ACCURACY OF DISTRIBUTION CURRENT TRANSFORMERS UNDER NON-SINUSOIDEAL EXCITATION

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1 ACCURACY OF DSTRBUTON CURRENT TRANSFORMERS UNDER NON-SNUSODEAL EXCTATON Astract K. Dnath School of Enginring Univrsity of Tasmania Hoart, Australia 7000 Th accuracy of CTs usd for mtring uross ar rquird to vry accurat as thy ar usd in tariff calculations. Dcads ago, th currnt flowing in distriution circuits could considrd mor or lss to of a urly sinusoidal form. n rcnt tims, howvr, such is not th cas. Many loads such as rctifirs, invrtrs and a host of othr lctronic dvi draw non-sinusoidal currnts. A non-sinusoidal currnt wavform can considrd to comosd of a ur sinusoid of th fundamntal owr frquncy and its harmoni. Sinc ths harmoni ar injctd into th systm th ammtrs and nrgy mtrs rad th comosit currnt, not just th fundamntal comonnt. Th masurmnts will, thrfor, rflct th actual currnts only if th CTs transform th harmoni in th sam roortion as th fundamntal comonnt. This ar rsnts th rsults of an invstigation on th accuracy of som commrcial currnt transformrs. 1. NTRODUCTON Currnt transformrs usd in masuring currnts in high voltag and high currnt circuits nd to hav high accuracy sinc thy may usd for tariff calculations. A sinusoidal rimary currnt is xctd to roduc a similar scondary currnt wav sha with a high transformation accuracy. Howvr, th currnt may contain harmonic distortion du to rctifying and othr tys of loads such as fluorscnt lams [1]. Th qustion thrfor ariss whthr th CTs rmain qually accurat in th rsnc of th harmoni. t is th uros of this ar to rsnt th rsults of an invstigation rformd on commrcial currnt transformrs to stalish thir haviour in th rsnc of harmoni. Although oth rotction and mtring ty of CTs wr usd in th invstigation, th rsults of only th lattr ty ar rsntd in this ar. 2. TEST METHODS AND EQUPMENT n addition to som othrs, th following two CTs wr mad availal to us y a owr utility for invstigation: Dll Ty TAT 1 15VA 50 Hz 150/5A Dll Ty TAT 2 30VA 50 Hz 300/5A Tsts rformd on oth CTs yildd similar rsults. Thrfor, rsults of only th first on ar rsntd in this ar. Th rimary winding of th CT was xcitd y a harmonic sourc and th currnts in oth th rimary and th scondary wr masurd. Th following two tys of instrumnts wr usd for th currnt masurmnts: ] 1. HP digital oscillosco (Modl 54602A) 2. Fluk 41 Powr Harmonic Analyzr. Both of th aov mtrs can rovid tru rms currnt valus. 2.1 Harmonic sour Two diffrnt tys of sour wr usd. Th first on is a singl-has half-controlld ridg rctifir fd from th mains owr suly. Th currnt drawn y th rctifying circuit was assd through th CT rimary winding as shown in Figur 1. Th harmonic contnts of th currnt can varid y varying th firing angl of th thyristors. Th advantag of this ty of sourc is that it is ralistic and rrsntativ of th kind of non-sinusoidal currnts xrincd in th ral world [2]. Th disadvantag is that th A CT Ac mains currnt A Primary currnt Half-controlld rctifir Rsistiv load Figur 1 Tst circuit with controlld rctifir as harmonic sourc

2 magnituds of th individual harmoni can not controlld at will for tst uross. Th scond ty of sourc usd is a rogrammal wavform gnrator [PWG]. Th quimnt consists of comutr softwar and hardwar including a digital to analog convrsion circuit. Sinc th outut of this gnrator is vry low, a owr amlifir was usd to dlivr th rquird tst currnt. This quimnt is caal of gnrating any aritrary wavform y scifying th ordr as wll as th magnitud of th harmoni, in addition to th fundamntal. An additional advantag of this gnrator is that it could gnrat a "ur" sinusoid in contrast to th somwhat distortd mains owr suly. Th tst circuit with this kind of harmonic sourc is shown in Figur 2. PWG currnt CT Primary currnt R s i s t i v L o a d Figur 2 Tst circuit with rogrammal wavform gnrator (PWG) as harmonic sourc. 2.2 Equivalnt circuit An quivalnt circuit of th tst CT was dtrmind y rforming th on-circuit and short-circuit tsts. Sinc a frquncy dndnt modl is considrd, tst voltags of varying frquncis wr usd. Figur 3 shows th kind of CT quivalnt circuit considrd [3] in this invstigation. Som authors us a slightly diffrnt quivalnt circuit [4]. Th aramtrs of th quivalnt circuit ar as follows: R = Primary winding rsistanc L = Primary lakag inductanc R = Rsistiv art of th magntizing imdanc Z L. = nductiv art of th magntizing imdanc Z C s = Stray caacitanc R s = winding rsistanc L s = lakag inductanc R = Rsistiv urdn (not shown) through which th currnt flows. Th xciting currnt is dndnt on Z and th scondary voltag rquird to driv th scondary 1 : N d a l / N R L L s R L Figur 3 Frquncy dndnt quivalnt circuit of a currnt Transformr. currnt through th total scondary circuit imdanc including th urdn. Sinc th scondary currnt may vary ovr a wid rang i.. from zro to ratd currnt. Th scondary currnt can xrssd as = N For a ractical CT, is not zro. Also, at high frquncis, th currnt can significant [5]. Thrfor th scondary currnt is diffrnt from th nominal /N. 2.3 Ratio corrction factor Th transformation accuracy of a CT can dfind in trms of its ratio corrction factor (RCF). Th turns ratio N multilid y th RCF quals th ratio of rimary currnt to scondary currnt. An idal CT will hav an RCF of unity. RCF = = = 1+ N C s c s Using this RCF factor, CT accuracy may also xrssd as an rror rcntag as follows: % rror = R s = RCF t is notd that th rcnt rror aroachs zro as th RCF aroachs unity. RCF is a function not only of and ut also of th i.. th urdn sulid y th CT. With a articular scondary currnt, incrass with frquncy and so dos th rcnt rror caus th scond trm of th RCF incrass. A dirct masurmnt of th currnts in th rimary and th scondary windings of th CT was rformd and th ratio corrction factor dtrmind. This was don at various frquncis and is shown in a latr sction.

3 F 2.4 On circuit tst With th "rimary winding" kt on, a voltag of 1 V rms was alid at th scondary. Th magnitud and has angl of th currnt drawn at th scondary wr masurd. This was ratd with a wid rang of frquncis (50 Hz to 400 khz). Plottd on a log-log ar, th on circuit imdanc shows a linar ris uto aout 125 khz and thn falls off as shown in Figur 4. Oviously, th imdanc twn 50 Hz and 125 khz is du to Z. Th straight lin can xrssd as log (Z oc ) = log (f) from which Z oc = f for f < 125 khz Figur 5 Phas angl of on circuit imdanc of 15VA 150/5A Dll currnt transformr Again, th quation of th straight lin for th Z oc which can considrd du to Z, twn 150 khz and 400 khz is givn y: log (Z oc ) = log(f) Z C s oc = Z = f = nf Short circuit tst For th uros of this tst, th "rimary" was handwound with sufficint numr of turns so that ratd rimary currnt was otaind. Short circuit tst was thn rformd for a wid rang of frquncis. Voltag and currnt magnituds as wll as th has diffrnc wr notd. Th short circuit imdanc curv is shown in Figur 6. Figur 4 On circuit imdanc of 15VA 150/5A Dll currnt transformr Th has angl of this imdanc rmains almost constant at 45 0 for a frquncy uto 4 khz as shown in Figur 5. Figur 6 Short circuit imdan (rfrrd to scondary sid) of 15VA 150/5A Dll currnt transformr Uto a crtain maximum frquncy, Z + Z << Z s and thrfor th short circuit imdanc can considrd to qual to Z + Z. s

4 Th scondary winding rsistanc can masurd dirctly y using a suital masuring dvic (a ridg circuit or a digital mtr). Th lakag inductanc of th scondary winding can stimatd y th following mthods: 1. A maximum valu for L s can stimatd y noticing any lack of rsonanc in th short circuit imdanc curv. 2. Th RCF of th CT can masurd as a function of frquncy and th valu of L s that givs th st fit for th RCF calculatd from th CT quivalnt circuit and th masurd RCF. Th slo of th short circuit imdan givs an aroximation of th rimary lakag inductanc (L ) of th hand-wound rimary. t may noticd in Figur 6 that th ortion twn 200 Hz and 30 khz is straight which can xrssd as Log (Z sc ) = log(f) ω + = ( L Ls ) f whr L is th rimary lakag inductanc rfrrd to th scondary sid and L s is th scondary lakag inductanc. This total inductanc as calculatd from th aov quation is 1.94 mh. As thr is no sign of any rsonanc u to 30 khz, L s may calculatd as L s 1 2 (2π 30,000) = mh Using MATLAB, th valu of L s that givs th st fit for th RCF is found to 0.56 mh. Th rsistanc of th scondary winding R s was found to 0.1 ohm. With all ths valus th quivalnt circuit of th CT was constructd and is shown in Figur 7. R 1 : N d a l T r a n s f o r m r L 2.91 f / f m H 0.1 o h m n F Figur 7 Frquncy dndnt quivalnt circuit for th CT undr invstigation 3. MEASURED DATA Using th tst circuit shown in Figur 1, th rimary currnt was adjustd to 51 ams (aout 33% of ratd currnt) corrsonding to a firing angl of Th xctd scondary currnt is 1.7 ams. Th actual masurd currnt was 1.73 ams. With th sam rimary currnt ut at a firing angl of 126 0, th scondary currnt was masurd to 1.72 ams. Th sam rocdur was ratd with 80% of ratd currnt (120 ams). Th rsults ar shown in Tal 1. Tal 1 Masurd currnts of th CT xcitd y rctifir currnt. Firing Angl (α) Primary Currnt Currnt Th maximum rrors hr ar 1.8% (1.73 ams instad of 1.7) and 1.3% (4.05 ams instad of 4). t may notd from th masurd data that th rror tnds to dcras as th currnt aroachs th ratd valu. Th aov masurmnts wr ratd with th scond harmonic sourc i.. th rogrammal wavform gnrator. Primary currnt consisting of th fundamntal and any on of th odd harmoni twn 3 to 11 wr injctd at on tim. Th magnitud of th harmonic was 20% of th fundamntal. Th scondary currnt was masurd to 1.71 or 1.72 ams for a rimary currnt of 51 ams as shown in Tal 2. Th scondary currnt dos not chang whn all of this frquncy comonnts ar addd so long as thir comind magnitud rmains within 20%. Th thortical transformation ratio of 30:1 is not availal vn for th ur 50 Hz inut (for a rimary currnt of 120 ams, th scondary currnt is 3.99 ams instad of 4). Howvr, it is notd with intrst that xactly 4 ams is masurd in Tal 2 Masurd scondary currnts of th CT xcitd y a rogrammal wavform gnrator. Harmonic ordr Currnt with = 51 A Currnt with = 120 A , , , , ,3,5,7,

5 th scondary whn th rimary consistd of many frquncis. Th ratio corrction factor curvs for th currnt transformr with various urdn rsistan ar shown in Figur 8. t may notd from this figur that for a urdn of 1 ohm or lss, th ratio corrction factor is vry clos to unity for frquncis uto 2 khz. As th urdn incrass, th transformation rror incrass for th sam frquncy rang ( 2 khz). Byond this frquncy rang of 2 khz (40th harmonic) th transformation accuracy dtriorats rgardlss of th urdn valu. Figur 8 Ratio corrction factor curvs for th currnt transformr with diffrnt urdn. Th has rror of th currnt transformr has n dtrmind for 50 Hz and its harmoni u to 2 khz for urdns of 0.2 ohm, 1 ohm, 3 ohms, 5 ohms and 10 ohms rsctivly. Phas angl rrors can xcd 2 0 vn at 50 Hz with high urdn say 10 ohms. Howvr, this rror rmains wll within th ound of 2 0 for uto th 40 th harmonic if th urdn is 3 ohms or lss. Evn with a urdn of 5 ohms, th has rror is vry clos to 2 0 as shown in Tal SUMMARY & CONCLUSONS Masurd data on CT accuracy has n rortd in this ar. Two diffrnt tys of harmonic sour wr usd with varying dgrs of rrsntation of ractical situations. t has n sn that th ratio corrction factor is vry clos to unity for low urdn (1 ohm or lss) for a frquncy rang of uto aout 2 khz i.. 40 th harmonic. Thr is a shar dtrioration of th RCF yond th 40 th harmonic vn with vry low urdn. t has also n osrvd that th has angl rror incrass, in gnral, with frquncy for a articular urdn. A maximum has rror of slightly aov Tal 3 Phas angl rror Burdn, Ohms f (Hz) Phas angl rror, dg k k k k dgrs has n found for a urdn of 10 ohms at a frquncy of 2 khz. Considral tim has n dvotd in dvloing a frquncy dndnt quivalnt circuit of th CT. Such a circuit can utilizd for th comutation of actual currnt transformation ratio at any frquncy. 5. REFERENCES [1] P. G. Kndall, "Harmoni in Powr Systm", Th Elctricity Council, Powr Systm Enginring Sris, [2] J. Arrillaga, D.A. Bradly and P.S. Bodgr. "Powr Systm harmoni", 1985, Wily, Nw York. [3] D.A.Douglass, "Currnt Transformr Accuracy with Asymmtric and High Frquncy Fault Currnts", EEE Transactions on Powr Aaratus and Systms, Vol. PAS-100 No. 3, March [4] V.J. Gosll and G.J. Sandrs, "Frquncy Rsons of distriution CTs", Procdings of AUPEC96, [5] Wright, "Currnt Transformrs: Thir transint and Stady Stat Prformanc", 1968, Chaman and Hall.