High Voltage Cables. Figure Layout of three, single-core cables

Transcription

1 High oltag Cabls 5.0 High oltag Cabls High oltag Cabls a usd whn undgound tansmission is quid. Ths cabls a laid in ducts o may b buid in th gound. Unlik in ovhad lins, ai dos not fom pat of th insulation, and th conducto must b compltly insulatd. Thus cabls a much mo costly than ovhad lins. Also, unlik fo ovhad lins wh tappings can asily givn, cabls must b connctd though cabl boxs which povid th ncssay insulation fo th joint. Cabls hav a much low inductanc than ovhad lins du to th low spacing btwn conducto and ath, but hav a cospondingly high capacitanc, and hnc a much high chaging cunt. High voltag cabls a gnally singl cod, and hnc hav thi spaat insulation and mchanical potction by aths. In th old pap insulatd cabls, th ath was of xtudd lad. Figu 5. ows th such cabls, as usually laid out. Th psnc of th ath intoducs ctain difficultis as cunts a inducd in th ath as wll. This is du to fact that th aths of th conductos coss th magntic filds st up by th conducto cunts. At all points along th cabl, th magntic fild is not th sam, Hnc diffnt voltags a inducd at diffnt points on th ath. This causs ddy cunts to flow in th aths. Ths ddy cunts dpnd mainly on (a) th fquncy of opation, (b) th distanc btwn cabls, (c) th man adius of th ath, and (d) th sistivity of th ath matial. 5. Pow loss in th Cabl Figu 5. - Layout of th, singl-co cabls Pow loss in th cabl can occu du to a vaity of asons (Figu 5.). Thy may b causd by th conducto cunt passing though th sistanc of th conducto - conducto loss (also somtims calld th copp loss on account of th fact that conductos w mainly mad out of copp), dilctic losss causd by th voltag acoss th insulation, ath losss causd by th inducd cunts in th ath, and intath losss causd by ciculating cunts in loops fomd btwn aths of diffnt phass. Th dilctic loss is voltag dpndant, whil th st is cunt dpndant. HFFFFFFFIHFI {FFFFFFFFFMLFFFFFFFMLFFFFFFF¾ Hat gnatd LFNFNFNFMJNK conducto loss dilctic ath & intath loss loss loss Figu 5. - Hat Tansf in a cabl du to losss

2 High oltag Cabls 5.. Dilctic loss Fo a pfct dilctic, th pow facto is zo. Sinc th cabl is not a pfct dilctic, th pow facto is not zo. Th cunt lads th voltag by an angl of lss than 90 o, and hnc th is a pow loss (Figu 5.3). If C is th capacitanc of th cabl, and E is th applid voltag, thn chaging cunt pow loss Th pow loss is popotional to E 5.. Conducto loss i E C & P E I cos 3 (,LQ/ E (i/cos /LQ/ ( C &WDQ/ and tan /, / 3 JFFFFFFFFFFFFFFFFFFF¾ E Figu Loss angl Th conducto loss Pc is givn by Pc I c watt wh c is th sistanc of th conducto and I is th cunt in th cabl Shath loss Th losss occuing in th ath of a cabl is usually obtaind by th mpiical fomula of Anold. Anold's fomula fo th ath loss P is givn by P 7.7 x 0-3 I m d watt wh m d I man adius of ath distanc btwn cabls (cnt to cnt) sistanc of full lngth of cabl cunt in cabl Th ath loss is usually about to 5 % of th conducto loss Intath Loss Intath losss a causd by th inducd mf btwn th aths causing a ciculating cunt. This loss is thus psnt only whn th aths of adjacnt cabls a connctd togth. Th aths nd to b connctd togth in pactic, as othwis spaking could occu causing damag to th aths. Th intath loss Pi can b calculatd as follows. Th mutual inductanc M btwn a co of on cabl and th ath of an adjacnt cabl is givn by Th voltag inducd Ei is givn by M µ d ln π Ei I. &0

3 High oltag Engining - J Lucas, 00 and th inducd cunt Ii is givn by Thfo th intath loss Pi is givn by nally, th ath sistanc >> &0 so that I i P [ + ] [ + ] i I E i ω M i P i I I Th intath loss is lag than th ath loss and may ang fom 0% to 50% of th copp loss. Thus th total pow loss (xclusiv of th dilctic loss) is givn as ω M + ω M ω M i ω M ω M. Total Pow loss Pc + P + Pi P loss I + I 7.7 x 0-3 d m + I ω M Sinc th whol xpssion is dpndant on I, w may xpss th loss in tms of an ffctiv sistanc ff. This givs th total pow loss in tms of th ffctiv sistanc as Ptotal I ff ff c x 0-3 d m + ω M Sinc th ath loss is usually vy small, th ffctiv conducto sistanc can b wittn as 5..5 Coss-bonding of Cabls ff + ω M c Whn th singl phas cabls a usd in pow tansmission, cunts a inducd in th aths and lad to ath ciculating cunts and pow loss. Ths may b substantially ducd, and th cunt ating of th cabl incasd by coss bonding of th cabls (Figu 5.4). Coss bonding of cabls a don xcpt fo vy ot lngths of cabl. a a a FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF HFFFFFFFFFFFFFFFI HFFFFFFFFFFFFFFFI HFFFFFFFFFFFFFFFI JNFFFFFFFFFFFFFFK JFFFFFFFFFFFFFFFK JFFFFFFFFFFFFFFNK b b b FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFFI HFFFFFFFFFFFFFFFI HFFFFFFFFFFFFFFOI JNFFFFFFFFFFFFFFK JFFFFFFFFFFFFFFFK JFFFFFFFFFFFFFFNK c c c HOFFFFFFFFFFFFFFI HFFFFFFFFFFFFFFFI HFFFFFFFFFFFFFFOI FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF JFFFFFFFFFFFFFFFK JFFFFFFFFFFFFFFFK JFFFFFFFFFFFFFFFK Figu Coss bonding of aths

4 High oltag Cabls Th continuity of ach cabl ath is bokn at gula intvals; th cabls btwn two adjacnt discontinuitis bing a mino sction. 3 mino sctions mak up a majo sction, wh th aths a solidly bondd togth and to ath. A sidual ath voltag xists, and th dsid balanc, giving ngligibl ath voltag btwn th solid goundd positions is achivd by tansposing th cabls at ach cossbondd sction. To pvnt xcssiv voltag build up at th coss bondd points, spcially duing faults, ths points a athd though non-lina sistos which limit voltag build up. Th cabl is also tansposd. (Figu 5.5) a HFFFFFFFFFFFFI a HFFFFFFFFFFFFI a FFFFFFFFFFFFFFFFFFFFFF HFFFFFFFFFFFFFFOI FFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFOI FFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFFI JNFFFFFFFFFFFFFFK JNFFFFFFFFFFFFFNK L L JFFFFFFFFFFFFFFNK M M FOF FOF F F b HFFFFFFFFFFFFFI b HFFFFFFFFFFFI b FFFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFOI FFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFOI FFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFOI JNFFFFFFFFFFFFFFK JNFFFFFFFFFFFFFNK L L JFFFFFFFFFFFFFFNK M M FOF FOF F F c HFFFFFFFFFFFFFI c HFFFFFFFFFFFI c FFFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFOI FFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFOI FFFFFFFFFFFFFFFFFFFFF HOFFFFFFFFFFFFFOI JNFFFFFFFFFFFFFFK JNFFFFFFFFFFFFFNK L L JFFFFFFFFFFFFFFNK M M FOF FOF FOF FOF F F F F 5. Impgnatd Pap Insulation Figu Non-lina sisto athing Th insulation consists mainly of pap tap impgnatd with compound. Th pap must b f fom lignous fibs and fom mtallic o oth conducting spots. Th compound with which th pap is insulatd ould b of such a consistncy that it is plastic at odinay tmpatus, and has no tndncy to dain away fom th cabl. Th impgnating compound vais fom manufactu to manufactu,but thy all a basd o paaffinic o naphthnic minal oil, with sin fquntly addd to low th viscosity and to impov its impgnating qualitis. Th pap is mad fom Manila fib o wood pulp. Impgnatd pap can withstand an lctic stss if about 5 to 0 tims that which could b withstood by dy pap insulation. Th dilctic stngth of impgnatd pap is about 00 to 300 k/cm. Initially, thy may b abl to withstand about 400 to 600 k/cm. Th caus of bakdown is usually th non-homognity of th dilctic. Whn a tst voltag is applid, th wakst pat of th dilctic bakdown and dtioation stats gtting mo and mo. This is accntuatd by th fact that th cabl is not caying th sam cunt all th tim. Th dtioation sults in th fomation of voids and gasss. Whn th voltag is aisd, ionisation o glow dischag can occu in th voids and ionic bombadmnt of th sufac. Som of th oil suffs condnsation and hydogn and oth gass a volvd. Thus th long tm bakdown stngth and th instantanous bak down stngths diff. This valu may dcas with tim du to dtioation to about 60 to 00 k/cm. In th cas of a badly impgnatd dilctic, th bakdown stss will continu to dcas and ultimatly lads to bakdown. With th us of a safty facto, not mo than about 40 k/cm is allowd in svic (Figu 5.6).

5 High oltag Engining - J Lucas, 00 b.d.v. 500 M 400 MFFFFFFFFFFFFFFFFFFund pssu (5 atmosphs) 300 M 00 MFFFFFFFFFFFFFFFFFFwithout pssu 00 M 0 OFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF¾ tim (hs) Figu Bakdown voltag chaactistic of pap insulation 5.. Poptis quid of cabl insulation Dilctics usd fo cabl insulation must hav th following poptis.. High Insulation sistanc. High dilctic stngth 3. ood mchanical stngth 4. Immun to attack by acids and alkali in th ang 0-00 o C 5. Should not b too costly 6. Should not b hygoscopic (tnding to absob wat), o if hygoscopic ould b nclosd in a wat tight coving. 5.. Pincipl undlying th dsign of high voltag cabl insulation By mans of dilctic tsts on cabls, it has bn obsvd that th long tm bakdown stss is incasd if th cabl is subjctd to pssu. This is du to th fact that th pssu discouags th fomation of voids. Evn fo a badly impgnatd cabl, th application of pssu impovs th pow facto (o loss tangnt) considably. If th cabl is subjctd to a pssu of about 5 atmosphs, th long tm dilctic stngth impovs to about 400 k/cm and a woking stss of about 50 k/cm may b usd (Figu 5.7). tan / bakdownm stss 400 M (k/cm) (a) (b) 300 M (b) (a) 00 M (c) (c) 0.0 M 00 M Applid stss tim LFFFNFFFNFFFPFFFNFFFNFFFF¾ 0 OFFFFFFFFFFFFFFFFFFFOFFFFFF¾ k/cm 00 (hs) (a) impgnatd ( atmos) (a) 5 atmosphs (b) badly impgnatd ( atmos) (b) 8 atmosphs (c) badly impgnatd (5 atmos) (c) atmosph Figu aiations with pssu

6 High oltag Cabls Compaison of th cuvs fo (a) wll impgnatd cabl at atmosphic pssu, (b) badly impgnatd cabl at atmosphic pssu, and (c) badly impgnatd cabl at a pssu of 5 atmosphs fo about 47 hous, ows th advantags of th pssu on th duction of pow facto. Futh th cuvs ow how th long tm bakdown stss is impovd by pssu. In modn high voltag cabls, with th us of btt matials, th pow facto has bn ducd fom about (0.007 to 0.0) to about (0.00 to 0.003). Fo high voltag cabls, impgnatd pap insulation is vy commonly usd. Th pap is poous and contains in itslf th impgnating compound. Th a no voids psnt as th oil is psnt btwn th lays of th pap which foms th insulation Pap insulatd pow cabls Th conducto of th cabl is standd, and this is lappd ound with th pap tap. It is fist hatd to about 00 oc taking ca not to bun it. A vacuum is thn applid fo 0 to 50 hous to gt id of any tappd ai insid th cabl, and whil still und vacuum, impgnating compound is poud into th tank and thaft a pssu of 50 p.s.i. (about 0.35 MN/m ) is applid. Impgnating of th pap pvnts void fomation in th dilctic, as voids can asily lad to th bakdown of th dilctic. As pap is hygoscopic, a samlss lad ath is xtudd ov th insulation so that no moistu will gt in. Fo high voltags, pssuisd cabls a usd wh th impgnatd pap insulation is kpt und pssu. A pssu of about 5 atmosphs is applid so that any potntial voids would b instantanously filld. Th pssu may b applid by having ith oil o gas und pssu. Whn th cabl is pssuisd, longitudinal infocmnt to pvnt bulging and infocmnt to pvnt hoop stss a usd. With pssuisd cabls, th long tm bakdown stngth dos not diff much fom th ot tm stngth, and as such using a safty facto, a woking stss of about 00 to 0 k/cm may b usd Insulation sistanc Fo a singl co cabl (figu 5.8), th insulation sistanc btwn th conducto and th out ath is givn by th following. ρ. x s π x l x û[ Figu Cabl coss-sction s wh l lngth of s ρ π l cabl (m) dx ρ ln( ) x π l i.. s ρ log0 ( ) x 0 M Ω l wh l lngth of cabl (km)

7 High oltag Engining - J Lucas, Capacitanc in a singl-co cabl Consid a singl co cabl (figu 5.9) with th following data. adius of co (m) adius of athd ath (m) q chag/unit lngth of cabl (C/m) D lctic flux dnsity chag dnsity (C/m ) 0 0 pmittivity of f spac /(4Œ[[ 9 ) F/m Consid an lmntal cylind of adius x and thicknss dx, and of lngth unity along th cabl. q D x π x x, x û[ qfigu Cabl coss-sction D π x lcticstss 9 D q 8x0 xq ε π ε ε x ε x 0 also, d v, d x so that 9 8x0 xq dx dx ε x i.. 8x0 ε 9 q log q log π ε ( /) ( /) capacitnac q ε 9 8x0 log ( /) F/m C ε log (/) 0 µ F/mil 0.04 ε log (/) 0 µ F/km (Fo impgnatd pap insulation, 0 3.5) 5..6 Th-co Cabls Whn th phas pow is bing tansmittd, ith th singl-co cabls o a singl th-co cabl may b usd. In th cas of th singl co cabls, th stss is adial, and its magnitud altnats with tim..0/ F F F F F F F F F F F. 3 3

8 High oltag Cabls.0/ F F F F F F F F F F F / F F F F F F F F F F F. 3 3 In th cas of th 3-co cabl, sinc th cnts of th cos li in a cicl, th lctostatic fild is a somwhat otating fild and not a pulsating on. Typical vaiations of th quipotntial sufacs, fo a fw points of th cycl a illustatd in figu 5.0. Fom ths it will b sn that th fild lins, which a ppndicula to th quipotntial lins, a not adial to th individual cos. Consquntly, th lctic stss is not adial, and tangntial componnts of stss xist. If pap insulation is usd aound ach cos, thn tangntial stsss will b applid along th sufac of th pap ath than just acoss it. Th lctical poptis of pap vais in diffnt dictions. Th ffctiv dilctic stss of pap insulation is much gat acoss th lays than along it. Thus th psnc of tangntial stss in pap insulation lads to gat isk of bakdown Th-co bltd typ Cabls Figu Equipotntial lins in th-co cabls In th cas of a 3-co cabl, th 3-cos a individually insulatd with pap insulation. Th fill spacs btwn th co insulation is also filld up with insulation, but dpiving ths of voids is much mo difficult. Blt insulation is usd on top of all th co insulations, and th lad ath is xtudd ov this. Ov th lad ath, th is gnally bitumn to pvnt damag. In buid cabls, additional potction is ncssay to pvnt damag. Th a two typs of amouing usd fo ths cabls. (i) Stl tap amouing - th stl tap is usually wound in two lays with opposit dictions of lay (ii) Stl wi amouing - th stl wis a laid in on o two lays.

9 High oltag Engining - J Lucas, 00 Capacitanc of 3-co bltd typ Th capacitanc btwn th conducto to nutal of 3-co bltd cabls (Figu 5.) cannot b obtaind by a simpl divation as fo th singl co cabl. Simon's xpssion can b usd to obtain this valu. conducto Th capacitanc p unit lngth to nutal is givn by If t thicknss of blt insulation T thicknss of conducto insulation d diamt of conducto 0 dilctic constant C0 log 0 t 0.5 T 0.03 ε t T +t T d Masumnt of capacitanc of 3-co cabls µ F/km Figu co bltd cabl Shath Cs In th-co cabls, capacitanc dos not hav a singl valu, but can b lumpd as own in figu 5.. C C Capacitanc btwn ach co and ath Cs Cs Cs Capacitanc btwn cos C Ths can b spaatd fom masumnts as dscibd in th following C sction. Figu 5. - Cabl Capacitancs Cs (a) Stap th 3 cos togth and masu th capacitanc btwn this bundl and th ath as own in figu 5.3. Cs Cs Masud valu Cm 3 Cs This givs th capacitanc to th ath as Cs Cm/3 (b) Connct of th cos to th ath and masu btwn th maining co and th ath (Figu 5.4) I HFFFFFFFFI ---M%ULJHL-K JFFFFFFFFK Figu Capacitanc masumnt Masud valu Cm C + Cs i.. C (Cm - Cs)/ (3 Cm - Cm)/6 C C Cs which givs th capacitanc btwn th conductos. FFFFFFI C HFFFFFFFFI FM%ULJHLFK JFFFFFFFFK Figu Capacitanc masumnt

10 High oltag Cabls Cs Th ffctiv capacitanc to nutal Co of any of th cos may b obtaind by considing th sta quivalnt (Figu 5.5). This givs 3C 3C C0 C s + 3C C 3 m 3C + 3 m - C 6 m Cs 3C Cs C 0 3 C m - 6 C m Figu Calculation of Co In th bakdown of actual 3-co bltd cabls, it is gnally obsvd that chaing occus at thos placs wh th stss is tangntial to th lays of pap. Thus fo th insulation to b ffctiv, th tangntial stsss in pap insulation ould b pfably avoidd. This can usually b accomplid only scning ach co spaatly (o by having individual lad aths fo ach of th cos), so that th cabl in ffct bcoms 3 individual cabls laid within th sam potctiv coving Hochstadt o "H" typ Cabl In this typ of cabl (Figu 5.6), th is no blt insulation. Th scning of individual cos is gnally thin and flxibl so that th is not much pow dissipation in thm. All th individual scns a athd so that th potntial at ths aths a all zo and thus th stss lins btwn th cos and scns would b now adial. pap insulation pap woming mtallisd pap copp wovn fabic lad ath conducto Figu H-typ cabl Th scns a thin so that th is hadly any cunt inducd. Th aths suounding th insulation of th cos consist of mtallisd pfoatd pap. Ths a wappd ound with copp wovn fabic (cotton tap into which a wovn copp wi). This out scn is in contact with th inn scns and is athd. Th cabl has th additional advantag that th spaation of th cos by thmal xpansion o mchanical displacmnt cannot intoduc stsss in th dilctic. Th mtallisd scns hlp to dissipat th hat. Ths a usd upto 66 k. In th H-typ cabl, th individual cos contain no lad coving. Th th cos a laid up with fills in th odinay way. If th cabl is to b buid, thn th cabl is amoud with stl wi and tap. Th womings of th H-typ cabl a full of oil S.L. typ Cabl Anoth dvlopmnt of th scning pincipl is th SL typ cabl (Figu 5.7). In this, ach co is scnd and thn individually athd with lad o aluminium. Ths do not hav an ovall lad ath.

11 High oltag Engining - J Lucas, 00 co insulation compound jut woming lad ath co cotton tap Th lctic fild in th insulation suounding ach co is natually adial and th function of th scns in this cas is to liminat th possibility of any stss acoss th claanc spac btwn co and ath. Th womings of th fill spacs in th S.L. typ cabls do not contain much oil as do not gt any lctic stss. Th th mtal athd cos, aft bing lappd with pap and cotton taps a laid with tad jut yan to gt a cicula fomation and thn wappd with hssian taps to fom a bdding fo th amouing. Th lctical and thmal advantags of H-typ cabls a also njoyd by th S.L. typ cabls. Ths cabls a suitabl fo hilly outs, as th absnc of oil in th fill spacs lssns th isk of oil dainag. Also, th S.L. typ constuction is usful on ot uns bcaus th tminating quipmnt is simplifid. Also th void fomation in th fill spacs a of no consqunc. Th spaat lad aths in th S.L. cabl a th sats of inducd cunts, but th sulting losss a small, and appa to b of no pactical significanc Copp Spac Facto Figu S L typ cabl Unlik in ovhad lins, insulation in cabls occupis a gat potion of th cabl spac. Thus high installation costs a involvd. Idally w would lik th insulation to occupy th minimum possibl thicknss. Thus w dfin a spac facto to indicat th utilisation of th spac. Th copp spac facto is dfind as copp spac facto coss-sction aa of conducto coss-sction aa of whol cabl Fo a singl co cabl, th bst spac facto is obtaind with a concntic aangmnt (Figu 5.8), as this givs th minimum conducto pimt fo th gatst conducto aa and givn insulation thicknss. Thus Spac facto / Fo th 3-co cabl (Figu 5.9), consisting of cicula conductos within a cicula ath, Figu 5.8 Spac facto 3 / wh T thicknss of co insulation, t thicknss of blt insulation t T and + T Howv, fo th 3-co cabl th cicula coss-sction is not th bst ap fo th conductos. Figu th-co cabl

12 High oltag Cabls Oth aps which givs btt spac factos a th lliptical apd conductos and th scto apd conductos (Figu 5.0). Figu Spcial aps of conductos to giv btt spac factos 5.3 Dilctic Stss in a Singl Co Cabl Th voltag diffnc acoss th conducto and th ath of a singl co cabl is givn by v q log π ε, also, q x π ε x so that x v x log It is sn that sinc x is th only vaiabl, th imum stss in th dilctic occus at th minimum valu of th adius x (i.. x ). i.. log Sinc it is quid that this imum stss in th dilctic ould b as low as possibl, diffntiating with spct to fo minimum givs d d 0 i.. log /. log i...78 Thus if th ovall diamt of th cabl is kpt fixd, thn / is th condition fo minimum. This valu of adius of conducto will gnally b lag than would b quid fo cunt caying capacity.

13 High oltag Engining - J Lucas, 00 Sinc /, th minimum valu of is givn by log / Sinc th adius of th conducto that would b givn fom th abov xpssion is lag than is ncssay fo cunt caying capacity, this valu of adius may b achivd by using Aluminium o hollow conductos. As can b sn (Figu 5.), th dilctic is not qually stssd at all adii, in a cabl of homognous insulation. Th insulation is fully stssd only at th conducto, and futh away na th ath th insulation is unncssaily stong and thus ndlssly xpnsiv Cabl ading fo Unifom Stss Distibution Th lctic stss in th dilctic may b mo qually distibutd by on of th two following mthods. (i) Capacitanc gading (ii) Intath gading 5.3. Capacitanc ading In this mthod of gading, th insulation matial consists of vaious lays having diffnt pmittivitis. Consid a cabl gadd by mans of 3 lays of insulation, as own in Figu 5., having pmittivitis 0, 0, 03, spctivly. Lt th out adii of ths lays by, and 3 spctivly, an th conducto adius. In od to scu th sam valu of imum stss in ach lay, th imum stsss in th lays a quatd. Lt th voltag acoss th inn-most lay of insulation b. Thn m 0 x Figu 5. - Stss Distibution q q π ε 0 ε π ε 0 ε q π ε 0 ε 3 m m m3 ε ε ε 3 log 0 x similaly, 3 can b dtmind Figu 5. - Capacitanc ading

14 High oltag Cabls Thfo th total voltag acoss th dilctic can b obtaind as follows. ln + ln ln + ln + ln +( ln +( - ) ln > log, sinc + - ) ln +( >, 3 ln - ) ln +( > - ) ln Hnc by gading th insulation, without incasing th ovall diamt of th cabl, th opating voltag can b aisd. A difficulty with this mthod is that w cannot obtain a wid ang of pmittivitis in pactic, as pap insulation has pmittivitis limitd to th ang.8 to 4.0. In th abov analysis, it has bn assumd that th imum pmissibl stss is th sam fo all th dilctics usd. If th imum stss in th th sctions a diffnt, and a,, 3 spctivly, thn th imum stsss ould b achd at th sam tim fo th most conomical opation of th insulation. This condition givs us th sult Intath ading ε ε 3 3 ε In this mthod of gading, th sam insulating matial is usd thoughout th cabl, but is dividd into two o mo lays by mans of cylindical scns o intaths (Figu 5.3). Ths intaths a connctd to tappings fom th supply tansfom, and th potntials a maintaind at such valus that ach lay of insulation taks its pop a of th total voltag. Th intaths a lativly flimsy, and a mant to cay only th chaging cunt. 3 Sinc th is a dfinit potntial diffnc btwn th inn and out adii of ach ath, w can tat ach sction spaatly as a singl co cabl. If,, 3,... a th potntial diffncs acoss th sctions of insulation, thn log log... Sinc th cabl insulation now consists of a numb of capacitos in sis, fomd by th spctiv intaths, all potntial diffncs,, 3,... a in phas. Thus, if is th phas to nutal voltag, w can also wit n m Figu Intath ading 0 x

15 High oltag Engining - J Lucas, 00 In th paticula cas that all th n lays hav th sam thicknss d, and if is th conducto adius, + d; + d; 3 + 3d;... n + n d + d log ( + d) log wh M n ( + (m -) d) m + d + d log... M + m d + (m -) d Th voltag acoss th m th sction is givn by m [ +(m - ) d] log M + m d +(m - ) d Hnc substituting fo th diffnt valus of m, w can obtain th voltag acoss th vaious lays that hav to b maintaind to giv qual imum stss in ach sction. In pactic, th is a considabl difficulty in aanging fo many intaths, this difficulty bing mainly associatd with th povision of th diffnt voltags fo th intaths, and as a sult it is usual to dsign a cabl of this typ with only on intath. This simplifis th dsign calculations, and th xpssion fo th imum stss thn givn by log + log Fo th pupos of compaison with th ungadd cabl, lt us fist tak th optimally dsignd ungadd cabl (i.. with / ), and intoduc an intath at a adius. Sinc and a both kpt fixd, is th only vaiabl, and th xpssion fo stss must b diffntiatd with spct to to obtain th condition fo th minimum valu of th imum stss. i.. -+ log + 0 considing, also log log 0 so that log This givs th solution.76.

16 High oltag Cabls.76 log.76 + log Howv, fo th cabl without intath, w hav /. Hnc, th addition of th intath aiss th imum applicabl voltag by 33%. Now lt us consid th cas of only th ovall diamt of th cabl bing fixd, and both and bing vaiabl. Thn fo minimum valu of th imum stss w hav 0, 0 i.. log - 0, also -+ log + 0 i.., -+ log + 0 This givs log - giving.88 log + log - + i Pssuisd High oltag Cabls In high voltag pap insulatd cabls, th application of pssu (about 3 atmosphs) incass th imum allowabl woking stss (aft applying a suitabl safty facto) fom about 50 k/cm to about 50 k/cm. In sup voltag cabls, th void contol is ffctd by pssuising th oil-impgnatd pap tap insulation by (a) pssuising th oil, and (b) applying gas pssu Oil-pssu cabls In oil filld cabls, th oil must b f to flow inod to tansmit th pssu. Th imum pssu of oil utilisd is about 0.35 MN/m (3.5 atmosphs o 50 p.s.i.). Du to th pssu of oil, th ath tnds to bulg out and thfo infocmnt of th athing is ncssay. A svoi maintains th quid pssu. Th cabl can now opat at a imum woking stss of 50 k/cm. In nomal, solid typ of cabl, th dying and impgnating a don bfo athing, whil in oil-filld cabls thy can b don aft athing by ciculating hot oil. Th oil filld constuction pmits a gat duction in siz of th cabl.

17 High oltag Engining - J Lucas, 00 Th a 3 main typs of oil filld cabls. Ths a (a) singl-co, conducto channl; (b) singl-co, ath channl; and (c) th-co, fill-spac channls. (a) Singl-co conducto channl Oil duct Lad ath hollow conducto pap insulation hlical ibbon infocmnt This typ of cabl own in figu 5.4 has a hollow conducto which acts as an oil channl, and is th simplst fom th point of viw of th cabl itslf. A disadvantag of this aangmnt is that th oil is at high voltag with spct to ath bing at th voltag of th conducto. Th copp stands of which th conducto is mad a laid ov a hlical mtal ibb, so that oil can ach th insulation. (b) Singl-co ath channl Figu Singl co conducto channl cabl goovd lad ath oil channls pap insulation Figu Singl co ath channl cabl lad ath button-stampd hlical spac ibbon In this typ (Figu 5.5), th oil channls a poducd ith by gooving th ath o by aanging spacs btwn ath and insulation. Th sistanc to oil flow in this typ is 6 to 8 tims that of typ (a), so that mo fding points a ncssay to maintain th pssu. An advantag is that th channls a at ath potntial so that joints and installation a simpl. (c) Th-co, fill spac channls lad ath pap insulation pap fill pfoatd oil-ducts Figu Th co fill spac channl cabl

18 High oltag Cabls In this typ (Figu 5.6), th oil channls a locatd in th fill spacs. Ths channls a composd of pfoatd mtal-ibbon tubing and a at ath potntial as-pssu cabls In as pssu cabls, a pssu of about.4 MN/m (4 atmosphs o 00 p.s.i.) is usd. Figu 5.7 ows th diffnt typs of gas pssu cabls. as Pssu (4 atmosphs) HFFFFFFFFFFFFFFFFFFFFFFFOFFFFFFFFFFFFFFFFFFFFFFI Extnal Pssu Intnal Pssu HFFFFFFFFFOFFFFFFFFFIHFFFFFFFFFFFFFFNFFFOFFFFFFFFFFI Pip lin typ slf-containd high pssu gas impgnatd typ gas -filld cuion pssuisd Extnal Pssu Cabls Pip lin typ Figu Typs of gas pssu cabls Stl pip-lin Nitogn at 00 p.s.i. thin mtal tap tiangula lad ath (mmban) Figu Pip lin typ cabl Th cabl, own in Figu 5.8, is manufactud in th usual way and th outsid is mad tiangula, and covd by a diaphagm lad ath. Th pip is filld with Nitogn subjctd to a pssu of 00 p.s.i. which is tansmittd to th insulation though th diaphagm. Th stl pip is laid fist, and th cabl is dawn in aftwads. Nitogn und pssu is thn intoducd into th pip. Th pssu is tansmittd to th mmban though th mmban. In th Slf-containd typ, an additional infocd lad ath is usd, but othwis th pincipl is th sam as that of th pip lin typ Intnal Pssu Cabls In th intnal pssu cabls, th gas is in contact with th dilctic.

19 High oltag Engining - J Lucas, 00 (a) as filld cabls lad alloy ath Annula gas passag Pap impgnation copp wovn fabic infocmnt tap cotton tap In ths cabls (Figu 5.9), spacs a lft btwn th convolutions so that th gas is btwn thm. Th psnc of Nitogn pvnts th fomation of voids. Th mthod of manufactu is such that th gas can mov fly insid packts, but cannot diffus outsid th insulation. (b) as cuion typ spaat gas cuions Figu as filld cabl FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ubb tap FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF sald Figu as Cuion Typ cabl (This typ own in Figu 5.30 is not of much pactical us but only of acadmic us). In this typ, a scnd spac is povidd btwn th lad ath and th dilctic, this spac poviding accommodation at all points along th lngth of th cabl fo th stoag of int gas und pssu. This stoag is maintaind by th subdivision of th scnd spac into a sis of gas cuions by mans of bais, with th sult that th cabl may b cut fo joining without losing gas fom mo than a ot lngth. (c) Impgnatd pssuisd cabl mtallisd pap scn mtal scn gas channl standd conducto (tinnd copp) Copp wovn fabic tap bind lad ath Figu Impgnatd Pssuizd cabl In th manufactu of this typ of cabl (Figu 5.3), povision is mad fo longitudinal gas flow, and th impgnating compounds usd a suitabl fo th high dilctic stsss ncssay fo high voltag cabls. Th cabl has a mass impgnatd pap dilctic and th impgnating oil is maintaind und a pssu of 00 p.s.i. by mans of nitogn. Spcial infocmnt is povidd to cat fo th lag hoop and longitudinal stsss st up.

20 High oltag Cabls Th co is standd and is covd with a mtallisd pap scn so as to obtain a compltly unifom stss. Th gas channl is in on of th fill spacs. 5.5 Thmal Dsign of Cabls Undgound cabls a installd in tnchs of ctangula coss-sction. Aft xcavation of th tnch, a lay of sand is placd in it to sv as a bdding, as own in Figu 5.3. Ai (T A) back fill dpth of buial undistubd gound sving cov til sand bdding insulation conducto ath Th lngth of cabl is pulld in along th tnch and covd with a futh lay of sand. Sand f fom flints and ston is mployd to avoid damag to th cabl sving duing pulling and initial back filling. Abov th cabl and sand bdding a placd cov tils to potct th cabl fom mchanical damag fom subsqunt xcavation activitis. Th xcavatd matial is placd in th tnch and stampd to consolidat it. Th minimum tnch width that can b convnintly xcavatd is about 700 mm (7 inchs), and fo safty asons, th minimum dpth of buial in nomal cicumstancs is 900 mm (36 inchs). An undgound cabl caying cunt will hav in addition to th conducto loss, dilctic loss and losss in th ath. Ths poduc hat which a conductd away fom th cabl to th sufac, poducing a tmpatu gadint. Whn mo than on singl co cabl is laid togth (as is quid fo th phas systms xcding 50 k), th hat poducd by on conducto affcts th oth and th hat factos nd to b modifid. Whn th spacing btwn th cabls is incasd, th hat poducd by th ciculating cunts btwn th cabls will incas whas th ddy cunt losss dcas. Thus th is an optimum spacing fo cabls and vaious altnativs may hav to b valuatd bfo th conomic aangmnt is finally slctd Cunt ating of Cabls ½FFFFFFFFF 7UHQFKZLWKFFFFF FFF ¾ Figu Coss-sction of Tnch and buid cabl In a cabl, th facto which ultimatly limits th cunt caying capacity is th imum opating tmpatu which may b sustaind by th cabl thoughout its lif without isk of damag o dtioation. As was discussd in an ali sction, th hat gnatd in th cabl is du to (a) ohmic loss in th conducto, (b) th dilctic loss in th insulating mdium and (c) th ath and intath losss. Th hat so gnatd is adiatd to th suoundings. Th cunt that can b caid dpnds on th conductivity of th suounding mdium as wll, so that th sam cabl would hav diffnt atings dpnding on whth th cabl is buid o not.

21 High oltag Engining - J Lucas, Thmal sistanc Sinc th flow of hat can b considd analogous to th flow of chag o cunt in th insulation, th thmal sistanc of th cabl and suoundings is masud in tms of th thmal ohm. Thmal Ohm: Th thmal ohm is th sistanc of a path though which a tmpatu diffnc of 0 C poducs a hat flow of watt. Thmal sistivity: Th thmal sistivity is th tmpatu dop in dg cntigad poducd by th flow of watt btwn th opposit facs of a mt cub of th matial. Consid a cabl buid und th sufac of th ath. FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF Figu Hat flow lins fom buid cabl Lt imum allowabl diffnc in tmpatu btwn th co and suoundings ( o C) Effctiv sistanc of conducto (including ffcts of ath loss) I Cunt caid by conducto H Hat poducd in th co (W) S' Thmal sistanc of dilctic S" Thmal sistanc of cabl outsid dilctic S S' + S" Total thmal sistanc of cabl Thmal sistanc of gound fom cabl to suoundings Fom th dfinition, th total tmpatu is btwn th conducto and th suoundings is givn by +6* Total pow loss dilctic loss (Wd) + ohmic loss (I ) At quilibium, th total pow loss must qual to th hat poducd. θ H W d + I θ S + i.. θ (Wd + I θ) (S + ) This givs th cunt ating of th cabl as I θ - W d (S +) θ (S +)

22 High oltag Cabls In calculating th flow if hat it is usful to to mmb th following analogis. Hat Elcticity Elctostatic Elctomagntic Tmpatu Diffnc Potntial diffnc Potntial diffnc magntomotiv foc (mmf) Hat Flow H Cunt I Elctic chag Q Magntic flux 3 Thmal sistanc S sistanc /Capacitanc luctanc If a mthod xists to study any of th abov phnomna, th analogous quantity can also b studid by compaison Thmal sistanc of singl-co cabl qui-tmpatu lins H qui-potntial lins q x dx lins of hat flow lins of chag flow x dx Figu Analogous hat-flow and chag-flow lins Th analysis of this poblm is simila to th analysis of th analogous lctostatic cas. Figu 5.34 ows ths two cass. In th hat poblm, H is th amount of hat gnatd p unit lngth of cabl, and in th cosponding lctostatic cas, q is th lctic flux flowing out p unit lngth. Fo th lctostatic cas, consid a gaussian cylind of adius x and thicknss dx. D. Œ[O TWKDW' TŒ[ q, ε π x wh ε ε 0 ε q q.. d x π ε x π ε log Considing th analogous hat flow cas, Lt d dop in tmpatu acoss dx k thmal sistivity

23 High oltag Engining - J Lucas, 00 Thmal sistanc is +WKDW Thmal sistanc of th-co cabls k. H. dx thn dθ π x k H intgation givs θ log π thmal sistanc k S log π Fo th-co cabls, th following two quip xpssions a usd. k 0. t (i) S ln 6 π T t thicknss of T thicknss of adius of.t T +t T wh blt insulation conducto insulation conducto Ω/ km 6 k ln (ii) S 6 π 3 wh a adius at which th cntsof adius of out adius of 6 - a a 3 conducto ach conducto lis dilctic Thmal sistanc of potctiv covings Sinc th potctiv coving of th cabl is in th fom of a cylind, th xpssion is of th sam fom as that fo a singl co cabl. k 3 - A/ S ln π + A/ wh 3 adius of out coving of cabl adius of lad ath A thicknss of amouing k thmal sistivity Thmal sistanc of gound aound cabl Insid th cabl constant tmpatu lins would all b concntic cylinds sinc th out lad ath is a conducto of hat. Th flow of hat would consquntly b adial. Howv, outsid th cabl, th qui-tmpatu lins would no long b concntic and th hat flow would go adially outwads fom th sufac of th cabl and nding up at th sufac of th gound nomally (assuming that th sufac of th ath is at a constant tmpatu).

24 High oltag Cabls H again, lt us analys using th analogy of th infinitly long conducto caying a chag q p unit lngth, placd at a distanc h abov th ath sufac (Figu 5.35). -H q h ath ath Hat flow h chag flow h H q Figu Effct of Eath Sufac This has th sam ffct as having a chag of -q at th sam distanc bnath th ath. Th ffct of th ath can b placd by an qual and opposit chag on th opposit sid of th sufac at th sam distanc fom th sufac. Th ffcts of th chag +q and -q can now b spaatly considd, and th sults supimposd. Each chag considd spaatly will giv is to adial flux lins. Th potntial diffnc btwn th chags causd by on of th chags is givn by q π log ε Th total potntial diffnc causd btwn th chags is twic that of th individual chag. This is qual to q - (- q) h q h log log π ε π ε h Thus th potntial diffnc to th nutal of ach conducto is givn as q π log ε h Analogy: Th tmpatu diffnc fom th hat souc to ath is givn by θ k H log π h

25 High oltag Engining - J Lucas, 00 Thus th thmal sistanc of th gound is givn by Whn applid to th pactical cas, it is found that th thotical thmal sistanc a found abov has to b multiplid by a facto of /3. This is bcaus w hav assumd th ath to b a plan of pfct conductivity (o constant tmpatu). Thus th modifid thmal sistanc of th gound fo pactical application is givn by A psntativ valu of th thmal sistivity k of th soil of avag moistu contnt is Cabls xposd to ai Th hat dissipation of a cabl xposd to th ai dpnds on th adiation. Fo a sufac in dict contact with th ai, with unstictd vntilation, th hat dissipation is givn by.5 H π ( θ s -θ a ) watt/cm of lngth wh 5.6 High oltag Buings Buings a insulatos which a usd to tak high voltag conductos though athd bais such as walls, floos, mtal, tanks tc. Th buings hav to povid lctical insulation of th conducto fo th woking voltag and fo vaious ov-voltags which may occu in svic and also hav to povid mchanical suppot against vaious mchanical focs Simpl cylindical buing k thmal sistanc xnal k H 3π θ k H log H π log h adius of cabl, usually of h lad ath, θ s tmpatu of cabl sufac, θ a ambint tmpatu, missivity constant whos valu vais with buing L t voltag to ath liv conductos athd bai adius x Figu Simpl cylindical buing Th simplst fom of buing is a cylind of insulating matial aound th conducto (Figu 5.36), with adial claanc t ( - ) and axial lngth L to suit lctical stngths of th insulating matial and suounding mdia.

26 High oltag Cabls In this cas, th voltag distibution with adius x is not lina so that th matial is not qually stssd. Th xpssions fo stss and voltag to ath x at adius x is givn by, x ln x Th imum stss in th buing occus at th conducto sufac (i.. at x ), so that so that th thicknss t quid fo th buing is givn by t xp t + ln x x ln +t log Thus as th voltag incass, th dimnsions quid bcom vy lag, so much so that fo vy high voltags, simpl cylindical buings of this fom a not satisfactoy. Upto about 66 k, poclain buings (with o without oil) may b usd Condns buing Th difficulty of th dimnsions incasing apidly is ovcom by th condns buing. In this cas, th busing is dividd into a numb of capacitos by concntic cylinds of mtallic foil o mtallic coatd pap. By pop choic of lngths of ths cylinds, it is possibl to obtain a naly unifom voltag distibution with adius (Figu 5.37). HI quipotntial HFfFFK athd flang cylinds FFFFFOFiFFFOFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF liv conducto FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFF FFFFNFfFFFNFFFFFFFFFF JFiFFI JK Figu Condns Buing Sinc th stss is now mad unifom, it must b qual to th atio of th applid voltag to th thicknss t' of th insulation. t, so that t As can b sn whn compaing with th simpl buing, th thicknss t' quid now is much lss than t.

27 High oltag Engining - J Lucas, 00 Exampl A condns buing fo an.m.s. voltag of 30 k to ath is dsignd to hav a unifom adial voltag gadint (Figu 5.38). Th insulating matial usd has a imum pmissibl woking voltag stss of 0 k/cm (pak). Assuming a unifom and vy small thicknss of insulation btwn ach succssiv foil, dtmin th adial thicknss t' of th buing. If th lngth of th buing at th outmost adius is 0 cm, dtmin th lngth at th sufac of th conducto (adius cm). Estimat also th thicknss t fo th buing without foils, if it is to hav th sam imum adial stss. 0 cm FFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFF FFOFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFOFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF ½FFFFFFFFFFFFFFFFFFFFFFF l FFFFFFFFFFFFFFFFFFFFFF¾ Figu Lngth of Condns Buing Sinc stss is unifom, t cm 0 Th pofil of th buing has th quation y a/x, at x t' +, y 0 cm, so that a 0(t' + ) 0(4.4 + ) thfo, x.y a 6.4 at x, y l thfo, l 6.4/x 6.4/ 3. cm In th absnc of foils, i.. + +t log log (+ t 8.34 t) log. t + t x cm Thus in th absnc of gading, it is sn that a much gat thicknss of insulation is quid (4.68 cm as compad to 4.4 cm). In addition to th simpl cylind buing, and th condns typ buing, th a oth typs of buings, which may consist of mo than on matial.