Intrnational Journal of Elctronics Enginring Rsarch. ISSN 0975-6450 Volum 9, Numbr 6 (2017) pp. 867-882 Rsarch India Publications http://www.ripublication.com Study of Distribution of Transint Voltags in th Winding of a Transformr Subjctd to VFTO and Lightning Surgs R.V. Srinivasa Murthy [1] Rsarch Scholar, Jain Univrsity, Bangalor, India. Pradipkumar Dixit [2] M.S. Ramaiah Institut of Tchnology, Bangalor, India. Abstract Dsign, up gradation and opration of powr ntwork rquirs rviw of various traits. Considr th xampl of transints in powr transformrs. Du to lightning and switching transints th voltag distribution along th winding bcoms non-linar. Th othr ffct is causing winding rsonanc, whn th frquncy of oscillation of th transint matchs th natural frquncy of th winding. This rsonanc ffct may caus partial ovrvoltag. Th study of surg voltag distribution in th winding of th transformr will hlp to idntify such strssd rgions. In th prsnt papr a simulation study of such transint voltag distribution du to lightning and VFTO surgs is prsntd. Th study is carrid out for th transformr mploying continuous disc, intrlavd and shildd winding. Kywords: Disc winding, intrlavd winding, shildd winding, Modling, Surg prformanc, Transformr. I. INTRODUCTION Powr transformrs play a vry important rol in powr systm. Powr Transformrs in th Transmission and Distribution ntwork or in industris ar affctd by lightning and switching surgs. Ths surg voltags whthr thy b systm gnratd or thos that occur du to natural phnomnon hav dtrimntal ffcts on transformr windings unlss protctiv masurs ar put in plac [1]. Switching oprations or
868 R.V. Srinivasa Murthy and Pradipkumar Dixit short circuit faults can caus VFTO s whos frquncy may rang from 10 s of KHz to 10 s of MHz and hav a lif span of dozns of microsconds. Th VFTO can b transmittd to transformr winding by th componnts of Gas Insulatd Sub-Stations (GIS). VFTO s can caus non-uniform voltag distribution in th transformr winding and also can caus voltag rsonanc du to th matching of transint frquncy with th natural frquncy of th winding. Du to ths two ffcts parts of th winding ar subjctd to mor strss causing insulation failur. Lightning surgs disturbs th rliability of distribution systms bcaus of damag of quipmnts and snsitiv loads [2]. Th fact that masurmnt of VFTO at such high frquncis is quit difficult and dmand skills and utmost car, maks computr simulation of switching opration attractiv. Simulation nabls to stimat th VFTO magnituds, thir ris tim, ffct on various componnts tc., with as and rasonabl accuracy vn bfor th actual commission of th GIS. An accurat simulation of th transint voltag distribution in HV winding of a larg powr transformr allows th dsignr to apply sufficint insulation in th aras of high strss, and at th sam tim rduc th xcssiv insulation of th wirs and lins in ordr to mak th transformr mor comptitiv. A practical importanc of rliabl simulations of th winding charactristics has bn long rcognizd by manufacturrs of larg and xpnsiv transformrs. Thy hav found that th savings on an optimizd insulation rprsnt a significant amount of mony. Ths savings projct on th ovrall cost of a transformr, and oftn dcid on th choic of supplir.[3] A bttr transint voltag analysis can b carrid out using digital computrs aftr propr modling of th transformr winding. With this analysis th dsign nginrs can com up with rliabl and possibly conomic insulation structur which is th main caus dciding factor of a transformr. II. PROBLEM DEFINITION It is th objctiv of th prsnt papr to invstigat th distribution of ovr voltags particularly switching surgs such as Lightning and VFTO in powr transformrs. Th dtaild study includs dsign, modling of an lctromagntic analogu modl of HV winding limb of a 11kV/415V 1MVA DYn 50Hz powr transformr. Transint analysis is carrid out for transformr mploying continuous disc, intrlavd and intr-shild windings for th cass of without skin ffct, with skin ffct and with both skin and mutual ffct. Th assumption is that th rspons of a wll constructd modl is fairly in good agrmnt with that of th actual transformr. For th purpos of analysis th HV winding of th transformr and th diffrnt gnrators ar modld using P-Spic/ORCAD.
Study of Distribution of Transint Voltags in th Winding of a Transformr 869 III. P-SPICE MODEL FOR TRANSIENT ANALYSIS An arly attmpt to analyz th voltag distribution along th transformr winding was mad by Wagnr. In this modl h usd standing wav thory on uniform windings whn subjctd to a unit stp voltag. A mor complicatd modl of a hlical winding was analyzd using travlling wavs by Rudnbrg.R[3]. This mthod was mor accurat as rflction at th far nd was takn into account. A laddr ntwork to rprsnt th transformr winding with ach sctions consisting of sris inductanc plus an intrsction capacitanc togthr with a shunt capacitanc to ground was introducd by Lwis [4]. In addition mutual inductancs btwn sts of windings wr introducd. Th laddr ntwork modl is usd in th prsnt papr for modling th HV winding of th powr transformr. A) Transformr Paramtrs: A 11kV/415v, 1MVA, DYn transformr modl is considrd for th study purpos. Th dtails of th transformr ar as follows. Outr diamtr of ach 11kV winding=0.417m Innr diamtr of ach 11kV winding=0.388m Axial lngth of ach 11kV winding=0.589m Numbr of discs in ach 11kV winding=66 Axial lngth of ach 11kV disc= 8.22m Avrag numbr of turns/ 11 kv disc= 12 Outr diamtr of ach 415V winding=0.358m Axial lngth of bar conductor for ach 11 kv disc= 0.077m Gap btwn two adjacnt discs of ach 11kV winding= 0.001m Innr diamtr of 6 th turn=0.414m Rsistanc of HV winding=1.07ω Ractanc of HV winding=364.14 Ω B) Winding dtails usd in th prsnt study For th purpos of simulation continuous disc winding, intrlavd winding and shildd winding ar considrd. a) Continuous disc winding : Highr rating transformrs primarily mploys disc winding. Th coils of th winding ar wound in th usual mannr starting from th cylindr and outward. Thn th coils ar transposd in th rvrs ordr. Slackning is don to mak th rvrsing asir and th conductor running from th drum is again tnsiond. Th procss hlps
870 R.V. Srinivasa Murthy and Pradipkumar Dixit continuous intr connction of coils without any soldrd joints. A typical continuous disc winding is shown in Fig. 1. Fig. 1. Continuous Disc Winding b) Intrlavd Winding : Continuous disc winding has th disadvantag of having low sris capacitanc. To ovrcom this disadvantag lctrostatic shilding was mployd till th invntion of intrlavd winding. Th first modl of th intrlavd winding was givn by G.F.Starn in 1950 and patntd it. Dispositioning of turns in a simpl way incrasd th sris capacitanc which in turn rsultd in nar uniform voltag distribution. A typical intrlavd winding is shown in Fig 2. [5] Fig 2. Intrlavd Winding c) Shildd winding: Placing a static ring btwn a pair of discs givs ris to lctrostatic shilding as shown in Fig. 3. Ths rings provid a larg qui-potntial surfac with a good cornr radius. This lads to rduction in voltag strss at th lin nd. Th arrangmnt also improvs sris capacitanc which in turn lads to uniform voltag distribution.
Study of Distribution of Transint Voltags in th Winding of a Transformr 871 Fig 3. Shildd Winding d) Paramtr Calculations for Disc, Intrlavd & shildd windings: Winding paramtrs and thir calculation for th transformr considrd ar discussd blow. i) Slf-inductanc Li of th disc coil Th slf inductanc of th 11kV disc coil is calculatd from th following quation [6] ii) Capacitanc to arth (Cg) Lo=4п 10 7 RN 2 1 {ln ( SR R ) 2} H (1) 1 A dlta connctd transformr winding with its sid limb winding impuls, will hav two componnts of Cg. Capacitanc btwn impulsd HV winding and arthd LV winding (C1) which can b calculatd using co-axial cylindr formula. c 1 = 2πє ln b a F/m (2) Capacitanc btwn impuls sid limb HV winding and transformr tank (C2), which can b calculatd by considring th tank as a co-axially halvd cylindr Th total ground capacitanc for disc is, c 2 = πє ln b a F (3) Cg=C1+C2. F (4) iii) Sris capacitanc for disc winding(csi) Sris capacitanc of a disc coil has two componnts Intr-turn capacitanc(ct)
872 R.V. Srinivasa Murthy and Pradipkumar Dixit This capacitanc is calculatd using th xprssion for th capacitanc btwn two axial cylindrical lctrods Intr-disc capacitanc(cd) Ct= 2пє ln b a F (5) For calculating Cd th adjacnt discs ar considrd as two paralll plat lctrods. Cd= єa d F (6) Th total sris capacitanc of a disc Whr, N1= No of turns pr disc. Cs = (Ct/N1)+(4/3 Cd) F (7) iv) Calculation of sris capacitanc for Intrlavd winding Du to simpl disposition of turns in som particular ways, adjacnt turns ar placd far away rsulting in incras in voltag btwn adjacnt turns. In th cas of intrlavd winding intr-disc capacitanc which has a rlativly low valu hardly affcts th sris capacitanc of th winding. Hnc only th intr-turn capacitanc is considrd for th calculation of sris capacitanc. C s = C T 4 [N D + (N D 1) 2 N D 2 (N D 2)] F (8) v) Sris capacitanc calculation for Shildd winding To calculat th sris capacitanc of th shildd winding w considr intr-turn capacitanc (CT) and capacitanc btwn shild and disc (Csu). Whr C s = CT=Intr-turn capacitanc ND=Numbr of turns /Disc R=Winding radial dpth C T (N 2N 2 D 1) + C sur + 7 C sur D 12 12 Csu= capacitanc btwn shild and first disc. F (9)
Study of Distribution of Transint Voltags in th Winding of a Transformr 873 Calculation of Csu This capacitanc is calculatd by trating both as cylindrical lctrods, Csu= 2пє 0є r ln b a F (10) Th calculatd valus of Slf inductanc of disc coil (Li), Capacitanc to arth (Cg) & Sris capacitanc ar shown in Tabl1. Tabl 1: Paramtrs of HV winding Paramtrs Continus Disc winding Intrlavd winding Shildd winding Slf inductanc of disc coil 0.196mH/Disc 0.196mH/Disc 0.196mH/Disc Capacitanc to arth 14.08 pf /Disc 14.08 pf /Disc 14.08 pf /Disc Sris capacitanc 1679.7pF/Disc 4177.36pF/Disc 6.474nF/Disc vi) Calculation of Mutual Inductanc Mutual inductanc btwn th turns is calculatd using Maxwll s xprssion which calculats th mutual inductanc btwn two co-axial circls. Th xprssion obtaind is a convrgnt sris. [6] L0=4πa[log 8a d 3d2 (1 + 16a2)] Nglcting highr ordr trms (11) a=radius of th coil d=distanc btwn th coils L0=4π 23.54[log ( 8 23.54 3 0.2882 ){1 + 1.288 16 23.542}] H (12) L12=n 2 M 0 = 19 2 832.86 = 0.3mH (13) Similarly mutual inductanc valus for othr sctions ar calculatd.
874 R.V. Srinivasa Murthy and Pradipkumar Dixit vii) Skin ffct calculations Th rsistanc of th winding taking skin ffct into considration is calculatd for both lightning and VFTO inputs which is shown in Tabl 2. Tabl 2: Rsistanc valus Typ of surg voltag Lightning impuls VFTO Rsistanc valus with skin ffct 0.0325Ω/Sction 0.0487Ω/Sction Th compltd modl of on limb of HV winding for PSPICE simulation is shown in Fig 4. Fig.4. Simulatd modl of HV winding. viii) Modling of lightning impuls gnrator Th modl diagram of lightning impuls gnrator with th calculatd valus of paramtrs is as shown in Fig 5. Fig.5. Lightning impuls gnrator
Study of Distribution of Transint Voltags in th Winding of a Transformr 875 Th simulatd wavform of th output of th gnrator is shown in Fig 6. Fig.6. Output voltag of th Lightning gnrator From th output wavform it is found that th valu of front tim of 1µs and fall tim of 50µs which is in agrmnt with th standard spcification 1.2/50µs±30%/±20%. ix) Modling of VFTO gnrator Th modl diagram of VFTO gnrator with th calculatd valus of th paramtrs is shown in Fig 7 and th simulatd wavform of th output of th VFTO gnrator is shown in Fig 8. Fig.7. VFTO Gnrator
876 R.V. Srinivasa Murthy and Pradipkumar Dixit Fig.8. Output voltag of th VFTO gnrator From th output wavform th masurd tim priod is 1.67µs and hnc th frquncy is 598kHz which is in agrmnt with [7]. IV. RESULTS AND DISCUSSIONS Th simulation study is carrid out on 1MVA transformr mploying continuous disc, intrlavd and shildd windings. Th surgs considrd ar lightning impuls and VFTO. Th surg analysis is don without taking skin ffct & coupling ffct, taking skin ffct only and taking both skin ffct and coupling ffcts. v o l t a g i n p u 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Without Skin & Mutual Effct With Skin Effct With Skin & Mutual 0-0.1 0 20 40 60 80 100 120 %Lgth of winding Fig 9. Voltag distribution along th winding subjctd to Lightning Impuls with Continuous Disc Winding
Study of Distribution of Transint Voltags in th Winding of a Transformr 877 Fig 9. Shows th graphs of pak voltag distribution along th ntir lngth of th winding obtaind for a 1MVA oil immrsd transformr mploying continuous disc winding subjctd to lightning impuls. Th voltag distribution is plottd for th cass of not considring skin and mutual ffct, considring only skin ffct and considring both skin and mutual ffct. For th first two cass th voltag distribution is almost similar whras for th last cas it is littl abov th two curvs. For xampl at 50% of th winding th pak voltag distribution for th first two cass is 0.517pu whras for th last cas it is 0.533pu. 0.9 v o l t a g i n p u 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 20 40 60 80 100 % Lngth of winding Without Skin & Mutual With Skin Effct With Skin & Mutual Fig 10. Voltag distribution along th winding subjctd to Lightning Impuls with Intrlavd Winding Fig 10 shows th graphs of pak voltag masurd ovr th ntir lngth of th winding obtaind for a 1MVA oil immrsd transformr mploying intrlavd winding subjctd to lightning impuls.th simulation study is carrid for th cass of without taking both skin and mutual ffct, taking only skin ffct and taking both skin and mutual ffct. From th graphs it is obsrvd that th distribution curvs for th cass of without skin and mutual and with only skin ar almost similar. Whras for th cas of both skin and mutual it is abov th two curvs. Hnc pak voltag distribution is high at ach lngth for th last cas compard to th first two cass.
878 R.V. Srinivasa Murthy and Pradipkumar Dixit v o l t a g 0.9 0.8 0.7 0.6 0.5 0.4 Without Skin & Mutual With Skin Effct i n p u 0.3 0.2 0.1 0 0 50 100 With Skin & Mutual % Lngth of winding Fig 11. Voltag distribution along th winding subjctd to Lightning Impuls with Shildd Winding Fig 11 shows th graphs of pak voltag masurd ovr th ntir lngth of th winding obtaind for a 1MVA oil immrsd transformr mploying Shildd winding subjctd to lightning impuls. Th simulation study is carrid for th cass of without taking both skin and mutual ffct, taking only skin ffct and taking both skin and mutual ffct. From th rspons curvs it is obsrvd that th curvs ar similar for without skin and mutual and with skin and mutual and for with only skin ffct is diffrnt. For th first two cass th dcay is almost at th sam rat. Whras for th last cas thr is a suddn ris at 50% of th lngth of th winding. 1.4 v o l t a g 1.2 1 0.8 0.6 Without Skin & Mutual With Skin Effct i n 0.4 p u 0.2 With Skin & Mutual 0 0 50 100 150 %Lgth of winding Fig 12. Voltag distribution along th winding subjctd to VFTO with Continuous Winding
Study of Distribution of Transint Voltags in th Winding of a Transformr 879 Fig 12 shows th graphs of pak voltag masurd ovr th ntir lngth of th winding obtaind for a 1MVA oil immrsd transformr mploying continuous disc winding and subjctd to VFTO. Th rspons curvs ar obtaind for th cass of without skin and mutual, with skin ffct and with both skin and both skin and mutual. Th rspons curvs shows that in all th thr cass thr is a ovrshoot of 1.28 p.u at th initial stag and thn dcras of pak distribution up to 30% of th winding, from 30% to 70 % of th winding th voltag distribution is approximatly uniform. Mor uniformity is sn in th cas of with both skin and mutual than th othr two cass. v o l t a g i n p u 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 50 100 150 % Lngth of winding Without Skin & Mutual With Skin Effct With Skin & Mutual Fig 13. Voltag distribution along th winding subjctd to VFTO with Intrlavd Winding Fig 13 shows th graph of pak voltag masurd ovr th ntir lngth of th winding obtaind for a 1MVA oil immrsd transformr mploying intrlavd winding and subjctd to VFTO. Th simulation study is carrid out for th cass of without taking skin and mutual ffcts, taking only skin ffct and taking both skin and mutual ffcts. From th distribution curvs it is obsrvd that thr is a ovrshoot of 1.28 pu for all th thr cass and thn th pak voltags start dcrasing. Th rspons curvs for all th thr cass ar coinciding up to about 45% and thn thy ar diffring. Th rspons curvs for th cas of with skin and mutual lis blow that of th othr two cass. In othr words th pak voltags aftr 40% of lngth is lss along th lngth of th winding for th cas of considring both skin and mutual than th othr two cass.
880 R.V. Srinivasa Murthy and Pradipkumar Dixit v o l t a g i n p u 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 50 100 150 % Lngth of winding Without Skin & Mutual With Skin Effct With Skin & Mutual Fig 14. Voltag distribution along th winding subjctd to VFTO with Shildd Winding Fig 14 shows th graph of pak voltag masurd ovr th ntir lngth of th winding obtaind for a 1MVA oil immrsd transformr mploying shildd winding and subjctd to VFTO. Th pak voltag distribution is plottd for th cass of without skin and mutual, with only skin ffct and with both skin and mutual ffct. From th graphs it is obsrvd that thr is a ovrshoot of pak voltag in all th thr cass at th initial lngth and it starts dcrasing. It is also obsrvd that th rsponss in th cass of without skin and mutual and with skin ar almost coinciding. Whras that of with skin ffct and coupling is lying just blow ths two cass. This indicats that th pak voltag distribution is littl mor uniform for th cas of with skin ffct and coupling than th othr two cass. 25 % d i f f r n c i n v o l t a g s 20 15 10 5 Publishd [8] 1MVA SHIELDED WINDING 0 0 50 100 % lngth of windings Fig 15. Comparison charts of publishd data and shildd winding
Study of Distribution of Transint Voltags in th Winding of a Transformr 881 Fig 15. Shows th charts comparing th charactristic curvs of 1MVA transformr mploying intrshild winding and th publishd data [8]. From th graph it is clar that % diffrnc of voltag is lss for th shildd winding compard to th publishd which mploys shild btwn turns. V. CONCLUSIONS In th prsnt papr PSPICE/ORCAD simulation studis on voltag distribution with standard lightning impuls and VFTO hav bn mad on impuls modl of a 1MVA 11/0.415 kv, 3-phas, 50 Hz, Dyn11 transformr with diffrnt winding configurations. Tim domain analysis of voltag distribution as a function of %lngth of th winding shows that Initial 20% of th winding is ovrstrssd. Significant damping of pak voltag has bn obsrvd with skin and mutual ffct. Voltag distribution is almost uniform aftr 40% of winding lngth whn subjctd to VFTO. With lightning impuls, shildd winding has lss voltag strss and with VFTO th pak voltag distribution is mor uniform whn compard to disc and intrlavd winding. %diffrnc in voltag in th cas of shild placd btwn th discs is lss compard to th shild placd btwn th turns of th winding. Th modl usd in th prsnt study is gnral and applicabl for th analysis of voltag distributions in th transformr windings during lightning and VFTO surgs. ACKNOWLEDGEMENT Th authors wish to acknowldg th support givn by th managmnt of East Wst Institut of Tchnology, M.S Ramaiah Institut of Tchnology and Jain Univrsity. REFERENCES [1] H.Rodrigo and H.Q.S.Dang Surg voltag Bhavior of Transformr winding IEEE confrnc, Pag no. 22-27, August 1999, Confrnc publication No.467. [2] Pantis N Mikropouls; Thomas.E.Tsovisis Sotiria; G.Kontoula Prformanc of Distribution Transformr Fding GSM Substations subjctd to Lightning impuls, IEEE Transactions on Powr dlivry, Vol: 29, Issu: 06, Pags 2570-2579, 2014.
882 R.V. Srinivasa Murthy and Pradipkumar Dixit [3] Rudnbrg.R Travrsing wav Prformanc of Coils and windings IEEE Transactions on Powr apparatus and systms, Vol.59, 1940, PP1031-1040. [4] Lwis T.J Laddr Ntworks rprsntation of transint bhavior of Transformrs and Machin windings, Procdings of IEEE, Vol: 10 Part 1 & 2, Pags 541-543, 1954. [5] S.V.Kulakarni &S.A.Khapard, Transformr Enginring Marcl Dkkr Inc., Ntwork, 2005. [6] F.W. Grovr, Tabls and Working Formula for Inductanc Calculations, Dovr Publications, Nw York. [7] Mark Florkowisky; Jakus Furgal and Piotr Pajak, Analysis of fast transint voltag distribution in Transformr windings undr diffrnt insulation conditions, IEEE transactions on Dilctrics&lctric insulation, vol19, No:6, pags 1991-1998,Dcbr 2012. [8] Mhdi Baghri; B.T.phung; Mohammd Salay Nadri Impuls voltag distribution and frquncy rspons of intrshild windings IEEE Elctrical Insulation Magazin, volum:32, issu:05, pags: 32-40, 2016