC Converter. IEEE Eletronics Letters. 1999, 35(7):523~524
53 M. H. Kheraluwala, R. W. de Doncker, D. M. Divan. Analysis, design and experimental evaluation of a high power high-frequency bi-directional DC/DC converter. EPE'91, 1991:568~573
54 M. N. Kheraluwala, R. W. Gascoigne, D. M. Divan, et al. Performance characterization of a high power dual active bridge DC-to-DC converter. IEEE Trans Industry Applications. 1992, 28(6):1294~1301
55孙慧贤,王群,杨卫新. ZVT PWM Buck变流器的改进.电气应用. 2005, 24(7):81~84
56 J. C. Jiang, W. G. Zhang, B. Shen. Analysis and Design of a Novel ZCT PWM Converter. IEEE PEDS'03, 2003, (1):126~130
57张立,赵永健.现代电力电子技术.科学出版社, 1992:98~105
58解永辉,丁道宏.一种新型缓冲电路研究.中国电源学会第11届年会论文集. 1995
59 D. C. Martins, F. J. M. de Seixax, J. A. Brilhante, et al. A Family of DC-DC PWM Converters using a New ZVS Commutation Cell. PESC'93, 1993:524~530
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61 D. M. Xu, C. Yang, L. Ma, et al. A Novel Single Phase Active-Clamped PFC Converter. APEC'97, 1997:266~271
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63 J. M. Zhang, X. G. Xie, X. K. Wu, et al. Stability Study for Paralleled DC/DC Converters. IEEE PESC, 2004:1569~1575
64 X. W. Zhou. Low-voltage High-efficiency Fast-transient Voltage Regulator Module. Virginia Polytechnic Technology University, 1999:39~49
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27 P. Barrade, S. Pittet, A. Rufer. Energy storage system using series connection of supercapacitors, with an active device for equalizing the voltages. EPFL, Swiss Federal Inst Technol, Lausanne, Switzerland, 2000
28 A. Schneuwly, R. Smith. Ultracapacitor to address power and redundancy needs of vehicles. EVS20, California, USA. 2003
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30张翀,毛永志.纯电动公交车是城市公交的发展方向.新材料产业. 2007, (8):54~55
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33 D. J. Adams, J. S. Hsu, R. W. Young, et al. Power Electronics and Electric Machinery Challenges and Opportunities in Electric and Hybrid Vehicles.Proceedings of the International Symposium on Automotive Technology and Automation, 1997:16~19
34 A. K. Adnanes, R. Nilsen, R. Loken, et al. Efficiency Analysis of Electric Vehicles, with Emphasis on Efficiency Optimized Excitation. IEEE Industry Applications Society Annual Meeting, 1993, (1):455~462
35范健文.电动汽车电气驱动系统.广西工学院学报. 2003, 14(2):51~55
36夏云.电动汽车动力驱动系统的研究现状和应用前景(2).微电机, 2003, 36(4):47~50
37范健文,马小强,吴彤峰.电动汽车电驱动系统控制技术.广西工学院学报. 2003, 14(3):25~28
38马宪民.电动汽车的电气驱动系统.西安公路交通大学学报. 2001, 21(3):83~86
39闫大伟,陈世元.电动汽车驱动电机性能比较.汽车电器. 2004, (2):4~6
40刑伟.电动汽车用永磁同步电动机及传动控制系统研究.沈阳工业大学硕士学位论文. 2004:2~5
41孙永伟.电动汽车控制系统保护及通讯技术的研究.沈阳工业大学硕士学位论文. 2004:4~6
42张承宁,谭建,孙逢春,等.电动公交大客车驱动系统控制特性分析.电工技术学报. 2004, 19(1):69~74
43张毅,杨林,朱建新,等.电动汽车能量回馈的整车控制.汽车工程. 2005, 27(1):24~27
44王子杰,黄妙华,邓亚东. EV再生制动系统的建模与仿真.武汉理工大学学报. 2001, 23(4):102~105
45 S. R. Cikanek. Electric Vehicle Braking Systems. 14th International Electric Vehicle Symposium. EVS14, Orlando, Fla., USA, 1997
46 K. E. Balley. Dynamic Model and Coordinated Control System for a Hybrid Electric Vehicle. 14th International Electric Vehicle Symposium. EVS14, Orlando, Fla., USA, 1997
47 F. Caricchi, F. Crescimbini, F. G. Capponi, et al. Study of bi-directional buck-boost converter topologies for application in electrical vehicle motor drives. Proc. of APEC'98, 1998:287~293
48 F. Caricchi, F. Crescimbini, A. Di Napoli. 20 kW water-cooled prototype of a buck-boost bidirectional DC-DC converter topology for electrical vehicle motor drives. Proc. of APEC'95, 1995:887~892
49 N. P. Filho, V. J. Farias, L. C. de Freitas. A novel family of DC-DC self-resonant PWM converter. Proc. of IECON'94, 1994:268~274
50林渭勋.现代电力电子电路.浙江大学出版社, 2002:316~327
51 E. S. Kim, K. Y. Joe, M. H. Kye, et al. An Improved Soft Switching PWM FB DC/DC Converter for Reducing Conduction Losses. Power Electronics, IEEE Transactions on. 1999, 14(2):258~264
52 H. L. Chan, K. W. E. Cheng, D. Sutanto. Bidirectional phase-shifted DC-DC Converter. IEEE Eletronics Letters. 1999, 35(7):523~524
53 M. H. Kheraluwala, R. W. de Doncker, D. M. Divan. Analysis, design and experimental evaluation of a high power high-frequency bi-directional DC/DC converter. EPE'91, 1991:568~573
54 M. N. Kheraluwala, R. W. Gascoigne, D. M. Divan, et al. Performance characterization of a high power dual active bridge DC-to-DC converter. IEEE Trans Industry Applications. 1992, 28(6):1294~1301
55孙慧贤,王群,杨卫新. ZVT PWM Buck变流器的改进.电气应用. 2005, 24(7):81~84
56 J. C. Jiang, W. G. Zhang, B. Shen. Analysis and Design of a Novel ZCT PWM Converter. IEEE PEDS'03, 2003, (1):126~130
57张立,赵永健.现代电力电子技术.科学出版社, 1992:98~105
58解永辉,丁道宏.一种新型缓冲电路研究.中国电源学会第11届年会论文集. 1995
59 D. C. Martins, F. J. M. de Seixax, J. A. Brilhante, et al. A Family of DC-DC PWM Converters using a New ZVS Commutation Cell. PESC'93, 1993:524~530
60 W. McMurray. Resonant snubbers with auxiliary switches. Industry Applications, IEEE Transactions on, 1993, 29(2):355~362
61 D. M. Xu, C. Yang, L. Ma, et al. A Novel Single Phase Active-Clamped PFC Converter. APEC'97, 1997:266~271
62陈坚.电力电子学-电力电子变换和控制技术.高等教育出版社, 2002:90~91
63 J. M. Zhang, X. G. Xie, X. K. Wu, et al. Stability Study for Paralleled DC/DC Converters. IEEE PESC, 2004:1569~1575
64 X. W. Zhou. Low-voltage High-efficiency Fast-transient Voltage Regulator Module. Virginia Polytechnic Technology University, 1999:39~49
65陈明,汪光森,马伟明.多重化双向DC-DC变换器电流纹波分析.继电器. 2007, 35(4):53~57
66 H. P. Xu, F. Z. Peng, K. Li. Multi-phase DC-DC converter with Bi-directional power flow ability for distributed generation system. PESC 2008, IEEE, 2008:2800~2805
67 M. Veerachary, T. Senjyu, K. Uezato. Signal flow graph modeling of DC-DC parallel converter. Industrial Electronics Society, 2000. IECON 2000. 26th Annual Conference of the IEEE, 2000, (4):2303~2308
68 M. Veerachary, T. Senjyu, K. Uezato. Signal flow graph nonlinear modelling of interleaved converters. Electric Power Applications, IEE Proceedings. 2001, 148(5):410~418
69 M. Veerachary, T. Senjyu, K. Uezato. Signal flow graph modelling of DC-DC parallel converter with coupled inductors. Power Conversion Conference, Osaka, 2002, 3:1352~1356
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