Theoretical Independence of Current and Torque Amplitudes of Synchronous Machine with Inductive Load from Frequency
DOI:
https://doi.org/10.24160/1993-6982-2019-5-68-72Keywords:
synchronous machine, inductive load, current, torque, amplitudeAbstract
The current and torque of an inductive synchronous electrical machine operating on an inductive load are considered. For an inductive synchronous machine operating on an inductive load, the following theorem is valid: the amplitude of the current through the inductive load of an inductive synchronous electrical machine does not depend on the rotation frequency. This theorem is proved by equating the Kirchhoff second law and the law of electromagnetic induction as applied to a rotating machine. The following theorem is also valid: the torque amplitude for an inductive synchronous electrical machine operating on an inductive load does not depend on the rotation frequency. This theorem is proved by analyzing the Ampere law as applied to a rotating machine.
It has been established that with an active load, the current and torque amplitudes depend linearly on the machine rotation frequency. With the machine operating on a capacitive load, the current and torque amplitudes are quadratic functions of the rotation frequency. The dependence of the machine power on the nature of its load is established. For an inductive load, the reactive electrical power is a linear function of the frequency; for a resistive load, the machine power is a quadratic function of the frequency; and for a capacitive load, its power is a cubic function of the frequency. For a synchronous capacitive machine operating on a capacitive load, the following theorems are valid:
The voltage amplitude across the capacitive load of a capacitive synchronous electrical machine does not depend on the rotation frequency. The torque amplitude for a capacitive synchronous electrical machine operating on a capacitive load does not depend on the rotation frequency.
References
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2. Boglietti A., Cavagnino A., Pastorelli M., Vagati A. Experimental Comparison of Induction and Synchronous Reluctance Motors Performance // Conf. Record of the 2005 Industry Appl. Conf. Fortieth IAS Annual Meeting. 2005. V.1. Pp. 474—479.
3. Bomela X.B., Kamper M.J. Effect of Stator Chording and Rotor Skewing on Performance of Reluctance Synchronous Machine // IEEE Trans. Ind. Appl. 2002. No. 1. Pp. 91—100.
4. Oprea C., Dziechciarz A, Martis C. Comparative Analysis of Different Synchronous Reluctance Motor Topologies // Proc. Intern. Conf. Environment and Electrical Eng. Palermo, 2015.
5. Fratta А., Troglia G.P., Vagati A., Villata F. Torque Ripple Evaluation of High-рerformance Synchronous Reluctance Machines // IEEE Trans. Ind. Appl. Mag. 1995. V. 1. No. 4. Pp. 14—22.
6. Haataja J.A. Comparative Performance Study of Four Pole Induction Motors and Synchronous Reluctance Motor in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
7. Ho Lee J., Lee K., Hyun Cho Y., Won Yun T. Characteristics Analysis and Optimum Design of Anisotropy Rotor Synchronous Reluctance Motor Using Coupled Finite Element Method and Response Surface Methodology // IEEE Trans. Magnetics. 2009. V. 45. Pp. 4696—4699.
8. Hofmann H., Sanders S.R. High-speed Synchronous Reluctance Machine with Minimized Rotor Loss // IEEE Trans. Industry Appl. 2000. V. 36. No. 2. Pp. 531—539.
9. Hortman M.B. Implementation and Evaluation of a Full-order Observer for a Synchronous Reluctance Motor. Georgia: School of Electrical and Computer Engineering Georgia Institute of Technology, 2004.
10. Hossein A., Abolfazl V. Rotor Geometry Parameter Optimization of Synchronous Reluctance Motor Using Taguchi Method // Przegląd Elektrotechniczny. 2013. V. 89. Pp. 197—201.
11. Hudak P., Hrabovcova V., Rafajdus P. Geometrical Dimension Induence of Multi-barrier Rotor on Reluctance Synchronous Motor Performances // Intern. Symp. Power Electronics, Electrical Drives, Automation and Motion. 2006. Pp. 346—351.
12. Kolehmainen J. Synchronous Reluctance Motor with Form Blocked Rotor // IEEE Trans. Energy Conversion. 2010. Pp. 450—456.
13. Haataja J. A Comparative Performance Study of Four-pole Induction Motors and Synchronous Reluctance Motors in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
14. Kamper M.J., Van der Merwe F.S., Williamson S. Directnite Element Design Optimization of the Cageless Reluctance Synchronous Machine // IEEE Trans. Energy Conversion. 1996. V. 11. No. 3. Pp. 547—555.
15. Moghaddam R.R. Synchronous Reluctance Machine (SynRM) Design // Thesis in Power Electrical Eng. Royal Institute of Technology, 2007.
16. Moghaddam R.R., Magnussen F., Sadarangani Ch. Theoretical and Experimental Reevaluation of Synchronous Reluctance Machine // IEEE Trans. Industrial Electronics. 2010. V. 57. No. 1. Pp. 6—13.
17. Попов И.П. Свободные гармонические колебания в электрических системах с однородными реактивными элементами // Электричество. 2013. № 1. С. 57—59.
18. Попов И.П. Зависимость реактивного сопротивления пьезоэлектрического преобразователя от механических параметров его нагрузки // Научно-технический вестник информационных технологий, механики и оптики. 2013. № 5 (87). С. 94—98.
19. Попов И.П. Емкостно-инертное устройство // Известия Санкт-Петербургского гос. электротехн. ун-та «ЛЭТИ». 2015. Т. 2. С. 43—45.
20. Попов И.П. Вращательные инертно-емкостные устройства // Вестник Самарского гос. техн. ун-та. Серия «Технические науки». 2011. № 3 (31). С. 187—192.
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Для цитирования: Попов И.П. Теоретически установленная независимость амплитуд тока и момента синхронной машины с индуктивной нагрузкой от частоты // Вестник МЭИ. 2019. № 5. С. 68—72. DOI: 10.24160/1993-6982-2019-5-68-72.
#
1. Bianchi N., Bolognani S., Bon D., Dai Pre M. Rotor Flux-Barrier Design for Torque Ripple Reduction in Synchronous Reluctance and PM-assisted Synchronous Reluctance Motors. IEEE Trans. Ind. Appl. 2009; 45;3: 921—928.
2. Boglietti A., Cavagnino A., Pastorelli M., Vagati A. Experimental Comparison of Induction and Synchronous Reluctance Motors Performance. Conf. Record of the 2005 Industry Appl. Conf. Fortieth IAS Annual Meeting. 2005;1: 474—479.
3. Bomela X.B., Kamper M.J. Effect of Stator Chording and Rotor Skewing on Performance of Reluctance Synchronous Machine. IEEE Trans. Ind. Appl. 2002;1: 91—100.
4. Oprea C., Dziechciarz A, Martis C. Comparative Analysis of Different Synchronous Reluctance Motor Topologies. Proc. Intern. Conf. Environment and Electrical Eng. Palermo, 2015.
5. Fratta А., Troglia G.P., Vagati A., Villata F. Torque Ripple Evaluation of High-рerformance Synchronous Reluctance Machines. IEEE Trans. Ind. Appl. Mag. 1995;1; 4:14—22.
6. Haataja J.A. Comparative Performance Study of Four Pole Induction Motors and Synchronous Reluctance Motor in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
7. Ho Lee J., Lee K., Hyun Cho Y., Won Yun T. Characteristics Analysis and Optimum Design of Anisotropy Rotor Synchronous Reluctance Motor Using Coupled Finite Element Method and Response Surface Methodology. IEEE Trans. Magnetics. 2009;45:4696—4699.
8. Hofmann H., Sanders S.R. High-speed Synchronous Reluctance Machine with Minimized Rotor Loss. IEEE Trans. Industry Appl. 2000;36;2:531—539.
9. Hortman M.B. Implementation and Evaluation of a Full-order Observer for a Synchronous Reluctance Motor. Georgia: School of Electrical and Computer Engineering Georgia Institute of Technology, 2004.
10. Hossein A., Abolfazl V. Rotor Geometry Parameter Optimization of Synchronous Reluctance Motor Using Taguchi Method. Przegląd Elektrotechniczny. 2013;89:197—201.
11. Hudak P., Hrabovcova V., Rafajdus P. Geometrical Dimension Induence of Multi-barrier Rotor on Reluctance Synchronous Motor Performances. Intern. Symp. Power Electronics, Electrical Drives, Automation and Motion. 2006:346—351.
12. Kolehmainen J. Synchronous Reluctance Motor with Form Blocked Rotor. IEEE Trans. Energy Conversion. 2010:450—456.
13. Haataja J. A Comparative Performance Study of Four-pole Induction Motors and Synchronous Reluctance Motors in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
14. Kamper M.J., Van der Merwe F.S., Williamson S. Directnite Element Design Optimization of the Cageless Reluctance Synchronous Machine. IEEE Trans. Energy Conversion. 1996;11;3:547—555.
15. Moghaddam R.R. Synchronous Reluctance Machine (SynRM) Design. Thesis in Power Electrical Eng. Royal Institute of Technology, 2007.
16. Moghaddam R.R., Magnussen F., Sadarangani Ch. Theoretical and Experimental Reevaluation of Synchronous Reluctance Machine. IEEE Trans. Industrial Electronics. 2010;57;1:6—13.
17. Popov I.P. Svobodnye Garmonicheskie Kolebaniya v Elektricheskikh Sistemakh s Odnorodnymi Reaktivnymi Elementami. Elektrichestvo. 2013;1:57—59. (in Russian).
18. Popov I.P. Zavisimost' Reaktivnogo Soprotivleniya P'ezoelektricheskogo Preobrazovatelya ot Mekhanicheskikh Parametrov Ego Nagruzki. Nauchno-tekhnicheskiy Vestnik Informatsionnykh Tekhnologiy, Mekhaniki i Optiki. 2013;5 (87):94—98. (in Russian).
19. Popov I.P. Emkostno-inertnoe Ustroystvo. Izvestiya Sankt-Peterburgskogo Gos. Elektrotekhn. Un-ta «LETI». 2015;2:43—45. (in Russian).
20. Popov I.P. Vrashchatel'nye Inertno-emkostnye Ustroystva. Vestnik Samarskogo Gos. Tekhn. Un-ta. Seriya «Tekhnicheskie Nauki». 2011;3 (31):187—192. (in Russian).
---
For citation: Popov I.P. Theoretical Independence of Current and Torque Amplitudes of Synchronous Machine with Inductive Load from Frequency. Bulletin of MPEI. 2019;5:68—72. (in Russian). DOI: 10.24160/1993-6982-2019-5-68-72.
2. Boglietti A., Cavagnino A., Pastorelli M., Vagati A. Experimental Comparison of Induction and Synchronous Reluctance Motors Performance // Conf. Record of the 2005 Industry Appl. Conf. Fortieth IAS Annual Meeting. 2005. V.1. Pp. 474—479.
3. Bomela X.B., Kamper M.J. Effect of Stator Chording and Rotor Skewing on Performance of Reluctance Synchronous Machine // IEEE Trans. Ind. Appl. 2002. No. 1. Pp. 91—100.
4. Oprea C., Dziechciarz A, Martis C. Comparative Analysis of Different Synchronous Reluctance Motor Topologies // Proc. Intern. Conf. Environment and Electrical Eng. Palermo, 2015.
5. Fratta А., Troglia G.P., Vagati A., Villata F. Torque Ripple Evaluation of High-рerformance Synchronous Reluctance Machines // IEEE Trans. Ind. Appl. Mag. 1995. V. 1. No. 4. Pp. 14—22.
6. Haataja J.A. Comparative Performance Study of Four Pole Induction Motors and Synchronous Reluctance Motor in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
7. Ho Lee J., Lee K., Hyun Cho Y., Won Yun T. Characteristics Analysis and Optimum Design of Anisotropy Rotor Synchronous Reluctance Motor Using Coupled Finite Element Method and Response Surface Methodology // IEEE Trans. Magnetics. 2009. V. 45. Pp. 4696—4699.
8. Hofmann H., Sanders S.R. High-speed Synchronous Reluctance Machine with Minimized Rotor Loss // IEEE Trans. Industry Appl. 2000. V. 36. No. 2. Pp. 531—539.
9. Hortman M.B. Implementation and Evaluation of a Full-order Observer for a Synchronous Reluctance Motor. Georgia: School of Electrical and Computer Engineering Georgia Institute of Technology, 2004.
10. Hossein A., Abolfazl V. Rotor Geometry Parameter Optimization of Synchronous Reluctance Motor Using Taguchi Method // Przegląd Elektrotechniczny. 2013. V. 89. Pp. 197—201.
11. Hudak P., Hrabovcova V., Rafajdus P. Geometrical Dimension Induence of Multi-barrier Rotor on Reluctance Synchronous Motor Performances // Intern. Symp. Power Electronics, Electrical Drives, Automation and Motion. 2006. Pp. 346—351.
12. Kolehmainen J. Synchronous Reluctance Motor with Form Blocked Rotor // IEEE Trans. Energy Conversion. 2010. Pp. 450—456.
13. Haataja J. A Comparative Performance Study of Four-pole Induction Motors and Synchronous Reluctance Motors in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
14. Kamper M.J., Van der Merwe F.S., Williamson S. Directnite Element Design Optimization of the Cageless Reluctance Synchronous Machine // IEEE Trans. Energy Conversion. 1996. V. 11. No. 3. Pp. 547—555.
15. Moghaddam R.R. Synchronous Reluctance Machine (SynRM) Design // Thesis in Power Electrical Eng. Royal Institute of Technology, 2007.
16. Moghaddam R.R., Magnussen F., Sadarangani Ch. Theoretical and Experimental Reevaluation of Synchronous Reluctance Machine // IEEE Trans. Industrial Electronics. 2010. V. 57. No. 1. Pp. 6—13.
17. Попов И.П. Свободные гармонические колебания в электрических системах с однородными реактивными элементами // Электричество. 2013. № 1. С. 57—59.
18. Попов И.П. Зависимость реактивного сопротивления пьезоэлектрического преобразователя от механических параметров его нагрузки // Научно-технический вестник информационных технологий, механики и оптики. 2013. № 5 (87). С. 94—98.
19. Попов И.П. Емкостно-инертное устройство // Известия Санкт-Петербургского гос. электротехн. ун-та «ЛЭТИ». 2015. Т. 2. С. 43—45.
20. Попов И.П. Вращательные инертно-емкостные устройства // Вестник Самарского гос. техн. ун-та. Серия «Технические науки». 2011. № 3 (31). С. 187—192.
---
Для цитирования: Попов И.П. Теоретически установленная независимость амплитуд тока и момента синхронной машины с индуктивной нагрузкой от частоты // Вестник МЭИ. 2019. № 5. С. 68—72. DOI: 10.24160/1993-6982-2019-5-68-72.
#
1. Bianchi N., Bolognani S., Bon D., Dai Pre M. Rotor Flux-Barrier Design for Torque Ripple Reduction in Synchronous Reluctance and PM-assisted Synchronous Reluctance Motors. IEEE Trans. Ind. Appl. 2009; 45;3: 921—928.
2. Boglietti A., Cavagnino A., Pastorelli M., Vagati A. Experimental Comparison of Induction and Synchronous Reluctance Motors Performance. Conf. Record of the 2005 Industry Appl. Conf. Fortieth IAS Annual Meeting. 2005;1: 474—479.
3. Bomela X.B., Kamper M.J. Effect of Stator Chording and Rotor Skewing on Performance of Reluctance Synchronous Machine. IEEE Trans. Ind. Appl. 2002;1: 91—100.
4. Oprea C., Dziechciarz A, Martis C. Comparative Analysis of Different Synchronous Reluctance Motor Topologies. Proc. Intern. Conf. Environment and Electrical Eng. Palermo, 2015.
5. Fratta А., Troglia G.P., Vagati A., Villata F. Torque Ripple Evaluation of High-рerformance Synchronous Reluctance Machines. IEEE Trans. Ind. Appl. Mag. 1995;1; 4:14—22.
6. Haataja J.A. Comparative Performance Study of Four Pole Induction Motors and Synchronous Reluctance Motor in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
7. Ho Lee J., Lee K., Hyun Cho Y., Won Yun T. Characteristics Analysis and Optimum Design of Anisotropy Rotor Synchronous Reluctance Motor Using Coupled Finite Element Method and Response Surface Methodology. IEEE Trans. Magnetics. 2009;45:4696—4699.
8. Hofmann H., Sanders S.R. High-speed Synchronous Reluctance Machine with Minimized Rotor Loss. IEEE Trans. Industry Appl. 2000;36;2:531—539.
9. Hortman M.B. Implementation and Evaluation of a Full-order Observer for a Synchronous Reluctance Motor. Georgia: School of Electrical and Computer Engineering Georgia Institute of Technology, 2004.
10. Hossein A., Abolfazl V. Rotor Geometry Parameter Optimization of Synchronous Reluctance Motor Using Taguchi Method. Przegląd Elektrotechniczny. 2013;89:197—201.
11. Hudak P., Hrabovcova V., Rafajdus P. Geometrical Dimension Induence of Multi-barrier Rotor on Reluctance Synchronous Motor Performances. Intern. Symp. Power Electronics, Electrical Drives, Automation and Motion. 2006:346—351.
12. Kolehmainen J. Synchronous Reluctance Motor with Form Blocked Rotor. IEEE Trans. Energy Conversion. 2010:450—456.
13. Haataja J. A Comparative Performance Study of Four-pole Induction Motors and Synchronous Reluctance Motors in Variable Speed Drives. Lappeenranta: Lappeenranta University of Technology, 2003.
14. Kamper M.J., Van der Merwe F.S., Williamson S. Directnite Element Design Optimization of the Cageless Reluctance Synchronous Machine. IEEE Trans. Energy Conversion. 1996;11;3:547—555.
15. Moghaddam R.R. Synchronous Reluctance Machine (SynRM) Design. Thesis in Power Electrical Eng. Royal Institute of Technology, 2007.
16. Moghaddam R.R., Magnussen F., Sadarangani Ch. Theoretical and Experimental Reevaluation of Synchronous Reluctance Machine. IEEE Trans. Industrial Electronics. 2010;57;1:6—13.
17. Popov I.P. Svobodnye Garmonicheskie Kolebaniya v Elektricheskikh Sistemakh s Odnorodnymi Reaktivnymi Elementami. Elektrichestvo. 2013;1:57—59. (in Russian).
18. Popov I.P. Zavisimost' Reaktivnogo Soprotivleniya P'ezoelektricheskogo Preobrazovatelya ot Mekhanicheskikh Parametrov Ego Nagruzki. Nauchno-tekhnicheskiy Vestnik Informatsionnykh Tekhnologiy, Mekhaniki i Optiki. 2013;5 (87):94—98. (in Russian).
19. Popov I.P. Emkostno-inertnoe Ustroystvo. Izvestiya Sankt-Peterburgskogo Gos. Elektrotekhn. Un-ta «LETI». 2015;2:43—45. (in Russian).
20. Popov I.P. Vrashchatel'nye Inertno-emkostnye Ustroystva. Vestnik Samarskogo Gos. Tekhn. Un-ta. Seriya «Tekhnicheskie Nauki». 2011;3 (31):187—192. (in Russian).
---
For citation: Popov I.P. Theoretical Independence of Current and Torque Amplitudes of Synchronous Machine with Inductive Load from Frequency. Bulletin of MPEI. 2019;5:68—72. (in Russian). DOI: 10.24160/1993-6982-2019-5-68-72.
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2018-11-06
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Electromechanics and Electrical Apparatus (05.09.01)
