多相感应电动机缺相建模与性能分析
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摘要
多相感应电机具有成本低、消耗材料少、结构简单、运行性能可靠、可以实现低电压、小电流、大容量,以及电机的谐波分量少,脉动转矩小等特点。同时,当多相电机定子绕组一相或者多相开路时仍可以继续起动和运行,因此,多相感应电机平衡和非平衡状态下的起动和运行特性引起了众多学者的研究兴趣。
本文以双三相感应电机为研究对象,由广义两相实变换推导出双三相感应电机定子绕组两相开路时的变换阵,得出双三相感应电机缺相时在静止坐标系下的广义α-β模型,基于建立的电机的动态模型,采用MATLAB/SIMULINK建立双三相感应电机定子绕组两相开路时的仿真模型。
结合多相感应电机逆变器供电时的常规模型,利用开关函数的理论,推导出双三相感应电机定子相缺失两相时逆变器供电的仿真模型。
通过计算机仿真结果,研究双三相感应电机在定子相缺失第一相和第六相时的动态特性,研究结果表明,当缺失第一相和第六相时,其在α-β子空间定子电压轨迹为圆形,其余各相的电流均相等,且没有转矩和速度脉动。对比定子相一相开路和两相开路的仿真结果,可知随着定子相开路相数的增加和开路相相位的不同,电机起动和运行特性差异较大。
对双三相感应电机定子相一相开路时,采用基于规则的空间电压矢量选择方法,实现不平衡运行时电机磁链和转矩的快速动态控制。
Since the eighties of the last century, with the development of power electronics and motor drives, the limitation of the number of phases of the drive being equal to that of the power supply was removed and opened the scope of exploring the multiphase motor. Multiphase machine has many advantages over the traditional three-phase motor drives such as reducing the amplitude and increasing the frequency of torque pulsation, reducing the stator current per phase without increasing the voltage per phase, lowering the dc link current harmonics and higher reliability. For that multiphase machine with capabilities to start and run even with one or more of its stator phases open-circuited when the winding structure is multiphase, recently, several papers studying the performance of multi- phase machine concerning when one or more stator phase open- circuited have been published.
In this paper, the author presents the modeling of dual-three-phase induction machine with two stator phase windings opened using vector space decomposition method. The model can be used analysis and control of the machine. The dynamic performance of the machine with structure unbalance is simulated with the help of MATLAB/SIMULINK.
Simulation model of dual-three-phase induction machine when two stator phase windings opened with voltage source inverter (VSI) is set up. This model is based on the theory of switch function and the conventional model of multiphase induction machine.
To study the dynamical performance of dual-three-phase induction machine under two stator windings open-circuited, simulations by means of MATLAB/SIMULINK are implemented using the model presented in this paper. For the sake of making comparison, two cases of the machine with lost a phase and lost two phase stator windings are simulated. The trace of stator voltage vector inα-βsubspace is a circle, which means the shape of the air-gap flux is also a circle. So, there not exists torque or speed ripple in steady state when 1st and 6th phase windings opened. Compared with dual-three-phase induction machine under two stator windings open-circuited and one stator windings open-circuited, diverse space place of lost stator phase has different influence on machine.
A rule based optimums election scheme of space voltage vector is proposed for direct torque control of dual-three-phase induction machine under two stator windings open-circuited. Fast torque response with low ripples of torque and flux is achieved.
本文以双三相感应电机为研究对象,由广义两相实变换推导出双三相感应电机定子绕组两相开路时的变换阵,得出双三相感应电机缺相时在静止坐标系下的广义α-β模型,基于建立的电机的动态模型,采用MATLAB/SIMULINK建立双三相感应电机定子绕组两相开路时的仿真模型。
结合多相感应电机逆变器供电时的常规模型,利用开关函数的理论,推导出双三相感应电机定子相缺失两相时逆变器供电的仿真模型。
通过计算机仿真结果,研究双三相感应电机在定子相缺失第一相和第六相时的动态特性,研究结果表明,当缺失第一相和第六相时,其在α-β子空间定子电压轨迹为圆形,其余各相的电流均相等,且没有转矩和速度脉动。对比定子相一相开路和两相开路的仿真结果,可知随着定子相开路相数的增加和开路相相位的不同,电机起动和运行特性差异较大。
对双三相感应电机定子相一相开路时,采用基于规则的空间电压矢量选择方法,实现不平衡运行时电机磁链和转矩的快速动态控制。
Since the eighties of the last century, with the development of power electronics and motor drives, the limitation of the number of phases of the drive being equal to that of the power supply was removed and opened the scope of exploring the multiphase motor. Multiphase machine has many advantages over the traditional three-phase motor drives such as reducing the amplitude and increasing the frequency of torque pulsation, reducing the stator current per phase without increasing the voltage per phase, lowering the dc link current harmonics and higher reliability. For that multiphase machine with capabilities to start and run even with one or more of its stator phases open-circuited when the winding structure is multiphase, recently, several papers studying the performance of multi- phase machine concerning when one or more stator phase open- circuited have been published.
In this paper, the author presents the modeling of dual-three-phase induction machine with two stator phase windings opened using vector space decomposition method. The model can be used analysis and control of the machine. The dynamic performance of the machine with structure unbalance is simulated with the help of MATLAB/SIMULINK.
Simulation model of dual-three-phase induction machine when two stator phase windings opened with voltage source inverter (VSI) is set up. This model is based on the theory of switch function and the conventional model of multiphase induction machine.
To study the dynamical performance of dual-three-phase induction machine under two stator windings open-circuited, simulations by means of MATLAB/SIMULINK are implemented using the model presented in this paper. For the sake of making comparison, two cases of the machine with lost a phase and lost two phase stator windings are simulated. The trace of stator voltage vector inα-βsubspace is a circle, which means the shape of the air-gap flux is also a circle. So, there not exists torque or speed ripple in steady state when 1st and 6th phase windings opened. Compared with dual-three-phase induction machine under two stator windings open-circuited and one stator windings open-circuited, diverse space place of lost stator phase has different influence on machine.
A rule based optimums election scheme of space voltage vector is proposed for direct torque control of dual-three-phase induction machine under two stator windings open-circuited. Fast torque response with low ripples of torque and flux is achieved.
引文
[1] Klingshirn EA. High Phase Order Induction Motors Part I, Description and Theoretical Considerations[J]. IEEE Trans Power App. Syst, 1983, 102(1): 47-59
[2] H. Xu, H. A. Toliyat, L. J. Petersen. Resilient Current Control of Fivephase Induction Motor under Asymmetrical Fault Conditions[C]. IEEE APEC, Mar. 2002:64-71
[3] R. Bojoi, M. Lazzari, F. Profumo, A. Tenconi. Digital Field Oriented Control for Dual-Three Phase Induction Motor Drives[J]. IEEE Trans. Ind. Appl, vol. 39(3), 2003 752-760
[4] R. Bojoi, A. Tenconi, F. Profumo, G. Griva, and D. Martinello. Complete Analysis and Comparative Study of Digital Modulation Techniques for Dual Three-Phase AC Motor Drives[C]. IEEE Power Electronics Specialists Conf,2002:851-857
[5] D. Hadiouche, L. Baghli, A. Rezzoug. Space Vector PWM Techniques for Dual Three-Phase AC Machine[C]. IEEE Industry Applications Society (IAS) Annu. Meeting, 2003:648-655
[6] Li jun Hou, Yan min Su, Lin Chen. Modeling and control of 15-phase induction machines. ICCA, 2002
[7] Ribeiro R. L. A, Jacobina C. B. A Strategy for Improving Reliability of Motor Drive Systems Using a Four-Leg There-Phase Converter[C]. IEEE Conf, 2001:385-391
[8] Emil Levi. Multiphase Electric Machines for Variable-Speed Applications[J]. IEEE Tans. Industrial Electronics, 1999, 55(5): 1893-1909
[9] Jahns T.M. Improved Reliability in Solid-State Drives for Large Asynchronous AC Machines by Means of Multiple-Independent Phase-Drive Units[J]. IEEE Trans, IA, 1980, 16(3):323-328
[10] Hamid A, Toliyat. Analysis of Concentrated Winding Induction Machine For Adjustable Speed Drive Application Port I (Motor Analysis)[J]. IEEE Trans. Energy Conv, 1991, 6(4):679-683
[11] Toliyat HA, Lipo TA, White JC. Analysis of Concentrated Winding Induction Machine for Adjustable Speed Drive Applications Part 2 (Motor Design and Performance)[J]. IEEE Trans. Energy Conversion, 1991, 6(4):685-692
[12] Gopakumar K, Ranganathan V. T, Bhat S. R. Split-Phase Induction Motor Operation from PWM Voltage Source Inverter[J]. IEEE Trans. IA, 1993, 29(5):927-932
[13] Zhao Y, Lipo T. A. Modeling and Control of a Multi-Phase Induction Machine with Structural Unbalance: Part 1. Machine Modeling and Multi-Dimensional Current Regulation[J]. IEEE Trans, EC, 1996, 11(3):570-577
[14]庄朝晖,唐伏良,熊有伦.多相感应电机空间电压矢量控制研究[J].电气传动, 2001, (5):9-12
[15] Bowes SR, Lai YS. The Relationship Between Space Vector Modulation and Regular-Sampled PWM[J]. IEEE Trans. Ind. Electron, 1997, 44(5):670-679
[16] J. R. Fu and T. A. Lipo, Disturbance-Free Operation of a Multiphase Current-Regulated Motor Drive with an Opened Phase[J]. IEEE Trans. Ind. Appl, 1994, (30)5: 1267-1274
[17] Ward E. E, Hater H. Preliminary Investigation of an Inverter-Fed 5-Phase Induction Motor[J]. Proc. Inst. Elect. Eng, 1969, 116(6):980-984
[18] White D. C, Woodson H. H. Electromechanical Energy Conversion[M]. New York: Wiley, 1959
[19] Pavithran K. N, Parimelalagan R. Studies on Inverter-Fed Five-Phase Induction Motor Drive[J]. IEEE Trans. PE, 1998, 3(2): 224-235
[20]王凤翔.交流电机的非正弦供电[M].北京:机械工业出版社, 1997
[21] P. Z. Grabowski, M. P. Kazmierkowski, B. K. Bose. A Simple Direct-Torque neuron-fuzzy control of PWM inverter fed induction motor drive[J]. IEEE. Trans Ind Electron. Vol47, 2000:863-870
[22] E. A. Klingshirn. Harmonic Filters for Six-Phase and other Multiphase Motors on voltage Source Inverters[J]. IEEE Trans Indus App, 1985, 21(4):8-12
[23] King K. G. A Three-Phase Transistor Class-b Inverter with Sine Wave Output and High Efficiency[C]. IEE Conf.1974, 204-209
[24] Toliyat H. A. Analysis and Simulation of Five-Phase Variable-Speed Induction Motor Drives under Asymmetrical Connections[J]. IEEE Trans. PE, 1998, 13(4):748-756
[25] N. P. Van der Duijn Schouten. Multiphase induction motors for integrated drives[C]. IEEE Conf. EMD, 1999:468-475
[26] Guo yi, Zheng Hua-Yao. Design of Ship electric Propulsion Simulation System[C]. The Fourth International Conference on Machine Learning and Cybernetics, 2005 ,9(2):1059-1063
[27] Direct Self-Contro1 of the Flux and Rotary Moment of a Rotary-Field Machine [P]. U, S. Patent 4678248, 1987(7)
[28] I. Takahashi, T. Noguchi. A New Quick-Response and High Efficiency Control Strategy of an Induction Machine[J]. IEEE Trans. IA, 1986, IA(22):820-827
[29] Yifan Zhao. Space Vector PWM Control of Dual Three Phase Induction Machine Using Vector Space Decomposition[J]. IEEE Trans On Ind. App. 1995, 31(5):1100-1109
[30] C. Lascu, I. Boldea, F. Blaabjerg. A Modified Direct Torque Control for Induction Motor Sensorless Drive[C]. In conf. Rec. IEEE-IAS Annu. Meeting, 1998:415-422
[31] Toliyat Ha, Xu H. A Novel Direct Torque Control(DTC) Method for Five-phase Induction Machines[C]. IEEE Annual Meeting, 2000:162-168
[32] Lin Chen, Kang-Ling Fang. A Novel Direct Torque Control For Dual-Three-Phase Induction Motor[C]. Proceedings of the Second International Conference on Machine Learning and Cybernetics, Xi’an, 2003:876-883
[33]周马山,欧阳红林,童调生.不对称多相PMSM的矢量控制[J].电工技术学报, 2004, 19(12):37-41
[34] P. C. Krause. Analysis of Electric Machinery[M]. McGraw-Hill Book Company, New York, 1986
[35] Dong Tian, Lin Chen, Lijun Hou, Juntao Pan. Modeling and Simulation of Dual-Three-Phase Induction Machine with Two Opened Phases[C]. Proceedings of the IEEE International Conference on Industrial Technology, Chengdu, 2008
[36] T. A. Lipo. A D-Q Model for Six-Phase Induction Machines[C]. Proc. International Conference on Electrical Machines, Athens, Greece, ICEM', 1980:860-867
[37] K. N. Pavithran, R. Parimelalagan, M. R. Krishnamurthy. Studies on Inverter-Fed Five-Phase Induction Motor Drive[J]. IEEE Trans. PE, 1988, 3( 4):224-235
[38] TolbertL M , Peng F Z. Multilevel Converters for Large Electric Drives[C]. IEEE-APEC. Conf. Rec , 1998:530-536
[39]潘晓晟,郝世勇.电机仿真精华50例[M].北京:电子工业出版社,2007
[40]张宜华,史惠康.精通MATLAB 5[M].北京:清华大学出版社,1999
[41] Boldea C L, Blaabjerg F. A Modified Direct Torque Control for Induction Motor Sensorless drive[J]. IEEE Trans. Ind. Appl, 2000, 36 (1):12 2130
[42] LeeB . K, Ehsani M. A Simplified Functional Simulation Model for Three-Phase Voltage-Source Inverter using Switching Fnction concept[J], IEEE Trans. IE, 2001, 48 (2):30 9-321
[43] Yu Qingguang, Li Pei, Hu Wenhua, eta1. Overview of STATCOM technologies[C]. Proceedings of the 2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies 2004(DRPT 2004). VoL2. Hong Kong, 2004:647-652
[44]杨影,吴志红,陶生桂.一种基于开关函数的电压源逆变器仿真模型[J].同济大学学报. 2006,34(11):1543-1547
[45] Sanchez. J. A, Vazquez. S. Carrasco. J. M. Digital Implementation Issues for a Three-Phase Power Converter Development Using a Repetitive Control Scheme[C]. IEEE Trans. IE, 2007, 667-672
[46]王兆安,黄俊.电力电子交流技术[M].北京:机械工业出版社, 1994
[47]雷穗芳,王辉.基于开关函数概念的VSI的仿真模型介绍[J].现代电子技术2003,1(144)
[48] S. Wei, B. Wu, Qianghua Wang. An Improved Space PWM Control Algorithm for Muti-Level Inverters[C]. The 4th International Power Electronics and Motion Control Conference, Vol. 3, 2004:1124-1129
[49] C. K. Lee, S. Y. R. Hui, H. Shu-hung Chung, Yash Shrivastava. A Randomized Voltage Vector Switching Scheme for Three-Level Power Inverters[J]. IEEE Trans on Power Electronics, 17(1), 2002:94-100
[50] T. G. Ha betler, F. Pastorelli. Direct Torque Control of Induction Machines using Space Vector Modulation, IEEE IAS'1991:428-436
[51] Judith Apsley. Analysis of Multiphase Induction Machines With Winding Faults[J]. IEEE Trans. Ind. Appl, 42(2), 2006:465-472
[52] Hyung-Min Ryu, Ji-Woong Kim, Seung-Ki Sul. Synchronous-Frame Current Control of Multiphase Synchronous Motor Under Asymmetric Fault Condition Due to Open Phases[J]. IEEE Trans. Ind. Appl, 42(4) 2006:1062-1070
[53] Deng Pan Zhu. Vecotor Control of Multiphase Permanent Magnet Synchronous Motors[D]. Faculty Science and Genie University. Quebec, Canada. 2006
[54] Zheng. Libo, Fletcher. John E, William. Barry W, He Xiangning. Dual-Plan Vector Control of a Five-Phase Induction Machine for an Improved flux pattern[J]. IEEE Transactions on Industrial Electronics, VOL55(5), 2008:1996-2005
[55] Liyong. Yang, Yinghong. Li, Yaai. Chen, Zhengxi. Li. A Novel Fuzzy Logic Controller for Indirect Vector Control Induction Motor Drive[C]. Proc. World Congr. Intelligent Control Autom. WCICA.2008:24-28
[56] Bahram-Kimiaghalam, Meisam-Rahmani, Hassan-Halleh. Speed & Torque Vector Control of Induction Motors with Fuzzy Logic Controller[C]. Int. Conf. Control., Auto. Syst, ICCAS.2008:360-365
[57] Subudhi. B, Kumar. Anish, Jena. D. Dspace Implementation of Fuzzy Logic based Vector Control of Induction Motor[C]. IEEE Reg 10 Annu Int Conf Proc TENCON, 2008
[58] Radu Bojoi, Giovanni Griva, Alberto Tenconi. Direct Torque Control for Dual Three-Phase Induction Motor Drives[J] . IEEE Trans. Ind. Appl, 41(6) 2005:1627-1636
[2] H. Xu, H. A. Toliyat, L. J. Petersen. Resilient Current Control of Fivephase Induction Motor under Asymmetrical Fault Conditions[C]. IEEE APEC, Mar. 2002:64-71
[3] R. Bojoi, M. Lazzari, F. Profumo, A. Tenconi. Digital Field Oriented Control for Dual-Three Phase Induction Motor Drives[J]. IEEE Trans. Ind. Appl, vol. 39(3), 2003 752-760
[4] R. Bojoi, A. Tenconi, F. Profumo, G. Griva, and D. Martinello. Complete Analysis and Comparative Study of Digital Modulation Techniques for Dual Three-Phase AC Motor Drives[C]. IEEE Power Electronics Specialists Conf,2002:851-857
[5] D. Hadiouche, L. Baghli, A. Rezzoug. Space Vector PWM Techniques for Dual Three-Phase AC Machine[C]. IEEE Industry Applications Society (IAS) Annu. Meeting, 2003:648-655
[6] Li jun Hou, Yan min Su, Lin Chen. Modeling and control of 15-phase induction machines. ICCA, 2002
[7] Ribeiro R. L. A, Jacobina C. B. A Strategy for Improving Reliability of Motor Drive Systems Using a Four-Leg There-Phase Converter[C]. IEEE Conf, 2001:385-391
[8] Emil Levi. Multiphase Electric Machines for Variable-Speed Applications[J]. IEEE Tans. Industrial Electronics, 1999, 55(5): 1893-1909
[9] Jahns T.M. Improved Reliability in Solid-State Drives for Large Asynchronous AC Machines by Means of Multiple-Independent Phase-Drive Units[J]. IEEE Trans, IA, 1980, 16(3):323-328
[10] Hamid A, Toliyat. Analysis of Concentrated Winding Induction Machine For Adjustable Speed Drive Application Port I (Motor Analysis)[J]. IEEE Trans. Energy Conv, 1991, 6(4):679-683
[11] Toliyat HA, Lipo TA, White JC. Analysis of Concentrated Winding Induction Machine for Adjustable Speed Drive Applications Part 2 (Motor Design and Performance)[J]. IEEE Trans. Energy Conversion, 1991, 6(4):685-692
[12] Gopakumar K, Ranganathan V. T, Bhat S. R. Split-Phase Induction Motor Operation from PWM Voltage Source Inverter[J]. IEEE Trans. IA, 1993, 29(5):927-932
[13] Zhao Y, Lipo T. A. Modeling and Control of a Multi-Phase Induction Machine with Structural Unbalance: Part 1. Machine Modeling and Multi-Dimensional Current Regulation[J]. IEEE Trans, EC, 1996, 11(3):570-577
[14]庄朝晖,唐伏良,熊有伦.多相感应电机空间电压矢量控制研究[J].电气传动, 2001, (5):9-12
[15] Bowes SR, Lai YS. The Relationship Between Space Vector Modulation and Regular-Sampled PWM[J]. IEEE Trans. Ind. Electron, 1997, 44(5):670-679
[16] J. R. Fu and T. A. Lipo, Disturbance-Free Operation of a Multiphase Current-Regulated Motor Drive with an Opened Phase[J]. IEEE Trans. Ind. Appl, 1994, (30)5: 1267-1274
[17] Ward E. E, Hater H. Preliminary Investigation of an Inverter-Fed 5-Phase Induction Motor[J]. Proc. Inst. Elect. Eng, 1969, 116(6):980-984
[18] White D. C, Woodson H. H. Electromechanical Energy Conversion[M]. New York: Wiley, 1959
[19] Pavithran K. N, Parimelalagan R. Studies on Inverter-Fed Five-Phase Induction Motor Drive[J]. IEEE Trans. PE, 1998, 3(2): 224-235
[20]王凤翔.交流电机的非正弦供电[M].北京:机械工业出版社, 1997
[21] P. Z. Grabowski, M. P. Kazmierkowski, B. K. Bose. A Simple Direct-Torque neuron-fuzzy control of PWM inverter fed induction motor drive[J]. IEEE. Trans Ind Electron. Vol47, 2000:863-870
[22] E. A. Klingshirn. Harmonic Filters for Six-Phase and other Multiphase Motors on voltage Source Inverters[J]. IEEE Trans Indus App, 1985, 21(4):8-12
[23] King K. G. A Three-Phase Transistor Class-b Inverter with Sine Wave Output and High Efficiency[C]. IEE Conf.1974, 204-209
[24] Toliyat H. A. Analysis and Simulation of Five-Phase Variable-Speed Induction Motor Drives under Asymmetrical Connections[J]. IEEE Trans. PE, 1998, 13(4):748-756
[25] N. P. Van der Duijn Schouten. Multiphase induction motors for integrated drives[C]. IEEE Conf. EMD, 1999:468-475
[26] Guo yi, Zheng Hua-Yao. Design of Ship electric Propulsion Simulation System[C]. The Fourth International Conference on Machine Learning and Cybernetics, 2005 ,9(2):1059-1063
[27] Direct Self-Contro1 of the Flux and Rotary Moment of a Rotary-Field Machine [P]. U, S. Patent 4678248, 1987(7)
[28] I. Takahashi, T. Noguchi. A New Quick-Response and High Efficiency Control Strategy of an Induction Machine[J]. IEEE Trans. IA, 1986, IA(22):820-827
[29] Yifan Zhao. Space Vector PWM Control of Dual Three Phase Induction Machine Using Vector Space Decomposition[J]. IEEE Trans On Ind. App. 1995, 31(5):1100-1109
[30] C. Lascu, I. Boldea, F. Blaabjerg. A Modified Direct Torque Control for Induction Motor Sensorless Drive[C]. In conf. Rec. IEEE-IAS Annu. Meeting, 1998:415-422
[31] Toliyat Ha, Xu H. A Novel Direct Torque Control(DTC) Method for Five-phase Induction Machines[C]. IEEE Annual Meeting, 2000:162-168
[32] Lin Chen, Kang-Ling Fang. A Novel Direct Torque Control For Dual-Three-Phase Induction Motor[C]. Proceedings of the Second International Conference on Machine Learning and Cybernetics, Xi’an, 2003:876-883
[33]周马山,欧阳红林,童调生.不对称多相PMSM的矢量控制[J].电工技术学报, 2004, 19(12):37-41
[34] P. C. Krause. Analysis of Electric Machinery[M]. McGraw-Hill Book Company, New York, 1986
[35] Dong Tian, Lin Chen, Lijun Hou, Juntao Pan. Modeling and Simulation of Dual-Three-Phase Induction Machine with Two Opened Phases[C]. Proceedings of the IEEE International Conference on Industrial Technology, Chengdu, 2008
[36] T. A. Lipo. A D-Q Model for Six-Phase Induction Machines[C]. Proc. International Conference on Electrical Machines, Athens, Greece, ICEM', 1980:860-867
[37] K. N. Pavithran, R. Parimelalagan, M. R. Krishnamurthy. Studies on Inverter-Fed Five-Phase Induction Motor Drive[J]. IEEE Trans. PE, 1988, 3( 4):224-235
[38] TolbertL M , Peng F Z. Multilevel Converters for Large Electric Drives[C]. IEEE-APEC. Conf. Rec , 1998:530-536
[39]潘晓晟,郝世勇.电机仿真精华50例[M].北京:电子工业出版社,2007
[40]张宜华,史惠康.精通MATLAB 5[M].北京:清华大学出版社,1999
[41] Boldea C L, Blaabjerg F. A Modified Direct Torque Control for Induction Motor Sensorless drive[J]. IEEE Trans. Ind. Appl, 2000, 36 (1):12 2130
[42] LeeB . K, Ehsani M. A Simplified Functional Simulation Model for Three-Phase Voltage-Source Inverter using Switching Fnction concept[J], IEEE Trans. IE, 2001, 48 (2):30 9-321
[43] Yu Qingguang, Li Pei, Hu Wenhua, eta1. Overview of STATCOM technologies[C]. Proceedings of the 2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies 2004(DRPT 2004). VoL2. Hong Kong, 2004:647-652
[44]杨影,吴志红,陶生桂.一种基于开关函数的电压源逆变器仿真模型[J].同济大学学报. 2006,34(11):1543-1547
[45] Sanchez. J. A, Vazquez. S. Carrasco. J. M. Digital Implementation Issues for a Three-Phase Power Converter Development Using a Repetitive Control Scheme[C]. IEEE Trans. IE, 2007, 667-672
[46]王兆安,黄俊.电力电子交流技术[M].北京:机械工业出版社, 1994
[47]雷穗芳,王辉.基于开关函数概念的VSI的仿真模型介绍[J].现代电子技术2003,1(144)
[48] S. Wei, B. Wu, Qianghua Wang. An Improved Space PWM Control Algorithm for Muti-Level Inverters[C]. The 4th International Power Electronics and Motion Control Conference, Vol. 3, 2004:1124-1129
[49] C. K. Lee, S. Y. R. Hui, H. Shu-hung Chung, Yash Shrivastava. A Randomized Voltage Vector Switching Scheme for Three-Level Power Inverters[J]. IEEE Trans on Power Electronics, 17(1), 2002:94-100
[50] T. G. Ha betler, F. Pastorelli. Direct Torque Control of Induction Machines using Space Vector Modulation, IEEE IAS'1991:428-436
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[52] Hyung-Min Ryu, Ji-Woong Kim, Seung-Ki Sul. Synchronous-Frame Current Control of Multiphase Synchronous Motor Under Asymmetric Fault Condition Due to Open Phases[J]. IEEE Trans. Ind. Appl, 42(4) 2006:1062-1070
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