2. Design of Three Phase Transformer

Transcription

1 . Desgn of Three Phase Transformer.1. Desgn dfferene beeen dsrbuon ransformer and poer ransformer (a) (b) Dsrbuon ransformer Sandard rangs 1, 16, 5, 6, 1, 16,, 5, 15, 4, 5, 6, 1, 15, 16,, 5 kva for 11 kv dsrbuon sysem and 1, 16,, 15, 4, 5, 6, 1, 15, 16,, 5 kva for kv sysem. Used n eler poer dsrbuon sysem. Operaes a lgh loads durng major pars of he day. Very hgh load fluuaon. Desgned for maxmum effeny a 6-7% of full load. More energy s los n ron loss ompared o opper loss hroughou he day so desgned for mnmum ron loss. Desgned for small value of leakage reaane for volage regulaon purpose. Desgned o operae for flux densy belo o he sauraon pon of he B-H urve. Usually prmary ndng s desgned for dela onneons and seondary ndng s desgned for sar onneon. Generally ol naural rulaon oolng mehod s used o manan he emperaure of he ransformer. Smaller n sze. Poer ransformer Sandard rangs above 5 kva and up o 1 MVA for above kv and up o 15 kv. Used a poer generang poer saons and ransmsson subsaon. Operaes a nearly full load durng major pars of he day. Load fluuaons s very less. Desgned for maxmum effeny a full load. More energy s los n opper loss ompared o ron loss hroughou he day so desgned for mnmum opper loss. Desgned for omparavely large value of leakage reaane for shor ru urren lmng purpose. Desgned o operae for flux densy near o he sauraon pon of he B-H urve. Usually prmary ndng s desgned for sar onneons and seondary ndng s desgned for dela onneon. Fored rulaon of ol s used o manan he emperaure of he ransformer. Larger n sze. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 1

2 . Desgn of Three Phase Transformer.. Desgn dfferene beeen ore ype ransformer and shell ype ransformer (a) Core ype ransformer Lmb Lmb Lmb Yoke (b) Lmbs are surrounded by he ndngs. No separae flux reurn pah s essenal. All lmb arres equal flux. Fgure. 1 Three phase ore ype ransformer Lamnaed ore s bul o form reangular frame. Wndng has poor mehanal srengh beause hey are no suppored or braed. Beyond one level s no possble o redue leakage beause hgh volage and lo volage ndng anno be subdvded o grea exen. Lmbs are surrounded by he ndngs so oolng s baer n ndng han lmb. Perms easer assemble of pars and nsulaon of ndng. Easy o dsmanle for manenane or repar. Muh smpler n desgn. Shell ype ransformer Lmb Lmb Lmb Yoke Fgure. Three phase shell ype ransformer Wndngs are surrounded by he lmbs. Separae flux reurn pahs s essenal. Cenral lmb arres hole flux and sde lmb arres half of he oal flux. Lamnaed ore s bul o form reangular frame. Wndng has exessve mehanal srengh beause hey are suppored or braed. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691)

3 . Desgn of Three Phase Transformer I s possble o redue leakage beause hgh volage and lo volage ndng an be subdvded by usng sandh ol. Wndngs are surrounded by he lmbs so oolng s baer n ore han ndng. Grea dffuly o assemble pars and nsulaon of ndng. Dfful o dsmanle for manenane or repar. More omplex n desgn... Oupu equaon of -phase ransformer Oupu equaon of ransformer s he mahemaal expresson relang kva rang h man dmenson. In -phase ransformer one ndo onans half of hgh volage () ndng and half of lo volage () ndng of o onseuve phase. To suh ndos forms enre assembly. Le, Q f = Oupu of ransfomer (kva) = Supply frequeny (Hz) = Maxmum flux (Wb) m = Maxmum flux densy (Wb/m ) m B = Curren densy (A/mm ) = Ressvy of onduor maeral (Ω-m) A = Ne ross seon area of ore (m ) = Gross ross seon area of ore (m ) g = Toal opper area n ndo (m ) = Toal area of ndo (m ) A A A K = Wndo spae faor T T I I a a V V = Number of hgh volage ndng urns = Number of lo volage ndng urns = Phase urren n hgh volage ndng (A) = Phase urren n lo volage ndng (A) = Cross seon area of hgh volage ndng onduor (mm ) = Cross seon area of lo volage ndng onduor (mm ) E E E = Phase volage of hgh volage ndng (V) = Phase volage of lo volage ndng (V) = Phase ndued emf n hgh volage ndng (V) = Phase ndued emf n lo volage ndng (V) = Volage per urn (V) Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691)

4 . Desgn of Three Phase Transformer A T a T a I I T T T I T I mmf of ndng mmf of ndng 4 A AT AT AT Also, ndo spae faor an be defned as K K K Toal opper area n ndo Toal area of ndo A A 4 AT A K A AT 4 Rang of -phase ransformer n kva Q V I 1 E I f T I 1 f m I T f B A m K A m K A K A 4.44 f 1 AT m Q.fB A K A 1 m Ths oupu equaon s applable o boh ore ype and shell ype ransformer. I helps o opmze desgn for mnmum loss, os, egh and sze. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 4

5 . Desgn of Three Phase Transformer.4. Derve equaon E =K Q. Also explan faors affeng he value of K Consderng oupu kva rang of one phase only. Q V I 1 m E I 1 f m I T f m AT 4.44 f T I m m 4.44 f 1 r,here r s onsan m r AT f m r r f Volage per urn, E E T m Q 4.44 f T m T r f 4.44 f E K Q f r Q Q Where, K 4.44 f r 1 Value of volage per urn depends on seleon of faor K, onsequenally hs faor basally depends on rao of ore ross seon area o opper area n ndo. Shell ype ransformer needs more ron maeral han opper maeral ompared o ore ype ransformer.e. value of K ll be hgher for shell ype ransformer. 1-phase ore ype ransformer needs more ron maeral han opper maeral ompared o -phase ore ype ransformer on per phase bass.e. value of K ll be hgher for 1- phase ore ype ransformer. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 5

6 . Desgn of Three Phase Transformer Dsrbuon ransformer s desgned for less ron loss ompared o poer ransformer.e. less ron maeral, hene value of K ll be lo for dsrbuon ransformer. The usual value of K for dfferen ypes of ransformer s, 1-phase shell ype ransformer: 1. o 1. 1-phase ore ype ransformer:.75 o.85 -phase shell ype ransformer: 1. -phase ore ype ransformer (Dsrbuon):.45 -phase ore ype ransformer (Poer):.6 o.7.5. Choe of flux densy for ransformer desgn Value of flux densy n he ransformer deermnes he ore area and yoke area, hene ompuaon of flux densy s very mporan and rual par n desgn. Normally flux densy s hosen near knee pon of he magnezaon urve h some margn o overome over fluxng, volage varaon and frequeny varaon. Magne maeral used for ore and yoke of ransformer are ho rolled slon seel and old rolled gran orened slon seel. Choe of flux densy may affe he performane parameer suh as no load urren, behavor under shor ru, ron loss, effeny and emperaure rse. Hgher value of flux densy resuls n redued ore area and hene here s a savng n ron. Wh he reduon n ore area, he lengh of mean urn of ndng ges redued hh furher saves onduor maeral. Lesser ron and opper maeral brngs don overall os, egh and sze of ransformer. Bu hgher value of flux densy nreases he ron loss hh resuls n lo effeny. Inreased ron loss auses hgh emperaure rse n ore. Flux densy o be hosen depends on he serve ondon of he ransformer. For dsrbuon ransformer hgh all day effeny s man desgn aspe and hene lo value of flux densy s hosen hh keeps don ron loss. The usual value of maxmum flux densy for Ho rolled slon seel ore maeral are: Poer ransformer: 1.5 o 1.45 Wb/m Dsrbuon ransformer: 1.1 o 1.5 Wb/m Cold rolled gran orened slon seel ore maeral are: Transformer up o 1 kv: 1.55 Wb/m Transformer above 75 kv: 1.6 Wb/m Transformer above 4 kv: Wb/m.6. Choe of urren densy for ransformer desgn The onduor n lo volage and hgh volage ndng s deermned afer hoosng suable value of urren densy. Temperaure rse may be hgh f hgher value of urren densy s seleed. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 6

7 . Desgn of Three Phase Transformer Curren densy seleon s sgnfan for I R loss, hene he load a hh maxmum effeny ours depends on. The level of I R loss requred s dfferen n dsrbuon and poer ransformer. Thus he value of urren densy s dfferen for dfferen ype of ransformer. Self-ooled ransformer: 1.1. A/mm Fored ar ooled ransformer:.. A/mm Fored ol ooled ransformer: A/mm.7. Seleon of ndo dmenson Leakage reaane of ransformer depends on dsane beeen adjaen lmbs. When dsane beeen lmbs are small, ndng s aommodaed by nreasng he hegh.e. ndng s long and hn. Ths arrangemen leads o lo value of leakage reaane. When dsane beeen lmbs are large, ndng s aommodaed by nreasng he dh.e. ndng s shor and de. Ths arrangemen leads o hgh value of leakage reaane. The area of ndo depends upon he oal onduor area and ndo spae faor. Toal area of ndo s defned as Toal opper area n ndo T a + T a A = = Wndo spae faor K Also A =H W The rao of hegh o dh H/W s seleed beeen o 4 o aheve suable arrangemen of ndng hegh and dh..8. Choe of ndo spae faor for ransformer desgn Wndo spae n ransformer s fully ouped by onduor maeral and nsulang maeral. Hene ndo spae faor s defned as he rao of oal opper area n ndo o oal area of ndo. K Toal opper area n ndo A Toal area of ndo A Value of K, depends on ransformer poer and volage rang. Follong empral formula s used for esmang he value of ndo spae faor. K K K 8 for ransformer rang above kva kv 1 for ransformer rang 5- kva kv 1 for ransformer rang of abou 1 kva kv Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 7

8 . Desgn of Three Phase Transformer (a) (b) Varaon n Wndo spae faor (K) h kva rang Transformers h he same volage rang bu dfferen kva rang () 1 kva () 1 kva, needs same nsulang maeral and large opper maeral for 1 kva ompared o 1 kva. Hene, ndo spae faor value nreases as poer rang of ransformer nreases. Varaon n Wndo spae faor (K) h kv rang Transformers h same poer rang bu dfferen kv rang () 11 kv () 11 kv, needs less opper maeral and more nsulang maeral n 11 kv ompared o 11 kv. Hene, ndo spae faor value dereases as volage level of ndng nreases..9. Seleon of ore ross seon for ransformer desgn In a ransformer, here are lo volage and hgh volage ndngs. The performane of a ransformer manly depends upon he flux lnkages beeen hese ndngs and lo reluane magne pah s requred o lnk flux beeen hese ndngs. Ths lo reluane magne pah s knon as ore of ransformer. Core seon of ransformer an be square or sepped. These shapes of ore an be advanages for rular ols. Dsrbuon and poer ransformer uses rular ols beause mehanal sresses produed a he me of shor ru are radal and hene here s no endeny for he ol o hange s shape. In small ransformer square ores are used. As he sze of ransformer nrease, sze of ore nrease and hene lo of useful spae s ased. Furher h he nrease n rumsrbng rle dameer, lengh of mean urn of ndng nreases, hh ll ll rse I R loss and onduor os. In large ransformer, ruform ores are used. For same ore area, spae ulzaon s baer n ruform ores ompared o square ore. Furher reduon n rumsrbng rle dameer, lengh of mean urn of ndng redues gvng lo I R loss and onduor os. a a b d a d a b q q Fgure. Square ore Fgure. 4 Cruform ore Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 8

9 . Desgn of Three Phase Transformer (a) (b) Square ore Crumsrbng rle dameer Gross area of ore aa d d 1.414a a.77d.5d Ne area of ore A Sakng faor, K = s Gross area of ore A Ne area of ore K A g s g.45d a a A d d A Ne area of ore.45d.58 Crumsrbng rle area d 4 Gross area of ore.5d.64 Crumsrbng rle area d 4 Cruform Core a b a b Gross area of ore ab b b A ab b g sn q ( d os q ) d snq d snq osq snq sn q snq dag To have maxmum area, dq g d d d( d snq sn q dq osq snq osq osq snq osq snq anq q 1.71 Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 9

10 . Desgn of Three Phase Transformer.9.618d Gross area of ore d sn sn 1.71 A.618d Ne area of orek A g A s.56d Ne area of ore.56d.71 Crumsrbng rle area d 4 Gross area of ore.618d.79 Crumsrbng rle area d 4 g Mos eonomal dmenson of sepped ores are gven as fraon of dameer of rumsrbng rle. In aual prae lamnaons are avalable n sandard sze o avod de varey and asage of maeral so, ransformer ores are made h sandard sep sze Fgure. 5 Mos eonomal dmenson of sepped ores By nreasng number of seps, he area of rumsrbng rle s more effevely ulzed. Mos eonomal dmensons of varous sep sze are abulaed belo. Area % of rumsrbng rle Square Cruform Three Four Gross area of ore Ne area of ore A = Kd Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 1

11 . Desgn of Three Phase Transformer.1. Seleon of yoke ross seon for ransformer desgn A yoke s a fxed magne par of ransformer ore hh omplees he flux pah. I s no surrounded by a ndng. Dy Yoke Hy Lmb Lmb Lmb Yoke Fgure. 6 Yoke dmensons Yoke h reangular ross seon s used for small ransformer, hoever for medum and large ransformer o or hree sepped yoke s used. Number of seps n yoke s muh lesser han seps n ore hene, unequal dsrbuon of magne flux along yoke ross seon ll gve rse o ron loss and no load urren n yoke. To overome above sad dffuly, ross seon area of yoke s aken 1 o % more han ross seon area of ore. Ne area of yoke, A 1.1 o 1. A y Wdh of yoke, D y Hegh of yoke, Ay H y D larges sampng sze y Flux densy n yoke, Flux n yoke y m B y Ne area of yoke A A y a y Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 11

12 . Desgn of Three Phase Transformer.11. Overall all dmensons of -Ø ransformer Hy H H Hy W Dy a a a W W d D d D d Fgure. 7 Overall dmensons D Dsane beeen ore ener (m) d Crumsrbng rle dameer (m) a Wdh of larges sampng (m) W Wdh of ndo (m) H Hegh of ndo (m) D Wdh of yoke (m) y H Hegh of yoke (m) y W Wdh of frame (m) H Hegh of frame (m) Hene, a a D W W a a a W D D a H H H H H H y y y Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 1

13 . Desgn of Three Phase Transformer.1. Seleon of ndng used for ransformer desgn In ransformer, ndng ype s hosen o mah desred eleral haraerss and adequae mehanal srengh. Some mes more han one ype of ndng may be suable. In hs ase, he ndng hh s smple n onsruon ll be used. Wndngs are usually of he follong ypes; (a) Cylndral ndng Core Core Fgure. 8 Cylndral ndng h rular onduor Fgure. 9 Cylndral ndng h reangular onduor Cylndral ndngs are layer ype and uses eher rular or reangular onduor. The layered ndng may have onduors ound n one, o or more layer and herefore, aordngly alled one, o or mul-layer ndng. I s used for large urren h number of parallel onduors loaed sde by sde n one layer. Parallel onduors have same lengh and loaed n almos same magne feld, hene hey are no ransposed. To layers of ylndral ndngs are separaed by an ol du n order o mprove ol oolng of nner layer. Cylndral ndngs h rular onduor are manly used for hgh volage rangs 6.6 kv, 11 kv, kv for poer rang up o 6 kva. Cylndral ndngs h reangular onduor are manly used for lo volage rangs.415 kv, 6.6 kv for poer rang up o 75 kva. (b) Cross over ndng Cross over ndng are used for hgh volage ndng of small ransformer. When ylndral ndngs are used for hgh volage ndng of small ransformer, volage beeen adjaen layers beomes oo hgh and hene beomes dfful o sele hkness of nerlayer nsulaon. Thus neessary o redue nerlayer nsulaon. I s aheved by dvdng ndng n number of ols separaed by a dsane of.5 o 1mm h he help of nsulang asher or ol du. The volage beeen adjaen ols should no exeed 8 o 1 vol, hene Volage rang of ndng Number of ol 8 o 1 Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 1

14 . Desgn of Three Phase Transformer In ross over ndng, he onduors are paper overed rular or reangular. Eah ols are ound over formers and onsss of number of layers. Core Col Core Col () Fgure. 1 Cross-over ndng h rular onduor Fgure. 11 Cross-over ndng h reangular onduor Complee ndng onss of ols onneed n seres. To end of ols are brough ou for seres onneon. Ousde end of one ol s onneed o nsde end of adjaen ol. Cross over ndng s used n he same range of rangs as ylndral ndngs. Cross over ndng have hgher srengh han ylndral ndng under normal operang ondon. Ths ndng have loer mpulse srengh han ylndral ndng. Helal ndng Helal ndngs are used for lo volage ndng of poer ransformer here number of ndng urns are small bu urren s hgh. These ype of ndngs are desgned h reangular onduor ross seon onneed n parallel and plaed h sde by sde n radal dreon. In order o seure mehanal srengh, reangular onduor h ross seon area no less han 1 mm s used for ndng. Usually () sngle helal () double helal () mul-layer helal ndngs are used for volage rangs of. o 15 kv for poer rang up o 1, kva. In sngle helal ndng onduors are plaed sde by sde o form one urn. Eah urn s separaed by spaers along he axal lengh. In double helal ndng onduors plaed sde by sde formng one urn are dvded no o parallel pah and hey are shfed o axal dreon o form o layer. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 14

15 . Desgn of Three Phase Transformer Double helal ndng s ommonly used beause less number of parallel onduor n radal dreon and large number of parallel onduor n axal dreon allos more axal magne feld o lnk h ndng. Magne feld s unform n axal dreon hle non-unform n radal dreon, herefore greaer magne regulary s aheved n double helal ndng. I ll resul n less I R loss and leakage reaane. (d) Fgure. 1 Sngle helal ndng Fgure. 1 Double helal ndng Mul-layer helal ndng s generally used for volage rang above 11 kv. I onsss of several ylndral layers ound and onneed n seres. Ouer layer s made shorer han nner layer o dsrbue apaane unformly. Mul-layer helal ndng s prefered o mprove surge behavor of ransformer bu mprovemen n surge behavor requres large apaane. I s aheved by redung radal deph of ndng. When radal deph of ndng redues, mehanal srengh of ndng beomes nferor. Therefore use of mul-layer helal ndng s resred. Helal ndngs are used for urren rage -4 A. Double helal ndng s used for he same range of volage used n sngle helal. Hoever urren rang for double helal ndng s e of sngle helal ndng. Ds ndng Ds ndngs are prmarly used n hgh apaor volage ransformer for urren rage 1-6 A. Ths ndng onsss of sngle layer ds ol ound h reangular onduor onneed n seres and parallel. Cols are ound sprally from ener ouards n he radal dreon. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 15

16 . Desgn of Three Phase Transformer Eah ol ress on pressboard spaers formng horzonal du. Wdh of radal ol du depends upon volage beeen adjaen ols, spef hermal loadng and naure of ransformer oolng. Core Col Col Spaer Fgure. 14 Ds ndng Fgure. 15 Arrangemen of spaer n ds ndng Number of ols should be hosen suh ha neessary ndng hegh ulzes sandard sze of onduor. Wndngs are desgned for volage o 11 kv normally uses 6 o 8 ols. Number of ols n onnuous ds ndng h apng a mddle should be mulple of four. Dsngushed feaure of onnuous ds ndng s ransposon of ols. Lo volage ndng desgn Number of urn T Curren I kva 1 V Conduor ross seon area a V E I Hgh volage ndng desgn Number of urn T Curren I kva 1 V Conduor ross seon area a V E I Ouer poson, lo urren apay and more number of avalable urn on hgh volage sde benefs shng. Hene, apngs are provded on hgh volage sde. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 16

17 . Desgn of Three Phase Transformer.1. Wndng ressane of -Ø ore ype ransformer T T I I a a r r Lm Lm ressvy of onduor maeral (Ω-m) Number of hgh volage ndng urns Number of lo volage ndng urns Phase urren n hgh volage ndng (A) Phase urren n lo volage ndng (A) Cross seon area of hgh volage ndng onduor (mm ) Cross seon area of lo volage ndng onduor (mm ) Ressane of hgh volage ndng (Ω) Ressane of lo volage ndng (Ω) Lengh of mean urn of hgh volage ndng (m) Lengh of mean urn of lo volage ndng (m) Lm Lm L Lm o Ressane of ndng r r Lm T Lm T Toal ressane referred o hgh volage ndng T R r r T Per un ressane I R r V a a.14. Wndng leakage reaane of -Ø ore ype ransformer learly sang he assumpons used Assumpons o Hgh volage and lo volage ndng have equal axal lengh. o Flux pah s parallel o he ndngs along he axal lengh. o Mmf requred o ron pah s neglgble. o Hgh volage ndng mmf and lo volage ndng mmf s equal, hene magnezng mmf and magnezng urren s zero. o Half of he leakage flux n he du lnks h eah ndng. o Lengh of mean urn of eah ndng s equal. o Reluane of flux pah hrough yoke neglgble. o Wndngs are unformly dsrbued, hene ndng mmf vares unformly from zero o AT from one end o anoher end. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 17

18 . Desgn of Three Phase Transformer LC x b bo b (a) Conduor seon Fgure. 16 Leakage flux dsrbuon n ore ype ransformer Consder a small nfne srp of dh dx a a dsane x from he edge of hgh volage ndng along s dh. Mmf aross srp Permeane of srp Flux n srp = Mmf x I b T 1 1 A Reluane L L L L C C C C Permeane Lm dx Lm A x Lm I T dx b L C dx Flux lnkages of he srp = x Lm x T I T dx b L b C Flux lnkages of hgh volage ndng Lm x 1 L b C d I T dx b d 1 b Lm x 1 L b C I T dx Lm b 1 I T L C Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 18

19 . Desgn of Three Phase Transformer (b) Du seon Mmf aross du = 1 1 Permeane of du = Reluane I T A A L Flux n du = Mmf Permeane = o I T b o L C Flux lnkages of hgh volage ndng due o du flux Half of flux n du T L b o I T T L C o L b o o I T L C L b o o o b o L L L L C C C C L Toal flux lnkages of hgh volage ndng 1 Lm b L b o o I T I T L L C C I T b b o Lm L o L C If, s assumed ha Lm Lm L Lm o Lm b b o I T L C Leakage nduane of hgh volage ndng Lm b b o L T L C Leakage reaane of hgh volage ndng Lm b b o x f T L C Smlarly,leakage reaane of lo volage ndng Lm b b o x f T L C Toal leakage reaane referred o hgh volage ndng T X x x T Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 19

20 . Desgn of Three Phase Transformer.15. Losses n -Ø ransformer and ondon for maxmum effeny Losses n ransformer are of o ypes () Copper loss (P) () Iron loss (P). Toal Copper loss P I R Toal ron loss P P P Iron loss n lmb + Iron loss n yoke P P Lmb Yoke Lmb Yoke Hegh of ndo Ne ron area Densy of lamnaon Sp. ron loss H A Densy of lamnaon Sp. ron loss Wdh of frame Ne area of yoke Densy of lamnaon Sp. ron loss W A Densy of lamnaon Sp. ron loss Toal loss y P P P Sray load loss C Transformer may be desgned for maxmum effeny.e. mnmum losses. Toal loss a full load P P Toal loss a any fraon x of full load Effeny a any fraon x of full load, dx Effeny s maxmum hen dx C x P P C x kva1 os x 1 os x kva x P P xq1 os 1 os x Q x P P 1 os 1 os 1 os 1 os x Q x P P Q x Q Q x P C C x Q 1 os x P P C x Q 1 os x P P Q 1 os x Q 1 os Q 1 os x C P C x Q 1 os x P P x Q 1 os x P C C x P P -x P C C P -x P C P x PC x Q 1 os x P P - x Q 1 os - x P Iron loss = Copper loss Consan loss = Varable loss C C C C Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691)

21 . Desgn of Three Phase Transformer.16. No load urren of -Ø ransformer When ransformer operaes a no load, urren a seondary ndng s zero bu prmary ndng dras small urren knon as no load urren. No load urren of a ransformer onsss of o omponen () Magnezng omponen (Im) () Loss omponen (Il). Toal magnezng mmf per phase AT o AT o Mmf of lmb + Mmf of yoke +Mmf of jons a l a l Mmf of jons y y Toal ron per phase P Toal ron loss Magnezng omponen of urren per phase I m AT T o Loss omponen of urren per phase P I l V No load urren per phase I I I o m l Magnezng omponen (Im) produes he magne flux n he ore, hle loss omponen (Il) produes real poer o feed oal ron loss. Magnude of magnezng omponen (Im) depends upon qualy of magne maeral used for ore and yoke, flux densy seleed and ype of jons. Magnude of loss omponen (Il) depends upon oal ron loss. Loss omponen (Il) s very small ompared o magnezng omponen (Im). No load urren s n order of perenage of raed urren of ransformer. Small ransformer:. 5. % of raed urren Medum ransformer: 1.. % of raed urren Large ransformer:.5. % of raed urren.17. Desgn opmzaon ondon for he mnmum os Desgn opmzaon s a ehnque n hh eran desgn varables are needed o be deermned o aheve he bes measurable performane under gven onsrans. Transformer an be desgned o make one of he quany () volume () egh () os (v) losses as mnmum. These requremens are onradory and no possble o sasfy all for one desgn. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 1

22 . Desgn of Three Phase Transformer Oupu equaon of ransformer Q.fB A K A 1.fB A A m m m As produ.fb δ 1 s onsan for gven rang, le assume A A M B A 4B A m m m Also, r AT K A A A 4 r A 4B m A M and A If, M C Toal os of ransformer ave maeral (Rs) C Toal os of ron (Rs) C Toal os of opper Spef os of ron (Rs/Kg) Spef os of opper (Rs/Kg) G Wegh of ron (Kg) G Wegh of opper (Kg) g g Densy of ron = (Kg/m ) Densy of opper = (Kg/m ) C C C G G A l g A L g m M M l g L g dc For mnmum os d m 1 1 M 1 l g M L g m M - l g M L g m M l g M L g m 1 l g L g m A l g L g m A l g A L g A m G G Cos of ron= Cos of Copper - Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691)

23 . Desgn of Three Phase Transformer.18. Area of ore affeed by egh of opper and ron Wegh of ron Rao Wegh of opper G A l g K A G L g m lg G A L g G m G A K 1 G lg Where, K 1 L g m Oupu equaon of ransformer Q.fB A K A 1 m G A.fB A K 1 m 1 G G.fB A K 1 m G G A l g A l g G A L g K A L g Q A G. 1 A fb K m 1 G 1 Q G.K fb G 1 m m m Effe of hange n lnear dmensons on oupu and losses of ransformer (a) (b) Consder o ransformer of same flux densy, urren densy, frequeny, ndo spae faor and ype h lnear dmenson n he rao of x:1. Le, ransformer h dmenson x s alled A and oher ransformer B. Effe on oupu Oupu of ransformer, Q fb A K A Where, A x and A x 4 Q A A x Effe on losses m Toal ron loss, P loss per un volume volume P x Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691)

24 . Desgn of Three Phase Transformer Toal opper loss, P I r I r Lm T Lm T a a a a a T Lm a T Lm Toal volume of opper P x.. Effe of hange n frequeny on losses, volage and leakage mpedane of ransformer (a) Effe on losses Spef ronloss Hyseress loss Eddy urren loss, P P P k f h e B k f B h m e m (b) () If volage of ransformer s onsan, he produ (fbm) ll be onsan. Le, produ fb K Eddy urren loss, P k f B Hyseress loss, P m e e m K kf e k e K h h m f onsan k fb K k f h f k K h f Inversely vares h frequeny Eddy urren loss ll reman onsan even hough frequeny s hanged and hyseress loss ll nrease h he derease n frequeny. Effe on volage Change n frequeny do no affe he volage of any sde of ransformer as volage depends on amoun of ndng. Hoever may hange he feld srengh of ore and possbly sauraon of. Effe on leakage mpedane Change n frequeny do no have muh effe on leakage mpedane. Leakage reaane ll nrease lnearly h he nrease n frequeny and ve versa. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 4

25 . Desgn of Three Phase Transformer Due o skn effe, effeve ressane ll nrease h he nrease n frequeny and ve versa. Ths effe s neglgble for he small hange n frequeny..1. Mehanal fores developed n ransformer ndngs (a) Transformer ndngs under normal operang ondons are subjeed o mehanal fores suh as o Fore of araon due o urren flong n same dreon o Fore of repulson due o urren flong n oppose dreon The magnude of fore on onduor s proporonal o produ of urren n onduor and nensy of magne feld due o neghborng onduor. Under normal ondon urren s small, so fores are moderae and no noeable. A he me of shor ru a full volage urren may reah o 1-5 mes full load urren hene, mehanal fores ll reah o 1-65 mes normal fores. For rular ol, fores are radal hene here ll no be any endeny o hange he shape of ol. Whle on reangular ol, fores are perpendular o onduor ha ll end o deform ol n rular form. Thus rular ols are preferred n ransformer ndng. Radal fore Fr X X L dfr dq R q Fgure. 17 Radal fore on ndng Ineraon of axal omponen of leakage flux h urren arryng onduor produes fore n radal dreon. Radal fore res o burs he ouer ndng and rush nner ndng. Ths s beause prmary and seondary ndng arres urren n oppose dreon and hene repulsve fore pulls ouer ndng and ompress nner ndng. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 5

26 . Desgn of Three Phase Transformer Insananeous mmf ang aross he du T T Flux densy n du H r L Average flux densy n du T L T L Radal fore ang on a srp a mean radus R hn an angle dθ of ol T R df T r Rdq T dq L L Toal nsananeous radal fore ang on he ol, F r df r dq R T L R T L Lm T L R T L (b) Axal fore Ineraon of radal omponen of leakage flux h urren arryng onduor produes fore n axal dreon. These fores res o squeeze he ndng ogeher n mddle. Wh symmeral ndng arrangemen, hese fores are neglgble even under shor ru ondon. In shell ype ransformer sandh ol has symmeral arrangemen hh ll have fore of repulson beeen eah par. Insananeous mmf of ndng T,Where T Number of urns n eah half ol Tn Flux densy n ndng H r W Average flux densy n ndng n T n n W Tn W Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 6

27 . Desgn of Three Phase Transformer T Toal axal fore ang on he ol, F T a Lm W Lm Tn W n n T Lm n W Lm T 8n W.. Effe of emperaure rse on ransformer (a) (b) Temperaure rse n ransformer s due o he onverson of loss developed n ndng and ore no he hea. Hea dreed o he oolng medum by he ay of radaon and onveon. Temperaure rse n ank h plan all Tank all dsspaes hea by boh radaon and onvon. A plan all ank dsspaes hea hrough radaon 6 W/m - o C and hrough onveon 6.5 W/m - o C for emperaure rse of 4 o C a an amben emperaure of o C. Toal loss Temperaure Rse, q Spef hea dsspaon Hea dsspaon surfae of ank P P P P 1.5S S Temperaure rse n ank h ubes If emperaure rse n ank h plan all exeeds spef lm, addonal ubes are aahed h he all o brng don he emperaure. Addonal ube ll nrease hea dsspaon surfae area, onveon rae bu ll brng don he radaon rae. Hene here s no hange by nreased surfae area so far as dsspaon of hea s onern h radaon. Bu nrease n hea dsspaon s more effeve n onveon due o pressure dfferene reaed by ol n ubes. Le, dsspaon surfae area nreased x mes by ank surfae area and onveon rae by 5%. l Lengh of ube (m) d Dameer of ube (m) a Area of eah ube (m ) n Number of ube Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 7

28 . Desgn of Three Phase Transformer Toal area of ube xs Toal hea dsspaon area S xs 1 x S xS x 1 xs 1 x Toal hea dsspaon by ank h ube= S xs x S Spef hea dsspaed by ank h ube Toal loss Temperaure rse, q Spef hea dsspaon Hea dsspaon surfae P P x qs x S P P 1 P P x qs P P x 1 x Toal area of ube Number of ube, n Area of eah ube xs dl 1 P P qs dl 1 x S S 1 P P -1.5S 8.8dl q.. Coolng mehods used for ol mmersed ransformer To dsspae he hea o surroundngs ar and ol s used as oolan. Transformer usng ar as oolan s alled dry ype and ol as oolan s alled ol mmersed. The mehod of oolng depends upon he () medum of oolng () Type of rulaon employed. They are abbrevaed h sandard noaon suh as Ar A, Gas G, Synhe ol L, Mneral ol O, Sold nsulaon S, Waer W Naural N, Fored F Coolan rulang nsde he ransformer omes n ona h ndng and ore, dependng upon he mehod oolan ransfers hea parally or fully o he ank alls from here s dsspaed o he surroundng medum. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 8

29 . Desgn of Three Phase Transformer (a) Ol naural ar naural (ONAN) Core Wndng Wndng Ol (b) Tank Fgure. 18 Ol naural ar naural (ONAN) oolng Ar oolng s no suffen and effeve for medum and large sze of ransformer. Ol has man advanage of hgh hea onduvy and hgh o-effen of volume expanson h emperaure. Hene all ransformers are mmersed n ol and hea generaed n ndngs and ore are dsspaed o he ol by onduon. In ol hea s ransferred by onveon. Durng onveon heaed ol ransfers hea o he ank alls from here hea s aken aay o he amben ar. Durng hs proess heaed ol ges ooled and falls bak o he boom. Therefor naural hermal head s reaed hh furher ransfer hea from heaed par o he ank all. Upo kva rang plan ank all s suffen o dsspae hea. Rangs hgher han kva ank all s nreased by provdng orrugaons, fns, ubes and radaors. Ol naural ar fored (ONAF) Ol Core Fan Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 9 Tank Fgure. 19 Ol naural ar fored (ONAF) Coolng

30 . Desgn of Three Phase Transformer () (d) Transformers are mmersed n ol here ol rulaon under naural head ransfers hea oards he ank all. In hs ype of oolng ehnques, ank s made hollo and ar s blon hrough o ool ransformer pars. Hea removal from nner ank all s nreased by 5-6 mes he onvenonal means. Hoever normal ay by ar blas s o use radaor banks of orrugaed ubes separaed from ank and ooled by ar blas produed by fan. Ol naural aer fored (ONWF) In hs ype of oolng ehnques, opper oolng ols are mouned above he ransformer ore bu belo he ol surfae. Man dsadvanage of hs mehod s employs aer nsde he ol ank and aer s a hgher head han ol. In ase of aer leakage, ges mxed h ol and redues deler srengh of ol. Waer nle and oule ppes are nsulaed n order o preven mosure from amben ar. Ol fored ar fored (OFAF) Ol Core Wndng Ol Pump Tank Hea Exhanger Fan Fgure. Ol fored ar fored (OFAF) oolng In large ransformer naural ol rulaon s no enough o ool ransformer, hene fored rulaon hrough ol pump s arred ou. A moor drven ol pump rulaes ol from ransform ank o exernal hea exhanger o ool he ol. In ol fored ar fored arrangemen ol s ooled by exernal hea exhanger usng ar blas produed by fan. Ol pumps and fans are no used all he me bu, hey are shed ON by emperaure sensors hen emperaure exeeds he lm. Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691)

31 . Desgn of Three Phase Transformer (e) Ol fored aer fored (OFWF) Ol Waer Inle Core Wndng Ol Pump Tank Hea Exhanger Waer Oule Fan Fgure. 1 Ol fored aer fored (OFWF) oolng In hs ol fored aer fored mehod ol s ooled n aer hea exhanger. Ths mehod s bes sued here oolng aer has large head. The pressure of ol s kep hgher han ha of aer so f any leakage ha ours ll be from ol o aer only. Hydroeler generang saons has large aer avalably, hene ransformer h OFWF oolng mehod s used here Shal Pael, EE Deparmen Desgn of DC Mahnes and Transformer (1691) 1