The Analysis of Induction Motor Rundown Regime Concomitant Electromechanical Processes in Two Phase Coordinate System α,β




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The Analysis of Induction Motor Rundown Regime Concomitant Electromechanical Processes in Two Phase Coordinate System α,β


Marina Konuhova, Riga Technical University, Guntis Orlovskis, Riga Technical University


Abstract- Nowadays different kinds of investigations linked to processes running in induction motor rotor circuit are topical. It might be explained by the fact that currents, electromagnetic torque value changes might be affected from stator terminal only. Nothing taking place in rotor circuit could be affected directly. Induction motor rundown regime attracts interest due to its particular feature: under unfavorable circumstances large inrush current and short-time shock nature mechanical forces at repeated motor switching at persistent stator field dangerous for induction motor can appear. Investigation and detailed research of induction motor rundown regime is important. Rundown regime occurs at any instance of induction motor switching. Rundown regime starts switching induction motor stator windings without power supply. Such switching can be purposeful or might occur because of some kind of network damages. Concomitant rundown regime in electromechanical processes determines success of the following induction motor operation regimes linked to different kinds of switching such as: self start at repeated closing and changeover, wye-delta start-up, reverse etc. Detailed research of transient electromechanical processes allows designing more optimal induction electrical drive. This article presents induction motor mathematical model in two phase coordinate system α,β, which allows comparing characteristics obtained in modeling and experimental way without additional transformations. Rotation frequency, residual voltage, electromagnetic torque, stator and rotor currencies, and stator and rotor flux linkages were obtained using this model. That gave the opportunity to analyze induction motor rundown regime concomitant processes.


Keywords – analysis, induction motor, mathematical model, reclosing, rundown regime, transient processes.


  1. Introduction

Induction motors are dominant consumers of power supply systems today. These motors are rather cheap and do not need large service expenses [1]. Thereto induction motors (IM) utilize about 60% of the energy produced in the European Union [2]. Therefore processes taking place in IM investigation remain topical even today. One of the most used in practice IM operation regimes is switching regime. Switching regime is accompanied by two processes: stator winding switching off and repeated closing. The most interesting for us is stator winding switching off process, respectively induction motor rundown regime investigation. The matter is that this regime specifies success of machine repeated closing in such regimes as self start, where for assuring important consumer power supply continuity automatic load transfer automation or repeated closing automation or reverse, wye-delta start-up etc. are used.

The overview of the sources in this field shows that issues dedicated to IM switching regimes have been extensively investigated, but in the recent years particular attention has been paid to electromagnetic transient processes [3-7]. The reason is success in development of fast-response switching automation causing respectable decrease of acting time in the recent years [8]. At IM repeated closing in short time the processes are analogical to synchronous machine operation with certain excitation determined by residual motor flux and residual voltage on terminals switching on [9]. At the moment of switching an inrush current appears initiating an increased torque and increased electrodynamical forces having an influence on the windings. Under such conditions it is impossible to ignore residual voltage after IM switching off and this argument led to deeper investigation of this issue. Papers [5-7] present transient process analysis for IM rapid switching. IM repeated switching variants depending on residual voltage and network vectors location for different IM operation load level are investigated. But this paper does not provide accurate mathematical model describing transient processes in rundown regime and at repeated closing for determination of inrush currents and torques. In paper [5] special attention is dedicated to determination of inrush currents and torques at IM repeated closing. In paper [7] investigation of IM group repeated closing after repeated closing automation and automatic load transfer and its impact on network is presented.

This article provides mathematical model in two phase coordinate system α,β, for IM rundown regime accompanying process investigation, which allows getting characteristics of rotation frequency, residual voltage, electromagnetic torque, stator and rotor currents flux linkages. Thus we get clear understanding of processes accompanying rundown regime.


  1. Rundown Regime Singularity

To model IM rundown regime we need to understand processes proceeding after IM stator windings switched off power supply.

We know that in accordance with commutation first rule “in circuit with active-inductive load the change of the current by step is impossible”. Electromagnetic energy accumulated in IM couldn’t be dispersed instantaneously. Electromagnetic energy is concentrated in the main magnetic circuit – excitation circuit and in stator and rotor dispersion magnetic fluxes. The remaining part of electromagnetic energy at the opening moment remains constant and supported by squirrel cage rotor windings.

Rundown regime takes place at IM stator winding switching off power supply. Power interruption might appear purposefully or due to any network emergency [10, 11].

Switching off IM power supply stator winding current value suddenly drops to zero. The faster the interruption is the higher voltage is induced in the stator winding because of the changes in electromagnetic flux interconnected with it.

Electromagnetic energy accumulated in IM remains constant and is supported by rotor winding. This circumstance is important because it allows coordinating final electromagnetic conditions before switching off and initial electromagnetic conditions of rundown regime.


  1. Assumptions

Conducting IM rundown regime analysis we assume the following [12]:

  • The motor maintains constant speed when switching off or reclosing is taking place;

  • Saturation is considered only in the calculation of the motor parameters. They remain unchanged for a given transient calculation. This gives a linear nature to the analysis of the transient circuits;

  • The neutrals of the motor and the power-factor correction capacitors are not grounded; consequently, the current of coordinate zero can be neglected. It is worth mentioning that the current and flux of coordinate zero, even if they exist, do not produce torque;

  • Multiple re-ignition and voltage escalation caused by switch-gears are not considered.




  1. Induction Motor Mathematical Model

IM mathematical model in two phase coordinate system can be presented in the following way:






(1)




(2)


where current values have been obtained from flux linkage expressions:






(3)


where




(4)





(5)


To model rundown regime at IM switching off moment we point start-up steady parameters.

Interrupting motor power supply we assume that stator circuit is broken instantly, stator currents are equal to zero [13].

Forced stator current nullification (7) initiates rotor currents change from rotor flux linkage vector invariability at switching moment condition.




(6)

Thus, IM rundown process behavior is determined by the following differential equation system:






(7)




(8)


The application of the provided model gives opportunity to get rotation frequency, current, flux linkages, electromagnetic torque, residual voltage characteristics in rundown regime for further estimation of safe repeated closing if fast-response automation is applied.


  1. Rundown Regime Characteristics Analysis

On the basis of IM mathematical model presented in the previous chapter IM was modeled with the following parameters (in relative units) [14]: ,, , , rundown regime.

After switching off the motor continues rotation by inertia. Motional energy is spent for overcoming all kinds of motion resistance. Therefore, the motor rotation frequency will decrease to zero after the time interval during which all the kinetic energy is completely expended (Fig.1).




Fig. 1. Rotation frequency curve in IM rundown regime

IM rotation frequency curve in rundown regime gives opportunity to determine exact IM rundown time or residual rotation frequency value at fixed time point after switching off power supply. Exact rotation frequency definition is needed for determination of driven mechanism behavior in such regimes as self start, reverse, repeated closing.

Thus, there is an opportunity to get rotation frequency curves for any IM with different load factors and load torques without application of graphic and analytic methods.

For mechanism exact stoppage it is important to know not only rotation frequency residual value but residual voltage value on stator terminal as well. Free rundown motor inducted electromotive force (EMF) value has decisive influence on the current of switching on at power supply renewal (Fig.2). Residual voltage may damp in several periods for small capacity motors but might continue for more that 5 seconds in large capacity machines [15].




Fig. 2. Residual voltage curve in IM rundown regime


Residual voltage curve at rundown regime gives an opportunity to define stator winding residual voltage damping time for any IM independent on its parameters and load type. Thus, there is an opportunity to define the time interval needed for residual voltage across stator winding that would be limited by 0.33 in the model, which assures safety of the following IM operation regimes [16].

Figures 3 and 4 present IM full current and electromagnetic torque characteristics in rundown regime.

Rundown regime currents and flux linkage curve analysis showed that in rotor circuit at the moment of IM switching off the rotor current changes step-wise (Fig.5) in contrast to stator circuit current, which drops to zero (Fig.6). Rotor flux linkages at IM switching off moment have damping nature (Fig.7) but stator flux linkages drops to zero instantaneously (Fig.8).

The swift increasing of rotor current at IM power supply interruption in a rundown process results in EMF induced there, the phase and value of which in aggregate with network voltage might have negative impact on IM at rapid reclosing.





Fig.3. IM current curve in rundown regime




Fig. 4. IM electromagnetic torque curve in rundown regime





Fig. 5. IM rotor current curve in rundown regime





Fig. 6. IM stator current curve in rundown regime





Fig. 7. IM rotor flux linkages curve in rundown regime




Fig. 8 IM stator flux linkages curve in rundown regime





Rotation frequency and residual voltage characteristics for the motor with squirrel cage rotor were made to estimate validity of the characteristics obtained in mathematical modeling experiments (Fig.11 and 12). Also the experiment to get IM with wound rotor stator and rotor currents in rundown regime was made (Fig. 9 and 10).

In Figure 9 it is shown that at the moment of motor switching off the stator current drops to zero instantly but rotor current changes stepwise (Fig.10). Comparison of rundown regime curves received by means of mathematical modeling and using oscillograph demonstrates that experimental characteristics completely concur with those obtained in the modeling process.





Fig. 9 Stator current oscillogram in IM with wound rotor rundown regime





Fig. 10 Rotor current oscillogram in IM with wound rotor rundown regime





Fig. 11 Residual voltage oscillogram in squirreled cage rotor IM rundown regime





Fig. 12. Rotation frequency oscillogram in squirreled cage IM rundown regime




  1. conclusions

Presented induction motor mathematical model in two phase coordinate system α,β, really allows analyzing rundown process concomitant electromechanical processes. With the help of this model it is possible to find out rotation frequency, residual voltage, electromagnetic torque, currents and flux linkages curves for any certain IM capacity with different load torques and different load characteristics.

The analysis of the received characteristics will give an opportunity to define residual rotation torque, permissible stator residual voltage value to ensure safe repeated IM closing in such regimes as: self start, wye-delta start-up, reverse etc.


ACKNOWLEDGMENT



This work has been supported by the European Social Fund within the project „Support for the implementation of doctoral studies at Riga Technical University”.

References

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  2. International Energy Ageny, key World Energy statistics 2007.

  3. Сивокобыленко В.Ф., Лебедев В.К., Кукий К.А. Mатематическое моделирование асинхронной нагрузки в режимах группового выбега и самозапуска.- Сб.Науч.трудов ДоНТУ. Серия: Электротехника и энергетика, вып.41:ДоНТУ. С.28-34, 2002.

  4. E.S.Koshevnikova, V.V.Chelpanov. Моделирование процесса самозапуска электродвигателей. Proceeding of the four All-Russian Scientific Conference with international participation (29-31 May 2007.) Part 2. Matem.Mod.Kraev.Zadachi,Samara State Technical Univ., Samara. pp.67-69, 2007.

  5. Faiz J., Ghaneei M., Keyhani A. Performance analysis of fast reclosing transients in induction motors. IEEE Trans. Energy Conversion Vol.14, No. 1. pp. 101-107. March 1999.

  6. Reynaud and P.Pillay. Reclosing transients in induction machines including the effect of saturation of the magnetizing branch and a practical case study. IEEE Transaction on energy conversion, Vol.9, No.2, pp.383-389, June 1994.

  7. Aiyuan W, Zhihao L, Wenbo L. Residual voltage analysis in reclosing process for induction machine. IEEE Proceedings of 7th World Congress on Intelligent Control and automation. Chongqing, China. pp. 4785-4788. June 2008.

  8. Терехов В.М. Системы управления электроприводов: Учебник для студ. Высш. Учеб. Заведений/ В.М.Терехов, О.И. Осипов; Под ред. В.М.Терехова.-М.: Издательский центр «Академия», 2005.-304 с.

  9. Домбровский В.В. Зайчик В.М. Асинхронные машины: Теория, расчет, элементы проектирования.- Л.: Энергоатомиздат. Ленинград. Отд-ие, 1990.

  10. Ketners K., Ketnere S., Klujevska S., Konuhova M. “Research of the induction motor’s self-starting mode”. Scientific proceedings of Riga Technical University, Power and Electrical Engineering, Riga: RTU, 2007. Vol.19. pp.124-130.

  11. Konuhova M., Ketners K., Ketnere E., Klujevska S. ”Investigation of the induction motor start up process using star-delta start”. Scientific proceedings of 4th International Conference on Electrical and Control Technologies of Kaunas University of Technology, Kaunas, Lithuania, May 7-8, 2009,pp.-215-218.

  12. John S.C. Htsui Non-simultaneous reclosing air-gap transient torque of induction motor: Part I, Analysis and computation logic. IEEE Trans. Of Energy Conv., Vol.EC-2,No.2, June 1987.

  13. Джафаров З.С., Мустафаев Р.И. Способы улучшения самозапуска двигателей собственных нужд ТЭС. Азербайджанский институт энергетики и энергетического проектирования. Проблемы энергетики №1, 2005.

  14. Асинхронные двигатели серии 4А: Справочник/А.Э.Соболевская, М.М. Шлаф, В.И.Афонин, Е.А. Соболевская.-М.:Энергоиздат,1982.

  15. P.Dalasta and S.Duran. High-speed breaker reclosing can put abnormal stress on your motors. Design and Equipment Application Section – Power, February 1958, pp.90-183.

  16. ANSI (NEMA) American National Standart for Polyphase Induction Motors for Power Generating Stations. ANSI Standart C50.41-2000.




Marina Konuhova was born in Riga, Latvia. She received the Dipl. Eng. Bachelor Degree in power and electrical engineering and Master Degree in power and electrical engineering at Riga Technical University in 2005 and 2007, respectively. From 2007 she was a doctoral student at Riga Technical University. She works at Riga Technical University at the Faculty of Electrical Machines and Devices as a researcher since autumn 2007. She is engaged in researching and modeling of induction motor and also processes connected with them.

    E-mail: Marina.Konuhova@rtu.lv



Guntis Orlovskis was born in Ludza, Latvia. He received Dipl. Eng. Bachelor Degree in power and electrical engineering and Master Degree in power and electrical engineering at Riga Technical University in 2008 and 2010 respectively. From 2010 he is a doctoral student at Riga Technical University. From 2002 until 2004 he was employed as an electrician in the Department of Electrical Machines Service at ABB Company. He works at Riga Technical University at the Faculty of Electrical Machines and Devices as a scientific assistant since autumn 2003. He is engaged in researching of electrical machines.

    E-mail: jott@inbox.lv






Марина Конюхова, Гунтис Орловскис. Анализ электромеханических процессов, сопровождающих режим выбега асинхронного двигателя в двухфазной системе координат α,β.

В данной работе представлена математическая модель асинхронного двигателя (АД) в координатной системе α,β. Использование координатной системы α,β является предпочтительным, т.к. позволяет без дополнительных преобразований сравнить результат одной из фаз. С помощью такой модели был проведен анализ электромеханических процессов АД, сопровождающих режим выбега. Режим выбега АД представляет интерес тем, что, в случае повторного включения с не затухшем поле статора могут возникнуть большие всплески тока и кратковременные механические усилия ударного характера, что является опасный для АД. Проведенный анализ показал, что в роторной цепи в момент отключения АД от источника питания, ток ротора возрастает и в процессе выбега с постоянной времени обмотки ротора падает до нуля. За счет этого тока индуктируется ЭДС на обмотке статора, которая так же затухает во времени. Однако остаточное напряжение на статорной обмотке может затухнуть через несколько периодов в машинах малой мощности, но может продлиться и более 5 секунд в машинах большой мощности. Таким образом, с помощью представленной математической модели, имеется возможность определить время, за которое остаточное напряжение на обмотке статора достигнет безопасного значения, для обеспечения безопасных последующих режимов работы АД, таких как: самозапуск с использованием автоматического ввода резерва и автоматического повторного включения; реверс; пуск со звезды на треугольник и пр.

Характеристики, полученные на модели для асинхронного двигателя в режиме выбега, были сопоставлены с характеристиками, полученными экспериментальным путем. Таким образом, представленная математическая модель АД в координатной системе α,β является адекватной и позволяет производить анализ электромеханических переходных процессов в режиме выбега асинхронной машины.


Koņuhova Мarina, Orlovskis Guntis. Asinhronā dzinēja izskrejas režīmu pavadošo elektromehānisko procesu analīze divfāžu koordinātu sistēmā α,β.

Šajā darbā aprakstīts asinhronā dzinēja (ADz) matemātiskais modelis koordinātu sistēmā α,β. Koordinātu sistēmas α,β izmantošana ir vēlama, jo ļauj bez papildus pārveidojumiem salīdzināt rezultātu vienai no fāzēm. Izmantojot šādu modeli tika veikta izskrejas režīmu pavadošo asinhrono dzinēju elektromehānisko procesu analīze. Pastiprināta uzmanība ir jāpievērš režīmam, kad asinhronais dzinējs darbojas izskrejas brīdī. Pie atkārtotas ieslēgšanas ja magnētiskais lauks nav norimis var parādīties lielas strāvas amplitūdas un īslaicīgi mehāniski triecieni uz dzinēja vārpstas, kas ir ļoti bīstami asinhronā dzinēja normālam darbam. Tā izrādījās, ka rotora ķēdē brīdī, kad asinhronais dzinējs tiek atslēgts no barošanas avota, rotora strāva pieaug un izskrejas procesā ar laika konstanti nokrītas līdz nullei. Šīs strāvas dēļ statora tinumā tiek inducēts EDS, kas tāpat rimst laikā. Tomēr paliekošais spriegums statora tinumā var norimt pēc vairākiem periodiem mazas jaudas mašīnās, bet var arī ilgt 5 un vairāk sekundes lielas jaudas mašīnās. Tādā veidā izmantojot aprakstīto modeli pastāv iespēja noteikt laiku pa kuru paliekošais spriegums statora tinumā sasniegs drošu vērtību, lai nodrošinātu drošus turpmākos asinhrono dzinēju darbības režīmus, tādus kā: pašpalaide izmantojot automātisko atpakaļ ieslēgšanu un automātisko atkārtoto ieslēgšanu, reversu, palaide no zvaigznes uz trīsstūri uc.

Raksturlielumi, kas iegūti izmantojot modeli asinhrono dzinēju izskrejas režīmā, tika salīdzināti ar raksturlielumiem, kas iegūti eksperimentālā ceļā. Tādā veidā aprakstītais asinhrono dzinēju matemātiskais modelis koordinātu sistēmā α,β ir adekvāts un ļauj veikt elektromagnētisko pārejas procesu analīzi asinhronās mašīnas izskrejas režīmā.



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