Theoetical Model fo Cooion ement in Ovehead Line Conducto Celio F. Baboa Geência de Soluçõe Tecnológica paa o Seto Elético Cento de Pequia e Deenv. em Telecomunicaçõe - CPqD Campina, SP, Bail gcelio@cpqd.com.b btact Thi pape peent an electomagnetic model fo aeing the zinc laye thickne of galvanized teel tand that fom cable ued in ovehead powe line, i.e., aluminum conducto teel-einfoced (CSR) and ovehead gound-wie (OHGW). The tatu of the teel galvanization povide an impotant indication of emaining cable life. The model i baed on the evaluation of eddy cuent induced in the zinc laye and it influence on a tet coil impedance that ha the cable a pat of it coe. The theoetical eult of the model ageed well with eult of expeiment, both fo the a cable containing only teel tand (e.g., OHGW) and a complete CSR cable. Thi model wa applied in the analyi of data collected by an inpection obot to be ued in ovehead powe line. Index Tem CSR cable, cooion detection, galvanization, ovehead line, eddy cuent. T I. INTRODUCTION HE ovehead powe line ae uually made of aluminum conducto teel einfoced (CSR), whee the inne teel tand povide the deied mechanical tength and the oute aluminum tand conduct the line cuent. One impotant facto that limit the evice life of thee conducto i intenal cooion, which i initiated by the lo of the zinc laye that cove the intenal teel tand. When thi laye i lot, the cooion poce between aluminum and zinc tand pogee fat, compomiing the integity of the conducto. thi cooion take place inide the conducto, it i not detectable by viual o infa-ed inpection, except when the cooion poduct ae lage enough to bulge the conducto but, at thi tage, the conducto' failue may be imminent. In ode to detect the cooion of CSR conducto in it ealy tage, an inpection ytem baed on the eddy cuent induced in the zinc laye wa developed in the 8' [, ]. Thi ytem i baed on a emote-contolled obot that weep the line and detect the eactance of a coil that ha the conducto a pat of it coe. Simila ytem uing the ame pinciple ae decibed in the liteatue [3,, ], a well a etimation of the conducto emaining life [, 7]. Othe technique to detect cooion in CSR conducto Thi wok wa financed, in pat, by Bazilian National Council fo Scientific and Technological Development (CNPq). can alo be found in the liteatue, and ome of them wee decibed by the Electic Powe Reeach Intitute (EPRI) [8, 9, ]. One of thee technique ue pemanent magnet to magnetize the teel wie and magnetic field eno to detect non-unifomitie in the field caued by cooion of the teel tand [,, 3]. Thi technique i baed on empiical efeence and detect cooion on an advanced tage, whee a ubtantial teel co-ection aea i lot. lthough the eddy cuent technique ha been widely ued in the field [,, ], to the bet of thi autho' knowledge, thee i no publihed theoetical appoach in ode to coelate the eno eading to the zinc laye thickne. Indeed, the inpection eult eem to be intepeted in an empiical way, i.e., the eno output fom an inpected conducto i compaed with output fom efeence ample of the ame conducto, but with known flaw. Theefoe, the aim of thi pape i to povide a theoetical model fo the cooion aement of ovehead line conducto baed on the eddy cuent method. Thi model i intended to povide the zinc laye thickne fom the ignal picked-up by a ening coil uounding the cable. The theoetical eult ae compaed with expeimental data obtained fom ample poduced in laboatoy, which uppot the popoed model.. Theoetical Model II. THE GLVNIZED STEEL STRND Thi ection analyze the epone of a teel tand when it i ubjected to a time-vaying longitudinal magnetic field. Let u conide a tand of length, a hown in Fig.. The teel coe i a cylinde of adiu, coveed by a zinc laye of thickne d. It i conideed that the zinc ha conductivity σ and pemeability μ, while the teel pemeability i ' " j, () whee µ i the fee-pace pemeability, µ' and µ" ae the eal and imaginay pat of the elative pemeability, epectively, and the dah above the ymbol denote a complex vaiable. The teel pemeability take into account the eddy cuent within the teel, o that it may be egaded a an effective pemeability. the intenity and fequency of the applied magnetic field ae kept contant in an inpection ytem, the effective teel pemeability i aumed to emain contant. nai do V Simpóio Baileio de Sitema Elético, Foz do Iguaçu PR, Bail. -// ISSN 77-
Fig.. Section of a galvanized teel tand and it dimenion. Fo a cuent i flowing in the zinc laye aound the teel coe of length, the coeponding magnetic field in the teel i: i H. () Conideing that the cuent ha a hamonic time-dependence, the magnetic flux in the teel i: H. (3) Subtituting () into (3), dividing by the cuent, and multiplying by the angula fequency ω give the fequencydependent impedance of the zinc laye: j X. () The eitance of the zinc laye i given by: R. () d The total zinc laye impedance i obtained fom () and (): Z j. () d If the teel coe i excited with a hamonic longitudinal magnetic field, the coeponding flux in the teel coe i: H, (7) and the induced voltage in the zinc laye i: V j H, (8) t Thi voltage will dive a cuent in the zinc laye that, by it tun, will give ie to a magnetic field given by: H V R Z. (9) Subtituting () and (8) into (9) give: H R j H d. () j d The total magnetic field T in the teel coe i given by the upepoition of the incident field and the eaction field R : H HT H H R. () j d Subtituting ω = π f in (), whee f i the fequency, and dividing by lead to the nomalized total field: j f d H N. () Equation () give the total nomalized magnetic field in a teel tand. Fig. how the dependency of N modulu with the zinc laye thickne, fo epeentative value of the elevant paamete. the output of a ening device i a function of N, it i clea fom Fig. that zinc laye thickne in the ange of inteet (e.g., fom to 8 µm) can be aeed fom the total magnetic field. Nomalized magnetic field,,8,,, 8 Zinc laye thickne (um) Fig.. Total nomalized magnetic field in a teel tand accoding to () a a function of zinc laye thickne. = mm, σ =.9 7 S/m, f = khz, µ =.7 - H/m, µ' = 3., and µ" =.. B. Steel Stand Magnetic Pemeability key paamete in the ue of () i the magnetic pemeability of a teel tand. Thi pemeability i defined in () a a complex vaiable, whee the eal pat (µ') i elated to the enegy toed in the magnetic field and the imaginay pat (µ") i elated to the loe. In ode to obtain expeimentally the teel tand pemeability, ome ample of tand wee taken fom diffeent CSR conducto and alo fom galvanized teel conducto ued a OHGW. The tet pocedue conited in electing a tand ample of about. m in length and emoving the galvanization by mean of acid attack. tet coil wa applied in the middle of the ample, wapping tightly a thin inulated coppe wie (. mm diamete) aound the tand, in ode to obtain a coil with tun. The eal and imaginay pat of thi coil wa meaued with a peciion LRC mete (HP 8). In ode to have efeence value, a imila coil wa built by wapping the wie aound a platic coe having the ame diamete a the teel tand. The teel pemeability component wee obtained a follow: X ', (3) X p R R " p, () X p whee X and X p ae the eactance of the teel-coe and platic-coe coil, and R and R p ae the eitance of the teelcoe and platic-coe coil, epectively. nai do V Simpóio Baileio de Sitema Elético, Foz do Iguaçu PR, Bail. -// ISSN 77-
Fig. 3 how the value obtained fo the teel tand fom a 3/8" diamete OHGW. It can be een that the eal component (µ' ) fall fat a the fequency inceae, and then goe aymptotically to. The imaginay component (µ" ) eache a maximum value aound khz and then alo fall cloe to the eal component. Thee meauement wee caied out at ambient tempeatue (3 C) and with an applied magnetic field equal to /m. In ode to ae the dependency of the pemeability with the intenity of the exciting magnetic field, ome eult ae hown in Fig., fo the fequency of khz. It can be een that the pemeability i elatively table in a wide ange of magnetic field intenity. It i impotant to highlight that in a detection device the fequency and the applied magnetic field intenity ae kept contant. Relative pemeability 3, Fequency (khz) Fig. 3. Relative pemeability of a teel tand a a function of fequency. Bold line: eal pat (µ ' ); Thin line: imaginay pat (µ" ). Relative pemeability 3 8 Magnetic field intenity (/m) Fig.. Relative pemeability of a teel tand a a function of magnetic field intenity at khz. Bold line: eal pat (µ ' ); Thin line: imaginay pat (µ" ). C. Expeimental Veification t thi point, it i inteeting to pefom an expeimental veification of (), a it i a key equation fo the model peented in thi pape. In ode to do o, a mall coil wa built, which ha at khz the eitance R =.8 Ω and eactance X =.93 Ω. It i eay to how that, when a teel tand i intoduced into thi coil, it impedance change to: whee: Z c R X k Q j X k P, () P H N ' ' H " ", () N Q H N ' H ' ", (7) c " N k, (8) H N ' and H N " ae the eal and imaginay pat of the nomalized magnetic field, epectively, and and c ae the coection aea of the teel tand and the tet coil, epectively. Fo the tet coil conideed, c = mm. N i function of the zinc laye thickne, the meauement of c fo teel tand with zinc laye of diffeent thicknee can povide a veification of (). Theefoe, a et of teel tand wa pepaed taking a. m ample fom the coe of diffeent CSR cable. Each tand wa weighted in a peciion cale. The galvanization wa completely emoved fom one tand of each coe, and the epective zinc laye thickne wa calculated fom the tand diamete and it ma eduction. The othe tand wee ubjected to the ame chemical teatment to emove the zinc, but the poce wa inteupted at diffeent tage. The emaining zinc laye thickne wa calculated fom the ma eduction and the aumption that all tand of the ame cable coe had the ame oiginal zinc laye thickne. Fig. how the modulu of the coil impedance a a function of zinc laye thickne fo teel tand taken fom the coe of an CSR, MCM cable (Dove), a calculated fom () and (). The teel tand adiu i. mm. Fig. alo how the expeimental value obtained fom the tand ample. It can be een that the coelation between theoetical and expeimental data i vey good, which uppot the electomagnetic model contained in (). Coil impedance (Ω) 3 3 Zinc laye thickne (µm) Fig.. Modulu of the tet coil impedance fo teel tand taken fom the CSR, MCM cable. Continuou line: calculated fom () and (); Dot: expeimental data obtained fom teated ample. The data in Fig. ae fo the modulu of the coil impedance. Fig. how the compaion of the eal and imaginay pat of the coil impedance. gain, thee i a good coelation between theoetical end expeimental eult. nai do V Simpóio Baileio de Sitema Elético, Foz do Iguaçu PR, Bail. -// ISSN 77-
Coil impedance (Ω) 3 3 Zinc laye thickne (µm) Fig.. Real and imaginay pat of the tet coil impedance fo teel tand taken fom the CSR, MCM cable. Thin line: calculated eal pat (eitive); Bold line: calculated imaginay pat (inductive); Coe: expeimental eal data; Tiangle: expeimental imaginay data. In the calculation hown in Fig. and, the zinc conductivity conideed i σ =,7 MS/m. Thi value wa obtained expeimentally and it i omewhat lowe than the conductivity of pue zinc (σ =,9 MS/m). Thi diffeence i likely to be due to impuitie in the zinc ued in the galvanization poce. The zinc conductivity wa obtained by weighting a m ample of galvanized teel tand and alo meauing it DC eitance with a milliohmmete (HP 38). The ample wa ubjected to a chemical teatment to emove all the galvanization and it weight and eitance wee meaued again. Baed on the tand dimenion (length and diamete), ma lo and inceae of eitance, it wa poible to obtain the zinc conductivity. Thi expeimental invetigation wa caied out fo teel wie fom the following cable: CSR 3, MCM (Blue Jay), CSR 79, MCM (Dake), CSR, MCM (Dove), and galvanized teel cable (3/8" OHGW). The eult wee imila to the one hown in Fig. and, which validate (). III. THE CSR CBLE The behavio of a galvanized teel tand wa invetigated in the peviou ection. Thi ection analyze the behavio of a goup of teel tand joined togethe to fom a cable coe, a well a the effect of the aluminum tand of an CSR cable.. Joining Steel Stand Excepting the malle CSR cable that have only a ingle teel tand, mot of CSR cable have eveal teel tand in the coe. common fomation i even tand, with one in the cente and ix tand twited aound the cental one, a hown in Fig. 7. Fig. 7. Seven-tand teel coe and the induced cuent. Fo a longitudinal inducing magnetic field, it i poible to identify two mode of induced cuent: the inta-tand and the inte-tand mode, a hown in Fig. 7. If the inte-tand cuent ae neglected, the effect of having eveal tand inide a ening coil may be modeled the upepoition of the effect of each tand. uming that the tand ae identical, (8) can be adapted in ode to conide n tand in the coil: k n. (9) c The validity of (9) wa veified expeimentally uing a tet coil of 8 tun, 7 mm length, and 3 mm diamete. The coil impedance with ai coe at khz i R =.7 Ω and X = 9.7 Ω. even-tand teel coe ample wa intoduced into the coil and the coil impedance wa meaued. Then one tand wa emoved fom the teel coe and the ix-tand coe wa meaued. Thi poce wa epeated, until only the cental tand emained. The obtained data how the coil impedance a a function of the numbe of teel tand. Fig. 8 how the expeimental data and the theoetical value calculated fom () and (9). It can be een that an excellent ageement wa obtained, which uppot the appoximation ued in the development of (9). Coil impedance (Ω) 7 3 3 7 8 Numbe of tand Fig. 8. Coil impedance modulu a a function of the numbe of tand. Continuou line: calculated value fom (); Dot: expeimental data. B. The luminum Stand Equation () give the epone of a galvanized teel cable that i commonly ued fo OHGW. Howeve, an CSR cable ha alo one o moe laye of aluminum tand aound the teel coe. Theefoe, it i neceay to model the effect of the aluminum tand on the epone of a ening coil. The inte-tand induced cuent on the aluminum laye could povide ome hielding effect to the teel coe. In ode to ae thi effect, ome expeiment wee caied out with ample of typical CSR cable. Each ample had it tand held tightly by uing platic tap and the inne teel tand wee emoved. The hollowed ample wa placed inide a coil excited with altenating cuent. mall pobe coil wa ineted inide the ample, and the voltage induced in thi pobe wa meaued. The expeiment wa epeated without the cable ample, fo the ame cuent in the inducing coil. nai do V Simpóio Baileio de Sitema Elético, Foz do Iguaçu PR, Bail. -// ISSN 77-
The eult obtained fo diffeent type of cable how that the hollowed cable doe not change ignificantly the magnetic field intenity inide the coil. The peence of the aluminum tand poduced a eduction on the magnetic field of le than % of the field meaued without the hollowed cable. Thi eult how that the hielding effect povided by the intetand cuent can be neglected. One poible explanation i that the contact eitance between the tand i lage enough to pevent the flow of ignificant cuent among the tand. Howeve, the cuent induced inide the aluminum tand need to be taken into account (ee the inta-tand cuent if Fig. 7). Thi phenomenon can be modeled by the ame appoach ued in Section II, auming that the cuent in the aluminum tand i confined in a laye defined by the kin depth δ. Fo a non-magnetic conducto, the kin depth i [7]: / f. () Fo intance, conideing the fequency f = khz and the aluminum conductivity (σ = 3. MS/m), the kin depth i 3 µm. the kin depth i not much hote than the tand adiu, an appoximate aumption i neceay in ode to obtain an effective tand adiu fo the application of (). It i aumed that % of the induced eddy cuent flow between the effective adiu e and the eal tand adiu and, of coue, the emaining % flow within e. It i eay to how that thi condition lead to: e.9. () The validity of thi appoximation can be aeed by meauing the epone of a tet coil with aluminum tand. In ode to do o, the teel coe wa emoved fom ample of Gobeak (CSR 3. MCM) and Patidge (CSR,8 MCM) cable. The eulting hollowed cable wee intoduced, one at a time, in a 3 mm diamete tet coil. The coil impedance wa meaued fo diffeent fequencie with and without the hollowed ample. Fig. 9 how the impedance meaued, a well a thoe calculated by () and (). It can be een a good ageement between the theoetical and expeimental eult, which uppot the popoed model fo the aluminum tand. Fig. 9 alo give the coil impedance without the cable, howing that the aluminum tand actually educe the coil impedance. cloe look into the eal and imaginay data how that the eitance inceae due to the loe in the aluminum and the inductance deceae due to the neutalization of the magnetic field within the tand. Coil impedance (Ω) 8 Fequency (khz) Fig. 9. Impedance of a coil containing a hollowed CSR cable. Bold line: coil impedance without cable; thin line: theoetical value fo.8 MCM cable; coe: expeimental data fo.8 MCM cable; dahed line: theoetical value fo 3, MCM cable; tiangle: expeimental data fo 3, MCM cable. C. The Complete CSR Cable Once the effect of the teel and aluminum tand have been modeled, () may be adapted in ode to povide the ening coil impedance fo a complete CSR cable: Z c k Q k Q j X k P k P R X, () a a a a whee P, Q, and k ae given by (), (7), and (8), epectively, uing the data fo the elevant tand, i.e., the ubcipt and a apply to the teel and aluminum tand, epectively. It i woth to emembe that, fo aluminum tand, µ ' = and µ " =. In ode to veify () expeimentally, two CSR cable wee ued. Fo each cable, two ample wee pepaed: one emained intact and the othe had it galvanization totally emoved. The zinc laye thickne wa calculated baed on the ma vaiation, a explained befoe. The ample wee intoduced into ening coil and the eulting impedance wee meaued. Fig..a how the expeimental value obtained fo the cable conideed, while Fig..b how the coeponding theoetical value. It can be een a good ageement between the expeimental and theoetical value: the diffeence emained below % fo the teel tand without galvanization and below % fo the galvanized tand. The highe diffeence fo the galvanized tand i likely due to the uncetaintie elated to the aement of the zinc laye thickne by the lo-of-ma poce. Fig. alo how the eult fo a 3/8" (9. mm) galvanized-teel ovehead gound wie (OHGW), fo compaion. nai do V Simpóio Baileio de Sitema Elético, Foz do Iguaçu PR, Bail. -// ISSN 77-
Tet coil impedance (Ω) (a) Tet coil impedance (Ω) (b) 8 8 Dove Patidge OHGW Dove Patidge OHGW Fig.. Impedance of a coil containing a complete CSR o OHGW cable. Ba with dahe: new galvanization; Ba with bick: no galvanization; (a) Expeimental data; (b) Theoetical data fom (). IV. CONCLUSION The electomagnetic model decibed in thi pape allow the aement of the zinc laye thickne of galvanized teel tand that fom CSR o OHGW cable, in ode to povide an indication of the emaining conducto life. The theoetical eult ageed well with eult of expeiment, which can be eaily epoduced. technique employing thi model ha been uccefully applied to a emote-contolled obot to inpect ovehead conducto. The field tial have been caied out in deenegized and enegized ovehead line, with conitent eult. In ode to apply the eddy cuent inpection in enegized line, the acquied data had to be poceed in ode to emove the powe cuent influence on the teel tand pemeability. Thi data poceing technique will be ubject of a futue publication. method fo detecting and locating flaw in ovehead tanmiion line," IEEE Tan. on Powe Delivey, vol., pp. 8-9, Jul. 99. [] Y. Kojima, J. Fukuda, T. Kumeda, J. Iinuma, and M. Endo, "Cooion detecto obot fo ovehead tanmiion line," Fujikua Technical Review, n., pp. 7-83, 99. [] S. D. Kim and M. M. Moco, "n application of olenoid eno fo inpecting deteioation of CSR conducto due to foet fie," IEEE Powe Engineeing Review, pp. -3, Oct.. [] D. G. Havad, G. Bellamy, P. G. Buchan, H.. Ewing, D. J. Hoock, S. G. Kinaamy, J. Motli, and K. S. Yohiki-Gavelin, "ged CSR conducto, Pat I: Tet pocedue fo conducto and line item," IEEE Tan. on Powe Delivey, vol. 7, n., pp. 8-87, pil 99. [7] D. G. Havad, G. Bellamy, M. K. Biada, C. G. Fajado, D. J. Hoock, J. R. Meale, J. Motli, M. Tabatabai, and K. S. Yohiki- Gavelin, "ged CSR conducto, Pat II: Pediction of emaining life," IEEE Tan. on Powe Delivey, vol. 7, n., pp. 88-9 pil 99. [8] "Inpection & aement of ovehead line conducto: tate-of-thecience epot," EPRI, Palo lto - C,, 8. [9] "Guide to help educe deteioation & extend life of field aged CSR conducto: pplication of available technologie to ae condition of conducto," EPRI, Palo lto - C,, 7. [] "New tool fo conducto evaluation: State of the at eview and pomiing technologie," EPRI, Palo lto - C, 3,. [] L. B. Gelle, D. Pophenoth, J. E. Udd, and D. Hutchinon, "Evaluation of electomagnetic ope tete: Joint Canadian-US wok," Mateial Evaluation, vol.., no., pp. -3, 99. []. V. Pinto J., M. Z. Sebao, C. R. S. C. Louenço, I. S. lmeida, J. Saad, and P. M. Louenço, "Remote detection of intenal cooion in conducto cable of powe tanmiion line," t Int. Conf. on pplied Robotic fo the Powe Induty, Monteal, Canada, Out.. [3] X. L. Jiang, Y. F. Xia, J. L. Hu, F. H. Yin, C. X. Sun, and Z. Xiang, "Optimal deign of MFL eno fo detecting boken teel tand in ovehead powe line," Poge in Elect. Reeach, vol., pp. 3-3,. [] "Diagnoi of intenal cooion technology fo CSR conducto of ovehead powe line", Fujikua New, n. 37, pp., July. [] "Ovehead line cooion detecto", Comon data heet n. PTP. vailable: www.comon.com/poduct/dataheet\ptp.pdf (acce. 8 Jan. 3). [] "Ovehead tanmiion line cooion uveying", tta dataheet. vailable: www.atta.com.au/ovehead-line-cooion-detection (acce. 8 Jan. 3). [7] E. Hallén, "Electomagnetic Theoy," John Wiley & Son Inc., 9. REFERENCES [] J. Sutton and K. G. Lewi, "The detection of intenal cooion in teeleinfoced aluminum ovehead tanmiion line," Poc. of UK Cooion'8, vol., pp. 3-39, Bimingham, UK, 98. [] P. H. Schwabe and D. Pike, "The meauement of cooion in ovehead powe line," nti-cooion, July, 988. [3] K. Komoda, T. Kawahima, M. Mineuma,. Mineyama, M. ihaa, Y. Ebinuma, T. Kanno, and M. Kiuchi, "Electomagnetic induction nai do V Simpóio Baileio de Sitema Elético, Foz do Iguaçu PR, Bail. -// ISSN 77-