51. IWK Internationales Wissenschaftliches Kolloquium International Scientific Colloquium

Transcription

1 5. IWK Internationales Wissenschaftliches Kolloquium International Scientific Colloquium PROCEEDINGS -5 Setember 006 FACULTY OF ELECTRICAL ENGINEERING AND INFORMATION SCIENCE INFORMATION TECHNOLOGY AND ELECTRICAL ENGINEERING - DEVICES AND SYSTEMS, MATERIALS AND TECHNOLOGIES FOR THE FUTURE Startseite / Inde: htt://

2 Imressum Herausgeber: Redaktion: Der Rektor der Technischen Universität llmenau Univ.-Prof. Dr. rer. nat. habil. Peter Scharff Referat Marketing und Studentische Angelegenheiten Andrea Schneider Redaktionsschluss: 07. Juli 006 Fakultät für Elektrotechnik und Informationstechnik Susanne Jakob Dil.-Ing. Helge Drumm Technische Realisierung (CD-Rom-Ausgabe): Institut für Medientechnik an der TU Ilmenau Dil.-Ing. Christian Weigel Dil.-Ing. Marco Albrecht Dil.-Ing. Helge Drumm Technische Realisierung (Online-Ausgabe): Universitätsbibliothek Ilmenau Postfach Ilmenau Verlag: Verlag ISLE, Betriebsstätte des ISLE e.v. Werner-von-Siemens-Str llrnenau Technische Universität llmenau (Thür.) 006 Diese Publikationen und alle in ihr enthaltenen Beiträge und Abbildungen sind urheberrechtlich geschütt. Mit Ausnahme der gesetlich ugelassenen Fälle ist eine Verwertung ohne Einwilligung der Redaktion strafbar. ISBN (Druckausgabe): ISBN (CD-Rom-Ausgabe): Startseite / Inde: htt://

3 5 st Internationales Wissenschaftliches Kolloquium Technische Universität Ilmenau Setember 5, 006 R. Stancheva, I.Iatcheva Effect of End Winding Transosition on the Electromagnetic Field in a Turbo-generator INTRODUCTION The stator core winding in ower turbo-generators has rather large rated electric current u to several thousands ameres. Of course it is referable the windings to be made of sections comosed of u to thirt conductors connected in arallel. To reduce the circulating currents induced in the conductors and the dissiative losses the conductors should be transosed at different ositions [, ]. For eamle the transosition begins from the to to the bottom of the slot and the conductors change their situations choosing available ositions in the end windings. The difficulties are due not onl to evaluate the circulating currents when are known the real ositions of the conductors [3] in design but eseciall to define the otimal design transositions [4]. This aer considers the first investigation ste. It resents a method for non comensated electromotive voltages and circulating currents evaluation aling FEM for the field analsis. The second ste including otimal transosition design for stator core slots and end windings of ower turbo-generator (TG) will be discuss later. The multi-section scheme of the stator winding is used. The magnetic field-electric circuit couled analsis is made for circulating currents determination. The method takes into account the demagnetied effect due to these currents. The comle electromagnetic ower incoming to the transosed winding is numericall evaluated on the basis of the Pointing vector. As a result the dislacement current and its coefficients, and the conductor number comle imedance are calculated. The general theoretical electromagnetic field model [5] allows making the following valuations:. Transosition influence on electromagnetic field in the end region of TG;. Non-comensated electromotive forces and circulating currents in the resence of transosition. An alication eamle is given, referring to the 00MW generator.

4 A SHORT REVIEW OF ELECTROMAGNETIC FIELD MODEL Aial section of the 00MW turbine-generator end region is shown in Fig.. l l 5 l l 4 l 3 Fig.. Aial section and end winding of 00MW turbine-generator The electromagnetic field is analed as quasi-three-dimensional and time-harmonic taking into account the actual currents of the three-hase stator and rotor windings, anisotro in the tooth one, edd currents in the conductive media and the generator state (load angle and ower factor). The describing equations are: r r r rot( ˆrot ν A) = ˆE σ + J e () r r A E = grad V -. t () Vector A r is the magnetic vector otential, E r is the electric field intensit, V is the scalar electric otential, νˆ and σˆ are tensors due to the magnetic reluctivit and electric conductivit of the anisotroic medium. The secific electric losses in unit volume of the conductors are due to the current densit J &r taking into account Joule s low as follows: - & [ σ ] J.J =. c (3) METHOD DESCRIPTION Multi-section scheme To simulate the magnetic field within and around the slots and end windings accuratel the transosed locations of each conductor are based on the ositions of sustaining sections in the stator core art of the winding and in outstanding arts of it. Between two sustaining sections the change of the ositions is ossible. These sections divide the

5 winding into several longitudinal arts which deend on the chosen model of transosition. In the resent aer referable model of transosition roosed in ersective TG is considered. It is conventionall denoted as scheme 360 / 540 / 360 and is shown in Fig.. In this case so-called bi-flu scheme of transosition is used. lend-left la/4 la/ la/4 lend-right Fig.. Preferable model of transosition- scheme 360 / 540 / 360 Conductors are on 540 degree intertwine in the slots and in the end winding the form two-to and bottom laers where intertwinement is made on 360 degree. Transosition of 540 degree means that each elementar conductor asses two times from one vertical row to the other. At the entr and the eit of the slot it is situated at different vertical rows and graduall changes its osition along the height of the slot similarl the siral. The conductor offset and its end are in different radial laers. In Fig. outgoing from the slot elementar conductors are shown b the bold line-if the are rising and b light line-when the are descending. In end winding transosition the rising elementar conductor at the left end winding is suitable to the descending elementar conductor at the right end winding and vice versa. The transosition is made at onl 80% of the whole end winding length (0% is art from the stator core end to the winding bending and the rest 0% is needed for elementar conductors solder). The change of elementar conductors ositions first hand outside the stator core as well as the influence of the real stator core skewing over the non comensated electromotive forces and circulating currents has been considered. Investigation has been made for 6 elementar conductors connected in double row arallel in the coil. So the number of elementar m conductors in the row is 8 =. Dimension of one conductor along the height of the b slot is than h m. At the issue ( = 0 ) of stator core the distance of the serial h

6 m number, with =,,..,, elementar conductor ais to the bottom of the slot (Fig.3) b is resented b relative coordinate k = ( ) acceting k =. The relative m h variable changes from k = to k = 0.5. Points where elementar conductors are m m bended along the end winding could be marked b: = kl ; = (0.5 k) ; 3 4 = (0.5 k) l and = ( k) l. The descritions made above refer to the geometr and geometrical arameters determining the wa of transosition in the end winding. + l I 4 I i h е 3 I b f c j d I h / kh a I o ϕ I I d I l Fig.3. Elementar conductors bending along the end winding Transosition influence on magnetic field Since end winding cross section is densel occuied b the two rows elementar arallel conductors it follows that to the art d, resectivel d, of one arbitrar elementar conductor a similar (removed arallel to the ais) conductor corresonds. It belongs to the other vertical row. Thus overlaing in region descending () conductors are considered in Fig.4. d one rising () and the relevant

7 I l end / J r h I J r d I α I Fig.4. Overlaing conductors from two vertical rows of end winding Sum between current densit vectors: and J crossing elementar conductors and resectivel gives as a result: J J 0 + J = ( J + J ) = J cos e α 0, (4) h whereα = arc tg because of the two laers winding. In the last eression l l =.8( l + l ) and l =.8( l 4 + l ) denotes the length of the to and the bottom winding laer. Thus the resulting current densit is obtained multiling current densit of the eciting current Je b the correction coefficient MW turbine-generators the following dimensions are valid: cos α. Taking into account that in 00 h = 0.5cm l + l 6cm the multilier iscos α = Diminution of the eciting current is under 4 = 0.8% and because of the linearit of investigated region it follows that at the same rate magnetic flu densit amlitude will decrease. Algorithm for electric field calculation in elementar conductors Investigation has been made of the end winding field suosing that magnetic vector otential A and magnetic flu densit B are known.. Ccle, number of which deends on the te of transosition, begins;. For the two laer winding l is determined; 3. Number of the elementar conductor is changed: = winding). The relative coordinate k is calculated; m,,..., and ( for two laer 4. Different arts (sections) of the transosing end winding are considered. Their geometrical arameters are determined taking into account the number of the

8 laer and the coordinates of the relevant section. Numbers i and j of finite element row and column, resectivel, are secified in the region. 5. Magnetic vector otentials are calculated. Field model [5] is suosed quasi-three dimensional. The three secial comonents of the magnetic field are accounted for. The field values are determined in one aial section of the machine considering the region of the end windings. For eamle under the sinusoidal ecitation the governing equations in Cartesian coordinates in this region are A& µ A& µ A& µ A& + µ A& + µ A& + µ π A& µ τ π A& µ τ π A& µ τ jωσ A& jωσ A& jωσ A& = J& = J& = J& The current densit comonents in (5) deend on the osition of the eciting current densit (Fig.3). The amlitude of the current densit is determined for I m elementar conductor number b the eression J e =, for =,,...,, S e e e.,, (5) where S is cross section of number elementar conductor. These values are the same for the to and the bottom laer of the winding. The electric circuit equations are given b the terms Here b U & and Z I& Z E& = U& for m =,,...,. (6) the outlet voltage of the stator winding and comle imedance of number elementar conductor are resectivel denoted. 6. Comle imedance Z of number elementar conductor is determined taking into account the dislacement current effect.the comle electromagnetic ower outgoing from transosed winding is numericall evaluated on the basis of the Pointing vector. Knowing the field values the conductor number comle imedance is calculated b the eression Z R m jω A A π π [ A + A ctg( ϕ)( A + A )] µ 0 r = e = ( τ τ e ) = & & dd. (7) I On the basis of equation (7) the term for resistance conductor is brought out R of number elementar

9 R m ω A A R = Im[ ]. A& + A& dd I µ 0 r = e = ( ) e (8) 7. Induced electric voltage E & is calculated aling equation E & ψ = t jω = 3 R m r = e = { e = jω A & ( Γ) [( A k.dl = jω + A q + A t [ A d + i, j i j ) + ( A k + A q + A Quantities used in the eression above are smbolied b: t )]}. A i, j d ] = (9) -the area of element e ; A A, A and A, A, A are and -comonents, resectivel k, q t k q t at three nodes k, q and t of element e ; R is number of the end winding sections in the resence of transosition. Equations (9) are solved for the left and the right arts of end windings at once considering the conditions imosed b multi-section scheme. 8. Relacing (7) and (8) in (6) so obtained sstem of field-circuit couled equations is solved with the relevant boundar conditions b using FEM. As a result the currents I & in transosed arallel conductors are calculated. Then using (9) e electromotive forces E & in these conductors are also determined. 9. Provided that transosition is aroimatel effective it is ossible to introduce equalit Z = Z =... = Z =... = Z m = Z. Than equivalent electromotive force E & eq of the whole winding bar is defined as the middle one m E & = E& eq =. (0) m Then the relative value of non comensated electromotive force is determined b the eression e 0.5m E& = m = E& m = E&. () CALCULATION RESULTS Electromagnetic field analsis The three comonents of the comle magnetic vector otential A &, A&, A& and electric

10 scalar otential V& have been calculated. Investigation of the magnetic flu distribution for the three comonents B &, & and B& has been also carried out. B Fig.5. Comonent A & of magnetic vector otential Fig.6. Comonent of magnetic vector otential A & Obviousl transosition effects deend mainl on A & (Fig.5) and A & (Fig.6) comonent of the magnetic vector otential and on the tangential comonent B & (Fig.7) of the magnetic flu densit. Because of this fact secial attention was aid to their

11 distribution in the region of stator end one as was shown in the mentioned figures. Fig.7. Comonent B & of magnetic flu densit Aling algorithm described above non-comensated electromotive forces e are calculated in relative units. The grahics are shown in: Fig.8- change along the height of the bottom bar; Fig.9-e change along the height of the to bar and in Fig.0- e curve along the height of the slot. From the bottom to the to of the slot radial dimension is changed from 0.63 to 0.80m. e

12 relative emf Fig.8. Non-comensated emf e distance, m in relative units along the height of the bottom bar relative emf distance, m Fig.9. Non-comensated emf e in relative units along the height of the to bar relative emf distance, m Fig.0. Non-comensated emf e in relative units along the height of the slot

13 If someone acceted that circulating currents deend onl on ohmic resistance of the conductors then in different scale these curves could resent the circulating current changes. Results show that values of non-comensated emf in the bottom bare are aroimatel two times bigger than in the to bar. The reason is due to the stator core end skewing. Electromotive force changes sign keeing its absolute value in two directions. CONCLUSIONS On the basis of magnetic field-electric circuit couled analsis electromagnetic field is calculated in a longitudinal section of turbogenerator in the resence of conductor s transosition. Electric field in the elementar transosed conductors is evaluated. Calculations are eecuted on the basis of the roosed algorithm. Eamle is referring to 00MW turbine generator. Influence of the eciting currents over roduced magnetic field decreases because of the transosition. Diminution of the eciting current is u to 0.8%. Taking into account the linearit of investigated region it follows that at the same rate amlitude of magnetic flu densit decreases. Non-comensated electromotive forces in transosed elementar conductors are calculated in relative units. Grahics are resented in relative units for electromotive forces and in different scale the are also valid for circulating currents. The results show that because of the stator core end skewing the values of noncomensated emf in the bottom bare are aroimatel two times bigger than in the to bar. Electromotive force changes it sign keeing its absolute value in two directions. References: [] X. Dein, Y.Hiuke,Y.Yinging, B.Baodong and N.Takahashi: Circulating current comutation and transosition design for large current winding of transformer with multi-section strateg and hbrid otimal method, IEEE Trans. on Magnetics, vol. 36, 000, [] Ю.А. Бобков: Исследование эффективности транспозиции проводников в лобовой части стержня статорной обмотки турбогенератора, Техн.электродинамика,, 989. [3] Ю.А. Бобков: Определение некомпенсированной разности э.д.с. в проводниках обмотки статора при большом скосе концевых пакетов сердечника турбогенератора, Электротехника,, 986, с. -3. [4] B.Baodong, X. Dein, C.Jiefan and F.Zhenao: Otimal transosition design of transformer windings b genetic algorithms, IEEE Trans. on Magnetics, vol. 3, 995, [5] R.Stancheva and I.Iatcheva: Numerical determination of oerating chart of large turbine generator, Int. Conf.on Electr. Machines ICEM 00, Belgium, Book of Abstr..39, Full tet on CD. [6] I.Ziari and A.Valedi: Identification of three hase induction motor arameters using average charge resonse of stator currents, Intern. Aegean Conference on Electrical Machines and Power Electronics, Turke, 004, Authors: Assoc. Prof. PhD. Rumena Stancheva, Assoc. Prof. Dr. Ilona Iatcheva Technical Universit of Sofia, 8, Kl. Ohridski Blvd 000 Sofia, Bulgaria Phone: Fa: rds@vmei.acad.bg, iiach@tu-sofia.bg