Asenkron makinede geçici olayları inceleme yöntemleri ve uygulamaları

Abstract

ÖZET Elektrik makinelerinde geçici olayların incelenmesinde kullanılabilecek bir yöntemin bulunması, uzun yıllar araştırmacıları meşgul etmiştir, îlk olarak R.H.Park, Blondel'in iki eksen teorisinden yararlanarak, kendi ismi ile anılan Park Dönüşümü'nü bulmuştur. Daha sonra W.V. Lyon sürekli hal simetrili bileşenlerinden hareketle, temelde matematiksel olarak Park vektörü ile özdeş, ani değer simetrili bileşenlerini tanımlamıştır. Günümüzde geçici :.olay incelemelerinde yaygın olarak kullanılan yöntem, işletme büyüklüklerinin uzay gösterici tanımları üzerine kurulmuştur. Uzay göstericisi ilk kez Kovâcs tarafından tanımlanmış, daha sonra Stepina'nın özgün katkılarıyla tüm elektrik makinelerinde kullanılabilecek genel geçerli bir matematiksel yapıya kavuşmuştur. Yukarıda sözedilen bütün yöntemlerde karmaşık büyüklük denklemleri kullanılmış, böylelikle karmaşık sayılarla çalışmanın sağladığı matematiksel kolaylıktan yararlanılmıştır. Temelde aynı amacı hedefleyen bu yöntemler üzerine yapılan çalışmalar ve uygulamaları son derece dağınıktır. Literatürde, aynı simetrisiz işletmenin veya arızanın herhangi iki yöntemle incelendiği ve sonuçların karşılaştırıldığı bir örneğe rastlanmamaktadır. Bu noktadan hareketle, çalışmada, bu yöntemlerin asenkron makineye uygulanışı ve birbirleri ile olan ilişkileri incelenmiştir, örnek olarak, bilezikli asenkron motörde yolverme direnci simetrisizliği dikkate alınmış, farklı yöntemlerle elde edilen sonuçlar ve doğruluğu tartışılmıştır. Aynı simetrisizlik dikkate alınarak, sürekli hal simetrili bileşenleri ile varılan çözümlerin, ani değer simetrili bileşenleri kullanılarak edinilen sonuçların özel bir hali olduğu gösterilmiştir. _ v _

SUMMARY THE METHODS OF TRANSIENT ANALYSIS İN THE ASYNCHRONOUS MACHINES AND APPLICATIONS This study presents the methods of transient analy¬ sis in the asynchronous machines by the means of symmetri- cal components of instantaneous values and space phasors. First of ali, the mathematical definitions of those met¬ hods are described and than, the voltage eguations are found out by using symmetrical components and space pha¬ sors quantities. Also, those eouations are separated d and q components of the rotor co-ordinate system. Furher- more the relations between those methods, and the rela- tions between steady state symmetrical components with syıranetrical components of instantaneous values (SKIV) are investigated, by applying SKIV to the slip ring induction motor with asymmetrical starting resistances. The operat- ing performance of that motor analyzed by the means of eguivalent circuits of steady state components. The historical development of transient analysis methods can be summarize, as follovs. The first transient analysis method is Park transformation, that was present- ed by R.H.Park in 1929, and has been used in salint pole synchronous machine. Because of using time varying guanti- ties, the analysis of transients by Park transformation is tedious and difficult. Having inspried by Fortescue, Lyon introduced the symmetrical components of instantaneous values for tran¬ sients in electrical machines. The mathematical represen- tation of SKIV is similar to symmetrical components in the phasor form. vo = ? ^u^v+V vu = l ^o+VV vp = l (vu+avv+a2vw) vv = l (vo+a2vp+avn) (1) vn = l (vu+a2uv+auw) vw - £ (vQ+avp+a2vn) _vi _in eguation (1)/ v denotes any operating guantities such a voltage, current and resistance. The steady state syıranetrical components can be analyzed only the stable operating guantities. it' s app- liance för transient phenoraenon is satisfactory. But, by using syıranetrical components of instantaneous values, either steady state ör transient solutions can be find out. Therefore it can be say briefly that, this develop- ment lid to later studies on this subject. And than Kovacs described the space phasor as a complex representation of fundamental space wave (the spa¬ ce means a guantity in the air gap which takes place bet- ween stator and rotor, such a current density, magnetic flux, ete.) and presented voltage eauations of the A.C. machines using space phasors. Kovacs investigated the re- lations between syıranetrical components of instantaneous values with space phasors and their d-q components during a long period of time also. Specially, the practical app- lications of engineering by those methods have been menti- oned in his publications. The other investigator J.Stepina had been contribu- ted the space phas'or method enormously. Stepina has been noted physical meaning of guantities of space phasors and their definations in the perpective of space harmonics. He analysed thad method mathematically, according to the theory of electrical machines. Moreover he proved that, the A.C. machines having unsymmetrical windings can also be analysed by using space phasor method. After those developments, the Japonese investiga¬ tor Yamaraura described Spiral Vector Theory in 1988. But that method was only a different mathematical representa¬ tion of the space phasors. So it was not a new method of transient analyzes. Hovever, that representaiton bring out some easiness to solve differantial voltage eauations. Firstly, the complex guantities in the electrotech- nic are defined in this study. After than, the symmetri- cal components of instantaneous values and the space pha¬ sor methods are given mathematically and their physical meanings and relations are discussed. in the A.C. machines the symmetrical components of instantaneous values and the space phasors of operating guantities described and the machine eguations are obtained by using those guantities. Also eguations in terms of d-g components are found out. Finally, the transient operating eguations of slip- ring induction motor with unbalanced starting resistances are obtained by using of symmetrical components of instan¬ taneous values. The steady state operation eguations are obtained by using transient operating eguations and compa- red with the results of analyses reported in the literatü¬ re, in which the same unsymmetrical operation was - vü -searched by using steady state symmetrical components. Furthermore the steady state operating performance of that motor is analysed in the case of given different ro¬ tor asymmetrisity by means of operation auantities such a stator and rotor voltages, currents and the torgue. The eguivalent circuits of the each symmetrical system are also investigated. Those eguivalent circuits can be combi- ned in the case of some electrical asymmetrisity in the rotor circuits. So, the slip-ring induction motor with ro¬ tor asymmetrisity represented only öne eguivalent circu¬ its and guantities are obtained by analyzing that motor circuit. in the study, the operating auantities of slip- ring induction motor with different rotor asymmetrisity are calculated by using a computer programme in Fortran language. For example the variations of symmetrical sys¬ tem torgues and total torgue of a slip-ring induction mo¬ tor in relation to rotor speed are shovm in Figüre l... Figüre 3 when the U phase of rotor is broken down. The results and conclusions of this study are as follows: 1. Studying of transient phenomena in asynchronous machi- nes by the means of space phasor descriptions instead of time dependent guantities is so convenient for the solving of problem. Solving of two differential volta- ge eguations, which are related stator and rotor, re¬ sults finding of operating guantities on the whole machine phases. /N M kNm 13 -.> 1 ' ~; / / ' 5-Ş i -: -/' l i i/ j ^' / ; İ,;£,,;1^ 0.1 `.2 O..Î D 4 05 0.6 C-7 0.8 0.9 l n/D-, Figüre l. The toroue-speed curve of positive symmetrical system when Ü phase of rotor is broken down. - viii -M ^ kNm 30 - 20 - 10 -/ '. _^^' i i /`^ _ 1.`. -. l ; __ ;>,-- _','.J 5i. 0.3 03 r..4 0.5 0.6 O.1* 0.6 09 l n/H-, Figüre 2. The torgue-speed curve of negative symmetrical system when U phase of rotor is broken down. 2.Every unsymmetrical transient operations can not be analysed by the method of space phasor so conveniently. The space phasor method is useful only in the unsymmet- rical feeding voltages. 3.Instantaneous values of symmetrical components, which describe space waves having definite degrees, are space indicators. Ali unsymmetrical transient phenomena can be analyzed by using the guantitive eauations of ins- tantaneous values. 4.Mathematical relations of these two methods are so simple and clear. Each of them analyses the same tran¬ sient phenomenon with different guantities and with the same result. 5.in this study the slip-ring induction motor with unsym¬ metrical rotor circuit is investigated by the method of symmetrical components of instantaneous values. Re¬ sult s of steady state which is founded out from the eguations of symmetrical components of instantaneous values is similar to that of literatüre which investi¬ gated the same phenomenon by using the method of ste¬ ady state symmetrical components. Finding out from sym¬ metrical components of instantaneous values, the solu- tion, which includes both transient and steady state operating guantities, is valuable in every situation. By the terms of solutions, symmetrical components of steady state is a values. - ±x -M/ s. M kNm 20 - 10-.-'/-. '/ x -10 r'..'' -20 -/ _jn,,i:ı/ O 0.1 0.3 03 0.4 0.5 0.6 0~ 0.8 0.9 l n/n-Figüre 3. The total motor torque-speed curve when U phase of rotor is broken down. 6.in the rotor asymmetrisity, the results, in relation with the auantities in d-q coordinate system, are founded out from d-q coordinate transformation is the same that of symmetrical components of instantaneous values. 7.The toraue of an induction motor having rotor asymmet¬ risity reduces in the half synchronous speed in res- pect to the guantity of asymmetrisity and the value of stator phase vinding. in certain values of unsymmetri- sity, the slip-ring induction motor operates as an asynchronous motor in half synchronous speed. 8.As a similar result 10, the motor current is changes in the half synchronous speed, heavily. - x -