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Guidelines for Current Transformers Selection for Protection SystemsLj. A. KojovicCooper Power SystemsFranksville, WI 53126

Abstract: If current transformer (CT) characteristics are notproperly selected for fault conditions, saturation will occurand relays can misoperate. To help protection engineersselect the appropriate CT, the IIEEE published twodocuments on CT performance and a~pplication.This papercompares the guidelines in these two documents andsuggests modifications that will make CT selection easierand more realistically estimate CT time-to-saturation.Keywords: Current Transformer, Saturation, TransientResponse, Protective Relaying, Digital Simulation

I. INTRODUCTIONCT performance characteristics are specified by ANSLIEEEStandard C57.13-1993 [1]. However, this standard onlycovers CT behavior under steady state and symmetrical faultconditions. In an actual power system, short circuit currentsmay have a significant DC offset, which may saturate CTSthat would not saturate under symmetrical fault conditions.Remanence in the CT core can also contribute to CTsaturation. Therefore, it is necessamy to use additionaltechniques to estimate CT performance under faultconditions.The IEEE published the following documents on CTperformance and application: 1) Power System RelayingReport 76-Chl 130-4 [2,3], and 2) IEEE Std C37.110-1996,IEEE Guide for the Application of Current TransformersUsed for Protective Relaying Purposes [4]. This papercompares the guidelines in these two documents andsuggests modifications that will make CT selection easierand more realistically estimate CT time-to-saturation.Section II presents the theory of CT operation. Secticm IIIcompares the two IEEE documents and proposes a modifiedmethod for CT selection. Guidelines are established toestimate CT time-to-saturation. Section IV includeslaboratory tests and computer simulations of CT transientresponse. The Alternative Transients Program (ATP) wasused for the computer simulations. ATP-based models,representing the protective relaying system and CTS, weredeveloped. They have proven useful in solving actualindustrial and utility distribution system problems.

H. CURRENT TRANSFORMER TRANSIENTANALYSISCurrent transformer equivalent circuit is shown in Figure 1.

ip RP~+ n+=-+

Rp, Lp -lb. Ls -

2~primary ;inding resistance and leakageinductancesecondary winding resistance and leakageinductance

Figure 1.Current Transformer Equivalent CircuitAn ideal CT will operate with an ampere-turn balance:

ip. np = iv.n., (1)where

ip, is - CT primary and secondary currentsnp,n~ - number of primary and secondary turns

An actual CT does not behave as an ideal transformer. TheCT secondary voltage is generated by the rate of flux changein the core, To produce flux in the CT core, magnetizing(exciting) current is needed. This current introduces ratioand phase errors. The equation of an actual CT can bewritten as:

v,1 p=;s+;m (2)where ip is primary current referred to the secondary, andim is magnetizing current.The fundamental transformer equation (3) applies to alltransformers including CTS.

whereE-B-A-f-n-

E==4.44BAnf (3)RMS voltage on the secondary winding [V]flux density [T]core cross section [m*]fi-equency[Hz]turns ratio

This equation can be used for steady state analysis, but inthis form, is not suitable for transient analysis. For transientanalysis, the CT equivalent circuit of Figure 2 applies.

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id RP Lp Ls isir@s-c>~lmrl I mx01$ RIRm Lm [tT

Lm - magnetizing inductanceEs - CTsecondary voltageimx - magnetizing current, realctivecomponentimr - magnetizing current, active componentRI - CT load (burden) including lead resistance

Rm - iron loss equivalent resistanceFigure 2. Current Transformer (CircuitDiagram

To simplifi CT tr~sient analysis, the C~ equivalent circuitof Figure 2 can be simplified as shown in Figure 3. CTparameters Rp, Lp, and Rm can be neglected. In thefollowing analysis Ls was also neglected, although in somecases it may be taken into consideration. Inter-windingcapacitance can also be neglected at the frequencies ofinterest to protection studies [5].

@ Es is~~1QCurrentsource ------i-

Figure 3. CT Representation fo~~ansient AnalysisRb=Rs+Rl (4)

CT time constant can be defined as ~2 = -& (5)RhThe magnetizing branch Lm is a non-linear element. It canbe estimated from the CT V-I characteristics which isreadily available. The Rb value is alsclusually provided. Lmand Rb data is sufficient to develop CT models.The most important transient condition to be considered forCT operation is an asymmetric short circuit current since,due to the DC component, the CT will saturate at lowercurrents than for symmetrical short circuit currents.The short circuit current can be expressed as:i(l) = Z&.k[sin(ax+ a p) + sin(a fp)e ] (6)where i(~ - current instantaneous value@ak - current peak value

lx - fault incidence angle- phase angle between vc)ltageand currentT: - primary circuit time constant

The most severe case is a full offset of short circuit currentwhich is obtained for ~_ ~ = ~ and represented by2equation:

-i(t) = IPgak[e cos(tot)] (7)Standards [1] specify CT behavior only under steady stateand symmetrical fault conditions. CT ratio error is specifiedto be 10?4.or less for fault currents 20 times the CT ratedcurrent and specified load. CTS are designed to meet thisrequirement. But, if a symmetric fault current exceeds 20times the CT rated current or if the fault current is smallerbut contains a DC offset (asymmetric current), the CT willsaturate and the secondary current will be distorted and havea reduced RMS value. Figure 4 demonstrates the levels of600/5 A, C100 CT saturation for different symmetric faultcurrents. CT ratio errors, calculated based on the currentRMS value, at different saturation levels are correlated toCT operating points on the V-I curve.03~___l_ lL_l_l_l Jl __ L__ L_ L_l_l LLl_l--l---l--l--t-l-l-l-i+- -+++-l-l-lll- 1 -1- -1- + -11-1+ + ~&a~~* - 1- - t- -1-llll- -L -,- J -,-1-!,. -- -Ts-ipmL-

with1.5Q totalload resistance , __L. CTratio _f_l.z 1111111g ill 111111

1- - -1.. -1--1 3:1:P ----- ,- - , -,- * -, ,.+ --

1- -----v --- ---- ____ -

1 1 J 1!. J __ -L _]_11111111!1Ill 1 I I 1 ,, : ,,, ;W,01101 102 103

CTPrima~ Current[A](referredtothesecondary)Figure 4. 600/5 A, C100Current Transformer Saturation

HI. METHODS FOR CT SELECTIONThe IEEE published two documents on CT performance andapplication. This section compares these documents andsuggests modifications to their guidelines for CT selection.These methods estimate if a CT will saturate under faultconditions, but they do not indicate the intensity ofsaturation and its possible impact on relay operation.Additional analysis is required to study the impact of CTsaturation on relay protection.Method #1: To make CT transient analysis easier for users,the Power System Relaying Report 76-Chl 130-4 [2,3]includes guidelines for CT selection. R fh-st defines asaturation factor (K.s)as

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~,=fi= Vk-.r (8)v, % &n

KSisthe ratio of the CT saturation voltage (J%)to the CTsecondary voltage (Vs) for a symmetrical fault. A higher Ksvalue indicates a greater safety margin.Report [2] includes a family of Ks curves that can be used toestimate CT transient response based on the Ks value fromwhich the time to CT saturation can be determined. Figure 5shows an example of Ks curves for primary circuit timeconstant T,=20 ms and current transformer time constantsT2=0.1, 0.3, 0.6, 1, 2, and 10 s. If the Ks value exceeclsthecurve for a particular Tz,the CT will not saturate.

T210 ,

r

.1 1111111 I 1111111

J1111111 10,,, ,!, ,,9 I I LIJIJl_. _-J_ LLl_lll ,. T1=20ms 1

8 -, -- -- --Z 11111111% 11111111- 7 -;------- 1 [11111;a 6 ~-+~~:{;:- 7.______ 0.3,

r 11111111111111 ) 1 Ill Ill~ 0.15- 1111111

r t 1! 11111 1 ! 111111

l-r TTITITl--r TrT r,T!1?7?1?1?1--- ?-?? FITl~

II~, 11111/li I !1111111 I

4l!l! 111

~ 3 !+++l H1--++ ++l+,+l---+ t-++,+,m ?ltlllll 1 111111! ! I 111111:EiLl&Mwdl1++.h4Hl---+ -+-+ +1.+ 1-+1---! -l-1 +1l+ll/L LL14u L-4- LLLIL UI.. -! LL.AI. AI1 10 100 1000

Figure 5.Time to Saturation [ins]

Saturation Factor (Ks) and Time to Saturationfor Primary Circuit Time CcmstantT,=20msand Different Current Transformer TimeConstants (TJThe procedure used to obtain Ks curves was as follows:Using the CT equivalent circuit of Figure 2, flux density inthe CT core for a resistive burden was approximated withEquation 9:

Flux density at the saturation point is(lo)CDnASetting B~=B(t)and rearranging yields

nThe second term of Equation 11 has a maximum vah~e forsin(cot)= -1. Therefore, the pessimistic value for Ks is:

K., = co ::TI(e-k-e-)+](12)

Ks curves in reference [2] are developed based on Equation12. Comparison of Ks curves for T1=20 ms and T,=l sobtained using Equation 11 with the Ks curve fromreference [2] (Equation 12) is shown in Figure 6. Themaximum value of Equation 11 defines the Ks above whichthe CT will not saturate. Therefore, a straight line wasdrawn starting from the maximum value. Also, thebeginning part- of the Ks curves (dotted lines in Figures 5and 6) are not drawn based on Equation 12 but wereadjusted to represent more realistic CT response sinceEquation 12 g;ves more pessimistic results in that region.The report does not explain this adjustment.

1

1 10 100 1000Time to Saturation [ins]

Figure 6. Saturation Factor (Ks) Curves for T1=20ms andT,=l SFigure 7 shows a family of Ks curves for T1=0.02, 0.04,0.06, 0.08, and 0.1 s and TJ= 0.1, 1, and 10 s developedbased on reference [2].

Time ConstantT 1 [s]Figure 7. Saturation Factor Curves vs. Primary Circuit (T,)and CT Time Constants (TJComments: Figure 7 indicates that for a CT with higher timeconstant T,, a higher value of Ks is required to avoid CTsaturation. This is p@ correct since the CT time constantincreases when Rb decreases. This incorrect result occursbecause the variable Rb exists on both sides of Equation 12.When calculating Ks curves, only the Rb on the right side ofEquation 12 was handled as a variable. However, when

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applying Ks curves, this error becomes corrected becauseKs must be first calculated from Equation 8, which includesRb. For a CT, Ks is higher with a smaller Rb and Ks issmaller with a higher Rb. Ks is then checked against the Kscurves in Figure 7 and the results become more realistic.Even though the fwst part of the Ks curves was adjusteddownward (dotted line, Figures 5 and 6), they still give morepessimistic results than actual CT transient response in thatregion.Method #2: IEEE Std C37.110-1996 [4] further simplifiesCT transient analysis by assuming T, to be infinite on theright side of Equation 12. This re,duces Equation 12 toequation 13:

[ -L)(Js=coTI le 1 +1 (13)From equation 13, time to saturation (t,) is() -1s=-T,.lrI l-~ =-T,.in 1-.=. (,4)aTI xl\ RI

T,=* where Xl and R, are primlarysystem reactancemRI and resistance up to the fault. Equation 141s included in [4].Comments: In Equation 14, Tz was assumed to be infinitewhich suggests Lm+Ls=cc or Rb=O. ,Again, this assumptionwas applied only to Tz of Equation 12, not to Ks which isalso dependent on Rb. This produces pessimistic results forCTS having small time constants such as auxiliary CTS andCTSwith low saturation voltages. This is shown in the nextsection.Proposed Method (Method #3): This paper proposes usingVkinstead of Ks (Equation 12) or t, (Equation 14) since itmakes it easier to visualize how a CT will perform. Fordetermining the CT time-to-saturation, the use of twoequations (Equations 15and 16) is also proposed.From Equation 11, Vk can be expressed as shown inEquation 15.k=R[++A-e-AFsin(u)l15)

ipwhere L = nTo estimate CT time to saturation, Equation 15 is used as is,with sin(cot)until its first peak as shown in Figure 8, Thisgives more realistic CT response for this time range. Afterthe first peak, sin(mt)=-1 is assumed which represents apessimistic value as given in Equation 16.

k=Rb[+He-6)Figure 9 shows a C800 CT time to saturation for a fault 20times the rated current, T1=0.02 s and Rb=O.5Q and 1 Q. Inthis case, the CT will not saturate for Rb=O.5 Q but willsaturate for Rb=1 Q afler 50 ms. Figure 10 extends theresults over a range of T1.

100C I I 1111111 I 1111 !111 I I 11111!1 I 1111111900 - _~~l_l~ll~l__l_l_l~l~l[_J JLIHlll__l_Ll_lulLI 1 1111 111 I I 1111111 I i 1111111 I 1111111_~~~l~l~l__l_l_l~l~l~_ I I 11111!1 I 1111111

~ 800 I I 1111!11 I 11111 [11

s I I 1111111 Ill: 600 -r Trlnrr[-i-r7 lr-TITll lT]l-(-r!7I 1 !111111 I 1111111

TITltr- TITlllT, i-,-r ,nflm.? ~~o --, ,,, ,,,,, - I 1 !111111 I 1111111g

I 1 1111111 I I 1111111 I l!ll [11I 11111111 1 I [111111 I 1! 11111

,(JO -- LLLI I-I I-I LILIU LJLIAILIL _l... Ll_l UUIll I 11111111 1 1 1111111 I [111111.,~3 ,@2 ,Wl 18 Id

Time toSaturation [s]Figure 8. Method #3 to Estimate the CT Time to Saturation900 ;;, ,!, ,,, ,, ,,, ,,800- C800CT 11 lll~~~f) 111111!

a!% 600--:+;+~-~:~---=

I 111111, ,111111~ I I 11111 Rb=O.5f) TrITIT.= I I 1111111 lnrl-7-r Tr17m~ I I 1)1111: 300-l T7Trt I- Ttlittl---t itt-l-tltlt

1*++I+HI--+* +*1+1+1100[+4 l--t+t14ulu44 &+ i-1+1+111111111, ,,, , 1,LUUl__l_LALl-l U l __ ALLL141A

I 11! 11111,,,, ,,, ,,, 1111,1,-1OC I , , ! I ,, I I $ , I ,,, , I I , ,,, .

10-3 , (y2 @ 1(PTime to Saturation [s]

Figure 9. Method #3 to Estimate CT Time to Saturation(CTClass: C800, Fault current: 20 times therated current, T1=0.02 s, CT Burden: 0.5 Qand 1Q) -= ____ -l----~-11 ----, - ----r,I,lnw -- - ,/A

- ;- -- -;-_ IfauM=20xrated ~.L-~?1 C800 c l .---I --;----i __________

f:I.- 1--.1 _ ,- Rb=lQ -!/_;__ --l II /7-- Rb=0,5.0 I

....~ 120w- _!. -. l-,--~~ 1ooo- -

&i(/

! 1-- ,----.1s --T800z -4

-j --.= J.--,; 6oo- -- I -~-l --, _ _ J -!. -1 -;--G __;b 400 --- -1 _-U le 1- --:-- -_!

Q

2oo- -: :=. -y __ 1- .- :____. ..-_e - - -. -- .=-_-- -------- _0.01 ----- - -0,04 0.040.03 0.02 0.020.01 0

0.06

FigurePrimaryCircuit Timeto Saturation[s]TimeC.nsta.t(T]) [s]

10. C800 CT Time to Saturation Curves usingMethod #3 for a 20 Times Rated Current Faultvs. the CT Vk, Tl, and Rb=O.5Q and Rb=l f2

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A comparison of Methods #1 and #2 to Method #3 isshown in Figure 11. Method #2 gives the most pessimisticresults for CTS with lower Vk suggesting the CTS willsaturate faster than in actual practice (the portion of thecurve from 1 ms to 10 ms in Figure 11). Method #1 hasslightly corrected this portion of the curve. Method #3 usessin(ot) in this range which gives results closer to resultsobtained by testing actual CTS.Methc~d#2 also incorrectlysuggests that in some CT applications, CTS need higher V~to avoid saturation than Method #1 and Method #3 wlhichgive more realistic results.

l-lIIIIIIII+-III

1-.11~.II++

J 11111 ..- LIllltl I111111 I--- ---711111 I111111 I-t tlil+-- t111111 IlLILIL --L111111 I1- Metimd #12- Method #23- Mcrimd #31111111+ *1+1+ --+

-L L LIIUI 11!1!1I 111111- _1 IltlllI 111111-1- f-l-l+ i-iI 111111

.- LLLIJUI 111111I 111111---- --I 1! 11111111111

-r-rrb7nIltllll

l-+ +1+1+1 111111111111 111111 Iltllll-50 I I I $ , ,111 1 , I IlL~ I1&3 l&2 1~1 lr@

Time to $atrrration [s]Figure 11. Comparison between Met!hod#3 and Methods#1 and #2 to Estimate CT Transient Behavior

IV. LABORATORY TESTS AND COMPUTERSIMULATIONSPaper [5] presented laboratory tests and computersimulations for a 600/5 A, C100 CT and simulations for a2000/5 A, C800 CT and demonstrated how tinle-to-saturation can be determined usin,g the three methodsdiscussed in Section III. Paper [5] also included an exampleof time-to-saturation estimation for an auxiliary CT.This paper compares three methods 10 determine the time-to-saturation for a 1200/5A current transformer for differentfault current levels. Time-to-saturation curves are plotted inthe same figure to demonstrate the impact of currents on CTsaturation and show what CT saturation voltage is necessaryto avoid saturation. Laboratory tests and computersimulations were performed. The ATP transient analysisprogram was used to simulate Cr transient behavior.Computer simulations were particularly usefid to investigatea CT transient behavior in the current range that was nottested in the laboratory. The transient responses of the CTmodels were compared to laboratory tests to confirm theiraccuracy.4.1. 1200/5 A CT Transient ResponseFigure 12 shows the measured V-I curve for a 1200/5 A CT.Several laboratory tests with full-offset currents were

performed at different current levels. Figures 13 to 15compare tested and simulated CT responses with Rb=2 Qand 6 kA and 10 kA faults with T1=30 ms. The tested andsimulated waveforms are very similar, verifying thecomputer modeling. Figure 16 shows the simulated primarytest current (24 kA full-offset) and the CT secondarycurrent. The estimated time to saturation using thesedifferent methods are presented in Figure 17and Table 1.

1111111 1 1 1 ! 11111 1 1 1111!11 I_r, . .. . . -i Tl-tl-rl--T - --rrnt-irI 1200/5A CT I I 1 111! 111 1 I )11111

1 1111111----- L---- _--_! _LL1-! Ll!-1 1111111 1 1 111111tlllllt I Itlllll 1 1 111! 111 I I 111111111 {111 1 111111{! 1 11111111 I I 11111!1111111 I 11111111 t 11111111 I I 111111

_~~~lql]l::~:l:lg~l~l~ :1:~~11~1~~ -1-l _lJ.lLI L_ J_ LL!_l LIL-1-1+ +1+11-- +-l- tHt.ll

-t-l+Htt l-++ +l+l-tl-- +-l-l -t+l+l t---l -+- HHEHE&z -1-14HU -1-44 *U UI- L-I-! 4LIL! L-4l-&uu LI 1111111 1 t 1111111 I ! 111111? _____ _____ ___1 1111111 1 1! 111111 I 1111111

.LIJu __l_l_l LIJl_(l-_J. -t_l_l LILIL__l_LL1-l LIL1111 ! 1411,,,,,, ,,!, ,,1, ,,

Illllllf!tllllll-1,~?,?,r-~r+~v, r

I 1! 11111 1 I 1111111 1 i 111111I 11111111 I I 1111111 1 1 111111

11! 1111! I I 1111111 I I 111111In 0.01 0.1 1 10

Current [A]Figure 12. V-I Curve for a 1200/5A CT

,1 1, ,, ,, 1 ! t 1 1 ,0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Time [s]Figure 13. Recorded and Simulated Primary CT TestCurrent (10 kA, Fully Offset, T1=30ms)

120 I I 1 I I I {

k,00 --- #!w--;---; ___l. loyx~=y__I I I I i4--f+ --!---&---& --&--:---&--{I i!60--; ---~40_-~ ---:~ 20 --: --U 0 -{ ----20 ---: l___-to - ~.; ~---111,1, -,1---- ,. --,-601 1 1 t I 1 t Io 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Time [s]

Figure 14. Recorded and Simulated Secondary CTCurrent (10 kA, Fully Offset, T,=30 ms)

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70605040

$30zg 20ku 10

0-lo-20xl o 0.02 0.04 0.06 0.08 0.1 0.12 O.1.t

Time [s]Figw-e15. Recorded and Simulated Secondary CT

Current (6 kA, Fully C)ffsct,T1=30ms)70605040~ 30:~ 205u 100-lo-200 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0,09

Time [s]Figure 16. Simulated Primary anclSecondary CT

Currents (24 kA, Fully C)ffset,T1=30ms)i2:m3000 -+-I I+HI+I - 24kA + 1+1H--l kl-l-l+l1 ,

-...10 100Time lmsl 1000 ------- ..

200

!lllllll! 1111 10 100Time [ins]..

Figure 17. Estimated CT Time-to-Saturation usingMethods #1, #2, and #3.

Table 1.Time-to-Saturation for a 1200/5A CT, T1=30msTime-to-Saturation [msl

6kA 10kA l2~kA- Method #1 [2] 23 9* 4.0*

W- Doted line region (approximated value) J.0

6.76.5

Comments: Table 1 indicates that both Method #1 andMethod #2 are more pessimistic than Method #3, whoseresults are closer to both tested and simulated results.

V. CONCLUSIONSThis paper compares two methods for selecting CTSpublished in IEEE documents on CT performance andapplication. Proposed modifications to these methods aresuggested to make CT selection easier and to obtain a morerealistic prediction of CT time-to-saturation. All threemethods predict if a CT will saturate under fault conditions,but they do not indicate the intensity of the saturation or itspossible impact on relay operation. Additional analysis isrequired to study the impact of CT saturation on relayprotection.References[1][2]

[3]

[4]

[5]

C57.13-1993 ANSI /IEEE Standard, Requirements ForInstrument Transformers.Transient Response Of Current Transformers, PowerSystem Relaying Report 76-Chl 130-4 PWR, IEEESpecial Publication, 1976.Transient Response of Current Transformers, IEEEPower System Relaying Committee, IEEE Trans. onPower Apparatus and Systems, Vol. 96, No. 6, 1977.IEEE Std C37. 110-1996, IEEE Guide for theApplication of Current Transformers Used forProtective Relaying Purposes.Lj. A. Kojovic, Behavior of Current Transformersduring Fault Conditions and Guidelines for theirSelection for Protection Systems, 27thAnnual WesternPower Relay Conference, October 24-26, 2000,Spokane, WA.

BiographyLjubomir A. Kojovic (SM 94) is Chief Power SystemsEngineer for Cooper Power Systems at the Thomas A.Edison Technical Center. He has a Ph.D. degree in powersystems with specialties that include protective relaying,testing, digital modeling, and systems analysis. Dr. Kojovicis included on the roster of experts for United NationsDevelopment Organization (UNIDO) and is a registeredProfessional Engineer in the State of Wisconsin. Dr. Kojovichas authored more than 100 technical papers.

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