5 Equivalent Circuits and Parameters of Power System Plant

Transcription

1 Equivlent Circuits nd Prmeters of Power System Plnt Introduction 5.1 Synchronous mchines 5. Armture rection 5. Stedy stte theory 5.4 Slient pole rotor 5.5 Trnsient nlysis 5.6 Asymmetry 5.7 Mchine rectnces 5.8 Negtive sequence rectnce 5.9 Zero sequence rectnce 5.10 Direct nd qudrture xis vlues 5.11 Effect of sturtion on mchine rectnces 5.1 Trnsformers 5.1 Trnsformer positive sequence equivlent circuits 5.14 Trnsformer zero sequence equivlent circuits 5.15 Auto-trnsformers 5.16 Trnsformer impednces 5.17 Overhed lines nd cles 5.18 Clcultion of series impednce 5.19 Clcultion of shunt impednce 5.0 Overhed line circuits with or without erth wires 5.1 OHL equivlent circuits 5. Cle circuits 5. Overhed line nd cle dt 5.4 References 5.5

2 Equivlent Circuits nd Prmeters of Power System Plnt 5.1 INTRODUCTION Knowledge of the ehviour of the principl electricl system plnt items under norml nd fult conditions is prerequisite for the proper ppliction of protection. This chpter summrises sic synchronous mchine, trnsformer nd trnsmission line theory nd gives equivlent circuits nd prmeters so tht fult study cn e successfully completed efore the selection nd ppliction of the protection systems descried in lter chpters. Only wht might e referred to s 'trditionl' synchronous mchine theory is covered, s tht is ll tht clcultions for fult level studies generlly require. Reders interested in more dvnced models of synchronous mchines re referred to the numerous ppers on the suject, of which reference [5.1] is good strting point. Power system plnt my e divided into two rod groups - sttic nd rotting. The modelling of sttic plnt for fult level clcultions provides few difficulties, s plnt prmeters generlly do not chnge during the period of interest following fult inception. The prolem in modelling rotting plnt is tht the prmeters chnge depending on the response to chnge in power system conditions. 5. SYNCHRONOUS MACHINES There re two min types of synchronous mchine: cylindricl rotor nd slient pole. In generl, the former is confined to nd 4 pole turine genertors, while slient pole types re uilt with 4 poles upwrds nd include most clsses of duty. Both clsses of mchine re similr in so fr tht ech hs sttor crrying three-phse winding distriuted over its inner periphery. Within the sttor ore is crried the rotor which is mgnetised y winding crrying d.c. current. The essentil difference etween the two clsses of mchine lies in the rotor construction. The cylindricl rotor type hs uniformly cylindricl rotor tht crries its excittion winding distriuted over numer of slots Network Protection & Automtion Guide 47

3 Equivlent Circuits nd Prmeters of Power System Plnt round its periphery. This construction is unsuited to multi-polr mchines ut it is very sound mechniclly. Hence it is prticulrly well dpted for the highest speed electricl mchines nd is universlly employed for pole units, plus some 4 pole units. The slient pole type hs poles tht re physiclly seprte, ech crrying concentrted excittion winding. This type of construction is in mny wys complementry to tht of the cylindricl rotor nd is employed in mchines hving 4 poles or more. Except in specil cses its use is exclusive in mchines hving more thn 6 poles. Figure 5.1 illustrtes typicl lrge cylindricl rotor genertor instlled in power plnt. Two nd four pole genertors re most often used in pplictions where stem or gs turines re used s the driver. This is ecuse the stem turine tends to e suited to high rottionl speeds. Four pole stem turine genertors re most often found in nucler power sttions s the reltive wetness of the stem mkes the high rottionl speed of two-pole design unsuitle. Most genertors with gs turine drivers re four pole mchines to otin enhnced mechnicl strength in the rotor- since gerox is often used to couple the power turine to the genertor, the choice of synchronous speed of the genertor is not suject to the sme constrints s with stem turines. Genertors with diesel engine drivers re invrily of four or more pole design, to mtch the running speed of the driver without using gerox. Four-stroke diesel engines usully hve higher running speed thn twostroke engines, so genertors hving four or six poles re most common. Two-stroke diesel engines re often derivtives of mrine designs with reltively lrge outputs (circ 0MW is possile) nd my hve running speeds of the order of 15rpm. This requires genertor with lrge numer of poles (48 for 15rpm, 50Hz genertor) nd consequently is of lrge dimeter nd short xil length. This is contrst to turine-driven mchines tht re of smll dimeter nd long xil length. Wek Strong Wek Strong N N Direction of rottion () S () S Figure 5.: Distortion of flux due to rmture rection N Figure 5.1: Lrge synchronous genertor 48 Network Protection & Automtion Guide

4 5. ARMATURE REACTION Armture rection hs the gretest effect on the opertion of synchronous mchine with respect oth to the lod ngle t which it opertes nd to the mount of excittion tht it needs. The phenomenon is most esily explined y considering simplified idel genertor with full pitch winding operting t unity p.f., zero lg p.f. nd zero led p.f. When operting t unity p.f., the voltge nd current in the sttor re in phse, the sttor current producing cross mgnetising mgneto-motive force (m.m.f.) which intercts with tht of the rotor, resulting in distortion of flux cross the pole fce. As cn e seen from Figure 5.() the tendency is to weken the flux t the leding edge or effectively to distort the field in mnner equivlent to shift ginst the direction of rottion. If the power fctor were reduced to zero lgging, the current in the sttor would rech its mximum 90 fter the voltge nd the rotor would therefore e in the position shown in Figure 5.(). The sttor m.m.f. is now cting in direct opposition to the field. Similrly, for opertion t zero leding power fctor, the sttor m.m.f. would directly ssist the rotor m.m.f. This m.m.f. rising from current flowing in the sttor is known s 'rmture rection' STEADY STATE THEORY The vector digrm of single cylindricl rotor synchronous mchine is shown in Figure 5., ssuming tht the mgnetic circuit is unsturted, the ir-gp is uniform nd ll vrile quntities re sinusoidl. Further, since the rectnce of mchines is normlly very much lrger thn the resistnce, the ltter hs een neglected. The excittion mpere-turns, AT e, produces flux Φ cross the ir-gp therey inducing voltge, E t, in the sttor. This voltge drives current I t power fctor cos -1 φ nd gives rise to n rmture rection m.m.f. AT r in phse with it. The m.m.f. AT f resulting from the comintion of these two m.m.f. vectors (see Figure 5.()) is the excittion which must e provided on the rotor to mintin flux Φ cross the ir-gp. Rotting the rotor m.m.f. digrm, Figure 5.(), clockwise until coincides with E t nd chnging the scle of the digrm so tht AT e ecomes the sic unit, where AT e = E t =1, results in Figure 5.(). The m.m.f. vectors hve thus ecome, in effect, voltge vectors. For exmple AT r /AT e is unit of voltge tht is directly proportionl to the sttor lod current. This vector cn e fully represented y rectnce nd in prctice this is clled 'rmture rection rectnce' nd is denoted y X d. Similrly, the remining side of the tringle ecomes AT f /AT e, which is the per unit voltge produced on open circuit y mpere-turns AT f. It cn e considered s the internl generted voltge of the mchine nd is designted E o. AT r AT r IX d E o AT e AT f () AT r AT AT e f AT e E t =1=V I AT e AT f () IX d E t (=V) IX E L L V (c) Figure 5.: Vector digrm of synchronous mchine The true lekge rectnce of the sttor winding which gives rise to voltge drop or regultion hs een neglected. This rectnce is designted X L (or X in some texts) nd the voltge drop occurring in it, IX L, is the difference etween the terminl voltge V nd the voltge ehind the sttor lekge rectnce, E L. IZ L is exctly in phse with the voltge drop due to X d, s shown on the vector digrm Figure 5.(c). It should e noted tht X d nd X L cn e comined to give simple equivlent rectnce; this is known s the 'synchronous rectnce', denoted y X d. The power generted y the mchine is given y the eqution: VE P= VIcosφ= sinδ X d Eqution 5.1 where δ is the ngle etween the internl voltge nd the terminl voltge nd is known s the lod ngle of the mchine. I I Equivlent Circuits nd Prmeters of Power System Plnt Network Protection & Automtion Guide 49

5 It follows from the ove nlysis tht, for stedy stte performnce, the mchine my e represented y the equivlent circuit shown in Figure 5.4, where X L is true rectnce ssocited with flux lekge round the sttor winding nd X d is fictitious rectnce, eing the rtio of rmture rection nd open-circuit excittion mgneto-motive forces. When pole is ligned with the ssumed sine wve m.m.f. set up y the sttor, corresponding sine wve flux will e set up, ut when n inter-polr gp is ligned very severe distortion is cused. The difference is treted y considering these two xes, tht is those corresponding to the pole nd the inter-polr gp, seprtely. They re designted the 'direct' nd 'qudrture' xes respectively, nd the generl theory is known s the 'two xis' theory. X d X L Equivlent Circuits nd Prmeters of Power System Plnt E o In prctice, due to necessry constructionl fetures of cylindricl rotor to ccommodte the windings, the rectnce X is not constnt irrespective of rotor position, nd modelling proceeds s for genertor with slient pole rotor. However, the numericl difference etween the vlues of X d nd X q is smll, much less thn for the slient pole mchine. 5.5 SALIENT POLE ROTOR E t Figure 5.4: Equivlent circuit of elementry mchine The preceding theory is limited to the cylindricl rotor genertor. The sic ssumption tht the ir-gp is uniform is very oviously not vlid when slient pole rotor is eing considered. The effect of this is tht the flux produced y rmture rection m.m.f. depends on the position of the rotor t ny instnt, s shown in Figure 5.5. V The vector digrm for the slient pole mchine is similr to tht for the cylindricl rotor except tht the rectnce nd currents ssocited with them re split into two components. The synchronous rectnce for the direct xis is X d = X d + X L, while tht in the qudrture xis is X q = X q + X L. The vector digrm is constructed s efore ut the pproprite quntities in this cse re resolved long two xes. The resultnt internl voltge is E o, s shown in Figure 5.6. In pssing it should e noted tht E 0 is the internl voltge which would e given, in cylindricl rotor theory, y vectorilly dding the simple vectors IX d nd V. There is very little difference in mgnitude etween E 0 nd E 0 ut sustntil difference in internl ngle; the simple theory is perfectly dequte for clcultion of excittion currents ut not for stility considertions where lod ngle is significnt. E' O IX d E O I q X q I d X d V Lg Armture rection M.M.F. Led Flux Flux I I q Dire ect xis po ole Figure 5.5: Vrition of rmture rection m.m.f. with pole position Qudr rture xis Pole xis Figure 5.6: Vector digrm for slient pole mchine I d 50 Network Protection & Automtion Guide

6 5.6 TRANSIENT ANALYSIS For norml chnges in lod conditions, stedy stte theory is perfectly dequte. However, there re occsions when lmost instntneous chnges re involved, such s fults or switching opertions. When this hppens new fctors re introduced within the mchine nd to represent these dequtely corresponding new set of mchine chrcteristics is required. The generlly ccepted nd most simple wy to pprecite the mening nd derivtion of these chrcteristics is to consider sudden three-phse short circuit pplied to mchine initilly running on open circuit nd excited to norml voltge E 0. This voltge will e generted y flux crossing the irgp. It is not possile to confine the flux to one pth exclusively in ny mchine, nd s result there will e lekge flux Φ L tht will lek from pole to pole nd cross the inter-polr gps without crossing the min ir-gp s shown in Figure 5.7. The flux in the pole will e Φ + Φ L. L Figure 5.7: Flux pths of slient pole mchine If the sttor winding is then short-circuited, the power fctor in it will e zero. A hevy current will tend to flow, s the resulting rmture rection m.m.f. is demgnetising. This will reduce the flux nd conditions will settle until the rmture rection nerly lnces the excittion m.m.f., the reminder mintining very much reduced flux cross the ir-gp which is just sufficient to generte the voltge necessry to overcome the sttor lekge rectnce (resistnce neglected). This is the simple stedy stte cse of mchine operting on short circuit nd is fully represented y the equivlent of Figure 5.8(); see lso Figure 5.4. L It might e expected tht the fult current would e given y E 0 /(X L +X d ) equl to E 0 /X d, ut this is very much reduced, nd the mchine is operting with no sturtion. For this reson, the vlue of voltge used is the vlue red from the ir-gp line corresponding to norml excittion nd is rther higher thn the norml voltge. The stedy stte current is given y: I d X L E = X g d X L X L () Synchronous rectnce X d Eqution 5. where E g = voltge on ir gp line An importnt point to note now is tht etween the initil nd finl conditions there hs een severe reduction of flux. The rotor crries highly inductive winding which links the flux so tht the rotor flux linkges efore the short circuit re produced y (Φ + Φ L ). In prctice the lekge flux is distriuted over the whole pole nd ll of it does not link ll the winding. Φ L is n equivlent concentrted flux imgined to link ll the winding nd of such mgnitude tht the totl linkges re equl to those ctully occurring. It is fundmentl principle tht ny ttempt to chnge the flux linked with such circuit will cuse current to flow in direction tht will oppose the chnge. In the present cse the flux is eing reduced nd so the induced currents will tend to sustin it. X d () Trnsient rectnce X f (c) Sutrnsient rectnce X d X f X kd Figure 5.8: Synchronous mchine rectnces Equivlent Circuits nd Prmeters of Power System Plnt Network Protection & Automtion Guide 51

7 Equivlent Circuits nd Prmeters of Power System Plnt For the position immeditely following the ppliction of the short circuit, it is vlid to ssume tht the flux linked with the rotor remins constnt, this eing rought out y n induced current in the rotor which lnces the hevy demgnetising effect set up y the shortcircuited rmture. So (Φ + Φ L ) remins constnt, ut owing to the incresed m.m.f. involved, the flux lekge will increse considerly. With constnt totl rotor flux, this cn only increse t the expense of tht flux crossing the ir-gp. Consequently, this genertes reduced voltge, which, cting on the lekge rectnce, gives the short circuit current. It is more convenient for mchine nlysis to use the rted voltge E 0 nd to invent fictitious rectnce tht will give rise to the sme current. This rectnce is clled the 'trnsient rectnce' X d nd is defined y the eqution: Trnsient current Eqution 5. It is greter thn X L, nd the equivlent circuit is represented y Figure 5.8() where: X X' d = X d X f + X d f + X E I' o d = X' L nd X f is the lekge rectnce of the field winding The ove eqution my lso e written s: X d = X L + X f where X f = effective lekge rectnce of field winding The flux will only e sustined t its reltively high vlue while the induced current flows in the field winding. As this current decys, so conditions will pproch the stedy stte. Consequently, the durtion of this phse will e determined y the time constnt of the excittion winding. This is usully of the order of second or less - hence the term 'trnsient' pplied to chrcteristics ssocited with it. A further point now rises. All synchronous mchines hve wht is usully clled dmper winding or windings. In some cses, this my e physicl winding (like field winding, ut of fewer turns nd locted seprtely), or n effective one (for instnce, the solid iron rotor of cylindricl rotor mchine). Sometimes, oth physicl nd effective dmper windings my exist (s in some designs of cylindricl rotor genertors, hving oth solid iron rotor nd physicl dmper winding locted in slots in the pole fces). Under short circuit conditions, there is trnsfer of flux from the min ir-gp to lekge pths. This diversion is, to smll extent, opposed y the excittion winding nd the min trnsfer will e experienced towrds the pole tips. d The dmper winding(s) is sujected to the full effect of flux trnsfer to lekge pths nd will crry n induced current tending to oppose it. As long s this current cn flow, the ir-gp flux will e held t vlue slightly higher thn would e the cse if only the excittion winding were present, ut still less thn the originl open circuit flux Φ. As efore, it is convenient to use rted voltge nd to crete nother fictitious rectnce tht is considered to e effective over this period. This is known s the 'sutrnsient rectnce' X d nd is defined y the eqution: where or Su-trnsient current I d = E Eqution 5.4 Xo d'' Xd X f Xkd X'' d = XL+ X X + X X + X X X d = X L + X kd d f kd f d kd nd X kd = lekge rectnce of dmper winding(s) X kd = effective lekge rectnce of dmper winding(s) It is greter thn X L ut less thn X d nd the corresponding equivlent circuit is shown in Figure 5.8(c). Agin, the durtion of this phse depends upon the time constnt of the dmper winding. In prctice this is pproximtely 0.05 seconds - very much less thn the trnsient - hence the term 'su-trnsient'. Figure 5.9 shows the envelope of the symmetricl component of n rmture short circuit current indicting the vlues descried in the preceding nlysis. The nlysis of the sttor current wveform resulting from sudden short circuit test is trditionlly the Current E I'' o d = X'' d E I'd = o X' d E Id = ir gp X d Time Figure 5.9: Trnsient decy envelope of short-circuit current 5 Network Protection & Automtion Guide

8 method y which these rectnces re mesured. However, the mjor limittion is tht only direct xis prmeters re mesured. Detiled test methods for synchronous mchines re given in references [5.] nd [5.], nd include other tests tht re cple of providing more detiled prmeter informtion. 5.7 ASYMMETRY The exct instnt t which the short circuit is pplied to the sttor winding is of significnce. If resistnce is negligile compred with rectnce, the current in coil will lg the voltge y 90, tht is, t the instnt when the voltge wve ttins mximum, ny current flowing through would e pssing through zero. If short circuit were pplied t this instnt, the resulting current would rise smoothly nd would e simple.c. component. However, t the moment when the induced voltge is zero, ny current flowing must pss through mximum (owing to the 90 lg). If fult occurs t this moment, the resulting current will ssume the corresponding reltionship; it will e t its pek nd in the ensuing 180 will go through zero to mximum in the reverse direction nd so on. In fct the current must ctully strt from zero nd so will follow sine wve tht is completely symmetricl. Intermedite positions will give vrying degrees of symmetry. This symmetry cn e considered to e due to d.c. component of current which dies wy ecuse resistnce is present. The d.c. component of sttor current sets up d.c. field in the sttor which cuses supply frequency ripple on the field current, nd this lternting rotor flux hs further effect on the sttor. This is est shown y considering the supply frequency flux s eing represented y two hlf mgnitude wves ech rotting in opposite directions t supply frequency reltive to the rotor. So, s viewed from the sttor, one is sttionry nd the other rotting t twice supply frequency. The ltter sets up second hrmonic currents in the sttor. Further development long these lines is possile ut the resulting hrmonics re usully negligile nd normlly neglected. 5.8 MACHINE REACTANCES Tle 5.1 gives vlues of mchine rectnces for slient pole nd cylindricl rotor mchines typicl of ltest design prctice. Also included re prmeters for synchronous compenstors such mchines re now rrely uilt, ut significnt numers cn still e found in opertion Synchronous Rectnce X d = X L + X d The order of mgnitude of X L is normlly p.u., while tht of X d is p.u. The lekge rectnce X L cn e reduced y incresing the mchine size (derting), or incresed y rtificilly incresing the slot lekge, ut it will e noted tht X L is only out 10% of the totl vlue of X d nd cnnot exercise much influence. The rmture rection rectnce cn e reduced y decresing the rmture rection of the mchine, which in design terms mens reducing the mpere conductor or electricl (s distinct from mgnetic) loding - this will often men physiclly lrger mchine. Alterntively the excittion needed to generte open-circuit voltge my e incresed; this is simply chieved y incresing the mchine ir-gp, ut is only possile if the excittion system is modified to meet the incresed requirements. In generl, control of X d is otined lmost entirely y vrying X d, nd in most cses reduction in X d will men lrger nd more costly mchine. It is lso worth Equivlent Circuits nd Prmeters of Power System Plnt Type of mchine Cylindricl rotor turine genertors 4 Pole I Air Cooled Hydrogen Hydrogen/ Multi-Pole Cooled Wter Cooled Slient pole genertors 4 Pole Multi-pole Short circuit rtio Direct xis synchronous rectnce X d (p.u.) Qudrture xis synchronous rectnce X q (p.u.) Direct xis trnsient rectnce X d (p.u.) Direct xis su-trnsient rectnce X d (p.u.) Qudrture xis su-trnsient rectnce X q (p.u.) Negtive sequence rectnce X (p.u.) Zero sequence rectnce X 0 (p.u.) Direct xis short circuit trnsient time constnt T d (s) Direct xis open circuit trnsient time constnt T do (s) Direct xis short circuit su-trnsient- time constnt T d (s) Direct xis open circuit su-trnsient time constnt T do (s) Qudrture xis short circuit su-trnsient time constnt T q (s) Qudrture xis open circuit su-trnsient time constnt T qo (s) NB ll rectnce vlues re unsturted. Tle 5.1: Typicl synchronous genertor prmeters Network Protection & Automtion Guide 5

9 Equivlent Circuits nd Prmeters of Power System Plnt noting tht X L normlly chnges in sympthy with X d, ut tht it is completely overshdowed y it. The vlue 1/X d hs specil significnce s it pproximtes to the short circuit rtio (S.C.R.), the only difference eing tht the S.C.R. tkes sturtion into ccount wheres X d is derived from the ir-gp line Trnsient Rectnce X d = X L + X f The trnsient rectnce covers the ehviour of mchine in the period seconds fter disturnce. This generlly corresponds to the speed of chnges in system nd therefore X d hs mjor influence in trnsient stility studies. Generlly, the lekge rectnce X L is equl to the effective field lekge rectnce X f, out p.u. The principl fctor determining the vlue of X f is the field lekge. This is lrgely eyond the control of the designer, in tht other considertions re t present more significnt thn field lekge nd hence tke precedence in determining the field design. X L cn e vried s lredy outlined, nd, in prctice, control of trnsient rectnce is usully chieved y vrying X L 5.8. Su-trnsient Rectnce X d = X L + X kd The su-trnsient rectnce determines the initil current peks following disturnce nd in the cse of sudden fult is of importnce for selecting the reking cpcity of ssocited circuit rekers. The mechnicl stresses on the mchine rech mximum vlues tht depend on this constnt. The effective dmper winding lekge rectnce X kd is lrgely determined y the lekge of the dmper windings nd control of this is only possile to limited extent. X kd normlly hs vlue etween 0.05 nd 0.15 p.u. The mjor fctor is X L which, s indicted previously, is of the order of p.u., nd control of the su-trnsient rectnce is normlly chieved y vrying X L. It should e noted tht good trnsient stility is otined y keeping the vlue of X d low, which therefore lso implies low vlue of X d. The fult rting of switchger, etc. will therefore e reltively high. It is not normlly possile to improve trnsient stility performnce in genertor without dverse effects on fult levels, nd vice vers. 5.9 NEGATIVE SEQUENCE REACTANCE Negtive sequence currents cn rise whenever there is ny unlnce present in the system. Their effect is to set up field rotting in the opposite direction to the min field generted y the rotor winding, so sujecting the rotor to doule frequency flux pulstions. This gives rise to prsitic currents nd heting; most mchines re quite limited in the mount of such current which they re le to crry, oth in the stedy stte nd trnsiently. An ccurte clcultion of the negtive sequence current cpility of genertor involves considertion of the current pths in the rotor ody. In turine genertor rotor, for instnce, they include the solid rotor ody, slot wedges, excittion winding nd end-winding retining rings. There is tendency for locl over-heting to occur nd, lthough possile for the sttor, continuous locl temperture mesurement is not prcticl in the rotor. Clcultion requires complex mthemticl techniques to e pplied, nd involves specilist softwre. In prctice n empiricl method is used, sed on the fct tht given type of mchine is cple of crrying, for short periods, n mount of het determined y its therml cpcity, nd for long period, rte of het input which it cn dissipte continuously. Synchronous mchines re designed to e cple of operting continuously on n unlnced system such tht, with none of the phse currents exceeding the rted current, the rtio of the negtive sequence current I to the rted current I N does not exceed the vlues given in Tle 5.. Under fult conditions, the mchine shll lso e cple of opertion with the product of I nd time in I N seconds (t) not exceeding the vlues given. Rotor construction Slient Cylindricl Mchine Mximum Mximum Rotor Cooling Type (S N ) I /I N for (I /I N ) t for /Rting continuous opertion during (MVA) opertion fults motors genertors indirect synchronous condensers motors direct genertors synchronous condensers indirectly cooled (ir) ll indirectly cooled (hydrogen) ll <= directly cooled Note 1 Note Note Note 1: Clculte s I = S N-50 I N x 10 4 Note : Clculte s ( I ) t = (SN -50) I N Tle 5.: Unlnced operting conditions for synchronous mchines (from IEC ) 54 Network Protection & Automtion Guide

10 5.10 ZERO SEQUENCE REACTANCE If mchine is operting with n erthed neutrl, system erth fult will give rise to zero sequence currents in the mchine. This rectnce represents the mchine's contriution to the totl impednce offered to these currents. In prctice it is generlly low nd often outweighed y other impednces present in the circuit DIRECT AND QUADRATURE AXIS VALUES The trnsient rectnce is ssocited with the field winding nd since on slient pole mchines this is concentrted on the direct xis, there is no corresponding qudrture xis vlue. The vlue of rectnce pplicle in the qudrture xis is the synchronous rectnce, tht is, X q = X q. The dmper winding (or its equivlent) is more widely spred nd hence the su-trnsient rectnce ssocited with this hs definite qudrture xis vlue X q, which differs significntly in mny genertors from X d. 5.1 EFFECT OF SATURATION ON MACHINE REACTANCES In generl, ny electricl mchine is designed to void severe sturtion of its mgnetic circuit. However, it is not economiclly possile to operte t such low flux densities s to reduce sturtion to negligile proportions, nd in prctice moderte degree of sturtion is ccepted. Since the rmture rection rectnce X d is rtio AT r /AT e it is evident tht AT e will not vry in liner mnner for different voltges, while AT r will remin unchnged. The vlue of X d will vry with the degree of sturtion present in the mchine, nd for extreme ccurcy should e determined for the prticulr conditions involved in ny clcultion. All the other rectnces, nmely X L, X d nd X d re true rectnces nd ctully rise from flux lekge. Much of this lekge occurs in the iron prts of the mchines nd hence must e ffected y sturtion. For given set of conditions, the lekge flux exists s result of the net m.m.f. which cuses it. If the iron circuit is unsturted its rectnce is low nd lekge flux is esily estlished. If the circuits re highly sturted the reverse is true nd the lekge flux is reltively lower, so the rectnce under sturted conditions is lower thn when unsturted. Most clcultion methods ssume infinite iron permeility nd for this reson led to somewht idelised unsturted rectnce vlues. The recognition of finite nd vrying permeility mkes solution extremely lorious nd in prctice simple fctor of pproximtely 0.9 is tken s representing the reduction in rectnce rising from sturtion. It is necessry to distinguish which vlue of rectnce is eing mesured when on test. The norml instntneous short circuit test crried out from rted open circuit voltge gives current tht is usully severl times full lod vlue, so tht sturtion is present nd the rectnce mesured will e the sturted vlue. This vlue is lso known s the 'rted voltge' vlue since it is mesured y short circuit pplied with the mchine excited to rted voltge. In some cses, if it is wished to void the severe mechnicl strin to which mchine is sujected y such direct short circuit, the test my e mde from suitly reduced voltge so tht the initil current is pproximtely full lod vlue. Sturtion is very much reduced nd the rectnce vlues mesured re virtully unsturted vlues. They re lso known s 'rted current' vlues, for ovious resons. 5.1 TRANSFORMERS A trnsformer my e replced in power system y n equivlent circuit representing the self-impednce of, nd the mutul coupling etween, the windings. A twowinding trnsformer cn e simply represented s 'T' network in which the cross memer is the short-circuit impednce, nd the column the excittion impednce. It is rrely necessry in fult studies to consider excittion impednce s this is usully mny times the mgnitude of the short-circuit impednce. With these simplifying ssumptions three-winding trnsformer ecomes str of three impednces nd four-winding trnsformer mesh of six impednces. The impednces of trnsformer, in common with other plnt, cn e given in ohms nd qulified y se voltge, or in per unit or percentge terms nd qulified y se MVA. Cre should e tken with multiwinding trnsformers to refer ll impednces to common se MVA or to stte the se on which ech is given. The impednces of sttic pprtus re independent of the phse sequence of the pplied voltge; in consequence, trnsformer negtive sequence nd positive sequence impednces re identicl. In determining the impednce to zero phse sequence currents, ccount must e tken of the winding connections, erthing, nd, in some cses, the construction type. The existence of pth for zero sequence currents implies fult to erth nd flow of lncing currents in the windings of the trnsformer. Prcticl three-phse trnsformers my hve phse shift etween primry nd secondry windings depending on the connections of the windings delt or str. The phse shift tht occurs is generlly of no significnce in fult level clcultions s ll phses re shifted eqully. It is therefore ignored. It is norml to find delt-str trnsformers t the trnsmitting end of Equivlent Circuits nd Prmeters of Power System Plnt Network Protection & Automtion Guide 55

11 Equivlent Circuits nd Prmeters of Power System Plnt trnsmission system nd in distriution systems for the following resons:. t the trnsmitting end, higher step-up voltge rtio is possile thn with other winding rrngements, while the insultion to ground of the str secondry winding does not increse y the sme rtio. in distriution systems, the str winding llows neutrl connection to e mde, which my e importnt in considering system erthing rrngements c. the delt winding llows circultion of zero sequence currents within the delt, thus preventing trnsmission of these from the secondry (str) winding into the primry circuit. This simplifies protection considertions 5.14 TRANSFORMER POSITIVE SEQUENCE EQUIVALENT CIRCUITS The trnsformer is reltively simple device. However, the equivlent circuits for fult clcultions need not necessrily e quite so simple, especilly where erth fults re concerned. The following two sections discuss the equivlent circuits of vrious types of trnsformers Two-winding Trnsformers The two-winding trnsformer hs four terminls, ut in most system prolems, two-terminl or three-terminl equivlent circuits s shown in Figure 5.10 cn represent it. In Figure 5.10(), terminls A' nd B' re ssumed to e t the sme potentil. Hence if the per unit selfimpednces of the windings re Z 11 nd Z respectively nd the mutul impednce etween them Z 1, the E A' ~ A A' B C B' C' () Model of trnsformer Z 1 =Z 11 -Z 1 Z =Z -Z 1 A B Z =Z 1 Zero us (c) 'T' equivlent circuit Lod B' A Z 11 Z Z 1 A' B' Zero us () Equivlent circuit of model r 1 +jx 1 r +jx A B R j X M A' Zero us (d) 'π' equivlent circuit B B' trnsformer my e represented y Figure 5.10(). The circuit in Figure 5.10() is similr to tht shown in Figure.14(), nd cn therefore e replced y n equivlent 'T ' s shown in Figure 5.10(c) where: Z = Z Z Z = Z Z Z = Z 1 Eqution 5.5 Z 1 is descried s the lekge impednce of winding AA' nd Z the lekge impednce of winding BB'. Impednce Z is the mutul impednce etween the windings, usully represented y X M, the mgnetizing rectnce prlleled with the hysteresis nd eddy current loops s shown in Figure 5.10(d). If the secondry of the trnsformers is short-circuited, nd Z is ssumed to e lrge with respect to Z 1 nd Z, then the short-circuit impednce viewed from the terminls AA is Z T = Z 1 + Z nd the trnsformer cn e replced y two-terminl equivlent circuit s shown in Figure 5.10(e). The reltive mgnitudes of Z T nd X M re of the order of 10% nd 000% respectively. Z T nd X M rrely hve to e considered together, so tht the trnsformer my e represented either s series impednce or s n excittion impednce, ccording to the prolem eing studied. A typicl power trnsformer is illustrted in Figure Three-winding Trnsformers If excittion impednce is neglected the equivlent circuit of three-winding trnsformer my e represented y str of impednces, s shown in Figure 5.1, where P, T nd S re the primry, tertiry nd secondry windings respectively. The impednce of ny of these rnches cn e determined y considering the short-circuit impednce etween pirs of windings with the third open. S Z s Z p Secondry P Tertiry Primry A Z T =Z 1 +Z B Z t A' B' Zero us (e) Equivlent circuit: secondry winding s/c T Zero us Figure 5.10: Equivlent circuits for two-winding trnsformer Figure 5.1: Equivlent circuit for three-winding trnsformer 56 Network Protection & Automtion Guide

12 Figure 5.11: Lrge trnsformer 5.15 TRANSFORMER ZERO SEQUENCE EQUIVALENT CIRCUITS The flow of zero sequence currents in trnsformer is only possile when the trnsformer forms prt of closed loop for uni-directionl currents nd mpere-turn lnce is mintined etween windings. The positive sequence equivlent circuit is still mintined to represent the trnsformer, ut now there re certin conditions ttched to its connection into the externl circuit. The order of excittion impednce is very much lower thn for the positive sequence circuit; it will e roughly etween 1 nd 4 per unit, ut still high enough to e neglected in most fult studies. The mode of connection of trnsformer to the externl circuit is determined y tking ccount of ech winding rrngement nd its connection or otherwise to ground. If zero sequence currents cn flow into nd out of winding, the winding terminl is connected to the externl circuit (tht is, link is closed in Figure 5.1). If zero sequence currents cn circulte in the winding without flowing in the externl circuit, the winding terminl is connected directly to the zero us (tht is, link is closed in Figure 5.1). Tle 5. gives the zero sequence connections of some common two- nd threewinding trnsformer rrngements pplying the ove rules. The exceptions to the generl rule of neglecting mgnetising impednce occur when the trnsformer is str/str nd either or oth neutrls re erthed. In these circumstnces the trnsformer is connected to the zero us through the mgnetising impednce. Where three-phse trnsformer nk is rrnged without interlinking mgnetic flux (tht is three-phse shell type, or three single-phse units) nd provided there is pth for zero sequence currents, the zero sequence impednce is equl to the positive sequence impednce. In the cse of three-phse core type units, the zero sequence fluxes produced y zero sequence currents cn find high reluctnce pth, the effect eing to reduce the zero sequence impednce to out 90% of the positive sequence impednce. However, in hnd clcultions, it is usul to ignore this vrition nd consider the positive nd zero sequence impednces to e equl. It is common when using softwre to perform fult clcultions to enter vlue of zero-sequence impednce in ccordnce with the ove guidelines, if the mnufcturer is unle to provide vlue. Equivlent Circuits nd Prmeters of Power System Plnt Network Protection & Automtion Guide 57

13 Connections nd zero phse sequence currents Zero phse sequence network Z T Zero us Z T Zero us Z T Zero us Equivlent Circuits nd Prmeters of Power System Plnt Z T Zero us Z T Zero us Zero us Zero us Z p Zero us Z t Z T Z T Z s Z p Zero us Z t Z s Z p Zero us Z t Z s Z p Zero us Z t Z s Z p Zero us Z t Z s Tle 5.: Zero sequence equivlent circuit connections 58 Network Protection & Automtion Guide

14 5.16 AUTO-TRANSFORMERS The uto-trnsformer is chrcterised y single continuous winding, prt of which is shred y oth the high nd low voltge circuits, s shown in Figure 5.14(). The 'common' winding is the winding etween the low voltge terminls wheres the reminder of the winding, elonging exclusively to the high voltge circuit, is designted the 'series' winding, nd, comined with the 'common' winding, forms the 'series-common' winding etween the high voltge terminls. The dvntge of using n uto-trnsformer s opposed to two-winding trnsformer is tht the uto-trnsformer is smller nd lighter for given rting. The disdvntge is tht glvnic isoltion etween the two windings does not exist, giving rise to the possiility of lrge overvoltges on the lower voltge system in the event of mjor insultion rekdown. Three-phse uto-trnsformer nks generlly hve str connected min windings, the neutrl of which is normlly connected solidly to erth. In ddition, it is common prctice to include third winding connected in delt clled the tertiry winding, s shown in Figure 5.14() Positive Sequence Equivlent Circuit The positive sequence equivlent circuit of three-phse uto-trnsformer nk is the sme s tht of two- or three-winding trnsformer. The str equivlent for three-winding trnsformer, for exmple, is otined in the sme mnner, with the difference tht the impednces etween windings re designted s follows: 1 ZL = ( Zsc c + Zc t Zsc t ) 1 ZH = ( Zsc c + Zsc t Zc t ) 1 ZT = ( Zsc t + Zc t Zsc c ) Eqution 5.8 where: Z sc-t = impednce etween 'series common' nd tertiry windings Z sc-c = impednce etween 'series common' nd 'common' windings Z sc-t = impednce etween 'common' nd tertiry windings When no lod is connected to the delt tertiry, the point T will e open-circuited nd the short-circuit impednce of the trnsformer ecomes Z L + Z H = Z sc-c, tht is, similr to the equivlent circuit of two-winding trnsformer, with mgnetising impednce neglected; see Figure 5.14(c). Z T Z s Z t Z e Zero potentil us () Two windings Z e Z p Zero potentil us () Three windings Figure 5.1: Zero sequence equivlent circuits L H V H I H N I L () Circuit digrm I L1 I H Z H I L -I H IT1 T (c) Positive sequence impednce L Z T I I L I T L L I L -I H Z T L V L Z L I L0 H I H1 Z LT Z LH L N Z Z T T H H I H0 Zero potentil us (d) Zero sequence equivlent circuit I H0 H Zero potentil us (e) Equivlent circuit with isolted neutrl I N T I L0 Z N Z HT Z X I T0 I H () Circuit digrm with tertiry winding I T0 Z Y Figure 5.14: Equivlent circuit of uto-trnsformer Equivlent Circuits nd Prmeters of Power System Plnt Network Protection & Automtion Guide 59

15 Equivlent Circuits nd Prmeters of Power System Plnt Zero Sequence Equivlent Circuit The zero sequence equivlent circuit is derived in similr mnner to the positive sequence circuit, except tht, s there is no identity for the neutrl point, the current in the neutrl nd the neutrl voltge cnnot e given directly. Furthermore, in deriving the rnch impednces, ccount must e tken of n impednce in the neutrl Z n, s shown in the following equtions, where Z x, Z y nd Z z re the impednces of the low, high nd tertiry windings respectively nd N is the rtio etween the series nd common windings. N Zx = ZL+ Zn ( N + 1) N Zy= ZH Zn ( N + 1) 1 Zz = ZT + Zn N + 1 Eqution 5.9 Figure 5.14(d) shows the equivlent circuit of the trnsformer nk. Currents I LO nd I HO re those circulting in the low nd high voltge circuits respectively. The difference etween these currents, expressed in mperes, is the current in the common winding. The current in the neutrl impednce is three times the current in the common winding Specil Conditions of Neutrl Erthing With solidly grounded neutrl, Z n = O, the rnch impednces Z x, Z y, Z z, ecome Z L, Z H, Z T, tht is, identicl to the corresponding positive sequence equivlent circuit, except tht the equivlent impednce Z T of the delt tertiry is connected to the zero potentil us in the zero sequence network. When the neutrl is ungrounded Z n = nd the impednces of the equivlent str lso ecome infinite ecuse there re pprently no pths for zero sequence currents etween the windings, lthough physicl circuit exists nd mpere-turn lnce cn e otined. A solution is to use n equivlent delt circuit (see Figure 5.14(e)), nd evlute the elements of the delt directly from the ctul circuit. The method requires three equtions corresponding to three ssumed operting conditions. Solving these equtions will relte the delt impednces to the impednce etween the series nd tertiry windings, s follows: Z = Z Z = Z N Z LH LT HT = Z s t s t s t N 1+ N ( ) N 1+ N ( ) ( ) Eqution With the equivlent delt replcing the str impednces in the uto-trnsformer zero sequence equivlent circuit the trnsformer cn e comined with the system impednces in the usul mnner to otin the system zero sequence digrm TRANSFORMER IMPEDANCES In the vst mjority of fult clcultions, the Protection Engineer is only concerned with the trnsformer lekge impednce; the mgnetising impednce is neglected, s it is very much higher. Impednces for trnsformers rted 00MVA or less re given in IEC nd repeted in Tle 5.4, together with n indiction of X/R vlues (not prt of IEC 60076). These impednces re commonly used for trnsformers instlled in industril plnts. Some vrition is possile to ssist in controlling fult levels or motor strting, nd typiclly up to ±10% vrition on the impednce vlues given in the tle is possile without incurring significnt cost penlty. For these trnsformers, the tpping rnge is smll, nd the vrition of impednce with tp position is normlly neglected in fult level clcultions. For trnsformers used in electricity distriution networks, the sitution is more complex, due to n incresing trend to ssign importnce to the stnding (or no-lod) losses represented y the mgnetising impednce. This cn e djusted t the design stge ut there is often n impct on the lekge rectnce in consequence. In ddition, it my e more importnt to control fult levels on the LV side thn to improve motor strting voltge drops. Therefore, deprtures from the IEC vlues re commonplce. IEC does not mke recommendtions of nominl impednce in respect of trnsformers rted over 00MVA, while genertor trnsformers nd.c. trction supply trnsformers hve impednces tht re usully specified s result of Power Systems Studies to ensure stisfctory performnce. Typicl vlues of trnsformer impednces covering vriety of trnsformer designs re given in Tles Where pproprite, they include n indiction of the impednce vrition t the extremes of the tps given. Trnsformers designed to work t 60Hz will hve sustntilly the sme impednce s their 50Hz counterprts. MVA Z% HV/LV X/R Tolernce on Z% < ± ± ± ± ± ± ±7.5 >00 y greement Tle 5.4: Trnsformer impednces - IEC Network Protection & Automtion Guide

16 MVA Primry kv Primry Tps Secondry kv Z% HV/LV X/R rtio MVA Primry kv Primry Tps Secondry kv Z% HV/LV X/R rtio % % ±10% % % ±10% % % % -0% % % % -0% % % % -0% % % % -0% % % % -0% % -18% % -0% % -15% % -0% ±10% % -0% ±10% % -0% % -15% % -0% 11/ % -15% % -4% 11/ ±10% % -4% 11/ % % % -15% % % % -0% % % % -0% % % Tle 5.5: Impednces of two winding distriution trnsformers Primry voltge <00kV MVA Primry Primry Secondry Tertiry Z% X/R kv Tps kv kv HV/LV rtio % -7.5% % -7.5% ±10% % -10% % -15% % -15% ±16.8% not known ±15% % Tle 5.6: Impednces of two winding distriution trnsformers Primry voltge >00kV MVA Primry Primry Secondry Secondry Tertiry Z% X/R kv Tps kv Tps kv HV/LV rtio ±15% % -5% % -5% % -5% % -5% % -15% ±10% Tle 5.8: Autotrnsformer dt MVA Primry Primry Secondry Z% X/R kv Tps kv HV/LV rtio 95 1 ±10% ±10% ±5% ±5% % -16.5% ±5% ±10% % -16.5% % -17.6% ±10% % -16.5% % -15% % % % -1.6% ±10% ±11.5% ±10% % -1.75% % -1% % -1% () Three-phse units MVA/ Primry Primry Secondry Z% X/R phse kv Tps kv HV/LV rtio / % -1.% / % -1.4% / - ±5% / % -1.% / % -1.% () Single-phse units Tle 5.7: Impednces of genertor trnsformers Equivlent Circuits nd Prmeters of Power System Plnt Network Protection & Automtion Guide 61

17 Equivlent Circuits nd Prmeters of Power System Plnt 5.18 OVERHEAD LINES AND CABLES In this section description of common overhed lines nd cle systems is given, together with tles of their importnt chrcteristics. The formule for clculting the chrcteristics re developed to give sic ide of the fctors involved, nd to enle clcultions to e mde for systems other thn those tulted. A trnsmission circuit my e represented y n equivlent π or T network using lumped constnts s shown in Figure Z is the totl series impednce (R + jx)l nd Y is the totl shunt dmittnce (G + jb)l, where L is the circuit length. The terms inside the rckets in Figure 5.15 re correction fctors tht llow for the fct tht in the ctul circuit the prmeters re distriuted over the whole length of the circuit nd not lumped, s in the equivlent circuits. With short lines it is usully possile to ignore the shunt dmittnce, which gretly simplifies clcultions, ut on longer lines it must e included. Another simplifiction tht cn e mde is tht of ssuming the conductor configurtion to e symmetricl. The self-impednce of ech conductor ecomes Z p, nd the mutul impednce G B R Series impednce Z = R + jx per unit length Shunt dmittnce Y = G + jb per unit length () Actul trnsmission circuit Y tnh ZY ZY X G () π Equivlent (c) T Equivlent Note: Z nd Y in () nd (c) re the totl series impednce nd shunt dmittnce respectively. Z=(R+jX)L nd Y=(G+jB)L where L is the circuit length. sinh ZY ZY Z Y Z Y = ZY tnh ZY ZY Z Y = ZY 1 10 Z tnh ZY ZY Z sinh B R Y tnh X ZY 17Z Y ZY ZY ZY Z tnh ZY ZY Y sinh ZY ZY Figure 5.15: Trnsmission circuit equivlents etween conductors ecomes Z m. However, for rigorous clcultions detiled tretment is necessry, with ccount eing tken of the spcing of conductor in reltion to its neighour nd erth CALCULATION OF SERIES IMPEDANCE The self impednce of conductor with n erth return nd the mutul impednce etween two prllel conductors with common erth return re given y the Crson equtions: De Zp = R f + j flog10 dc De Zm = f + j flog 10 D Eqution 5.11 where: R = conductor.c. resistnce (ohms/km) dc = geometric men rdius of single conductor D = spcing etween the prllel conductors f = system frequency D e = equivlent spcing of the erth return pth = 16 p/f where p is erth resistivity (ohms/cm ) The ove formule give the impednces in ohms/km. It should e noted tht the lst terms in Eqution 5.11 re very similr to the clssicl inductnce formule for long stright conductors. The geometric mens rdius (GMR) of conductor is n equivlent rdius tht llows the inductnce formul to e reduced to single term. It rises ecuse the inductnce of solid conductor is function of the internl flux linkges in ddition to those externl to it. If the originl conductor cn e replced y n equivlent tht is hollow cylinder with infinitesimlly thin wlls, the current is confined to the surfce of the conductor, nd there cn e no internl flux. The geometric men rdius is the rdius of the equivlent conductor. If the originl conductor is solid cylinder hving rdius r its equivlent hs rdius of 0.779r. It cn e shown tht the sequence impednces for symmetricl three-phse circuit re: Eqution 5.1 where Z p nd Z m re given y Eqution Sustituting Eqution 5.11 in Eqution 5.1 gives: Z = Z = R+ j flog 1 10 D dc Z = R f + j flog o Z = Z = Z Z 1 p Z = Z + Z o p m m 10 De dcd Eqution Network Protection & Automtion Guide

18 In the formul for Z 0 the expression dcd is the geometric men rdius of the conductor group. Where the circuit is not symmetricl, the usul cse, symmetry cn e mintined y trnsposing the conductors so tht ech conductor is in ech phse position for one third of the circuit length. If A, B nd C re the spcings etween conductors c, c nd then D in the ove equtions ecomes the geometric men distnce etween conductors, equl to ABC. Writing D c = dcd, the sequence impednces in ohms/km t 50Hz ecome: Z = Z = R+ j0. 145log Zo = ( R )+ j0. 44log Eqution CALCULATION OF SHUNT IMPEDANCE It cn e shown tht the potentil of conductor ove ground due to its own chrge q nd chrge -q on its imge is: V Eqution 5.15 where h is the height ove ground of the conductor nd r is the rdius of the conductor, s shown in Figure Similrly, it cn e shown tht the potentil of conductor due to chrge q on neighouring conductor nd the chrge -q on its imge is: V' =qlog Eqution 5.16 where D is the spcing etween conductors nd nd D is the spcing etween conductor nd the imge of conductor s shown in Figure Since the cpcitnce C=q/V nd the cpcitive rectnce X c =1/ωC, it follows tht the self nd mutul cpcitive rectnce of the conductor system in Figure 5.16 cn e otined directly from Equtions 5.15 nd Further, s lekge cn usully e neglected, the self nd mutul shunt impednces Z p nd Z m in megohm-km t system frequency of 50Hz re: Z' p Z' 1 10 m =qlog D' D = j0. 1log 10 = j0. 1log e e h r 10 h r D' D ABC dc Eqution 5.17 Where the distnces ove ground re gret in reltion 10 D D e c h h to the conductor spcing, which is the cse with overhed lines, h=d. From Eqution 5.1, the sequence impednces of symmetricl three-phse circuit re: Z = Z = j0. 1log Z Eqution 5.18 It should e noted tht the logrithmic terms ove re similr to those in Eqution 5.1 except tht r is the ctul rdius of the conductors nd D is the spcing etween the conductors nd their imges. Agin, where the conductors re not symmetriclly spced ut trnsposed, Eqution 5.18 cn e re-written mking use of the geometric men distnce etween conductors, ABC, nd giving the distnce of ech conductor ove ground, tht is, h, h, h c, s follows: Z = Z = j0. 1log Z 1 10 o ' Conductor Rdius r Figure 5.16 Geometry of two prllel conductors nd nd the imge of (') = j0. 96log 1 10 = j0. 1log D D r ' D rd ABC r D' 8hhh r A B C Erth Eqution 5.19 Equivlent Circuits nd Prmeters of Power System Plnt Network Protection & Automtion Guide 6

19 .80 A B C A A A=.5m U n (kv) (m) R R1 W X Equivlent Circuits nd Prmeters of Power System Plnt R1 W Y Single circuit Single circuit U n = 6kV/90kV U n(kv) 6 90 (m) K.00 - N.0.0 d R1 W Y Single circuit U n = 6kV/66kV/90kV Y c c d 6 kv(k) kv (N) Doule circuit U n= 6kV/90kV Single circuit U n = 90kV Doule circuit U n = 6kV/66kV/90kV U n (kv) (m) =.7m =4.6m R1 W Y R1 W Y Single circuit U n = 110kV Doule circuit U n = 18kV Doule circuit U n = 170kV Figure 5.17: Typicl OHL configurtions (not to scle) 64 Network Protection & Automtion Guide

20 d c n1 p n R1 W X R R1 W A B C.5 4. c d n n n n p Y.40 R1 W X Single circuit U n = 45kV 9.74 Single circuit U n = 45kV X 8.5 R1 W X Doule circuit U n = 45kV Doule circuit U n = 40kV Doule circuit U n = 45kV Doule circuit U n = 40kV Equivlent Circuits nd Prmeters of Power System Plnt Single circuit U n = 550kV Doule circuit U n = 550kV Single circuit U n = 800kV Figure 5.17(cont): Typicl OHL configurtions (not to scle) Network Protection & Automtion Guide 65

21 Equivlent Circuits nd Prmeters of Power System Plnt 5.1 OVERHEAD LINE CIRCUITS WITH OR WITHOUT EARTH WIRES Typicl configurtions of overhed line circuits re given in Figure Tower heights re not given s they vry considerly ccording to the design spn nd nture of the ground. As indicted in some of the tower outlines, some tower designs re designed with numer of se extensions for this purpose. Figure 5.18 shows typicl tower. In some cses, the phse conductors re not symmetriclly disposed to ech other nd therefore, s previously indicted, electrosttic nd electromgnetic unlnce will result, which cn e lrgely eliminted y trnsposition. Modern prctice is to uild overhed lines without trnsposition towers to reduce costs; this must e tken into ccount in rigorous clcultions of the unlnces. In other cses, lines re formed of undled conductors, tht is conductors formed of two, three or four seprte conductors. This rrngement minimises losses when voltges of 0kV nd ove re involved. It should e noted tht the line configurtion nd conductor spcings re influenced, not only y voltge, ut lso y mny other fctors including type of insultors, type of support, spn length, conductor sg nd the nture of terrin nd externl climtic lodings. Therefore, there cn e lrge vritions in spcings etween different line designs for the sme voltge level, so those depicted in Figure 5.17 re only typicl exmples. When clculting the phse self nd mutul impednces, Equtions 5.11 nd 5.17 my e used, ut it should e rememered tht in this cse Z p is clculted for ech conductor nd Z m for ech pir of conductors. This section is not, therefore, intended to give detiled nlysis, ut rther to show the generl method of formulting the equtions, tking the clcultion of series impednce s n exmple nd ssuming single circuit line with single erth wire. The phse voltge drops V,V,V of single circuit line with single erth wire due to currents I, I, I flowing in the phses nd I e in the erth wire re: V = ZI + ZI + ZcIc + ZeIe V = ZI + ZI + ZcIc + ZeIe Vc = ZcI + ZcI + ZccIc + ZceIe 0 = ZeI + ZeI + ZecIc + ZeeIe Eqution 5.0 where: Z = R f + j flog10 De dc De Z = f + j flog10 D nd so on. The eqution required for the clcultion of shunt voltge drops is identicl to Eqution 5.0 in form, except tht primes must e included, the impednces eing derived from Eqution Figure 5.18: Typicl overhed line tower 66 Network Protection & Automtion Guide