A Mathematical Review Study on Dynamical Models of Symmetrical Three-Phase Induction Machine in Various Reference Frames

Yıl 2024, Cilt: 14 Sayı: 3, 1401 – 1430, 15.09.2024

Mehmet Ali Usta

https://doi.org/10.31466/kfbd.1472193

Öz

This paper presents dynamic models of a three-phase induction machine in various reference frames widely employed in alternating-current (ac) machine analysis. The main objective is to derive and explain the machine model in relatively basic terms by using the idea of rotating reference frame theory. Many matrix manipulations and complex frame-to-frame transformations performed to obtain an advanced model from primitive dynamical equations are presented in a more compact and easy-to-understand way. Therefore, this paper reviews a detailed, yet simple and understandable mathematical background on the dynamic models of the induction machine. Furthermore, a unified and broadly applicable simulation model is proposed for simulating the dynamic behavior of the machine in any desired reference frame. The simulation model has also a modular and user-friendly structure. For the simulation studies, Matlab/Simulink environment is preferred due to its popularity. A Simulink machine model with several subsystems is explicitly given. The simulation study is realized for a small power induction machine operating under both load and no-load conditions. The variations of three-phase currents, electromagnetic torque, and rotor mechanical speed as well as the rotor flux-linkage components are shown. The key features of each reference frame are discussed, especially through the measured rotor flux-linkage components.

Anahtar Kelimeler

Induction machine, Reference frame theory, Dynamic model, Simulation model

Kaynakça

• Abu-Rub, H., Iqbal, A., and Guzinski, J. (2012). High performance control of ac drives with Matlab/Simulink models. West Sussex, UK: John Wiley & Sons.
• Akherraz, M. (1997). Pspice-assisted dynamic modeling and simulation of induction motor drives. IEEE International Electric Machines and Drives Conference Record (pp. MB1/8.1-MB1/8.3). Milwaukee, WI, USA.
• Brereton, D. S., Lewis, D. G., and Young, C. G. (1957). Representation of induction-motor loads during power-system stability studies. Transactions of the American Institute of Electrical Engineers. Part-III: Power Apparatus and Systems, 76(3), 451-460.
• Bose, B. K. (2002). Modern power electronics and ac drives. New Jersey, NJ: Prentice Hall.
• Krause, P. C., and Thomas, C. H. (1965). Simulation of symmetrical induction machinery. IEEE Transactions on Power Apparatus and Systems, PAS-84(11), 1038-1053.
• Krause, P. C., Wasynczuk, O., and Sudhoff, S. D. (2002). Analysis of electric machinery and drive systems (2nd ed.). New Jersey, NJ: IEEE Press.
• Krishnan, R. (2001). Electric motor drives – Modeling, analysis, and control. New Jersey, NJ: Prentice Hall.
• Kron, G. (1951). Equivalent circuits of electric machinery. New York, NY: John Wiley & Sons.
• Lee, R. J., Pillay, P., and Harley, R. G. (1984). D,Q reference frames for the simulation of induction motors. Electric Power Systems Research, 8(1), 15-26.
• Li, Q., and Hu, J. (2010). Simulation model of induction motor based on Labview. Third International Conference on Intelligent Networks and Intelligent Systems (pp. 273-276). Shenyang, China.
• Lipo, T. A., and Consoli, A. (1984). Modeling and simulation of induction motors with saturable leakage reactances. IEEE Transactions on Industry Applications, IA-20(1), 180-189.
• Melkebeek, J. A. (2018). Electrical machines and drives – Fundamentals and advanced modelling. Springer International Publishing.
• Novotny, D. W., and Lipo, T. A. (1996). Vector control and dynamics of ac drives. New York, NY: Oxford University Press.
• Ozpineci, B., and Tolbert, L. M. (2003). Simulink implementation of induction machine model – A modular approach. IEEE International Electric Machines and Drives Conference (pp. 728-734), Madison, WI, USA.
• Park, R. H. (1929). Two-reaction theory of synchronous machines generalized method of analysis – part I. Transactions of the American Institute of Electrical Engineers, 48(3), 716-727.
• Q’Rourke, C. J., Qasim, M. M., Overlin, M. R., and Kirtley, J. L. (2019). A geometric interpretation of reference frames and transformations: dq0, Clarke, and Park. IEEE Transactions on Energy Conversion, 34(4), 2070-2083.
• Shi, K. L., Chan, T. F., and Wong, Y. K. (1997). Modelling of the three-phase induction motor using Simulink. IEEE International Electric Machines and Drives Conference Record (pp. WB3/6.1-WB3/6.3). Milwaukee, WI, USA.
• Slemon, G. R. (1988). Modelling of induction machines for electric drives. IEEE Transactions on Industry Applications, 25(6), 1126-1131.
• Stanley, H. C. (1938). An analysis of the induction machine. Electrical Engineering, 57(12), 751-757.
• Vas, P. (1998). Sensorless vector and direct torque control. New York, NY: Oxford University Press.
• Wack, P. (2011). Dynamics and control of electrical drives. Chennai, India: Springer-Verlag Berlin Heidelberg.

Simetrik Üç Fazlı Asenkron Makinanın Çeşitli Referans Çerçevelerinde Dinamik Modelleri Üzerine Matematiksel Bir İnceleme Çalışması

Yıl 2024, Cilt: 14 Sayı: 3, 1401 – 1430, 15.09.2024

Mehmet Ali Usta

https://doi.org/10.31466/kfbd.1472193

Öz

Bu makale, alternatif akım (aa) makine analizinde yaygın olarak kullanılan çeşitli referans çerçevelerinde üç fazlı asenkron makinanın dinamik modellerini sunmaktadır. Temel amaç, dönen referans çerçeve teorisi fikrini kullanarak makina modelini nispeten basit terimlerle türetmek ve açıklamaktır. İlkel dinamik denklemlerden gelişmiş bir model elde etmek için gerçekleştirilen birçok matris manipülasyonu ve karmaşık çerçeveden çerçeveye dönüşümler, daha kompakt ve anlaşılması kolay bir şekilde sunulmaktadır. Bu nedenle, bu makale asenkron makinanın dinamik modellerine ilişkin ayrıntılı, ancak basit ve anlaşılır bir matematiksel arka planı gözden geçirmektedir. Bundan başka, makinanın dinamik davranışını istenen herhangi bir referans çerçevesinde simüle etmek için birleşik ve geniş çapta uygulanabilir bir simülasyon modeli önerilmektedir. Simülasyon modeli aynı zamanda modüler ve kullanıcı dostu bir yapıya sahiptir. Simülasyon çalışmalarında popülerliği nedeniyle Matlab/Simulink ortamı tercih edilmektedir. Birkaç alt sisteme sahip bir Simulink makina modeli açıkça verilmiştir. Simülasyon çalışması hem yük hem de yüksüz koşullar altında çalışan küçük güçlü bir asenkron makina için gerçekleştirilmiştir. Üç fazlı akımların, elektromanyetik torkun ve rotor mekanik hızının yanı sıra rotor akı bileşenlerinin değişimleri gösterilmektedir. Her bir referans çerçevesinin temel özellikleri, özellikle ölçülen rotor akı bileşenleri aracılığıyla tartışılmaktadır.

Anahtar Kelimeler

Asenkron makina, Referans çerçeve teorisi, Dinamik model, Benzetim modeli

Kaynakça

• Abu-Rub, H., Iqbal, A., and Guzinski, J. (2012). High performance control of ac drives with Matlab/Simulink models. West Sussex, UK: John Wiley & Sons.
• Akherraz, M. (1997). Pspice-assisted dynamic modeling and simulation of induction motor drives. IEEE International Electric Machines and Drives Conference Record (pp. MB1/8.1-MB1/8.3). Milwaukee, WI, USA.
• Brereton, D. S., Lewis, D. G., and Young, C. G. (1957). Representation of induction-motor loads during power-system stability studies. Transactions of the American Institute of Electrical Engineers. Part-III: Power Apparatus and Systems, 76(3), 451-460.
• Bose, B. K. (2002). Modern power electronics and ac drives. New Jersey, NJ: Prentice Hall.
• Krause, P. C., and Thomas, C. H. (1965). Simulation of symmetrical induction machinery. IEEE Transactions on Power Apparatus and Systems, PAS-84(11), 1038-1053.
• Krause, P. C., Wasynczuk, O., and Sudhoff, S. D. (2002). Analysis of electric machinery and drive systems (2nd ed.). New Jersey, NJ: IEEE Press.
• Krishnan, R. (2001). Electric motor drives – Modeling, analysis, and control. New Jersey, NJ: Prentice Hall.
• Kron, G. (1951). Equivalent circuits of electric machinery. New York, NY: John Wiley & Sons.
• Lee, R. J., Pillay, P., and Harley, R. G. (1984). D,Q reference frames for the simulation of induction motors. Electric Power Systems Research, 8(1), 15-26.
• Li, Q., and Hu, J. (2010). Simulation model of induction motor based on Labview. Third International Conference on Intelligent Networks and Intelligent Systems (pp. 273-276). Shenyang, China.
• Lipo, T. A., and Consoli, A. (1984). Modeling and simulation of induction motors with saturable leakage reactances. IEEE Transactions on Industry Applications, IA-20(1), 180-189.
• Melkebeek, J. A. (2018). Electrical machines and drives – Fundamentals and advanced modelling. Springer International Publishing.
• Novotny, D. W., and Lipo, T. A. (1996). Vector control and dynamics of ac drives. New York, NY: Oxford University Press.
• Ozpineci, B., and Tolbert, L. M. (2003). Simulink implementation of induction machine model – A modular approach. IEEE International Electric Machines and Drives Conference (pp. 728-734), Madison, WI, USA.
• Park, R. H. (1929). Two-reaction theory of synchronous machines generalized method of analysis – part I. Transactions of the American Institute of Electrical Engineers, 48(3), 716-727.
• Q’Rourke, C. J., Qasim, M. M., Overlin, M. R., and Kirtley, J. L. (2019). A geometric interpretation of reference frames and transformations: dq0, Clarke, and Park. IEEE Transactions on Energy Conversion, 34(4), 2070-2083.
• Shi, K. L., Chan, T. F., and Wong, Y. K. (1997). Modelling of the three-phase induction motor using Simulink. IEEE International Electric Machines and Drives Conference Record (pp. WB3/6.1-WB3/6.3). Milwaukee, WI, USA.
• Slemon, G. R. (1988). Modelling of induction machines for electric drives. IEEE Transactions on Industry Applications, 25(6), 1126-1131.
• Stanley, H. C. (1938). An analysis of the induction machine. Electrical Engineering, 57(12), 751-757.
• Vas, P. (1998). Sensorless vector and direct torque control. New York, NY: Oxford University Press.
• Wack, P. (2011). Dynamics and control of electrical drives. Chennai, India: Springer-Verlag Berlin Heidelberg.

Toplam 21 adet kaynakça vardır.

Ayrıntılar

Kaynak Göster

Download or read online: Click here