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Abstract A new technique for the correction of distorted

current waveforms in the secondary windings of current

transformers (CTs) when the magnetic core is saturated, is

presented. The technique is based on the integration of theinduced voltage in a tertiary winding. The exciting current is

determined using a function that describes the magnetization

process in the core, and by adding it to the distorted secondary

current, a more faithful reproduction of the primary current

wave is obtained. The initial magnetic flux in the core is

determined by analogical integration of the voltage across the

tertiary winding, from the pre-fault state up to the instant in

which the current reaches 150% of the load current. Due to the

large air gap length, the remnant flux in the core is ignored.

Index Terms Air-gapped CTs, current transformer,

distortions, power system protection, saturation, waveform

compensation.

I. INTRODUCTION

HE fault currents in electric power systems present asinusoidal component plus a dc decaying component. The

first produces a sinusoidal magnetic flux in the currenttransformer (CT) core. The second produces an initiallyincreasing flux which may lead to a high saturation level in thecore. This may cause severe distortions in the secondarycurrents supplied to protective relays. As consequences, thefollowing problems may arise [1]:

1) Relays can operate inadequately;2) Relays may not be sensitive to the distortions that reduce

the root-mean-square value of the secondary current;3) Relay operations may be delayed, for the reason cited in

the previous item.4) Fault locators may not show the correct indication.Those occurrences can cause thermal and electrodynamics

damages, loss of coordination in the protection relays, anddifficulty of location of the faulted point, or loss of systemstability. Then, it is necessary to develop techniques thatprovide the best accuracy in the process of transformation, toavoid such disturbances. This task has been accomplished byseveral methods and mathematical tools used in the area ofdigital signal processing, applicable to the field of powersystem protection.

The initial works about the mitigation of the distortions insecondary currents of CTs considered the problem by means ofhardware [2]-[3].

With the development of the microprocessors, numericaltechniques for detection the CT core saturation and correctionof the secondary current waveform were developed. Conradand Oeding [4] is the first reference about this matter. Theauthors proposed a method in which the magnetic flux areobtained by numerical integration of the secondary current; inaddition, a function that describes the minor hysteresis loops inthe iron core is used to obtain the excitation current; so, thecorrection is performed adding this current to the distortedsecondary current. A similar method was proposed by [5].Additionally, a method to calculate the core flux prior the faultwas presented, which was based on the periodicity of the fluxwaveform in the steady state. The algorithm was tested in real

time using a DSP. The reported results were good. However,this technique was not able to estimate the residual flux in theCT core. The same authors presented a method to detect theinstants of the core saturation, which was based on third orderdifference functions [6]. Later, this method was combined withanother based on second order difference functions to estimatethe residual flux in the CT core [7].

The discrete wavelet transform was proposed by Li et al. [8]to detect the CT saturation, in conjunction with a regressiontechnique destined to correct the secondary current wave.

Methodologies based on least squares curve fitting werepresented by Pan et al. [9], El-Naggar and Gilany [10] and

Hooshyar and Sanaye-Pasand [11]. Despite the refinedmathematical treatment, these methods impose an intenseburden of computation to the relay.

Wiszniewski et al. [12] suggested a simple method toreconstruct the primary current waveform. However, theaccuracy might degrade if the primary fault current containsharmonics and noise.

Techniques based on artificial neural networks (ANNs) fordetection and correction were proposed by Yu et al. [13],Khorashadi-Zadeh and Sanaye-Pasand [14], and Segatto andCoury [15]. These methods might require a substantial amountof network training.

Correction of Distorted Current Waveforms in

the Secondary of Current TransformersFagner A. Pereira, Francisco das Chagas F. Guerra, Edson G. da Costa,Member, IEEE, and Benemar

A. de Souza, SeniorMember, IEEE

Universidade Federal de Campina Grande - UFCG

T

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II. CURRENT TRANSFORMER MODEL

The CT equivalent electric circuit is shown in Fig. 1. A thirdwinding (tertiary) superimposed to the secondary is used,which is made by a thin wire, with the purpose to provide thevoltage u3 that will be integrated for determination of themagnetic flux in the CT core.

Fig. 1. The current transformer equivalent circuit.

Fig. 1 shows the resistances and leakage inductances of thewires and burden (Rw, Lw, Rr, Lr), as well as the nonlinearmagnetizing inductance of the iron core (Lm) and the linearinductance of the gap (Lg). The magnetic core properties arerepresented by the following expression, where is the fluxlinkage in the secondary winding and is the electricconductance related to the iron core losses:

)()]([)(

)]([)( 3 tutfdt

tdtftie +=

+= ( 1 )

The function ie (t) = f [(t)] describes the CT saturationcurve (in peak values). So, the trajectories in the phase plane

- iedetermined by (1) describe asymmetric minor loops. Theparameter is determined by trial-and-error method, bycomparing dynamic loops - iein 60 Hz obtained by computersimulations with those registered in laboratory.

For the circuit of Fig. 1, it follows that:

dttuttt )()()( 300 += ( 2 )

)(][)( 3 tutftie +)(= ( 3 )

)()()( 21 tititi e += ( 4 )

The term (t0) of (2) is the remanent flux in the magnetic

core, R, plus the initial secondary flux linkage 0imposed bythe primary current when it reaches 150% of the rated current.The remanent flux in the magnetic core is reduced to anegligible value by the air gap (CT class TPZ). However, 0cannot be neglected because small increases of cause largeincreases in iewhen the core saturates.

III. THE PROPOSED METHOD

The correction of the secondary current waveform isaccomplished in accordance to the test setup block diagramshown in Fig. 2. The interface system has three inputs (1,2,3)and three corresponding outputs which are connected to supply

the IED (Intelligent Electronic Device). The current in the

secondary winding (N2turns) is applied in the input port 1 andis converted in a proportional voltage. The tertiary winding (N3turns) is connected to the port 2 through an analogicalintegrator. In this winding the current is negligible. Thus, thevoltage u3is also applied to the port 3.

Fig. 2. Test setup block diagram.

The proposed correction method of the secondary currentwaveform is accomplished by the following way:

1) The voltage proportional to the current i2 in secondarywinding and the induced voltage in tertiary winding, u3,are registered.

2) The integral of u3(t) is determined by an analogicalintegrator connected to tertiary winding, which allows themeasuring of initial flux linkages, (t0). So, the initialflux is measured, and not estimated using second orderdifferences as proposed by [7].

3) Evaluations of three successive current samples aremade. If they are larger than 150% of the maximum loadcurrent, the secondary flux linkage is calculated by (2),using the trapezoidal integration method.

4) Calculation of the exciting current, ie, using the saturationcurve and the constant , in accord to (3).

5) Calculation of the corrected secondary current, bysumming ieto the current i2, in accordance to (4).

The voltage u3applied to the port 3 is necessary to calculate numerically, because the analogical integrator only givesadequate values of only about 1/6 of cycle in 60 Hz, after thefault occurrence.

IV. HARDWARE IMPLEMENTATION

The electric circuit used to obtain the primary current isshown in Fig. 3.

Fig. 3. Circuit used to obtain the primary current waveform.

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The transmission line is reproduced by a series associationof three pairs of iron core reactors with non-magnetic gap toassure linear properties up to 40 A. The time constant of theartificial transmission line is 150 ms. In normal conditions, thecurrent is limited by a resistive loadRL= 1.9 k.

The fault is simulated by closing the synchronous switch,which consists in a triac controlled by a circuit based on amicrocontroller PIC16F877. So, the fault incidence angle maybe set in the range 0o-180o.

The CT used in the laboratory measurements has a coremade of grain oriented silicon steel, with the following data:magnetic path length: 0.342 m; gap length: 0.001 m; corecross-section area: 0.00132 m2; lamination thickness: 0.3 mm;stacking factor: 0.95; core weight: 3 kg; turns ratio (primary /secondary / tertiary): 240 / 240 / 240; rated primary current: 5A; rated secondary current: 5 A; secondary winding resistance:0.64 ; secondary winding leakage inductances: negligible;

core electric conductance, : 0.00083 S; rated burden: 1.2 .The saturation curve and the major dynamic loop - ie(60

Hz), obtained in laboratory, are shown in Fig. 4.

0.00 4.00 8.00 12.00 16.00 20.00

Time ( s )

0.00

0.20

0.40

0.60

0.80

FluxLin

kage(V.s

)

Fig. 4. Major dynamic loop and saturation curve measured in 60 Hz.

A way to fit the saturation curve is to use a sequence of

points with coordinates (ie, ) in an ordinate table [16]. Avalue of ie corresponding to an intermediate value of isobtained using a search routine and linear interpolation. So,the parameter is used, as indicated in (3).

After computer simulation studies, the proposed algorithmwas implemented in laboratory, using a microcomputer and a16-bit data acquisition board. The sampling rate was 333samples/cycle.

V. RESULTS

Two different secondary burden are considered in thelaboratory measurements, whose impedances are 4.3 + j 0

and 2.6 +j3.6 , in 60 Hz.

To evaluate the performance of the algorithm, the transienterror, T,is calculated at every sampling instant:

(%)100.2 1

12

F

FN

I

iiK = (5)

where KN is the turns ratio of the CT, i2

is the secondarycurrent, i1Fis the primary current and I1Fis the RMSvalue ofthis current in symmetrical regime.

Fig. 5 and Fig. 8 show the primary and secondary currents.Fig. 6 and Fig. 9 show the instantaneous RMS values of thesecurrents.

The transient errors are shown in Fig. 7 and Fig. 10.Fig. 11 and Fig. 12 show the current waves in symmetrical

regime.

0.02 0.04 0.06 0.08 0.10

Time ( s )

-20.00

-10.00

0.00

10.00

20.00

30.00

Current(A)

PRIMARY

SECONDARY - DISTORTED

SECONDARY - CORRECTED

Fig. 5. Current waveforms Burden: 4.3 +j0 .

0.00 0.04 0.08 0.12 0.16 0.20

Time ( s )

0.00

4.00

8.00

12.00

16.00

CurrentRMS

(A)

Fig. 6. Current RMS versus time Burden: 4.3 +j0 .

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0.00 0.10 0.20 0.30 0.40 0.50

Time ( s )

-20.00

0.00

20.00

40.00

60.00

80.00

TransientError(%)

CORRECTED

DISTORTED

Fig. 7. Transient error Burden: 4.3 +j0 .

0.22 0.24 0.26 0.28 0.30

Time ( s )

-20.00

-10.00

0.00

10.00

20.00

30.00

Current(A)

PRIMARY

SECONDARY - DISTORTED

SECONDARY - CORRECTED

Fig. 8. Current waveforms Burden: 2.6 +j3.6 .

0.00 0.10 0.20 0.30 0.40 0.50

Time ( s )

0.00

4.00

8.00

12.00

16.00

CurrentRMS(A)

Fig. 9. Current RMS versus time Burden: 2.6 +j3.6 .

0.00 0.10 0.20 0.30 0.40 0.50

Time ( s )

-20.00

0.00

20.00

40.00

60.00

TransientError(%)

CORRECTED

DISTORTED

Fig. 10. Transient error Burden: 2.6 +j3.6 .

0.48 0.48 0.48 0.49 0.49

Time ( s )

0.00

4.00

8.00

12.00

16.00

Current(A)

PRIMARY

SECONDARY (CORRECTED)

SECONDARY ( DISTORTED)

Fig. 11. Current waveforms in symmetrical regime Burden: 4.3 +j0 .

0.49 0.50 0.50 0.50

Time ( s )

0.00

4.00

8.00

12.00

16.00

Current(A)

PRIMARY

SECONDARY (CORRECTED)

SECONDARY ( DISTORTED)

Fig. 12. Current waveforms in symmetrical regime Burden: 2.6 +j3.6 .

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Table I shows the maximum transient errors, T, that occurin the correction processes.

TABLEIMAXIMUM TRANSIENT ERRORS

BURDEN()

TDISTORTED(%)

TCORRECTED(%)

4.3+j0.0 70.9 7.52.6+j3.6 52.1 4.0

Table II shows the magnitude error, S. and phase error, ,of the secondary fault currents in symmetrical regime. Themagnitude error is calculated by the following expression, inwhich the RMS values are considered:

(%)100.1

12

F

FNS

I

IIK = (6)

TABLEIIMAGNITUDE AND PHASE ERRORS IN SYMMETRICAL REGIME

BURDEN()

SDISTORTED

(%)

SCORRECTED

(%)

DISTORTED

(O)

CORRECTED

(O)

4.3+j0.0 2.8 -0.03 8.7 0.012.6+j3.6 12.2 0.52 4.3 0.42

The magnetic trajectories in the phase plane - ie for theresistive burden are shown in Fig. 13. These trajectoriesdescribe asymmetric minor loops, because the inclusion of theconstant in (3).

-4.00 0.00 4.00 8.00 12.00

Excitation Current ( A )

-0.20

0.00

0.20

0.40

0.60

FluxLinkage(V.s

)

Fig. 13. Magnetic trajectories in phase plane - ie Burden: 4.3 +j0.0 .

VI. CONCLUSION

The success of the secondary current correction is extremelydependent of the accurate determination of the initial flux inthe instant of the fault occurrence. In other methods, the initialflux is determined by estimation. However, such processes can

cause significant errors. In the proposed technique, the initialflux imposed by the primary current is measured by ananalogical integrator, inside a time interval that result accuratevalues. Moreover, the gap reduces the residual flux to anegligible value.

The loss of accuracy caused by the increase of the excitingcurrent is compensated by the numeric processing performedby the IED. In consequence, it is possible to use the same typeof CT in the protection and in the measurement.

The proposed correction method avoids the CT oversizing.Thus, the magnetic core dimensions become smaller and theratio and phase errors are reduced. The inserted air gap allowsan additional reduction of the core, because the secondary timeconstant, the remanence and the magnetic induction decrease.

Another advantage of this technique is that it is notnecessary the knowledge of the impedances of the load,secondary winding and connection wires to calculate the

secondary excitation voltage. This practice causes significanterrors, because not always such impedances are preciselyknown. Another problem is that any change of its valuesrequests modifications in the settings of the IED.

The CT must have a tertiary winding. However, this is not asignificant problem, because this type of CT is easily availablein the trade. Many CTs are manufactured with two or morelow current windings. Moreover, these characteristics can bespecified in the proposal of acquisition of those devices,without practically to increase the cost of CT, because thecurrent in tertiary winding is very low. So, this winding can bebuilt with thin wire, which is used for measurement of theinduced voltage to calculate the magnetic flux in the iron core.

The presented results indicate that the proposed methodcorrects the distorted secondary current in a satisfactory wayand the errors introduced by the iron core CTs are significantlyreduced.

ACKNOWLEDGMENT

The authors thank Prof. W. L. A. Neves of FederalUniversity of Campina Grande for his stimulating interest inthis work and his suggestions.

REFERENCES

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[4] T. Conrad and D. Oeding, A method to correct the distorted secondarycurrents of current transformers, inProc. PSCC, 1987, pp. 311315.

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[7] Y. C. Kang, U. J. Lim, S. H. Kang, and P. A. Crossley, Compensationof the distortion in the secondary current caused by saturation andremanence in a CT,IEEE Trans. Power Del., vol. 19, no. 4, pp. 1642-1649, Oct. 2004.

[8] F. Li, Y. Li, and R. K. Aggarwal, Combined wavelet transform andregression technique for secondary current compensation of current

transformers,IEE Proc.Gener. Transm. and Dist., vol. 149, no. 4, pp.497-50, Jul. 2002.[9] J. Pan, K. Vu, and Y. Hu, An efficient compensation algorithm for

current transformer saturation effects, IEEE Trans. Power Del., vol.19, no. 4, pp. 1623-1628, Oct. 2004.

[10] K. M. El-Naggar, and M. I. Gilany, A discrete dynamic filter fordetecting and compensating CT saturation, Elect. Power Syst.

Research, vol. 77, pp. 527-533, 2006.[11] A. Hooshyar and M. Sanaye-Pasand, Accurate measurement of fault

currents contaminated with decaying DC offset and CT saturation, vol.27, no. 2, pp. 773-783, Apr. 2012.

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Fagner de Araujo Pereira was born in CampinaGrande, Brazil, in 1982. He received the B.Sc. andM.Sc. degrees in electrical engineering from theUniversidade Federal de Campina Grande (UFCG),Campina Grande, Brazil, in 2010 and 2012,respectively, where he is currently pursuing the D.Sc.degree. Currently, he is teaching in the Escola TcnicaRedentorista (ETER), Campina Grande, Brazil. Hisresearch interests include electronic circuits and digitalsignal processing.

Francisco das Chagas Fernandes Guerrawas bornin Antenor Navarro, Brazil, in 1954. He received theB.Sc. and M.Sc. degrees in electrical engineeringfrom the Universidade Federal da Paraiba (UFPB),Campina Grande, Brazil, in 1977 and 1982,respectively, and D.Sc. degree in UniversidadeFederal de Campina Grande (UFCG), in 2007.Currently, he is teaching in the Department ofElectrical Engineering, UFCG, Campina Grande,Brazil. His research interests include magneticcircuits, power quality and power system protection.

Edson G. da Costa (M03) was born in 1954 inRibeiro, Brazil and started his academic career inAreia, Brazil. He obtained the B.Sc., M.Sc. and D.Sc.degrees, all in electrical engineering, respectively in1978, 1981 and 1999 (Federal University of Paraba).Since 1978, he is teaching in the Federal University ofCampina Grande (UFCG), Brazil. His researchinterests include high voltage equipments, electric fieldmapping, partial discharges, finite element method,surge arresters and insulation systems. Dr. Guedes is amember of IEEE, CIGR and SBA.

Benemar Alencar de Souza (M02SM05)received the B.Sc., M.Sc., and Ph.D. degrees inelectrical engineering from the Federal Universityof Paraba, Campina Grande, Brazil, in 1977, 1981,and 1995, respectively. Currently, he is anAssociate Professor with the Department of

Electrical Engineering at the Federal University ofCampina Grande. His main research activities areon optimization methods applied to power systems,electromagnetic transients, power quality and faultdiagnostic.