Trnsformer Internl Fult Modeling in ATP A. Avendño, B. A. Mork, H. K. Høidlen Astrct An importnt spect to investigte wen designing trnsformer protection scemes is te protection ginst internl fults. Altoug te ccurte modeling nd simultion of internl fults cn e n importnt tool for protection engineers, tere is presently no trnsformer model in ATP wit tis cpility. Tis pper investigtes on te development of trnsformer windingfult models sed on two different sources of informtion: 1) test-report dt nd 2) design informtion. Simultion results will e compred to l mesurements nd conclusions regrding teir ccurcy sll e given. Keywords: Internl fults, trnsformer model, lekge rectnce, finite element metod, ATP/EMTP. P I. INTRODUCTION OWER trnsformers re frequently suject to vriety of electromgnetic trnsients during teir operting lifespn. Tese impose stresses in windings nd oter components tt my led to immedite or long-term filure. Internl fults develop s consequence of tese overstresses nd if left undetected, cn result in ig repir nd replcement costs for utility. Trnsformer protection relys re tus required to operte for internl fults nd te ccurte simultion of tese cn ecome n importnt tool for te development of dequte protection scemes. Relevnt work in tis re s focused on uilding internl fult models for EMTP sed on rules of consistency, lekge nd proportionlity pplied to te fulted winding sections [1]. Te metod s te drwck of resorting to empiricl correction fctors tt decrese te ccurcy of te model wenever winding sections of irregulr geometry re encountered or wen smll sections tt do not rec full window eigt must e studied (wic is usully te cse). Tis prolem cn e voided troug te development of trnsformer models sed on te Finite Element Metod [2]. Tis my e te most ccurte pproc for tis purpose ut it requires te knowledge of detiled design informtion tt in most cses is not redily ville. A model uilt from only fctory test-report informtion cn e prcticl lterntive ut its ccurcy is unknown. Tis pper descries some prcticl metods for modeling internl fults ccording to te type of prolem nd mount of informtion ville wit te A. Avendño nd B. A. Mork re wit te Deprtment of Electricl nd Computer Engineering, Micign Tecnologicl University (MTU), Hougton, MI 49931 USA (e-mil of corresponding utor: vedno@mtu.edu). H. K. Høidlen is wit te Deprtment of Electric Power Engineering, Norwegin University of Science nd Tecnology (NTNU), Trondeim, Norwy (e-mil: ns.oidlen@elkrft.ntnu.no). Pper sumitted to te Interntionl Conference on Power Systems Trnsients (IPST2011) in Delft, te Neterlnds June 14-17, 2011 ojective of creting suitle model for ATP in ny cse. Tis pproc works wit lekge prmeters directly troug n dmittnce formultion since under lod conditions te voltge nd current distriution in te windings is determined y te lekge flux. Te excittion crcteristics were dded externlly troug topologiclly-correct dulity-derived core model tt includes zero-sequence inductnce, mking te complete trnsformer model suitle for trnsient simultions in EMTP/ATP. In order to determine if model sed on only test-report dt (wic is te type of informtion usully ville) cn give cceptle results, n internl fult model ws developed for 500-kVA 11430Y/235Y V lyer-lyer concentric winding core-form distriution trnsformer using two different sources of informtion: 1) test-report dt nd 2) design informtion (for comprison). Te min cllenge ere ws to determine te sort-circuit rectnce etween fulted sections using ec source of informtion. Bot modeling pproces sll e descried nd ve een implemented in te Alterntive Trnsients Progrm (ATP). Teir ccurcy ws determined y compring te simulted line nd fult current wveforms for turn-to-ground nd turn-to-turn fult conditions ginst lortory mesurements. Conclusions nd recommendtions re lso given t te end of te pper. II. INTERNAL FAULT MODEL A. Generl Approc Te generl pproc for te development of te proposed models ws to crete new expnded iger-order lekge inductnce model for te trnsformer. Te numer of sections in wic te windings needed to e split into depended on te type of fult to e simulted. For turn-to-ground fults, te fulted coil d to e split into two sections s seen in Fig. 1). For turn-to-turn fults, tree sections were necessry s in Fig. 1). Tis llowed ccess to new terminls tt corresponded to te position in te winding were te fult occurred nd te desired connections could e mde to ground or to noter section of te winding. Isort H1 H10 I I Iline VH1 H1 Isort c H10 I I Ic Iline ) ) Fig. 1. Internl fult winding sections for Pse-1 of te HV-winding. VH1
Besides te simultion of te internl fult current, te model reproduced te originl sort-circuit evior wen te pproprite coils were connected in series. B. Lekge Representtion Once te lekge rectnces were clculted, te lekge prt of te internl-fult model ws represented y winding resistnce mtrix nd n inverse inductnce mtrix. Te mtrices were creted following te procedure descried in [3] for te representtion of single-pse -coil trnsformers troug n dmittnce formultion. Tis gve te well-known representtion of trnsformers for sort-circuit nd power flow studies (1) As recommended for trnsient studies, te resistive nd inductive prts were seprted y uilding from te rective prt of te sort-circuit dt. Te winding resistnces ten formed digonl mtrix, nd (2) Te extension to tree-pse ws mde y including te zero-sequence inductnce externlly in te core model nd y mking te pproprite connections etween te winding terminls. Tis procedure ws implemented in te sme mnner regrdless of turn-to-ground or turn-to-turn model. Te only difference ws te numer of coils tt needed to e represented. III. CALCULATION OF LEAKAGE REACTANCE BETWEEN FAULTED SECTIONS A. From Test-Report Dt Since te typicl informtion ville in test report or trnsformer nmeplte for tis purpose is te stndrd sortcircuit impednce, te lekge rectnce etween sections ws clculted using only tis prmeter. Te per-pse formultion descried next is sed on te splitting of te HVwinding into sections, denominted s windings,,,. Te LV-winding ws kept s is ut it cn e split in similr mnner. Consider te originl trnsformer wit n equivlent sortcircuit impednce (referred to te HV-side in tis cse) etween windings nd. An individul impednce ws ssigned to ec winding ssuming tt te equivlent impednce divides eqully etween ot in per-unit. In oms, tis gve /2 (3) / (4) were is te turns rtio / / (per pse). Since te winding d to e split into sections, ws divided proportionlly ccording to / (5) / (6) / (7) were,,, re te numer of turns of ec new section nd re frction of te totl numer of turns. (8) 1 (9) Clculting te individul impednce of ec section, (10) (11) (12) Te voltge for ec section cn lso e defined: (13) (14) (15) For winding, nd sty te sme. Te equivlent inry rectnce etween ny two sections nd ws clculted wit (16) from te imginry prts of te respective impednces nd using te corresponding turn-rtios. Te rel prts of (10)-(12) gve te resistnce of te new windings. (16) Te inry rectnces were ten converted to per-unit vlues using common VA se nd te corresponding se voltge of te section eing referred to. From ere, te metod of Section II. B. ws implemented to represent te terminl crcteristics of te trnsformer for ec pse. B. From Design Informtion Wen design informtion ws ville, te inry rectnce etween sections could e clculted in different wys depending on te spe nd size of te new windings. 1) Rectngulr Geometry, Full Window Heigt Wen tere is uniform distriution of mpere turns etween ec pir of windings, te lekge flux due to te sort-circuit current is predominntly xil, except t te winding ends, were tere is fringing effect due to sorter return pt for te lekge flux troug te core lims nd yoke. Te lekge rectnce etween sections could ten e clculted using te common formuls for trnsformers wit concentric windings nd flux tues [4]: 2 (17)
1 3 1 3 (18) k1 [1-(k1+k2)]NI k1ni H / (19) 1 1 (20) k2 = + k2ni c d H -(k1+k2)ni x were is te re of te Ampere-Turn Digrm, is te Rogowski fctor ( 1, is te mgnetic permeility of free-spce, is te winding eigt, is te rted numer of turns of te reference side,, nd re te men dimeters nd, nd re te rdil depts of te first, gp, nd second winding, respectively. Fig. 2 sows te lekge field distriution etween sections nd wen te HV-winding ws split in two sections of equl eigt nd uniformly distriuted mpere-turns. Axis of symmetry Core Fig. 3. Resolution of lekge mgnetic field distriution for xilly ssymetricl windings. 3) Irregulr Geometry For cses of irregulr or non-stndrd winding configurtions, te lekge rectnce could not e esily ndled y clssicl nlyticl metods. Te Finite Element Metod (FEM) ws te most suitle tecnique for clculting te flux distriution under tese conditions. Te prolem could e solved troug mgnetosttic study strting wit Mxwell s equtions for stedy-current cses, x LV winding N xh J (21) B0 (22) H D D g D N were H is te mgnetic field intensity, J is te current density t point nd B is te mgnetic flux density. Defining te vector H for isotropic medi, HB/µ (23) R ihv Fig. 2. Lekge mgnetic field distriution etween sections nd. 2) Rectngulr Geometry, Unequl Heigts Wen it ws desired to clculte te rectnce etween sections of unequl mpere-turn per eigt distriution (e. g., wen one of te sections ws too smll to rec full window eigt), te conventionl formuls for concentric windings did not yield ccurte results since te lekge flux ws no longer predominntly xil, ut d now n dditionl cross-flux component in te rdil direction wit mgnitude dependent on te degree of xil symmetry etween te sections. In tis cse, te rectnce clcultion ws resolved into two seprte components: one relted only to te xil flux nd te oter depending on te rdil flux component. For te first, conventionl formuls for concentric windings could e used nd for te second, conventionl formuls for pncke or interleved windings were used. Te totl rectnce ws te sum of te two rectnces [4]-[6]. Referring to Fig. 3, te ssymetricl winding is replced wit windings nd. Winding is of equl mpere-turn per eigt distriution s winding, nd winding s n mpere-turn per eigt distriution suc tt te ddition of mpere-turns long te window eigt of nd gives te sme mpere-turns s winding. T T x were µ is te mgnetic permeility of te mteril, ten xb µj (24) Due to (22), it sould e possile to express B s BxA (25) were A is te mgnetic vector potentil. Mking A0 (26) A is completely defined. Tking te curl of (25), we ve AµJ (27) wic is Poisson s eqution for te vector potentil nd is te generl form of te eqution solved y commercil FEM softwre. Once solution for te vector potentil ws otined, te instntneous energy stored in winding could e clculted y evluting (28) only over te volume of te winding 1 2 (28)
Te totl mgnetic energy ws given y te sum of te energy stored in ec winding. Alterntively, te totl mgnetic energy stored in te stedy field over te volume of te core window could e clculted y 1 2 (29) Te totl mgnetic energy ten defined te totl lekge inductnce referred to ny one specific winding 2 / (30) were is te nominl current of winding. IV. ADDING THE CORE MODEL Te core representtion generted y te Hyrid Trnsformer Model [8] ws implemented in ATPDrw using open-circuit test dt t different excittion levels s n input to n XFMR model for te 500-kVA trnsformer. Te coreloss resistnce, current, nd flux linked vlues were cquired from te.lis file of te XFMR circuit nd were input into resistive, liner, nd nonliner inductive elements s sown in Fig. 4. nd represent te nonliner lims nd yokes respectively, nd represents te zero-sequence pt troug te tnk. L4 n : 1 α β γ P S n : 1 P S Zl Zl Zl Zy Fig. 4. Core ttced to N+1 t winding. Te ttcment of te core to te lekge model ws mde troug idel trnsformers of unity-turns rtio representing te,, terminls of n infinitely-tin +1 t coil t te surfce of te core leg. Te rectnce etween te core nd te primry nd secondry coils ws estimted s in [8], [9]. For te cse of two-winding trnsformer wit concentric windings, 0.5 (31) 2 (32) Since te primry or secondry windings d to e split into su-coils to simulte internl fults, te procedure of Section III. A. ws pplied to te vlues of (31) nd (32) to clculte te rectnce etween sections nd te core winding. Zy n : 1 P S L4 V. INTERNAL-FAULT STUDY Internl-fult lortory tests were mde to encmrk te simultions using te ville tps on te HV-winding. Fig. 5 is scemtic of te HV-coil wic consisted of 81/2 lyers nd ±2x2.5% tps (sded regions). Sections nd for te turn-to-ground fult study re lso sown. Te HV-winding ws energized wit reduced 3-pse voltge for cses were te LV-winding ws ot open- nd sort-circuited. Wit te pproprite connections, turn-to-ground fults were pplied on one pse t time, were te ottom 5% of te coil ws sorted. Turn-to-turn fults were pplied in similr mnner, were te point corresponding to 5% of te coil ws sorted to noter corresponding to 2.5%. 1 1 2 3 4 5 6 7 8 8 1 2 3 2 4 5 6 7 Fig. 5. HV-winding tp nd lyer rrngement, 500-kVA trnsformer. A. Modeling Approc Since te geometry of te fulted sections ws of irregulr spe, 2D-FEM model ws creted using COMSOL for te outer leg of te trnsformer in order to clculte te lekge rectnce etween sections. A model tt uses only test-report dt s n input ws lso creted for comprison. Te influence of te core ws included in te FEM simultions wit core model tt represented te totl core reluctnce seen from te outer leg [10]. Since it ws n xisymmetric model, te yoke eigt vried long te rdil direction to give constnt yoke re. Te core-to-coil rectnces were clculted using (31) nd (32). After ll te rectnces were clculted, te procedure of Section II. B. ws followed to crete lekge description for ATP were te [A] nd [R] mtrices were input troug user-specified lirry component. Te connection etween te fictitious winding nd dulity-derived core model ws mde y referencing te,, nodes of te idel trnsformers of Fig. 4 in [A]. Fig. 6 sows te complete model implemented in ATPDrw wit turn-to-ground fult eing simulted on Pse-A of te HVwinding wile te LV-winding ws sort-circuited. SRC [A][R] LIB CB α β CORE γ Fult Fig. 6. Internl fult model implemented in ATPDrw. 1 HV A B C LV 2 4
VI. RESULTS A. Sort-Circuit Rectnce Tle I sows te mesured nd clculted per-pse rectnce vlues etween sections, (95 nd 5% of te HVcoil, respectively), nd te LV-coil given y te two models. Te results sow tt te pproc were te Finite Element Metod is used long wit (30) yields muc closer results to te mesurements tn y using (16). Te typicl sort-circuit rectnce given in test report or nmeplte is mesured under lnced, stedy-stte conditions. Altoug te vlues clculted using te test-report pproc represent n exct iger-order equivlent circuit of te windings, te ctul lekge flux pt under fult conditions is not eing dequtely represented. TABLE II BENCHMARKING OF LINE AND INTERNAL FAULT CURRENTS (PEAK A) Test IA Mes IA Sim %e IA Isc Mes Isc Sim %e Isc T-G_oc 0.96 0.98 2.08 18.89 19.42 2.8 T-G_sc 14.65 14.74 0.61 19.62 20.93 6.67 T-T_oc 0.51.55 7.84 18.99 19.94 5.0 T-T_sc 6.54 6.67 1.98 20.19 21.19 4.95 Fig. 8 sows te mgnetic flux density in te window re during 5% turn-to-ground internl fult. Fig. 9 sows te mgnetic vector potentil contour during 5-2.5% turn-to-turn fult were lrge rdil component cn e oserved. In ot plots te LV-winding is open-circuited. TABLE I CALCULATED REACTANCE VALUES BETWEEN COIL SECTIONS FROM TEST- REPORT AND DESIGN DATA MODELS (Ω REFERRED TO TEST WINDING). Rectnce Mesured Test-Report %e T-REP FEM %e FEM Model Model X_-L 8.86 9.617 8.54 8.71-1.69 X_- 58.56 98.63 68.42 56.48-3.55 X_-L 0.187 0.2725 45.72 0.1774-5.13 Compring te clculted vlues using te FEM model nd (30) wit previous mesurements, te mximum percent error mgnitude encountered ws of 5.13%. Te differences in vlues cn e due to te fct tt in te FEM model te complete winding cross-section ws considered s solid current-crrying conductor ut in relity tere is insultion etween turns tt decreses te conducting re, wic in turn increses te current density of ec winding, resulting in lrger mgnetic energy tt would yield iger lekge inductnce. Additionl sources of error cn e due to te omission of te winding led tt connects to te HV-using, mnufcturing tolernces, nd smll mesurement errors. B. Simultion of Internl Fults-FEM Model Fig. 7 sows plot of te line nd fult currents of Pse-A wen te ottom 5% of te HV-winding ws sorted to ground. Tere is sligt pse-error of 4.5 due to te difference etween mesured nd modeled impednces ut overll te simultion sows good greement wit te mesurements. Tle II sows more simultion results for 5% turn-to-ground nd 5-2.5% turn-to-turn fults (LV-coils open nd sort-circuited). Current (A) 20 15 10 5 0-5 -10-15 IA mes Isc mes IA sim Isc sim -20 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Time (s) Fig. 7. Internl fult 5%-to-ground, LV open-circuited, 500-kVA trnsformer. Fig. 8. Mgnetic flux density, 5% turn-to-ground fult, LV open-circuited. Fig. 9. Vector potentil, 5-2.5% turn-to-turn fult, LV open-circuited. VII. CONCLUSIONS In tis work, internl fult models uilt from fctory testreport nd design informtion were developed nd teir ccurcy ws compred. It ws determined tt te clcultion of lekge rectnce etween fulted winding sections ws more ccurte wen FEM model ws constructed using design informtion. A mximum error mgnitude of 5.13% ws otined wit tis pproc, giving internl fult simultions wit mximum error mgnitude of 7.84% in te
currents. Tis error considerly grew wen using only te 2- winding sort circuit impednce to crete iger-order lekge model for te trnsformer under study. Tis lst model did not ccurtely represent te internl sort-circuit evior of te trnsformer since te lekge rectnce etween fulted sections (determining te line nd fult currents) depends not only on te numer of sort-circuited turns, ut lso on teir geometry nd position in te winding. Since tis needs to e tken into ccount, design informtion is tus necessry for its ccurte clcultion. VIII. FUTURE WORK An investigtion of internl fults on dditionl trnsformers of different size nd configurtion sll e mde in order to etter evlute te test-report dt model. Since design informtion defining winding dimensions is lredy source of informtion for te Hyrid Trnsformer Model in ATPDrw, te metods descried in Sections III. B. 1) nd III. B. 2) could e implemented in te XFMR to simulte internl fults wen te resulting sections re of rectngulr geometry. For irregulr winding geometries, 3-D FEM model cn e investigted in order to improve ccurcy. An nlyticl formultion could lso e implemented s n lterntive to FEM model ut wit some simplifictions in order to fcilitte te nlysis of te prolem [12]-[14]. Some of tese re te ssumption of infinite permeility of te core, negligile effects of ducts nd insultion in windings, nd tt te sum of mpere-turns etween windings is lwys zero. A comprison wit FEM clcultions could e mde to investigte its ccurcy. [11] H. W. Dommel, Electromgnetic Trnsients Progrm Reference Mnul (EMTP Teory Book), Portlnd, OR, Prepred for BPA, Aug. 1986. [12] E. Billig, Te clcultion of te mgnetic field of rectngulr conductors in closed slot, nd its ppliction to te rectnce of trnsformer windings, Proc. IEE-Prt IV: Institution Monogrps, vol. 98, no. 1, pp. 55-64, 1951. [13] A. Boyjin, Lekge rectnce of irregulr distriutions of trnsformer windings y te metod of doule Fourier series, AIEE Trns. Power App. Syst., vol. 73, Pt. III, pp. 1078-1086, Oct., 1954. [14] L. Rins, Trnsformer rectnce clcultions wit digitl computers, AIEE Trns. Power App. Syst., vol. 75, pt. 1, pp. 261-267, 1956. X. BIOGRAPHIES Alejndro Avendño ws orn in Tijun, México, on Jnury 19, 1982. He received te B.S. degree in Electromecnicl Engineering from Instituto Tecnológico de Tjun in 2004. In 2005 e ws wrded wit scolrsip from te Ntionl Reserc Council of Mexico (CONACYT) nd joined te Deprtment of Electric & Computer Engineering t Micign Tecnologicl University. He is now P.D. cndidte t MTU. Bruce A. Mork (M'82) ws orn in Bismrck, ND, on June 4, 1957. He received te BSME, MSEE, nd P.D. (Electricl Engineering) from Nort Dkot Stte University in 1979, 1981 nd 1992 respectively. From 1982 troug 1986 e worked s design engineer for Burns nd McDonnell Engineering in Knss City, MO, in te res of susttion design, protective relying, nd communictions. He s spent 3 yers in Norwy: 1989-90 s reserc engineer for te Norwegin Stte Power Bord in Oslo; 1990-91 s visiting resercer t te Norwegin Institute of Tecnology in Trondeim; 2001-02 s visiting Senior Scientist t SINTEF Energy Reserc, Trondeim. He joined te fculty of Micign Tecnologicl University in 1992, were e is now Professor of Electricl Engineering, nd Director of te Power & Energy Reserc Center. Hns K. Høidlen ws orn in Norwy in 1967. He received is MSc nd PD from te Norwegin University of Science nd Tecnology in 1990 nd 1998 respectively. He is now professor t te sme institution wit specil interest of electricl stress clcultions nd modeling. IX. REFERENCES [1] P. Bstrd, P. Bertrnd, M. Meunier, A trnsformer model for winding fult studies, IEEE Trns. Power Del., vol. 9, no. 2, pp. 690-699, Apr. 1994. [2] H. Wng, K. L. Butler, Finite element nlysis of internl winding fults in distriution trnsformers, IEEE Trns. Power Del., vol. 16, no. 3, Jul. 2001. [3] V. Brndwjn, H. W. Dommel, I. I. Dommel, Mtrix representtion of tree-pse N-winding trnsformers for stedy-stte nd trnsient studies, IEEE Trns. Power App. Syst., vol. PAS-101, no. 6, pp. 1369-1375, Jun. 1982. [4] S.V. Kulkrni, S.A. Kprde, Trnsformer Engineering Design nd Prctice, New York, NY: Mrcel Dekker, Inc., 2004. [5] H. O. Stepens, Trnsformer rectnce nd losses wit nonuniform windings, Electricl Engineering, vol. 53, pp. 346-49, Fe. 1934. [6] A. K. Swney, A Course in Electricl Mcine Design, Deli, Indi: Dnpt Ri & Sons, 1994. [7] S. Jmli, M. Ardeili, K. Aszde, Clcultion of sort circuit rectnce nd electromgnetic forces in tree pse trnsformer y finite element metod, Proc. 8t Int. Conf. on Electricl Mcines nd Systems, vol. 3, pp. 1725-1730, Sept. 2005. [8] B.A. Mork, F. Gonzlez, D. Iscenko, D. L. Stuem, J. Mitr, Hyrid trnsformer model for trnsient simultion-prt I: Development nd prmeters, IEEE Trns. Power Del., vol. 22, pp. 248-255, Jn. 2007. [9] B.A. Mork, F. Gonzlez, nd D. Iscenko, Lekge inductnce model for utotrnsformer trnsient simultion, presented t te Interntionl Conference on Power System Trnsients, Montrel, Cnd, 2005. [Online]. Aville: ttp://www.ipst.org/ipst05ppers.tm. [10] E. Bjerkn, Hig frequency modeling of power trnsformers - Stresses nd dignostics, Doctorl Tesis, Norwegin University of Science nd Tecnology, Trondeim, Norwy, 2005.