A NEW CURRENT TRANSFORMER SATURATION DETECTION ALGORITHM

Transcription

1 A NEW CURRENT TRANSFORMER SATURATION DETECTION ALGORITHM CHAPTER 5 I uit protctio schms, whr CTs ar diffrtially coctd, th xcitatio charactristics of all CTs should b wll matchd. Th primary currt flow o ach of th CTs that ar parallld ad/or diffrtially coctd ca b gratly diffrt ad thrby th prformac calculatio is vry difficult. Modr bus/grator/trasformr protctio schm utilizs high impdac ovr-voltag rlays, low impdac ovrcurrt rlays, ad mdium impdac prctag rstrait rlays which rquir ddicatd CTs to sur propr opratio of rlays. Still, i may cass, protctio CTs ar ot slctd ad/or matchd proprly. Hc, xtral fault currt havig log DC tim costats lads to saturatio of CTs which i tur maloprats bus/trasformr diffrtial rlays. Th subsqut sub-sctios discuss problms coutrd by diffrt tchiqus, a w currt trasformr saturatio dtctio algorithm, tstig of th proposd CT saturatio dtctio algorithm usig fild data 5.1 INTRODUCTION Th diffrtial protctio ds to trip or ot withi short tim (ms dpds o th trasit compot of fault currt. This compots dcay vry slowly durig fault as pr tim costat of li. Hc, i powr systms, it is cssary to aalyz trasit prformac of CT for ddicatd diffrtial protctio schm. CT has to trasform primary currt to scodary sid i ormal as wll as faulty coditio ad its rlativ tolrac caot xcd th limits. Howvr, saturatio of CT may impact o its prformac durig its opratig stat. Most of th CTs us iro cor to maximiz th flux likag btw primary ad scodary widigs. Howvr, th oliar xcitatio charactristics ad ability to rtai larg flux (rmat flux i cors may lad CT to saturat. May studis o th aalysis of stady-stat ad trasit bhavior of iro-cord CTs hav b rportd i th litratur [105], [130], [182], [207]. 100

2 This chaptr puts forward a w CT saturatio dtctio tchiqu which dpds o saturatio dtctio idx (D that is drivd usig drivativs of currt sigals ad Nwto s backward diffrc formulas. 5.2 CURRENT STATE OF THE ART Though th mai fuctio of th protctiv CT is to faithfully trasform th maximum possibl currt udr ormal as wll as durig faulty coditios, its saturatio is ivitabl. Th amout of saturatio dpds o th magitud of fault currt, rmac flux, magitud of th DC compot, primary & scodary tim costat of CT ad burd o scodary sid of CT [24], [196]. Svral mthods hav b suggstd by rsarchrs for dtctio of CT saturatio. Kag t al. [200] prstd a algorithm basd o calculatio of flux availabl i cor of CT usig scodary currt. Howvr, th prim limitatio of this algorithm is that th valu of rmac flux rmais zro durig iitial calculatio which is ot tru i all situatios. Thraftr, Fradz t al. [39] proposd impdac-basd CT saturatio dtctio algorithm for busbar diffrtial protctio. But th rquirmt of both voltag ad currt sigals for dtctio of CT saturatio is th mai disadvatag of this schm. Latr o, Pa t al. [94] dscribd CT compsatio algorithm basd o covrsio of currt wavform distortd by CT saturatio to a compsatd currt wavform. Howvr, this schm is comparativ slowr tha othr schms as it rquirs o ad half cycl (aftr icptio of fault to calculat compsatd valu of currt. Villamaga t al. [139] suggstd a CT saturatio dtctio schm basd o th zro-squc diffrtial currt gradit with rspct to th bias currt. Howvr, th said algorithm may maloprat durig fault ot ivolvig groud as th amout of zro-squc diffrtial currt maily dpds o th ivolvmt of groud i th fault. Aftrwards, authors of rfrcs [203] ad [12] suggstd a CT saturatio dtctio schm basd o scod ad third currt diffrc fuctio. Nvrthlss, fixd valu of thrshold may ot b abl to dtct vry low saturatio coditio ad prsc of ois & harmoic durig fault coditio may maloprat th abov two schms. Thraftr, Hog t al. [209], [208] prstd Wavlt-basd tchiqus for CT saturatio dtctio. But suscptibility of Wavlt agaist ois which may prst durig fault is th fudamtal disadvatag of th said two schms. Latr o various rsarchrs hav proposd diffrt tchiqus of CT saturatio dtctio basd o ural twork (NN/combiatio of NN with othr artificial itlligc (AI tchiqus [47], [70], [194]. Howvr, larg 101

3 traiig sts, tdious traiig procss, ad a larg umbr of uros ar th svral disadvatags of th ural twork basd schms. Furthrmor, svral saturatio dtctio tchiqus hav also b proposd by rsarchrs usig diffrt approachs such as Taylor sris xpasio, mathmatical morphology, phasor computatios, wavform aalysis ad diffrc fuctios of CT scodary currt sampls [64], [197], [44], [13], [53]. Howvr, most of th abov schms may ot giv satisfactory rsults i cas of ivolvmt of dcayig DC compot, ois i fault currt ad rmac flux i th cor of CT. Morovr, th majority of ths schms hav ot b tstd i ral tim or usig actual fild data or i laboratory viromt. I ordr to rctify th said problm, a w algorithm for CT saturatio dtctio has b prstd i this chaptr. Th proposd schm has b tstd by gratig various saturatio cass o CT modl availabl i PSCAD/EMTDC softwar packag [84]. Subsqutly, th sam algorithm has also b validatd by dvlopig a tst bch of CT i laboratory viromt. 5.3 PROPOSED METHOD FOR CT SATURATION DETECTION Durig th ormal opratio of powr systm, CT rplicat fudamtal frqucy compot which is siusoid i atur. Howvr, th scodary currt may distortd durig powr systm fault which oft cotai a dcayig DC offst. Th drivativs of th scodary ca b subsqutly usd to ispct th wav shap proprtis of th currt sigal. Basd o this pricipl, a w idx has b drivd to dtct saturatio i various opratig coditio of CT. Th, th variatios of this idx alog with filtr durig typical fault currt/systm coditio hav b compard with adaptiv thrshold. Th subsqut sub-sctio dscribs th proposd pricipl ad dtctio algorithm Proposd Algorithm May factors such as DC compot i fault, siz of cor, flux dsity i cor, scodary burd tc, may lad to saturatio of th CT cor, ad caus sigificat distortio of th scodary currt wavform [02]. Figur 5.1 shows th simplifid quivalt circuit of a CT for trasit aalysis with th total impdac i scodary circuit i.. th sum of scodary lakag impdac, lad impdac, ad th load impdac, giv by Z b = (R b + jωl b. 102

4 i 1 i 2 i c i m i f L b R c L m R b Figur 5.1 Simplifid quivalt circuit of a CT for trasit aalysis Assum furthr that th magtizig impdac Z m is a paralll combiatio of th cor loss rsistac R c ad th magtizig iductac L m. Th primary currt i 1 (t durig trasit aalysis of CT ca b giv by, t / ΤP i 1( t = I max cos( ωt θ cosθ for t 0 (5.1 = 0 for t < 0 Whr, I max is th pak valu of siusoidal stady stat fault currt, T P is th primary tim-costat ad θ is th fault iitiatio agl. It has b assumd that th valu of prfault currt is almost zro bfor th icptio of th fault (t<0. Th scodary currt of CT is rprstd as, i (t = I i 2 max Rc cosθ (R +R c b t / Τ T T [ τ 2 (si ϕ cosϕ ta θ cos ϕ] ϕ t / Τ T cos ( ωτ *si( ωt θ ϕ τ T cosθ t / ΤS t / ΤP (t = A + B - C*si( ωt -θ - (5.2 2 ϕ Whr, ta ϕ = ωτ, τ = ( R clm + RbLm / Rb Rc T P ad T S ar primary ad scodary tim costat, rspctivly, ad A & B ar costats. I quatio (5.2, th first ad scod xpotial trms dcay with th tim costats T S ad T P, rspctivly, whras th magitud of th siusoidal trm is giv by, ωts C = I max ω TScosϕ = Imaxsiϕ = I max whr, taϕ = ωt S ( ( ωt Th discrt tim vrsio of i 2 (t is obtaid by cosidrig t=h. S 103

5 i H / Τ / 2π S H ΤP = A + B - C * si( - θ - ] (5.4 N 2 ϕ [ Whr, H is th samplig itrval, N is th umbr of sampls pr cycl ad is th rct sampl. Th first diffrc of i 2 [] is giv by quatio ( = i 2 [ ] = A(1 - i (H/T S 2[ -1] * ( H/T S + B(1 (H/T P * ( H/T P π 2π π π C 2si si θ ϕ + N N N 2 (5.5 If th samplig rat is 4 khz (80 sampls pr cycl for a powr systm frqucy of 50Hz, th samplig itrval H= 0.25ms. By cosidrig T S = 1s ad T P = 0.02s, th valu (H/T of (1 S (H/T ad (1 P ar xpotially rducd to ad , rspctivly [203], [64]. This idicats that th xpotial trms i 1 ar cosidrably rducd ad hav gligibl valus sic th tim costats ar larg. Ths valus ar furthr rducd for CTs of highr protctio class as th scodary tim costat of such CTs ar i th rag of 3 to 10s [64]. At th sam tim, th magitud of a siusoid trm π C 2si dpds o samplig rat N. N Th followig quatios ca b drivd for th scod, third & fourth diffrc of th CT scodary currt. 2 = = i2[] - 2i2[-1] + i2[ 2] = A(1 (H/Ts 2 (H/Ts +B(1 (H/Tp 2 (H/Tp 2 π 2π 2π C 2si si θ ϕ N N N (5.6 3 = = (5.7 = A(1 i2[] - 3 i2[-1] + 3i2[-2] - i2[- 3] (H/Ts 3 (H/Ts + B(1 (H/Tp 3 (H/Tp 3 π 2π 3π π C 2si si θ ϕ + N N N 2 104

6 4 = = i - 4 i + 6 i - 4 i + i (5.8 2[] = A(1 2[-1] (H/Ts 4 2[-2] (H/Ts 2[-3] + B(1 2[-4] (H/Tp 4 (H/Tp 4 π 2π 4π C 2si si θ ϕ N N N Dtaild aalysis of saturatio dtctio has b carrid out usig quatio (5.5 to quatio (5.8. Hr, it has b obsrvd that th accuracy of saturatio dtctio is stadily icrasd as o mov from 2- poit formulas (quatio-5.5 to 5- poit formulas (quatio-5.8. It is tru that ay furthr icras i formulas (byod 5-poit will dfiitly rduc saturatio dtctio rror. But at th sam tim it will ucssarily icras th amout of calculatio. Hc, author has drivd a saturatio dtctio idx (D usig quatios (5.5 to (5.8 ad Nwto s backward diffrc formulas [114]. Thy ar giv as: D 3 = + + H ( D 4 = H Whr, H is samplig itrval ( Takig th diffrc of quatios (5.9 & (5.10, a saturatio dtctio idx (D ca b calculatd ad giv by quatio (5.11. [ 0.25 i i i i ] 1 D = D 4 D 3 = 2[] 2[ -1] 2[ -2] 2[ -3] i 2[ - 4] (5.11 H Whr is rct sampl. This idx (D is compard with adaptiv thrshold (discussd i sctio to stimat start ad d poit of CT saturatio Coditio for CT Saturatio Dtctio π Th valu of D is much largr tha th costat trm C 2si availabl i N siusoidal part of quatio (5.8 durig CT saturatio. This trm is usd to driv adaptiv thrshold (T h alog with svral othr trms such as amout of maximum fault currt (I max stimatd usig Fourir algorithm ad safty factor (λ which dpds o low pass filtr. Hc, th adaptiv thrshold is giv as blow, 4 T h 4 π = λ * 2 *Imax * C * 2si (5.12 N 105

7 Th said valu of adaptiv thrshold is capabl to dtct small to havy saturatio coditio as it dpds o magitud of fault currt ad λ compard to th schm giv i [203] which uss fixd thrshold valu Proposd Saturatio Dtctio Flowchart Figur 5.2 shows th flowchart of th proposd algorithm. Iitially, currt sampls of bay CTs ar acquird by data acquisitio systm through first ordr low pass filtr which ffctivly rmovs th ois prst i th scodary currt. Th fault dtctio algorithm is usd to discrimiat btw th fault ad ormal coditio [170]. Start Rad Currt Sampls (I R, I Y ad I B of bay CTs Low Pass First Ordr Filtr Fault Dtctio Algorithm No Fault Dtctd? Nxt st of sampls Ys CT saturatio stimatio block Computatio of D ad T h as pr q. (6.11 ad (6.12, rspctivly No Is D > T h Ys CT saturatio dtctd/bgis Is D < T h Ys Ed of CT saturatio Figur 5.2 Algorithm of CT saturatio Dtctio Whvr a fault is dtctd by th fault dtctio algorithm, post fault sampls of all phass of coctd bay CTs ar st to th CT saturatio stimatio block. I this block, th valu of D is calculatd usig fiv poit formulas (quatio-5.11 for ach cycl ad is big cotiuously compard with adaptiv thrshold. Wh th valu of D xcds 106

8 thrshold valu, startig poit of CT saturatio is dtctd (D > T h ad thraftr d of saturatio is oticd wh th valu of D gos blow thrshold valu. 5.4 SYSTEM STUDY Figur 5.3 shows sigl li diagram of a portio of Idia powr systm twork cosistig of thr sourcs rprstd by Thvi s quivalt. Ths sourcs ar coctd to th commo bus through bay L1, L2 & L3, rspctivly. Th modl, as show i Figur 5.3, is simulatd usig th PSCAD/EMTDC softwar packags. G1 G2 L1 (80km L2 (50km CB1 CB2 CB3 CT L3 (100km G3 F xt1 F xt2 F xt3 Figur 5.3 Sigl li diagram of powr systm modl To validat th proposd algorithm, th CTs locatd o bay L3 ar aalyzd which uss Jils Athrto modl [188] availabl i PSCAD/EMTDC softwar packag. All th tst cass ar gratd by simulatig faults o bay L3 with varyig fault ad systm paramtrs. Ths paramtrs ar Fault Icptio Agl (FIA, fault rsistac (R f, typs of fault (Ftyp ad Fault Locatios (FL o li L3 (F x1, F x2, F x3. Th li ad sourc paramtrs ar giv i Appdix-E. Samplig frqucy of 4 khz, which is i th rag of th commo samplig frqucis i digital rlayig schm for a systm opratig at a frqucy of 50 Hz, is usd i this study. Morovr, th prformac of CT udr trasit coditio is also xamid with du cosidratio of ffct of burd rsistac, rmac flux, DC offst ad whit ois prst i currt sigal. 5.5 SIMULATION RESULTS OF DIFFERENT SATURATION CONDITIONS Th proposd CT saturatio dtctio mthod is vry fast cosidrig adaptiv thrshold. Howvr, just aftr fault icptio, CT scodary currt has a poit of iflctio. Hc, D may hav a larg valu at th xt sampl of a fault istat; th proposd algorithm may dtct this istat as th start of saturatio. To avoid malopratio udr this situatio, th proposd algorithm starts aftr a currt that xcds thr tims th ratd scodary currt for thr succssiv sampls [203]. I ordr to tst ffctivss of th proposd schm udr varyig systm coditios, a larg umbrs of simulatio cass hav b gratd. Diffrt paramtr 107

9 valus which hav b chos to produc th trasit rspos of CT ar rmac flux dsity, burd rsistac ad prsc of DC offst & ois. Cosidrig all ths paramtr valus, aroud 900 simulatios cass wr gratd ad th ffctivss of th proposd schm has b validatd for all ths tst cass. Howvr, th rsults of som sampl cass ar show i upcomig sctio Effct of DC Compot ad Scodary Burd o CT Saturatio Th ffct of CT saturatio for ay diffrtial protctio schm is of crucial importac particularly durig a high currt xtral fault. By chagig th CT scodary burd rsistac, diffrt dgrs of CT saturatio ca b obtaid [188]. Th prformac of th proposd schm durig CT saturatio is carrid out by simulatig diffrt faults o bay L3 at diffrt locatios (5 km, 10 km ad 20 km from th bus with varyig systm paramtrs. Figur 5.4 (a ad (b show th CT primary & scodary currt ad th valu of D & thrshold (T h, rspctivly, durig L-g fault (R-g o bay L3 at 20 km without CT saturatio ad DC compot. Figur 5.4 Wavform of CT primary & scodary currt ad valu of D & T h (a, (b without CT saturatio (c, (d with CT saturatio, rspctivly It has b obsrvd from Figur 5.4 (b that th magitud of D rmais wll blow th adaptiv thrshold throughout th fault tim ad hc, o saturatio is dtctd by th proposd algorithm. Figur 5.4 (c & (d show th prformac of th proposd 108

10 schm i prsc of dcayig DC compot alog with th valu of burd rsistac R b = 1 Ω. It is to b otd from Figur 5.4 (d that th valu of D crosss th thrshold valu aftr o cycl laps from poit of fault icptio (start of saturatio ad rmais abov th thrshold valu for xt thr succssiv cycls. Th saturatio ds wh th valu of D gos wll blow th thrshold valu. Furthr, i ordr to authticat th algorithm udr various dgrs of saturatio, th burd rsistac of CT scodary has b chagd. Figur 5.5 (a & (b ad (c & (d show th prformac of th proposd algorithm for L-L (R-Y fault o bay L3 at 5 km durig burd rsistac (R b quals to 3 Ω ad 6 Ω, rspctivly. It is to b otd from Figur 5.5 (b ad (d that th proposd schm is capabl to dtct svr CT saturatio coditio i prsc of dcayig DC compot. Figur 5.5 Wavform of CT primary & scodary currt ad valu of D & T h udr CT saturatio coditio (a, (b for R b = 3 Ω ad (c, (d for R b =6 Ω, rspctivly Effct of Rmat Flux o CT Saturatio Th amout of rmat flux i th cor dpds o factors such as magitud of primary currt, th burd o scodary circuit ad th amplitud & tim costat of dcayig DC compot. Dpdig upo th dirctio of flux stup i th cor durig th rgizatio of CT i prsc of rmat flux, a larg part of scodary currt of CT may saturat [196]. I this situatio, th prformac of protctiv class CT is iflucd by this rmac or rsidual magtism ad may rach up to 90% of th 109

11 saturatio flux [82]. Figur 5.6 (a & (b ad (c & (d show th primary & scodary currts ad valu of D & thrshold for a thr-phas (R-Y-B fault at 10 km o bay L3 durig 0.5 Ω burd rsistac with 0% ad 90% rmat flux dsity, rspctivly. This rmat flux dsity was st i th cor of CT prior to icptio of fault. It is to b otd from Figur 5.6 (b ad (d that th proposd algorithm is capabl to dtct th saturatio itrval (by comparig th valu of D ad thrshold irrspctiv of th lvl of rmac flux prviously prst i th cor of CT. Figur 5.6 Wavform of CT primary & scodary currt ad valu of D & T h durig (a, (b 0 % rmac flux ad (c, (d 90 % rmac flux, rspctivly Effct of Nois Suprimposd i Scodary Currt To valuat th proposd algorithm, acquird currt sigals from PSCAD/EMTDC softwar ar pollutd with whit Gaussia ois by cosidrig diffrt sigal-to-ois ratios (SNR i MATLAB viromt. Th SNRs ar st to 20db, 30db ad 40dB to pollut th origial currt sigals. Thraftr, ths oisy currt sigals ar filtrd by a low pass first ordr Buttrworth filtr which dimiishs th highr ordr harmoics ad ois. Th proposd algorithm is tstd by chagig th cut-off frqucy of th filtr for prfct saturatio dtctio. Iitially, cut-off frqucy was st to 1600 Hz ad it is gradually dcrasd up to 200 Hz with samplig frqucy of 4 KHz. Figur 5.7 (a & (b show th primary & scodary currt of CT ad valu of D & thrshold durig R-Y-g fault o bay L3 at 5 km with R b =3Ω, SNR=40 db ad cut off frqucy=300 Hz. It has 110

12 b obsrvd form Figur 5.7 (b that th proposd algorithm accuratly dtcts start ad d of saturatio. Hr, th magitud of D & thrshold ar cosidrably rducd at low cut-off frqucy du to which th proposd algorithm givs mor fficit rsults i trms of saturatio dtctio i th prsc of harmoics ad ois. Figur 5.7 (a wavform of CT primary & scodary currt ad (b valu of D & T h durig SNR=40db cotaid by CT scodary sigals Effct of Typs of Fault ad Fault Icptio Agl (FIA Th systm show i Figur 5.3 was subjctd to various typs of faults such as L-g, L-L, L-L-g ad L-L-L/L-L-L-g. Th rsults ar giv i Figur 5.4 to Figur 5.7 of subsctio-5.5. It has b obsrvd that th proposd algorithm dtcts CT saturatio coditio for both balacd ad ubalacd faults. I ordr to idtify th ffct of fault icptio agl (FIA o CT saturatio, various simulatio cass has b gratd by varyig th FIA btw 0 o to Figur 5.8 (a ad (b show th primary & scodary currt of CT ad valu of D & T h, for L-g (R-g fault applid at 5 km o bay L3 with R b = 3 Ω ad FIA θ=45 0. Th simulatio rsults for th sam fault coditio with FIA θ=135 0 ad R b = 5 Ω ar show i Figur 5.8 (c ad (d. It has b obsrvd from Figur 5.8 (b & (d that though th magitud of dcayig DC 111

13 compot is affctd by FIA, th proposd schm corrctly idtifis th start ad d poits of CT saturatio. Figur 5.8 Wavform of CT primary & scodary currt ad valu of D & T h durig (a, (b FIA θ=45 0 ad R b = 3 Ω ad (c, (d FIA θ=135 0 ad R b = 5 Ω, rspctivly 5.6 PRACTICAL VALIDATION OF THE PROPOSED ALGORITHM Hardwar Stup I ordr to valuat prformac of th proposd algorithm durig CT saturatio coditio, a laboratory tst bch, as show i Figur 5.9, is dvlopd. Hr, protctiv class (5P10 rsi cast typ CT havig CT ratio= 10/5 A, burd= 5 VA ad voltag ratig= 660 V is usd. Furthr, various quipmts such as rlay tstig kit, rhostat, switchs ad clamp-o mtr ar also usd for th dvlopmt of th said laboratory prototyp. Hr, tstig kit is usd to ijct high currt (0-250 A i th primary of CT ad variabl rhostat is usd as a scodary burd rsistac. I ordr to rcord ad compar th wavform of CT scodary currt, a high rsolutio four chal Digital Storag Oscilloscop (DSO is usd. I additio, clamp-o typ currt ssor prob is also usd which covrts CT scodary currt sigals ito quivalt voltag sigals. Thraftr, ths data ar giv to DSO whr a samplig is carrid out at a rat of 80 sampls/cycl. Subsqutly, ths sampld data ar loadd i MATLAB softwar usig USB port of DSO ad furthr utilizd for tstig of th proposd CT saturatio dtctio algorithm. 112

14 Figur 5.9 Hardwar stup of laboratory tst bch Rsults of Prototyp I ordr to validat th proposd algorithm, various cass hav b gratd usig th said laboratory prototyp by chagig burd rsistac from 0 Ω to 12 Ω ad primary currt of CT from 10 A to 120 A. Figur 5.10 (a shows th wavform of CT scodary currt durig saturatio alog with zoomd viw of crtai portio of sigal capturd by DSO durig 100 A primary currt ad R b =12 Ω. Figur 5.10 (a CT scodary currt sigal of DSO durig 100 A primary currt ad 12 Ω burd rsistac ad (b algorithm rsults i trm of D ad T h for th said coditio 113

15 Th prformac of th proposd algorithm i trms of D ad T h ar show i Figur 5.10 (b for th zoomd viw of slctd portio as show i Figur 5.10 (a. It has b obsrvd from Figur 5.10 (b that th proposd schm corrctly dtcts svr CT saturatio coditio as th valu of dtctio idx xcds thrshold valu (dtcts oly startig poit as thr is o d poit for th collctd data. 5.7 COMPARISON OF THE PROPOSED ALGORITHM WITH EXISTING SCHEME It has b obsrvd by th author that th schms basd o scod ad third diffrc fuctios of th sampld currt sigals [64], [203] may ot b abl to idtify th d poit of saturatio. Morovr, th abov two schms may maloprat i cas of vry low saturatio of CT, particularly durig havy load variatio. Covrsly, th proposd algorithm provids accurat rsult irrspctiv of lvl of saturatio. This fact ca b asily udrstood by obsrvig th comparativ valuatio of th abov two schms with th proposd schm as show i Figur Figur 5.11 (a CT primary & scodary currt, (b valu of dl 2 & T h1 durig scod diffrc [64], (c valu of dl 3 & T h2 durig third diffrc [203], (d valu of D ad T h for proposd algorithm Th CT primary & scodary currt durig B-g fault o bay L3 at 50 km with mior CT saturatio havig R b =0.06 Ω is show Figur 5.11 (a. Th magitud of drivativ (Dl 2, Dl 3 ad D & thrshold (T h1, T h2 ad T h durig scod diffrc of th sampld currts (quatio-5.6 [64], third diffrc of th sampld currts 114

16 (quatio-5.7 [203] ad usig fiv poit formulas of th proposd algorithm (quatio ar show i Figur 5.11 (b, (c ad (d, rspctivly. It is to b otd from Figur 5.11 (b ad (c that th valu of Dl 2 ad Dl 3 rmais wll blow th rspctiv thrshold T h1 ad T h2 udr mior CT saturatio coditio. O th othr had, as show i Figur 5.11 (d, th proposd algorithm accuratly dtcts th saturatio itrval. 5.8 CONCLUSION I this chaptr, a w CT saturatio dtctio algorithm has b prstd. Th proposd algorithm dpds o a saturatio dtctio idx (D which is drivd usig drivativs of currt sigals ad fiv poit Nwto s backward diffrc formulas. Iitially, th saturatio dtctio idx (D is drivd usig drivativ of CT scodary currts. Basd o th maximum fault, ssitivity of filtr ad samplig rat a adaptiv thrshold is dcidd. Th calculatd idx is cotiuously compard with th adaptiv thrshold (T h to stimat start ad d poit of CT saturatio. I ordr to improv accuracy of th proposd schm, a low-pass first ordr Buttrworth filtr is usd to supprss ois ad harmoics which may prst i CT scodary currt. Th validatio of th proposd algorithm is carrid out by gratig various simulatio cass cosidrig CT modl availabl i PSCAD/EMDC softwar packags. Ths cass ar gratd by varyig paramtrs such as rmac flux, FIA, burd rsistac ad prsc of DC offst & ois. Th proposd algorithm is also validatd by producig various CT saturatio cass i laboratory viromt usig dvlopd CT tst bch. Rsults obtaid from both simulatio ad hardwar stups idicat ffctivss of th proposd algorithm to dtct CT saturatio coditio. At th d, a comparativ valuatio of th proposd algorithm is also carrid out with th xistig schms ad its prformac is foud to b suprior compar to th xistig schms. Hc, th proposd algorithm ca b practically implmtd i a xistig digital diffrtial rlayig schm. 115