Behaviour of Current Transformers (CT's) under severe saturation conditions

Transcription

1 Behavour of Current Tranforer (CT') under evere aturaton condton Héctor. O. acual Electrcal Engneerng Departent Natonal Unverty of La lata 9, La lata, Argentna Jorge L. Dapé Electrcal Engneerng Departent Natonal Unverty of La lata 9, La lata, Argentna Joé A. Rapalln Electrcal Engneerng Departent Natonal Unverty of La lata 9, La lata, Argentna Abtract - Modern protectve yte requre a fathful reproducton of prary hort crcut current. Often, pecally n hgh power ntallaton, an portant part of the current, durng a few cycle at leat, the d.c. coponent, whch caue evere aturaton condton, f the current tranforer not correctly elected and eployed. redcton of the behavour of thee devce durng the frt -4, when d.c. coponent hgher, becoe a ut. Many odel have been preented to ulate current tranforer, but only oe of the are well uted for tranent condton. Th paper preent a coparon between predcted reult, fro accepted odel, and real condton one, fro hgh power laboratory tet. Sgnfcatve dfference, that tend to dappear wth te, have been found n certan cae. Keyword: Current tranforer, aturaton.. INTRODUCTION It portant to be able to deterne the behavour of a CT wthn a certan range of accuracy when t appled a prary current whch contan a d.c. coponent that ay caue t aturaton, nce th wll allow to predct the behavour of related equpent, uch a that aed at protectng power electrc yte, whch due to th tuaton ght ake an ncorrect operaton wthn the perod nvolved. Th paper how the theoretcal and experental reult obtaned fro typcal CT', ephang on the frt cycle of the tranent event, and tate oe conderaton on ther applcablty.. EQUIVALENT CIRCUIT OF A CURRENT TRANSFORMER. Fg. how the typcal equvalent crcut of a tranforer. R L R L p fe R fe L ag ag R bur L bur R, L : prary leakage pedance. R, L : econdary leakage pedance. R bur, L bur : burden pedance. R fe, L ag : dervaton branch. p : prary current. : econdary current. fe : current derved by the branch repreentng the core loe. ag : current derved by the agnetng branch. A uual, all agntude ut be referred to one de of the tranforer. In th work they are condered a referred to the econdary de. -. Conderaton on the equvalent crcut. In order to ncorporate the hytere loop nto the uggeted odel, two alternatve way can be taken. On one hand, conderng the ron core loe (by ean of a varable retance R fe ) eparately fro the agnetng current (by ean of a varable nductance L ag ). On the other hand, ntroducng the ron core loe nto the agnetng branch and conderng the hytere loop dynac n th branch. The latter ha been choen to perfor the analy hereby preented, nce n th way the poblty to ntroduce the odel whch predct the hytere loop dynac n the CT core durng the tranent tuaton ore traghtforward ([],[],[3],[4],[5] or [6]). Accordng to uual conderaton for thee cae, t aued that R = contant, and nce the prary leakage pedance doe not affect the behavour of the CT, the followng plfed equvalent crcut obtaned: p v R L L R bur Fg.. Splfed equvalent crcut of the a current tranforer. L bur Fg.. Equvalent crcut of a tranforer.

2 -. Matheatcal odel repreentng the equvalent crcut of the CT. Fg., how that the prary current the u of two coponent: + p = () Baed on [7] and conderng that the path taken by flux a a functon of current avalable (by ean of a tet perfored on the econdary de of the CT), and tatng a lnear trajectory between the pont ued a, t poble to pot (). = ( ) () In equaton () the ubcrpt agned to and value, whch correpond to the tart of the lnear egent of the current-flux curve n whch the ulaton calculu tuated and the lope of uch egent, whch change when flux value exceed ether lt of uch egent. Subcrpt refer the value obtaned at preent ulaton te (t). For whch = + K K = + Cobnng the econdary pedance of the CT wth the burden we get: (3) R + j ω L = ( R + Rbur) + j ( ω L + ω Lbur) (4) Takng nto account the aforeentoned, voltage v hown n Fg., wll be (5) furtherore: where v = R + L (5) v = (6) = N φ, the total lnked flux, N beng the nuber of turn and φ the equvalent flux per turn, hence: = R + L by approxatng the dervatve by ean of a dfference quotent, where ubcrpt and refer to the value at the preent te tep (t) and the precedng te tep ( t ), (8) obtaned. ( ) ( + ) ( ) = R + L (8) fro whch we get (9) n whch J a contant value throughout ulaton, and h a htory varable, (where htory varable the one whoe value for ulaton correpond to te tep t ). where h J + J (7) = h (9) = R + L = J d () d another contant: d R L = J Conderng the equaton developed o far and relatng (), (3) and (9): = + p by ubttutng ter t poble to relate the flux value to the prary current, whch : p K h = () + J Wth the reult fro () and ubttutng n (9), econdary current obtaned. Once thee value are obtaned, varable h updated, o that thee varable are condered a value for the next ulaton te tep. Thu, wth calculated value and the value of h obtaned, whch wll be the h for the next ulaton tep.

3 h = J d Conderng the aforeentoned, varable odfed when lope change t value. K wll be The curve obtaned are thoe n Fg. 3 and 4, whch how that for thee tranforer the hytere loop area neglgble for the current aount nvolved. Th algorth pert a fat oluton for the repreentaton of a CT; t can therefore be ued n real te applcaton to obtan the current gnal to feed protecton relay n order to analye ther behavour. 3. MEASUREMENTS ON THE CURRENT TRANSFORMER. The neceary to be ntroduced n the atheatcal odel have been obtaned fro two CT' and they are: Fg. 3: Flux-current curve of tranforer. Tranforer : Rato: 4/5 Accuracy cla: Rated burden: VA R (econdary wndng retance):.87 Ω. R bur (burden retance connected to econdary wndng):.34 Ω L bur (burden nductance connected to econdary wndng):. Tranforer : Rato: /5 Accuracy cla:.5 Rated burden: 3 VA R (econdary wndng retance):.83 Ω. R bur (burden retance connected to econdary wndng):.6 Ω L bur (burden nductance connected to econdary wndng):. Fg. 4: Flux-current curve of tranforer. Fg. 5 how the hytere loop obtaned fro another tet perfored on tranforer, wth current value about te lower than thoe n Fg Obtanng the hytere loop feedng the CT through the econdary wndng. The CT' have been fed fro the econdary de, wth the prary de open crcuted. By ntegratng the voltage acro econdary ternal, and conderng the value of R, we get: or: = v nt t R dt = t ( v ec R) dt n both equaton current the eaured current, whle v nt the ntegral of the voltage n connecton ternal v ec. Fg. 5: Flux-current curve of tranforer, low current appled. Conderng that the current and flux value nvolved n the tet perfored on the tranforer are around the value hown n Fg. 3 and 4, the to be ued wll be thoe hown n thee fgure. Therefore, we need not conder a odel whch predct the flux path takng nto account the hytere loop area. 4. RESULTS OBTAINED. The current appled to the prary de of tranforer and, are repectvely thoe hown n Fg. 6 and 7. The value of the econdary current,

4 eaured and calculated by the ethodology developed above are preented n Fg. 8 and 9..5 x 4.5 Current (A) Te (ec) Fg. 6. rary current eaured n the tet (CT ). Current (A).5 x Te (ec) Fg. 7. rary current eaured n the tet (CT ). It oberved fro Fg. 8 and 9 that there are dfference between eaured and calculated value. Fg.. CT conderng a leakage reactance of. Ω to 5 Hz The dfference between eaured and calculated current (Fg. 8) are attrbuted to the fact that n aturaton condton the leakage reactance doe not have a contant value (uually neglgble), a generally condered n th type of CT odel, but t adopt dfferent value n functon of the aturaton degree. The ethodology uually eployed (te 3-) to obtan the flux-current graphc (Fg. 3 and 4) doe not conder the eparaton between the leakage flux and the flux that ut be entered a n the agnetng branch of the CT odel (Fg. ), whch provde another ource of error to the calculated value. When leakage flux neglgble eaured and calculated value tend to be lar, a hown n Fg CONCLUSIONS. Fg. 8. Secondary current eaured and calculated n CT. Fg. 9. Secondary current eaured and calculated n CT. In order to deterne the effect produced by conderng a contant value for nductance L, we have ncluded n the odel of tranforer a leakage reactance equal to. Ω at 5 Hz, (a uch hgher value than expected n th achne), and o obtanng the reult hown n Fg., apprecably lar to thoe n Fg. 8: Fro the analy perfored, and takng nto account the conderaton tated n -, t oberved (Fg. 8, 9 and ) that the value obtaned by ulaton lgthtly dffer fro the actual value n the cycle where agnetc aturaton ore portant. A follow fro Fg., a contant value for the leakage reactance, do not prove draatcally ulaton reult. The dfference between ulated and eaured value are attrbuted to the fact that the leakage reactance value ha not been condered a a varable, nce the leaked flux vare takng dfferent value n functon of the core aturaton degree. On the other hand, flux eaureent (te 3-), take nto account the value of uch reactance. In order to obtan a degree of approxaton hgher than the actual value, the leakage reactance varaton pattern hould be known throughout the developent of ulaton, and the leaked flux hould be eparated fro the one ntroduced a n the odel by ean of the curve hown n Fg. 3 and 4. It noteworthy that n thoe current tranforer whch n aturaton condton have a low flux leakage, the value obtaned by th type of ulaton, wth the conderaton tated above, wll be cloer to the actual value. Fro the aforeentoned, t ut be taken nto account that when a CT repreented wth a odel a that

5 of Fg., ubtted to evere aturaton condton, falure to conder leakage flux varaton can gve re to dfference between the calculated and eaured econdary current at the frt tage of the tranent (Fg. 8), whch ay lead to error n the reult of the ulaton, and to wrong concluon when thee reult are ntended to deterne the behavour of the protecton relay. 6. REFERENCES [] S. Ray, "Dgtal ulaton of B/H excuron for power yte tude", roc. IEE, Vol. 35, t C, No. 3, May 988, pp. -9. [] S.N. Talukdar and J.R. Baley, "Htere Model for Syte Stude", IEEE Tranacton on ower Apparatu and Syte, Vol. AS-95, No. 4, July/Augut 976, pp [3] D. O'Kelly, "Sulaton of Tranent and Steady-tate Magnetaton Charactertc wth Hytere", IEE roceedng, Vol. 4, No. 6, June 977, pp [4] F. de Leon, A. Selyen, "A Sple Repreentaton of Dynac Hytere Loe n ower Syte Tranforer", IEEE Tranacton on ower Delvery, Vol., No., January 995, pp [5] Ncke Meneenl, "Nonteratve Dynac Hytere Modellng for Real-Te Ipleentaton", IEEE Tranacton on ower Syte, Vol.3, No.4, Noveber 998, pp [6] J.G. Frae, N. Mohan and T. Lu, "Htere Modelng n Electroagnetc Tranent rogra", IEEE Tranacton on ower Apparatu and Syte, Vol. AS-, No. 9, Septebre 98, pp [7] J. R. Martí, L. R. Lnare and H. W. Doel, "Current Tranforer and Couplng-Capactor Voltage Tranforer n Real-Te Sulaton", IEEE Tran. on ower Delvery, vol., no., pp , January 997. [8] M. Kezunovc, "Experental evaluaton of EMTbaed current tranforer odel for protectve relay tranent tudy", IEEE Tran. on ower Delvery, vol. 9, no., pp , January 994. [9] Rchard Boll, Soft Magnetc Materal, Seen Aktengeellchaft Heyden, Brtan, 979. [] Enrque Ra, Tranforadore de potenca, de edda y de proteccón, Marcobo, Barcelona, 97 ( edcón). [] E.E. Staff del M.I.T., Crcuto Magnétco y Tranforadore, Reverté, Argentna, 984. []. F. Van Eldk y. Cornelu, Aparato de Corrente Alterna con Núcleo de Herro, Bbloteca Técnca hlp, arannfo, Epaña, 964. [3] Spnadel, Crcuto Eléctrco y Magnétco, Tea Epecale, Nueva Lbrería, Argentna, 98.