Evaluaion of CT auraion mpac for Various 87L Applicaions Zhihan Xu (GE Digial Energy), Ma rocor (GE Digial Energy) lia Voloh (GE Digial Energy), Mike Lara (NC-Lavalin) Absrac This paper will explore requiremens for he line curren differenial funcion (87L) wih regards o he impac of curren ransformer (CT) sauraion for various 87L applicaions. ercen differenial elemens ypically cope wih CT sauraion using proper resrain bu also have algorihms designed o olerae CT errors including CT sauraion. How o use resrain seings and hese algorihms properly for a given applicaion is no an easy ask and is no undersood well by proecion engineers. Therefore, how o esimae reliabiliy of he differenial during CT sauraion condiions is no an easy ask a all. The paper will firs explain he general knowledge of CT fundamenal and sauraion. econdly, he paper will invesigae securiy and dependabiliy aspecs of he 87L during CT sauraion caused by inernal and exernal fauls. Then, echniques ha have been used or can be used in 87L o reduce CT requiremen and improve relay securiy are discussed. A pracical analysis ool is presened for differen applicaions, including breaker-and-a-half or ring configuraions, o analyze reliabiliy of 87L during CT sauraion, evaluae he differenial relay securiy, invesigae he effec of adjusing 87L seings, choose he proper size of CT and examine he possibiliy of reducing CT requiremen. A more accuracy mehod is described as well o esimae he CT ime o sauraion. ndex Terms Line Differenial Relay, ecuriy and Dependabiliy, CT auraion, Time o auraion. CT FUNDAMENTAL Curren Transformer (CT) is simply a ransformer designed for he specific applicaion of convering primary curren o a secondary curren for measuremen, proecion and conrol purposes [1], []. Apparenly, a CT is like any oher kind of ransformer, which consiss of wo windings magneically coupled by he flux in a saurable seel core. A ime varying volage applied o one winding produces magneic flux in he core, which induces he volage in he second winding o deliver he secondary curren. The ransformer draws an exciing curren o keep he core excied [3]. imilarly, CT s experience copper losses, core losses, eddy curren losses and leakage flux. o he secondary curren of a CT is no a perfecly rue replica of he primary curren in magniude and here may exis a small phase shif. ince AC volage is ime varying, he flux, he exciing curren, he volage and curren induced in he second winding are also ime varying. For ransformers, i is common o use a hyseresis loop o relae he flux in he core o he exciing curren, as illusraed in Figure 1. During he normal load condiion, he exciing curren is very small and non-sinusoidal. A. Elecrical circui model The acual performance of a CT, and he equivalen circui model used for analysis purposes, are idenical o ha of any oher ransformer, as illusraed in Figure.
v e φ φ iφ i e Figure 1. Relaion of flux and exciing curren in CT deal CT T X R Vs X E R E E V B Z B N1 N Figure. CT equivalen circui model V is he secondary CT exciing volage, V B is he CT erminal volage across exernal burden, is he primary curren, T is he oal secondary curren, is he secondary load curren, E is exciing curren, R E is he exciing resisance (negligible), X E is he exciing reacance (nonlinear due o nonlinear magneizaion process, negligible during complee sauraion or 1-1 ohms), R is he secondary resisance, X is he leakage reacance (negligible in Class C CTs) [4], Z B is he burden impedance (including secondary devices and leads), and N/N1 is he CT urns raio. Besides he hyseresis curve shown in Figure 1, he CT secondary exciaion characerisics curve is a more pracical way o represen he CT seady-sae performance, which is normally provided by manufacurers and can be easily verified during field ess. The exciaion curve maps he relaionship beween he roo-mean-square (rms) value of he secondary exciing volage (V ) and he rms value of he secondary exciing curren ( E ). The Figure 3 shows a 5:5A CT exciaion characerisic obained during a field es.
1 3 auraion volage Exciing Volage (V, rms) 1 1 1 1 1-1 Knee poin volage (157V) per EC Knee poin volage (148V) per EEE 1 - CT Raio: 5/5A econdary resisance:.78 ohm 1-5 1-4 1-3 1-1 -1 1 1 1 Exciing Curren (A, rms) Figure 3. A CT secondary exciaion characerisics obained from he es n EEE C37.11-7 sandard, he knee poin volage is defined as he poin in he curve where a 45 degree line drawn angen o he abscissa. The knee-poin is no he poin of sauraion. The sauraion volage is graphically locaed by he cross poin of he sraigh lines of he exciaion curve [1]. n EC 61869- sandard, he knee poin volage is defined as he volage applied o he secondary erminals of he ransformer, which, when increased by 1%, will resul in he rms value of he exciing curren o increase by 5% []. The seady sae exciing reacance (X E ) can also be calculaed from he exciaion curve and is nonlineariy is illusraed in Figure 4. 1 4 Exciing Reacance (ohms) 1 3 1 1 1 1-5 1-4 1-3 1-1 -1 1 1 1 Exciing Curren (A, rms) Figure 4. Exciing reacance calculaed from he exciaion curve in Figure 3
Ture econdary Curren (rms, pu) Considering he same 5:5A CT, he relaion beween rue and ideal secondary currens is shown in Figure 5, where rue secondary curren would experience sauraion under he higher faul curren or larger CT burden. The ideal secondary curren is equal o he primary curren divided by he CT raio. Burden=1 ohm Burden= ohms Burden=4 ohms Burden=8 ohms 15 1 5 5 1 15 deal econdary Curren (rms, pu) Figure 5. deal and rue secondary currens B. Compuer simulaion models Many echniques have been proposed o model he behavior of iron-cored curren ransformers used for proecive relaying purposes [5]. Many power sysem ransien simulaion ools provide he CT componens o simulae faul ransien for relay sudies. Elecromagneic Transien rogram (EMT) provides hree nonlinear CT models, a rue nonlinear model (Type-93) and wo pseudo-nonlinear models (Type-96 and Type-98) [6]. The performance of he CT models has been experimenally evaluaed, and he comparison indicaes ha CT models in EMT give he saisfacory resuls for mos of he cases [7]. Elecromagneic Transiens including DC (EMTDC) program provides a Lucas model [8], and a model based on he Jiles-Aheron heory of ferromagneic hyseresis [9]. The EEE ower ysem Relaying Commiee (RC) proposed a simplified CT model based on he assumpion of he single-valued sauraion curve as shown in Figure 6, where he porion of waveform in he below-knee-poin region has been ignored due o is negligible effec on he overall soluion if he exciing curren eners ino he sauraed region [1].
Vs lope=1/ Exciaion Volage (V, rms) Acual curve implified Curve 1A Exciaion Curren (A, rms) Figure 6. implified CT model proposed by RC The secondary curren is calculaed by he following equaions, i ( ) i ( ) i ( ) (1) s s e i p( ) is( ) () N 1 i e( ) sgn( ( )) ( ) (3) V R ( ) ( 1) ( 1) (4) dis ( ) Ris ( ) Lb Rie ( ) ( ) d (5) 1 1 1 Lb ( ) R V R 1 sin ( ) d (6) where, i s is he insananeous secondary curren, i s is he insananeous ideal secondary curren, i e is he insananeous exciing curren, i p is he insananeous primary curren, N is he CT urn raio, λ is he insananeous flux linkage, ω = πf, R is he oal burden resisance, L b is he burden inducance, is he slope obained from he exciaion curve, V s is he exciing volage where he exciing curren is equal o 1A, and Δ is he inegraion ime sep.
Curren (pu of faul) An Excel spreadshee has been developed by he EEE RC for he purpose of easy applicaion [11]. This EEE RC CT model has been verified by muliple paries [1] and validaed in a high curren laboraory [1]. The laboraory obained sauraed CT waveforms agreed o he EEE RC CT model waveforms very closely. Therefore, his simplified CT model can be used for CT sauraion modeling and is used in his paper as well.. CT URATON When he exciing volage is greaer han he knee volage in he exciaion curve, he CT eners he sauraed region, where he exciing curren ( E ) is no longer negligible. Therefore, he raio error ( E / 1%) of he exciing curren o he secondary curren increases and he secondary curren ( ) is disored, no being sinusoidal anymore. A. AC sauraion AC sauraion, also called seady sae sauraion, is caused by he symmerical curren wih no DC componen. A se of AC sauraion examples is shown in he figure below. 1.5 1 Raio Curren CT Raio: 8/5 Burden: ohms Vs@1A: 33 V DC offse: %.5 -.5 auraed econdary Curren (15-65kA) -1-1.5.15..5.3.35.4.45.5 Time (s) Figure 7. Examples of AC sauraion n order o avoid ac sauraion, he secondary sauraion volage, V X, mus saisfy he following equaion. V X Z (7) where, is he primary curren divided by he urns raio, and Z is he oal secondary burden (R + X + Z B ). can be observed ha he AC sauraion may be caused by he higher primary curren, lower raio CT (such as ground CT), or larger CT burden (long lead lengh, and/or small AWG wire gage). Therefore, he AC sauraion can be avoided by properly increasing he CT sauraion volage, CT raio, or decreasing CT burden.
Curren (pu of faul) n real applicaions, a commonly used rule of humb is o selec a CT wih he volage raing of a Class C CT a leas wice ha required for he maximum seady sae symmerical faul curren [1]. B. DC sauraion DC sauraion, also called ransien sauraion, is commonly caused by he DC componen in he faul curren, unipolar half wave curren or remnan flux in he CT. Once he ransiens decay enough or vanish so ha he sauraed region is no enered, he CT would ge back o he seady sae. is well known ha he ransien shor-circui curren is defined by he following equaion: i( ) R E L sin sin( ) e where, E is he sysem volage, R is he sysem resisance, L is he sysem inducance, α is he faul incepion angle, θ is he impedance angle, T is he ime consan of he primary sysem. Considering he wors case condiion where α-θ=9, he faul curren conains he highes DC offse. A se of DC sauraion examples caused by he fully DC offse is shown in he figure below. / T (8).5 Raio Curren CT Raio: 8/5 Burden: ohms Vs@1A: 33 V DC offse: 1% 1.5 1.5 -.5-1 auraed econdary Curren (15-65kA)..3.4.5.6.7.8 Time (s) Figure 8. Examples of DC sauraion To avoid DC sauraion (bu ignoring effec of remanence), he required sauraion volage is given below, V X X Z (1 ) (9) R
where, X/R is he primary sysem X/R raio. Comparing Eq. (7) wih Eq. (9), i can be found ha he knee poin volage o avoid dc sauraion mus be (1+X/R) imes ha required for avoiding AC sauraion. C. Conribuing facors o CT sauraion Regarding a specified CT, mosly, here are four facors which conribue o CT sauraion: High primary faul curren Excessive secondary burden Heavy DC offse in curren Large percen remanence Apparenly, he increase in primary faul curren will increase secondary curren, sequenially, increase exciing volage, ener ino he sauraed region and significanly increase exciing curren. As a resul, he secondary curren is grealy reduced and disored. Boh Figure 7 and Figure 8 show he sauraed secondary currens. Larger CT burdens increase exciing volage under he same faul curren, and increase exciing curren. Then CT is more likely o saurae. As indicaed by he analysis of Eq. (8), he maximum DC componen of a faul occurs when he insananeous volage is zero. Then he DC componen sars decaying according o he ime consan of he primary power sysem. The larger ime consan will resul in he longer decaying process, and hen longer CT sauraion period. Remanence, also called remanen flux or residual flux, is he magneic flux ha is reained in he magneic circui afer he removal of he exciaion. Remanence may remain in eiher posiive or negaive direcion. When he CT is subjec o subsequen faul curren again, he flux changes will sar from he remanen value. Then he shifed remanence may worsen he ransien response by pushing he core ino deeper sauraion wihin shorer ime if he remanence and insananeous flux have he same direcion, or improve he ransien response by keeping he core away from he deeper sauraion if he remanence and insananeous flux have he opposie direcion.. MACT OF CT URATON ON 87L The Eq. (9) describes he crierion of sizing CT o avoid DC sauraion. However, i is no always pracical or possible o saisfy for differen applicaions. n pracice, i is rarely possible o compleely preven he occurring of CT sauraion for differen faul evens. The disored secondary curren caused by CT sauraion would ineviably affec he performance of curren-based proecion elemens, such as overcurren, direcional overcurren, disance, differenial and ohers. The performance requiremens of CT for various proecion applicaions have been inroduced in [13], [14]. This secion will discuss he impac of CT sauraion on line curren differenial relays.
A. Effec on curren phasor esimaion Mos of curren-based proecion funcions are using he curren phasor. This secion will discuss he effec of CT sauraion on one of mosly used phasor esimaion echniques, Discree Fourier Transform (DFT). should be menioned ha in he real implemenaion of relays, some filering echniques may be applied o remove DC decaying ransiens, or he cosine filer is used for phasor esimaion, however, hese echniques are no considered in his paper. The phasor of he secondary curren is calculaed by DFT as below, 1 NC i ( p.5) / NC i e p 1 NC i ( p.5) / NC ( it ie ) e p NC1 NC1 i ( p.5) / NC it e ie p NC p NC NC NC e i ( p.5) / NC (1) T NC T E 1 NC ie p e i ( p.5) / NC where,, T and E are he phasors of he rue secondary curren, ideal secondary curren and exciing curren, i, i T and i E are he insananeous currens, NC is he amoun of samples per cycle. can be found ha an error exiss beween rue and ideal curren phasors caused by he exciing curren (i E ). ince here are many facors affecing he sauraion process and he exciing curren is a quie nonlinear quaniy, i is hard o give an accurae and definie analysis based on Eq. (1). Therefore, some assumpions are applied for furher analysis, Wihou sauraion, he rue and ideal currens have he exac same samples. During sauraion, he rue curren samples are zero. auraion is repeaed each half cycle wih he same paern. There is no dc offse. The ime o sauraion longer han half cycle is no considered since he differenial relays normally operae a he high speed. An example of sauraed curren wih assumpions is shown below, where he ime o sauraion is around.86 ms a 6 Hz.
Curren (pu) 1.5 1 deal Curren auraed Curren.5 -.5-1 -1.5.5.1.15..5.3.35 Time (s) Figure 9. Example of simplified sauraed curren Applying DFT o he sauraed and ideal currens shown in he above figure, he magniude and angle of phasors are shown in Figure 1. 1 deal Curren auraed Curren -1 - deal Curren auraed Curren Magniude (pu).8.6.4. Angle (degree) -3-4 -5-6 -7-8 -9 -.1 -.5.5.1.15..5.3 Time (s) -1 -.1 -.5.5.1.15..5.3 Time (s) Figure 1. Magniude and angle of currens in Figure 9 Then, he ime o sauraion is adjused from o.5 cycle, exclusively. Afer applying DFT analysis for each scenario, he fracion of he ideal rms and magniude, and he angle shif from ideal are illusraed in Figure 11.
1 1 RM (pu of ideal) Magniude (α, pu of ideal).8.6.4. 8 6 4 Angle hif from deal (β, degree, leading) 5 1 15 5 3 Time o sauraion (1/64 cyc) Figure 11. RM, magniude and angle shif of sauraed currens can be concluded ha: Boh rms and fundamenal magniude will decrease under sauraion. The deeper sauraion, he larger decrease. The rms is always higher han he fundamenal magniude under he same sauraion since he harmonics are considered in he rms value. The angle is becoming leading. The deeper sauraion, he larger leading angle. The maximum angle shif is 88 degree leading in Figure 11 and he wors case shall be normally less han 9 degree. should be menioned as well ha in real cases, he sauraion process is quie dynamic; as a resul, boh he magniude and angle are changing dynamically hrough he faul process as shown in he following figures. 1 auraed Curren and Magniude (pu of faul) 1.5 1.5 -.5-1 -1.5..4.6.8.1.1.14 Time (s) p=15ka p=65ka Angle hif (degree, leading) 1 8 6 4..4.6.8.1.1.14 Time (s) p=15ka p=65ka Figure 1. Fundamenal magniude and angle shif of wo sauraed currens
B. Effec on 87L Using he resul in Figure 11, he phasor of he sauraed curren can be expressed as, (11) DEAL where, is he phasor of he sauraed curren, DEAL is he magniude of he ideal curren, is he ime o sauraion, he magniude reducing facor α is expressed as a funcion of, and he angle advancing facor β is also expressed as a funcion of. The angle of he ideal curren is assumed o zero. The funcions α( ) and β( ) can be approximaed by he hree-order and wo-order Fourier series respecively as below,.916.6565 cos(4.34.38 cos(8.648.434 cos(1.97 6.39 cos(9.466 ).349 sin(4.34 ).161 sin(8.648 61.55 36.5 cos(4.733 ).1394 sin(1.97,.5 cycle ).474 sin(9.466,.5 cycle ) 49.84 sin(4.733 Considering a radiional dual slope percenage differenial scheme, he differenial (operaing) signal for an N-erminal line is defined as,... (14) DFF 1 N The resrain signal is given as, RE N ) ) ) ) ) (1) (13) 1... (15) The operaing condiions are he differenial signal exceeds a consan pickup level, DFF K (16) and exceeds a percenage of he resraining signal, DFF DFF L1* L* RE RE, when RE B, or L1 L B, oherwise where, L1 and L are he slope rae of slope 1 and, and B is he break poin. The effecs of sauraed currens caused by inernal and exernal fauls will be discussed in his secion. 1) auraion caused by inernal fauls Considering a wo-erminal line wih inernal fauls, he local CT has no sauraion and he faul curren phasor is θ L, where, is he faul curren magniude and θ L is he impedance (17)
angle. The remoe CT experiences sauraion and he curren phasor is α( )K (β( )+γ+θ L ), where, γ is an angle difference olerance facor o accommodae angle error, and K is a magniude difference olerance facor o accommodae, Differen faul curren level a he remoe end Differen CT performance beween CTs locaed a wo erminals Model difference beween simplified sauraion and real sauraion Oher errors caused by DC offse, asymmerical sauraion, ec. ince θ L has no effec on he differenial calculaion, i can be ignored, and hen he local and remoe curren phasors are expressed as, L R ( ) K ( ( ) ) The differenial curren is hen given as, DFF L R 1 ( The resrain curren is given as, RE L R 1 ( ( ) K ) K ( ( ( ) K ) K ( ( ) ) ) ) n his scenario, is normally greaer han he break poin B, so he operaing signal is deermined by he following condiion, L RE DFF 1 ( L1 L) B Because (L1-L) is always less han, a more sric operaing condiion is given below, i.e., L DFF RE 1 (18) (19) () (1) () 1K ( ) L 1 K cos( ) ( K) 1 K L1 K Furhermore, he above equaion can be expressed as, 1 (3) 1 1 K cos( ) ( K) 1K L The Dependabiliy Facor (DF) is defined below o demonsrae he dependabiliy of he differenial funcion during inernal fauls, (4)
DF 1 K cos( ) ( K) 1 K Using he approximaion equaions (1) and (13), he dependabiliy facor wih differen K and γ is illusraed below. (5) 1 1.98 Dependabiliy Facor.96.94.9.9.88.86 5 1 15 5 3 Time o sauraion (1/64 cyc) K=1 γ (degree) Dependabiliy Facor.95.9.85 -.8 5 1 15 5 3 Time o sauraion (1/64 cyc) K= - γ (degree) 1 1 Dependabiliy Facor.95.9.85.8 K=5 Dependabiliy Facor.95.9.85.8 -.75 K=1 -.75 5 1 15 5 3 Time o sauraion (1/64 cyc) γ (degree).7 5 1 15 5 3 Time o sauraion (1/64 cyc) γ (degree) Figure 13. Dependabiliy facor inernal fauls Observed from Figure 13, he 87L funcion would correcly operae on inernal fauls if he dependabiliy facor is greaer han.7, which also means he seing of L shall be less han.7 according o Eq. (4). Acually in real applicaions, L is normally se o a value less han.7. can be concluded ha he sauraed currens caused by inernal fauls will rarely resul in he failure o operae, if a proper resrain of he higher slope is se.
Even he above analysis and conclusion is based on he simplified sauraed waveforms, hey can sill be applied for he real applicaions based on he following facors: Tolerance facors K and γ already accommodae he magniude difference, magniude error, and angle error. A more sric operaing condiion, Eq. (), increases he resrain region and reduces he relay dependabiliy in he analysis; forunaely, he higher slope in he radiional dual slope percenage plane would provide more dependabiliy for he sauraion caused by inernal fauls. ) auraion caused by exernal fauls imilarly, considering a wo-erminal line wih exernal fauls closed o he remoe end, he local CT has no sauraion and he faul curren phasor is, where, is he faul curren magniude. The remoe CT experiences sauraion and he curren phasor is α( )K (β( )+γ+18 ), where, K is a olerance facor, which value is around 1, and γ is he angle error. The local and remoe curren phasors can be expressed as, L R ( ) K The differenial curren is given as, DFF L R 1( The resrain curren is given as, RE L R ( ( 1( ( ) 18 ) K ) K ( ( ( ) K ) K ) ( ( ) ) ) 18 n his scenario, is normally greaer han he break poin B, so he operaing signal is deermined by he following condiion, L RE DFF 1 ( L1 L) B ncreasing he securiy by removing he erm, (L1-L) B, i.e., L DFF RE 1 1K ( ) L 1 K cos( ) ( K) 1 K L 1 K The ecuriy Facor (F) is defined below o demonsrae he securiy of he differenial funcion during exernal fauls, 1 ) (6) (7) (8) (9) (3) (31)
ecuriy Facor F 1 K cos( ) ( K) 1K imply assuming γ=, he securiy facor F wih differen K is illusraed in Figure 14. (3) 1.9.8.7.6.5 Misoperaions K=.9 K=1. K=1.1 L=.7.4.3..1 5 1 15 5 3 Time o sauraion (1/64 cyc) Figure 14. ecuriy facor exernal fauls can be observed ha here exiss possibiliy of misoperaion even hough he 87L securiy has been increased by Eq. (3). A similar resul can be observed in he radiional percenage differenial plane, he differenial-resrain loci is shown in Figure 15, assuming p=6 and 8 pu, K=1, and γ=. 16 14 K=.3 B=3 L1=3% L=6% 1% Line Differenial Curren (pu) 1 1 8 6 4 -> Operaing Zone Misoperaions Resrain Zone p=6pu p=8pu 4 6 8 1 1 14 16 Resrain Curren (pu) ->.5 cyc Figure 15. Differenial characerisics exernal fauls
can be concluded ha CT sauraion caused by exernal fauls, paricularly when i is more severe a one CT carrying he whole faul curren in breaker-and-a-half applicaions or when CTs are differen a opposie line erminals, inroduces a spurious differenial curren ha may cause he differenial proecion o misoperae. V. TECHNQUE UED TO MROVE CT URATON TOLORENCE FOR 87L ALCATON has been menioned ha i is no always pracical o avoid CT sauraion in real applicaions by using Equaions (7) and (9) o size CT. Therefore, some echniques have o be applied in relays o deal wih problems caused by CT sauraion. Based on he analysis in he previous secion, proecion engineers are mosly concerned wih he echniques o increase he securiy during sauraion caused by exernal fauls. Exernal faul deecors are commonly applied in bus or ransformer proecion. These mehods deec exernal fauls before he occurrence of CT sauraion o preven relay misoperaion on exernal fauls. auraion deecion echniques have been developed as well o block/unblock he operaion of proecion elemens. These algorihms are slower han he exernal faul deecors ha specially use sampled-based deecion echniques, because sauraion deecors would be assered unil he occurrence of CT sauraion. ome compensaion mehods have been proposed o reconsruc he disored secondary curren waveform caused by sauraion condiions. Then, he reconsruced and undisored waveform will be used for relay calculaions. However, here sill have some issues for real implemenaion, such as precision, speed and compuaion burden. Wih respec o he applicaion of curren differenial relays, one or more exra securiy measures lised below can be applied upon he deecion he exernal faul. Add a porion of curren disorions such as harmonics, sauraed CT signal and noise, ino he resrain signal; herefore, he resrain region is adapively increased. Dynamically swich he differenial seings o more secure values o deal wih exernal fauls. Normally, he more secure seings would resul in he larger resrain region. Consanly use he ransien bias as he addiional resrain signal. An exernal faul or a sudden surge of he load curren will cause a posiive change (dela) in he resrain curren, and hen his dela signal is mixed ino he ransien bias o increase he resrain signal. f he dela signal vanished, he ransien bias would sar decaying exponenially. A echnique uilizing he adapive resrain and CT sauraion deecion is explained below in deails [15], [16]. The adapive resrain characerisic dynamically adjuss he operaing-resrain boundary which is he decision boundary beween siuaions ha are declared o be a faul and hose ha are no. The adapive decision process is based on an on-line compuaion of he sources of
measuremen error. ources of error include power sysem noise, ransiens, inaccuracy in line charging curren compuaion, curren sensor gain, phase and sauraion error, clock error, and asynchronous sampling. The relay compues he error caused by power sysem noise, CT sauraion, harmonics, and ransiens. These errors arise because power sysem currens are no always exacly sinusoidal. The inensiy of hese errors varies wih ime; for example, growing during faul condiions, swiching operaions, or load variaions. Curren ransformer sauraion is included wih noise and ransien error. The measuremen error, also called goodness of fi, is compued as a sum of squared differences beween he acual waveform and an ideal sinusoid over one daa window. NC/ 1 4 4 LOC _ ADA _ A( k ) iloc _ A( k p) LOC _ MAG _ A NC NC (33) p where, LOC_ADA_A is he local phase A adapive resrain erm, NC is he amoun of samples per cycle, i LOC_A is he local phase A samples afer he dc removal filering, and LOC_MAG_A is he local phase A magniude. A dedicaed mechanism is applied in he line curren differenial relay o cope wih CT sauraion and ensure securiy of proecion for exernal fauls. The relay dynamically increases he weigh of he adapive resrain porion ( LOC_ADA_A in Eq. (33)) in he oal resrain quaniy, bu for exernal fauls only. The following logic is applied: Firs, he erminal currens are compared agains a hreshold of 3 pu o deec overcurren condiions ha may be caused by a faul and may lead o CT sauraion. For all he erminal currens ha are above he 3 pu level, he relaive angle difference is calculaed. Depending on he angle difference beween he erminal currens, he adapive resrain curren is increased by he muliple facor of 1, 5, or.5 o 5 as shown in Figure 16. As seen from he figure, a facor of 1 is used for inernal fauls, and a facor of.5 o 5 is used for exernal fauls. This allows he relay o be simulaneously sensiive for inernal fauls and robus for exernal fauls wih a possible CT sauraion. f more han one CT is conneced o he relay (breaker-and-he half applicaions), he CT sauraion mechanism is execued beween he maximum local curren agains he sum of all ohers, hen beween he maximum local and remoe currens o selec he secure muliplier MULT. A maximum of wo (local and remoe) is seleced and hen applied o adapive resrain.
arg(loc/rem)=18 (exernal faul) MULT=5 MULT=abs(arg(LOC/REM) 5/18 MULT=1 MULT=1 arg(loc/rem)= (inernal faul) Figure 16. Adapive resrain muliplier MULT in he above figure denoes a muliplier ha increases resrain if CT sauraion is deeced. The final resraining curren is calculaed as a sum of squared local and all remoe resrains (assuming wo erminals here). RETT _ A LOC _ RETRANT REM _ RETRANT _ A LOC _ RETRANT _ A REM _ RETRANT _ A _ A LOC _ TRAD _ RET _ A MULTLOC _ A LOC _ ADA _ A MULT REM _ TRAD _ RET _ A REM _ A REM _ ADA _ A Where, RET_A is he final phase A resrain curren, LOC_RETRANT_A is he final local phase A resrain curren, REM_RETRANT_A is he final remoe phase A resrain curren, LOC_TRAD_RET_A is he radiional local phase A resrain curren, REM_TRAD_RET_A is he radiional remoe phase A resrain curren, MULT LOC_A is local phase A muliplier obained from Figure 16, and LOC_ADA_A is he local phase A adapive resrain obained from Eq. (33). The Eq. (34) is based on he adapive sraegy. When he adapive porion of he resrain curren is small, he resrain region shrinks. When he adapive porion of he resrain curren increases, he resrain region grows o reflec he uncerainy of he measuremen. Raising he resrain muliplier corresponds o demanding a greaer confidence inerval and has he effec of decreasing sensiiviy, while lowering i is equivalen o relaxing he confidence inerval and increases sensiiviy. Thus, he resrain muliplier is an applicaion adjusmen ha is used o achieve he desired balance beween sensiiviy and securiy. V. A CT URATON ANALY TOOL FOR 87L The quesions were recenly raised for he pracicaliy of he EEE (1+X/R) crieria, especially for applicaions wih he low CT raio bu high faul curren [17]. Ulimaely, uiliy cusomers are (34)
looking for he relay manufacurer recommendaions and warranies for he CT selecion a heir sysem wih paricular relay models. CT selecion recommendaions are differen from one manufacurer o anoher and here canno be any sandard giving specific recommendaions. is possible o verify relay performance for a given applicaion by modelling CTs wih RTD or any oher simulaion ools, bu his is no always available o uiliy cusomer, is expensive and requires lo of effors and ime. is relay manufacurers responsibiliy o confirm he CT/relay sysem applicaion since only he relay manufacurer knows he proprieary design of he proecion relay [18]. Besides relay algorihms, complexiy arises from he faul curren disribuion in breaker-and-a-half applicaions, possible differen CT raios or even differen CT characerisics in real life applicaions. n order o analyze he line curren differenial relay reliabiliy during CT sauraion caused by an exernal faul, invesigae he effec of adjusing 87L seings, choose he proper size of CT and examine possibiliy of reducing CT requiremen, i is possible o develop a ype of CT sauraion analysis ool ha is able o emulae he CTs and he relay behavior. The following descripion is an example of such a ool. The ool uilizes he CT model and CT sauraion calculaion algorihm proposed by he EEE RC, and simulaes he analog/digial signal processing and daa calculaions exacly exising in he line curren differenial relay. seamlessly incorporaes he CT performance and relay sysem applicaion. The Figure 17 shows he example of he inerface of such analysis ool. Figure 17. CT sauraion analysis ool For he sysem where he CTs are already insalled, he CT and sysem parameers are known. The users can use he following procedure o analyze he reliabiliy of he 87L relay during CT sauraion and invesigae he effec of adjusing 87L seings. elec he single CT or breaker-and-a-half configuraion for each erminal. A leas one CT shall be seleced a each erminal. f only a single CT is applied in one erminal, check any one CT from ha end. pecify he CT behind which he exernal faul is locaed.
Choose he sysem frequency, 6Hz or 5Hz. Based on he daashee provided by he CT manufacurer, inpu he CT parameers for each CT, including inverse of sauraion curve slope, secondary volage (Vs) a 1A exciing curren, CT primary curren, CT secondary curren. The deails can be referred o he EEE RC documens [1] and [11]. Deermine he corresponding primary circui X/R raio. Calculae he oal CT burden for each CT, including CT secondary winding resisance, loop lead resisance, and he relay burden a raed secondary curren. npu he per-uni DC offse in primary curren, normally se o 1 (1%) for he wors case analysis. npu he per-uni remanence, normally se o for he seleced CTs. Deermine he maximum faul curren supplied by each seleced CT which is no closed o he exernal faul. The maximum faul curren for he CT closed o he faul is he summaion of currens flowing hrough all oher CTs. These currens are in primary amperes. e he 87L seings of a percenage differenial characerisic, including pickup level, resrain slope 1, resrain slope, and break poin. Click he Analyze buon, hen he CT secondary currens, differenial curren, resrain curren and operae signal will be illusraed. An example is shown in Figure 18. Try differen faul locaions and faul disribuion hrough all CTs. should be noed ha, Applicaion is considered safe when resr / diff >1.5 wih seleced seings and all faul scenarios considered. Adjusing he 87L seings, especially Resrain, is helpful o increase he securiy during CT sauraion caused by exernal fauls. n he case o size CTs, normally, CT primary and secondary currens can be pre-deermined by some crieria, such as maximum load condiions. The inverse of sauraion curve slope is almos idenical for he same CT model, so i can be calculaed from he CT daashee. Therefore, he users are mosly concerning he selecion of V value. The following procedure can be used. e V o zero and use he approximae CT secondary winding resisance (R CT ) for all he CTs o be sized. The ool will auomaically examine he differen V, saring from 3V o 5V in seps of -5V. Once a misoperaion is deeced, he ool will sop calculaion and give he boundary V. elec he CT having he maximum faul curren or highes CT primary curren, add a 1%~14% safey margin o he boundary V, find he rue V and secondary winding resisance from he CT daashee, and inpu hese values ino he ool for his CT only. Repea he above sep unil all he CTs are sized. Try differen faul locaions and faul disribuion hrough all CTs.
Figure 18. Analysis ool resuls V. TME TO URATON Because curren in an inducance canno change insananeously, CTs ake ime o saurae. This is an imporan facor in he design and applicaion of proecive relays. For example if a relay uses digial signal processing o adjus he securiy of a proecive funcion afer CT sauraion has been deeced, he relay mus have an adequae number of samples prior o sauraion in order o make his deerminaion. An EEE repor [19] gives he deailed discussion and curves from which he ime o sauraion can be esimaed. The EEE sandard [1] gives a conservaive equaion o esimae he ime o sauraion. T V X ( R RB ) T1 ln1 T1 ( ( R RB )) (35)
where, T is he ime o sauraion, T 1 is he primary sysem ime consan, V X is he sauraion volage, is he primary curren divided by he urns raio, R is he secondary winding resisance, and R B is he burden resisance. A more deailed equaion is described in [], where he dc offse and percen remanence are included. T T1 (1 percen remanence ) Vx 1 T T1 ln1 (36) TT 1 ( pu offse ) ( R RB ) cos where, T is he secondary sysem ime consan, and cosφ is he secondary power facor. However, some case sudies have demonsraed he resuls calculaed by Eq. (35) and Eq. (36) are no consisen wih he one observed from he EEE RC model described in ecion -B. To have a definie reference, he observed ime o sauraion is referred o as he ime inerval beween he faul incepion and he firs momen a which he difference beween he ideal and sauraed waveforms is greaer han 1% of he symmeric faul curren. This observed value is measured from he sauraed curren waveform obained by he EEE RC model. Taking hree of DC sauraion scenarios in Figure 8 as examples, he observed and calculaed ime o sauraion are lised below. Faul Curren (ka) Table 1: Observed and Calculaed Time o auraion Time o auraion (ms) Observed value Calculaed by (35) Calculaed by (36) 15 6.33.93 7.39 35 4.66-1.11 3.8 65 3.8-1.79 1.65 Obviously, here exiss large error beween he observed and calculaed values; even he invalid negaive values are esimaed by Eq. (35). Therefore, a more accurae esimaion mehod is explained below o esimae he ime o sauraion of a full DC sauraion (assuming remanence is zero). CT sauraion facor K capabiliy curve is defined as, K T T T T 1 / T / 1 T e e sin( ) 1 where, ω is he radian sysem frequency πf, T 1 is he primary sysem ime consan and T is he secondary CT ime consan, which can be approximaed by, T V N ( R ) (37) (38)
where, N is he CT raio, V is he CT secondary volage a 1A exciing curren obained from CT exciaion curve, and R is he oal CT burden. CT limiing facor K _LM is defined by he following equaion, K V N _ LM (39) R where, is he primary faul curren. Finally, CT ime o sauraion can be found as a projecion of he inersecion of he CT sauraion K capabiliy curve and CT limiing facor K _LM as illusraed in he figure below. Figure 19. llusraion of CT sauraion capabiliy curve and limiing facor Taking he same examples, he ime o sauraion calculaed by he new mehod is compared wih he observed values, as abulaed below. Table : Observed and Calculaed Time o auraion by New Mehod Faul Curren (ka) Observed value Time o auraion (ms) Calculaed by new mehod 15 6.33 6.5 5 5.6 5.33 35 4.66 4.71 45 4.3 4.31 55 4.1 4. 65 3.8 3.8 can be observed ha he esimaion error of he proposed mehod is normally less han.ms for he cases sudied. The esimaion error would become larger when he ime o sauraion is longer. The reason is he porion of waveform in he below-knee-poin region has been ignored in
he RC model; however, his region has a non-negligible effec for sligh CT sauraion. Overall, he sligh CT sauraion (which means longer ime o sauraion) would have less impac on he dependabiliy and securiy of 87L, which can be confirmed from Figure 13 and Figure 14. should be menioned ha he well-mached resuls in Table are obained from he wo differen models. The RC model is based on he single-valued sauraion curve and he proposed mehod is based on he secondary flux curve. V. CONCLUON By analyzing and simulaing he simplified sauraion curren waveforms on he percenage differenial characerisic plane, i has been concluded ha, The sauraion caused by inernal fauls will rarely resul in he failure o operae. The sauraion caused by exernal fauls, paricularly when i is more severe a one CT carrying he whole faul curren in breaker-and-a-half applicaions or when CTs are differen a opposie line erminals, inroduces a spurious differenial curren ha may cause he differenial proecion o misoperae. The echniques ha have been used in 87L o olerae CT errors, reduce CT requiremen and improve relay securiy are discussed. An adapive resrain logic and CT sauraion deecion mehod is explained in deails. eamlessly incorporaing he CT performance and relay sysem applicaion, a pracical CT sauraion analysis ool is presened o analyze reliabiliy of 87L during CT sauraion, evaluae he differenial relay securiy, invesigae he effec of adjusing 87L seings, choose he proper size of CT and examine he possibiliy of reducing CT requiremen. This ool can also be applied for differen applicaions, including breaker-and-a-half or ring configuraions. Furhermore, a more accurae mehod is described o esimae he ime o sauraion. V. REFERENCE [1] EEE Guide for he Applicaion of Curren Transformers Used for roecive Relaying urposes, EEE andard C37.11-7, April 8. [] EC nsrumen ransformers ar : Addiional requiremens for curren ransformers, EC andard 67869-, epember 1. [3] R. Hun, L. evov, and. Voloh, "mpac of CT Errors on roecive Relays - Case udies and Analysis," in roc. he Georgia Tech Faul & Disurbance Analysis Conference, May 19-, 8. [4] EEE andard Requiremens for nsrumen Transformers, EEE andard C57.13-1993, June 1993. [5] Working Group C-5 of he ysems roecion ubcommiee of he EEE ower ysem Relaying Commiee, "Mahemaical Models for Curren, Volage, and Coupling Capacior Volage Transformers," EEE Transacions on power delivery, vol. 15, no. 1, pp. 6-7, January. [6] Elecric ower Research nsiue, Elecromagneic Transien rogram (EMT) Rule Book, ER EL-4541, April 1986. [7] M. Kezunovic, L. Kojovic, A. Abur, C. W. Fromen, D. R. evcik, and F. hillips, "Experimenal Evaluaion of EMT-based Curren Transformer Models for roecive Relay Transien udy," EEE Transacions on power delivery, vol. 9, no. 1, pp. 45-413, January 1994.
[8] J. R. Lucas,. G. McLaren, and R.. Jayasinghe, "mproved simulaion models for curren and volage ransformers in relay sudies, " EEE Trans. on ower Delivery, vol. 7, no. 1, pp. 15-159, January 199. [9] U. D. Annakkage,. G. McLaren, E. Dirks, R.. Jayasinghe, and A. D. arker, "A curren ransformer model based on he Jiles-Aheron heory of ferromagneic hyseresis," EEE Trans. on ower Delivery, vol. 15, no. 1, pp. 57-61, January. [1] Working Group Repor of he EEE ower ysem Relaying Commiee, Theory for CT Calculaor, hp://www.pes-psrc.org/repors/ct_%1-1-3.zip, 3. [11] Working Group Repor of he EEE ower ysem Relaying Commiee, CT Calculaor, hp://www.pes-psrc.org/repors/ct_%1-1-3.zip, 3. [1] B. Kaszenny, J. Mazereeuw, and H. DoCarmo, "CT auraion in ndusrial Applicaions Analysis and Applicaion Guidelines," in roc. he 6h Annual Conference for roecive Relay Engineers, March 7-9, 7. [13] Working Group Repor of he Wesern ysems Coordinaing Council, Relaying Curren Transformer Applicaion Guide, hps://www.wecc.biz/reliabiliy/relaying%curren% Transformer%Applicaion%Guide.pdf, June 1989. [14]. Ganesan, "elecion of curren ransformers and wire sizing in subsaions," in roc. he 59h Annual Conference for roecive Relay Engineers, April 4-6, 6. [15] M. G. Adamiak, W. remerlani, and G. E. Alexander, "A New Approach o Curren Differenial roecion for Transmission Lines," in roc. he Elecric Council of New England roecive Relaying Commiee Meeing, Ocober -3, 1998. [16] GE publicaion GEK-11963, L9 Line Curren Differenial ysem - nsrucion Manual, 14. [17] R. E. Cossé, Jr., D. G. Dunn, and R. M. piewak, " CT auraion Calculaions: Are They Applicable in he Modern World? - ar : The Quesion," in roc. eroleum and Chemical ndusry Technical Conference, epember 1-14, 5. [18] R. E. Cossé, Jr., D. G. Dunn, R. M. piewak,. E. Zocholl, T. Hazel, and D. T. Rollay, "CT auraion Calculaions - Are hey Applicable in he Modern World? - ar, roposed Responsibiliies," in roc. eroleum and Chemical ndusry Technical Conference, epember 17-19, 7. [19] EEE RC Repor, Transien Response of Curren Transformers, EEE ublicaion 76 CH 113-4 WR, January 1976. [] A. Wu, "The Analysis of Curren Transformer Transien Response and s Effec on Curren Relay erformance," EEE Trans. on ndusry Applicaions, vol. A-1, no. 4, pp. 793-8, May/June 1985. X. BOGRAHE Zhihan Xu received he B.c. and M.c. degrees in power engineering from ichuan Universiy, he second M.c. degree in conrol sysems from he Universiy of Albera, and a h.d. degree in power sysems from he Universiy of Wesern Onario. He is a Lead Applicaion Engineer wih GE Digial Energy in Markham. His areas of ineres include power sysem proecion and conrol, faul analysis, modeling, simulaion, and auomaion. He is a professional engineer regisered in he province of Onario. Ma rocor is currenly a Technical Applicaion Engineer a GE Mulilin and has been wih GE Mulilin for over 5 years. Ma earned Bachelor of cience in elecrical engineering from Louisiana ae Universiy in Baon Rouge, LA in 1 and an MBA from LU in 5. He has been working in he
elecrical power field in various capaciies since 1997. He specializes in power sysem sudies and proecion and conrol relay applicaions. He is a licensed professional engineer in he sae of Louisiana lia Voloh received his Elecrical Engineering degree from vanovo ae ower Universiy, Russia. Afer graduaion he worked for Moldova ower Company for many years in various progressive roles in roecion and Conrol field. He is currenly an applicaions engineering manager wih GE Mulilin in Markham Onario, and he has been heavily involved in he developmen of UR-series of relays. His areas of ineres are curren differenial relaying, phase comparison, disance relaying and advanced communicaions for proecive relaying. lia auhored and co-auhored more han 3 papers presened a major Norh America roecive Relaying conferences. He is an acive member of he RC, member of he main RC commiee and a senior member of he EEE. Mike Lara received his BEE degree from Texas A&M Universiy in 199. He spen 4 years wih ExxonMobil and anoher 6 years wih LyondellBasell as a ower ysems Engineer and rojec Manager. He joined NC-Lavalin in as a enior Elecrical Design Engineer and has spen he las 15 years in ha capaciy specializing in medium and high volage subsaions and proecive relaying sysems for perochemical insallaions. He is a rofessional Engineer regisered in he sae of Texas.