yu2010

1340 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 3, JULY 2010

Detection and Correction of SaturatedCurrent Transformer Measurements Using

Decaying DC ComponentsChi-Shan Yu, Member, IEEE

AbstractWhen fault currents contain decaying dc components,current transformers (CTs) face the risk of becoming saturated.Traditionally, fault current waveform or CT model analyses wereused to detect CT saturation. This paper analyzes the decayingdc components in fault currents to detect CT saturation. Thedecaying dc component in fault currents is first estimated usingphasor-based computations. Such a component is then used to de-fine a detection index. The proposed detection index can be easilyused to detect CT saturation because its value in an unsaturatedperiod is within a pre-known range. After CT saturation has beendetected, the current samples and phasors in the latest unsatu-rated period are used to correct the saturated current samples.The proposed algorithm was tested using MATLAB/SIMULINKsimulator and realized on a DSP Starter Kit to demonstrate itseffectiveness and applicability.

Index TermsCurrent transformers, decaying dc component,phasor, saturations.

I. INTRODUCTION

C URRENT transformers (CTs) are used to measure thefault currents in protection relays. If the fault currents arepurely sinusoidal, CTs can measure as much as 20 times therated currents with acceptable error [1]. However, if the mea-sured fault current contains a decaying dc component or if anauto-reclosure follows a permanent fault [2], the CT may be-come saturated even if the fault current is not very large. Thesaturated CT may cause distorted measurements and inaccuraterelay operations.

In recent decades, many algorithms [3][10] have been pub-lished to address CT saturation problems. CT model-based algo-rithms [3][5] can simultaneously achieve detection and correc-tion of CT saturation. In the fault period, the predicted excitationcurrents are used to detect and correct the CT saturation. Math-ematical equations [3] or neural networks [4], [5] can be used toobtain the excitation currents. Another approach is to analyzethe time-domain fault current waveforms [6][10]. The mainidea behind this approach is that current waveforms are non-smooth at the beginning and end of a CT saturated period. In [6],[7], discrete wavelet transform (DWT) was used to detect thenon-smooth variations. In [8], the difference functions of current

Manuscript received May 27, 2009; revised October 01, 2009, November 24,2009. First published April 19, 2010; current version published June 23, 2010.This work was supported by the National Science Council under Grant NSC96-2628-E-027-115-MY2. Paper no. TPWRD-00401-2009.

The author is with the Department of Digital Technology Design, NationalTaipei University of Education, Taipei, Taiwan, R.O.C. (e-mail: [email protected]).

Digital Object Identifier 10.1109/TPWRD.2010.2045137

samples were used to detect CT saturation. In [9], a gradient-based criterion was used to detect the non-smooth variations.In [10], a simpler algorithm that used an identified referencepoint was proposed to discriminate saturated periods. After thesaturated periods were identified, other algorithms were used tocorrect the saturated current samples. Regression or least-squareanalyses on the unsaturated samples [6], [10] were widely usedfor corrections. An artificial intelligence method [7] was alsoused to correct the saturated samples.

CT saturation can be accurately detected using the algorithmsproposed in [3][10]. However, some problems may still arise.For example, the performances of CT model-based algorithms[3][5] may be degraded when the CT parameters are changed.Moreover, mild CT saturation cannot easily be detected usingwaveform-based algorithms [6][9]. Because the detection al-gorithms of [6], [7] were developed based on edge-trigger con-cepts, the saturation period has the chance to be discriminatedas an unsaturated period.

Generally, CT saturation is caused by the decaying dc com-ponent in a fault current. When a CT is saturated, the param-eters of the decaying dc component will be changed. Hence,this paper attempts to use the information contained in such acomponent to detect CT saturation. To achieve this goal, the de-caying dc component is estimated using a phasor-based compu-tation, and the decaying factor in the decaying dc component isused to define a detection index. When a CT is unsaturated, thisindex will be within a small pre-known range. When a CT issaturated, this index will oscillate within a wide range. Thus, alevel-trigger concept can be developed to detect CT saturation.When a saturated current is detected, the current samples andphasors in the latest unsaturated period are used to correct thesaturated current. Although the proposed detection index is de-signed based on the variation of a decaying factor, ac saturationcan still be detected using the proposed index. The proposed al-gorithm was tested using the MATLAB/SIMULINK [11] simu-lator to demonstrate its effectiveness. A DSP Starter Kit (DSK)for TMS32C6416 [12] was also used to evaluate the real-timeapplicability of the proposed algorithm.

II. THE PROPOSED DETECTION ALGORITHM

A. The Saturation Detection IndexTo define a detection index, a fault current containing a

fundamental component and a decaying dc component is de-scribed as follows:

(1)0885-8977/$26.00 2010 IEEE

YU: DETECTION AND CORRECTION OF SATURATED CT MEASUREMENTS 1341

where and denote the magnitude and phaseangle of the fundamental component, respectively. and de-note the magnitude and time constant of the decaying dc compo-nent, respectively. If the fault current is measured by samplesper cycle, the th sample of the fault current can be representedas follows:

(2)

where the sampling time , the sampling angleand the decaying factor .

In an unsaturated current measurement, the decaying factorvaries within a small range, although the time constant for a de-caying dc component varies within a wide range. For example,if the sampling frequency is 3840 Hz and the pos-sible time constant of a decaying dc component varies within0.1 to 5 cycles, the corresponding decaying factor only varieswithin a small range [0.8553, 0.9969]. However, when the cur-rent is saturated, the measured will be outside of that smallrange. Thus, the value of a decaying factor can be used toidentify whether a CT is saturated or not.

In this paper, the decaying factor was estimated using thephasor-based computations. To achieve this estimation as fast aspossible, the fractional cycle discrete Fourier transform (DFT)[13] was used to compute a current phasor. The obtained currentphasor has the following form:

(3)

where denotes the accurate fundamental phasor anddenotes the phasor domain decaying dc component. Meanwhile,the subscript denotes that the phasor is obtained just afterthe th sample is measured. When the th sample ismeasured, the phasor can be represented as follows:

(4)

To reduce the computational burden, recursive DFT [13] wasused to update the new phasor . Comparing the phasors

and obtained by the recursive DFT, the relationsbetween , and are as follows:

(5)

where . When the th sample is mea-sured, the phasor can also be obtained by the recursiveDFT computations. Using the relation (5), the division of twophasor differences and can beexpressed as follows:

(6)

Thus, the magnitude of a decaying factor can be estimated asfollows:

(7)

Then, also using the relation (5), the magnitude of the phasordomain decaying dc component can be estimated as follows:

(8)

In most cases, the estimated can be used to detect CT sat-uration. However, when the decaying dc component of a faultcurrent is very small and the CT is unsaturated, the relation be-tween three consecutive current phasors will have the followingrelation:

(9)

Substituting relation (9) into (7), the numerator and the denom-inator of will be very small. Thus, if the estimated isdirectly used to detect CT saturation, numerical stability prob-lems may be met when the decaying dc component is very small.To increase the numerical stability, and are combined todefine a detection index (DI) as follows:

(10)

where the constant is a weighting gain whose value dependson the magnitude of the decaying dc component of a fault cur-rent. If the decaying dc component is large, the constant isset as a small value. While the decaying dc component of a faultcurrent is very small, the constant can be set as a large valueto prevent the numerical problem. Following these two ideas,the rule to obtain the constant is designed as follows.

The rule to obtain the constant :

IF

ELSE

END

In the rule mentioned above, the ratio is used to eval-uate the magnitude of a decaying dc component. The level value10 is selected to ensure the constant is set when the de-caying dc component is very small.

To tolerate the measurement noise, the threshold boundary ofthe detection index is defined as [0.85,1.05]. Thus, the proposedCT saturation detection algorithm is described as follows.


The algorithm to detect CT saturation:

IF four consecutive DI are in the boundary [0.85, 1.05]The CT is not saturated and

ELSE

The CT is saturated and

END

Using the proposed algorithm, CT saturation can be detected.The following three conditions are used to explain the opera-tions of the proposed detection algorithm.

1) Condition 1: If the decaying dc component of a fault cur-rent is large, the ratio will be smaller than 10.Under this condition, the constant will be set as 0.005,and (10) is approximated to (7). Thus, CT saturation canbe detected by judging whether the value of (10) is in thethreshold boundary or not.

2) Condition 2: If the decaying dc component of a fault cur-rent is very small and the fault current is unsaturated, theratio will be larger than 10. Under this condition,the constant will be set as 1, and the weighting currentphasor will dominate the numerator and the denomi-nator of (10). Thus, the value of (10) will approximate tounity, and an unsaturated period can be detected.

3) Condition 3: If the decaying dc component in a fault cur-rent is very small and the fault current is saturated, the mag-nitude of the current phasor will be decreased due to theincrease in the magnetizing current. The phasor differences( and ) and the magni-tude of the phasor domain decaying dc componentwill be increased due to the saturated waveform distortion.Under this condition, the ratio will be smaller than10 and the constant is set as 0.005. Thus, CT saturationcan be detected by judging whether the value of (10) is inthe threshold boundary or not.

B. The Fault Detection IndexGenerally, the CT saturation detection algorithm needs to be

activated by a fault detection algorithm. In this paper, the suddenchange in current phasor magnitude is used to detect a fault.To achieve this, one adaptive threshold value is defined asfollows:

(11)

where and are the mean and standard deviation values ofthe current phasor magnitude , respectively. The most recent

phasors were used to obtain , while the most recentphasors were used to obtain . Meanwhile, the gain wasselected. To prevent this detection from being too sensitive, theminimum value of the standard deviation was limited to

. If three consecutive are larger than the thresholdvalue , it can then be concluded that a fault is detected.After a fault is detected, the CT saturation detection algorithmis activated.

C. Adaptive Tuning of the Threshold ValuesGenerally, the threshold boundary [0.85,1.05] can be used to

detect CT saturation under various line impedance values. How-ever, for a specific transmission line, the threshold boundary canbe adaptively tuned to improve the detection performance. Theproposed tuning procedures are described as follows.

1) After a fault is detected, the threshold boundary [0.85,1.05]is used to discriminate the first un-saturated period.

2) After the end of the un-saturated period is detected, alldetection indices obtained in the latest unsaturated pe-riod are used to obtain the new threshold boundary as

. The threshold values and areobtained as follows:

(12)

where and are the mean and standard deviationvalues of all of the detection indices in the latest un-satu-rated period, respectively. The gain was selectedfor gaining the . To prevent this detection from beingtoo sensitive, the minimum value of the standard deviationis limited to .

3) Next, the new threshold boundary is used forCT saturation detections.

III. THE PROPOSED CORRECTION ALGORITHM

Using the proposed detection algorithm, the saturated andthe unsaturated current waveform periods can thus be discrim-inated. When a CT is unsaturated or before the end of the firstunsaturated period is detected, the measured current samples areused directly. When the end of an unsaturated period is detected,the proposed algorithm begins to correct the saturated samples.

When a CT is saturated, the current measurements and thecurrent phasors in the latest unsaturated period are used to obtainthe current waveform parameters. Assume that the CT saturationwas detected just after the th current sample was measured, andthat there are unsaturated current phasors obtained in the latestunsaturated period . Using theunsaturated phasors, three summation variables , andare defined as follows:

(13)

(14)

(15)

Using the three summation variables and the relation of (7), theaveraged decaying factor in the latest unsaturated period canbe obtained as follows:

(16)


Fig. 1. Flowchart of the proposed CT saturation detection/correction algo-rithm.

Then, applying the concepts of (3)(5), the accurate funda-mental phasor can be obtained as follows:

(17)

Considering the time domain waveform, can be obtainedusing the averaged computations as follows:

(18)

Finally, the corrected current sample can be obtained asfollows:

(19)

The proposed CT saturation detection/correction algorithm isdescribed using a flowchart shown in Fig. 1. At first, the pro-posed algorithm is in the no fault stage where the fault detec-tion algorithm proceeds. After a fault is detected, the proposedalgorithm comes into the unsaturated stage and the CT satura-tion detection algorithm is activated. After the end of an un-saturated period is detected, the proposed algorithm comes intothe saturated stage. In the saturated stage, the current measure-ments and current phasors in the latest unsaturated period areused to correct the saturated current measurements. The correc-tions continue until the beginning of a new unsaturated periodis detected. Then, the proposed algorithm goes back to the un-saturated stage and the CT saturation detection will continue.The loop between the unsaturated and the saturated stages canbe stopped by a relay when a relay has received enough faultmeasurements.

IV. SIMULATION EVALUATIONSIn this section, the proposed algorithm was evaluated by a

simple power system shown in Fig. 2. The parameters of this

Fig. 2. Single-line-diagram of a sample power system.

Fig. 3. CT magnetizing curve with the saturation point (9.52 A, 0.48 Vs).

TABLE IPARAMETERS OF THE SIMULATION SYSTEM

system and the CT model are listed in Table I. The CT modeldescribed in [14] was used to model the CT. The magnetizingcurve of the CT is shown in Fig. 3, which was generated by theATP [15] with the saturation point of (9.52 A, 0.48 Vs). The testpower system was simulated using the MATLAB/SIMULINKsimulator. Fault currents were measured at Bus S and pre-fil-tered using second order Butterworth low-pass filters with 360Hz cut-off frequency. The filtered analog measurements werethen sampled by 3840 Hz (64 samples per cycle). The fractionalcycle DFT was used to obtain the phasors for all the simulations.The window length of the fractional cycle DFT is eight samples(1/8 cycle).

In the following simulations, the error index (EI) [10] is usedto evaluate the accuracy of the rms value. The rms value of acurrent signal is defined as follows:

(20)

where (the sample number per cycle). The error index(EI) is defined as follows:

% (21)


where denotes the rms current on the CT primaryside, denotes the rms current on the CT secondary side,and denotes the turns ratio of a CT.

A. Demonstrations of the Proposed Algorithm Using CaseStudies

In the following tests, the proposed algorithm was evaluatedusing some specific cases, such as severe saturation, mild satu-ration, high remanence, and ac saturation cases.

Case 1: Severe Saturation Case: In this case, a three phaseshorted fault was used to demonstrate the performances of theproposed algorithm under a severe saturation condition. Thefault occurred at 0.05 s, at a 0.3 per-unit distance away fromBUS S, and with a 0.1 fault resistance. Fig. 4(a) depicts thecurrent waveforms, in which the corrected, saturated, and idealcurrents are compared. All currents are referred to the CT pri-mary side. The ideal current denotes the current which ignoresthe CT measurement effects. The proposed detection index ispresented in Fig. 4(b). The fault and CT saturation detectionresults are shown in Fig. 4(c). Using the EI index to evaluateaccuracy, the EI index is significantly reduced from 48.8% (sat-urated current) to 1.71% (corrected current).

Fig. 4(b) shows that the detection index performs a transienthigh value just after occurring a fault (0.05 s) to cause a momen-tary saturation detection result of . This is caused by themixed-data windowing effect of a DFT computation [13]. Sincethe proposed correction algorithm begins to correct the saturatedcurrent after the end of the first unsaturated period has been de-tected, this windowing effect will not affect the performance ofthe proposed algorithm.

Fig. 4 also shows that the windowing effect delays theproposed detection index entering the threshold boundary

at the end of each saturated period. However, theproposed detection index can detect the beginning of a saturatedperiod very fast. Indeed, the main purpose of a saturation de-tection algorithm is to identify the unsaturated current samplesfor waveform corrections. Thus, the accuracy of identifying anunsaturated current sample is more important than the accuracyof identifying a saturated current sample. Although a time delayis inevitable for the proposed phasor-based algorithm to detectthe end of a saturated period, the proposed detection algorithmcan ensure the accuracy of the identified unsaturated currentsamples. Thus, the identified unsaturated current samples canbe used to accurately correct the saturated current.

Case 2: Mild Saturation Case: In this case, an A-phasegrounded fault was used to demonstrate the performances ofthe proposed algorithm under a mild saturation condition. Thefault occurred at 0.05 s, at a 0.7 per-unit distance away fromBUS S, and with a 2 fault resistance. Fig. 5(a) shows thecorrected, saturated and ideal A-phase current waveforms.Notably, the CT is not saturated in the first fault cycle, andthe saturation is very mild in the second fault cycle. The cor-rected, saturated, and ideal current waveforms are shown inFig. 5(a), respectively. The obtained detection index is shownin Fig. 5(b), while the saturation detection result is shown inFig. 5(c). Although the saturation is very mild, the proposedalgorithm can still be used to correct the saturated current. Itcan be noted that the corrected and the ideal current waveforms

Fig. 4. Simulation results for a severe saturation case. (a) A-phase currentwaveforms. (b) Proposed detection index. (c) Saturation and fault detectionresults.

Fig. 5. Simulation results for a mild saturation case. (a) A-phase current wave-forms. (b) Proposed detection index. (c) Saturation and fault detection results.

are almost overlapping because the corrected current is veryaccurate. Using the EI index to evaluate accuracy, the EI indexis reduced from 2.18% (saturated current) to 0.61% (correctedcurrent). Thus, the proposed algorithm can work properly in amild saturation case.

Case 3: Various Remanence Case: The remanence in a CTcore may be large after the auto-reclosure operation for a per-manent fault. The presence of larger remanence may make the


Fig. 6. Simulation results of case 3. (a) Flux waveforms of various remanences.(b) A-phase current waveforms under various remanences.

CT becoming saturated easily. In this case, the same A-phasegrounded fault used in case 2 was assumed to be already tripped,and the fault was reclosed at 0.05 s. For ease of simulations, var-ious remanences (25% (0.12 Vs) and 50% (0.24 Vs)) were di-rectly set at the beginning of each simulation and the proposedalgorithm was activated as soon as the circuit was reclosed.Fig. 6(a) shows the fluxes under various remanence conditions.Fig. 6(b) shows the saturated and corrected current waveformsunder various remanence conditions. Meanwhile, the ideal cur-rent waveform is also compared in Fig. 6(b). Using the proposedalgorithm, the EI indices for the 25% and 50% remanence condi-tions are reduced from 24.9%% and 28.7% to 1.95% and 3.53%,respectively. Thus, the proposed algorithm can work properlywhen various remanences exist.

Case 4: Very Large Remanence Case: In this case, the samereclosure condition of case 3 was used, and 96% remanence(0.46 Vs) was directly set at the beginning of the simulation andthe proposed algorithm was activated as soon as the circuit wasreclosed. The simulation results are shown in Fig. 7. Fig. 7(a)shows that the first unsaturated period is very short because theremanence is very large. In Fig. 7(b), the obtained DI did not sat-isfy the unsaturated condition until the second fault cycle. Afterthe end of the first detected unsaturated period, the proposed al-gorithm begins to correct the saturated current. Since the currentdistortions have been accurately corrected, the corrected and theideal current waveforms are almost overlapping. Using the EIindex to analyze the results after the second fault cycle, the EIis reduced from 20.3% (saturated current) to 0.69% (correctedcurrent). Thus, the proposed algorithm can work properly undera very large remanence condition.

Case 5: AC Saturation Case: If a fault current does notcontain a decaying dc component or a CT does not contain alarge remanence, a CT will not easily become saturated, unlessthe fault current is very large [1] or a CT has a large burden.This phenomenon is called ac saturation of a CT. In this case,an A-phase grounded fault occurring at a 0.1 per-unit distanceaway from BUS S with a 0.1 fault resistance is tested. To

Fig. 7. Simulation results of case 4. (a) A-phase current waveforms. (b) Pro-posed detection index.

Fig. 8. Simulation results of case 5. (a) A-phase current waveforms. (b) Pro-posed detection index. (c) Saturation and fault detection results.

perform ac saturation condition, the CT burden is increasedfrom 0.7 to 4.5 and the fault inception time is changedfrom 0.05 s to 0.0535 s. This fault inception time can causethat the A-phase fault current does not contain a decaying dccomponent. Meanwhile, such a large CT burden can make aCT becoming saturated easily.

The simulation results are shown in Fig. 8. As can be seenin Fig. 8(a), the first unsaturated period is too short to be de-tected. In Fig. 8(b), the obtained DI did not satisfy the unsat-urated condition until the second fault cycle. After the end ofthe first detected unsaturated period, the proposed algorithm be-gins to correct the saturated current. Notably, the corrected andthe ideal current waveforms are almost overlapping because thecorrected current is very accurate. Using the EI index to ana-lyze the results after the first fault cycle, the EI is reduced from


TABLE IIPERCENTILE ANALYSES OF THE EI INDEX FOR STATISTICAL EVALUATIONS

13.9% (saturated current) to 0.12% (corrected current). Obvi-ously, although the proposed detection index is designed basedon the variations of a decaying factor, ac saturation can still bedetected using the proposed index.

B. Statistical EvaluationsTo analyze and demonstrate the performance of the proposed

algorithm under normal fault conditions in detail, different faulttypes, inception angles (0-degree to 270-degree), fault locations(0.1 to 0.5 p.u. location from Bus S), short-circuit capacities(1500 to 3000 MVA), fault resistances (0.1 to 4 ), phase anglesbetween the voltages and (10-degree to 20-degree), CTburden impedance (0.7 to 1 ), and CT burden power factor (0.5to unity) were considered to generate over 5800 cases. In allthe simulation cases, the CT saturation occurred in about 3900cases.

The EI index was used to analyze the A-phase current wave-forms of all cases, and the percentile method [10], [16] was usedto analyze the percentage distribution of all the computed EI re-sults. Table II shows the analysis results of the saturated andcorrected currents. The maximum EI of the saturated currents is60.6% which occurred in a severe three-phase shorted fault case.Using the proposed algorithm, the maximum EI of the correctedcurrents is therefore reduced to 7.77%, which also occurred ina severe three-phase shorted fault case. The averaged EI for allcases is 0.72%. In considering the corrected current results indetail,90% of the EI are smaller than 2.05%. Thus, the proposedalgorithm can support accurate correction currents under var-ious fault conditions and CT conditions.

C. Evaluation With Considering Low Order HarmonicCurrent Sources

Here, harmonic current sources (4% at the second and 4%at the third harmonics) were injected from the position of thevoltage to evaluate the performance of the proposed algo-rithm under an active low-order harmonic environment with cur-rent % which exceeds the current harmonic limi-tation recommended in [17]. For ease of comparison, the samethree-phase shorted fault used in case 1 is also tested in this case.The simulation results are shown in Fig. 9. As can be seen, inthe pre-fault and the unsaturated periods, the computed detec-tion index contains an oscillation which is caused by the injectedharmonics. Notably, the oscillation is larger in a pre-fault periodas the fault current with a larger fundamental component can

Fig. 9. Simulation results with considering harmonic sources. (a) A-phase cur-rent waveforms. (b) Proposed detection index. (c) Saturation detection results.

TABLE IIIEI INDEX ANALYSES FOR THE HARMONIC CURRENTS

WITH DIFFERENT MAGNITUDES

reduce the effect of the injected harmonics. Using the proposedalgorithm, CT saturation detections are almost not affected bythe injected harmonics. However, the injected harmonics mayaffect the accuracy of the corrected waveform. This is becausethe proposed CT saturation detection algorithm does not needvery accurate phasor computations but the waveform correctiondoes. When using the EI index to evaluate the accuracy, the EIindex is reduced from 49.4% (saturated current) to 5.61% (cor-rected current). Compared with the results of case 1, the accu-racy of the corrected current is moderately affected by the in-jected harmonic currents with 5.66% current THD.

To evaluate the performance of the proposed algorithm underdifferent harmonic magnitudes, all the magnitudes of the in-jected harmonic currents were reduced from 4% to 3%, 2%,and 1%. The EI indices of the corrected currents are all listedin Table III. Notably, the EI index decreases when the magni-tudes of the injected harmonics decrease. Thus, if the magni-tudes of the injected current harmonics satisfy the limitationsrecommended in [17], the proposed algorithm is only slightlyaffected by the injected harmonics.D. Realization of the Proposed Algorithm on a DSP

In this subsection, the proposed algorithm was implementedon a 1-GHz TMS320C6416T DSP Starter Kit (DSK) [12] toverify whether the proposed algorithm could satisfy the realtime requirement.


C language was used to develop the DSP program which in-cludes the fractional cycle recursive DFT subroutine, the faultdetection subroutine, the saturation detection subroutine, andthe saturation correction subroutine. The transformation of aphasor from a rectangle form to a polar form and the divisioncomputation of phasors were accomplished using the CORDICalgorithm [18]. To accelerate the program speed, the DSP pro-gram was programmed using the Q16 fixed-point arithmetic.Thus, the precision for a number can be achieved as . CodeComposer Studio (CCS) v3.1 [19] was used to develop the pro-gram, by which we can debug the program and analyze the pro-gram performances.

The performance of the DSP program was evaluated using theprofile analysis tool in CCS to indicate the memory usage andthe execution time. The total memory required for all DSP pro-grams was less than 11 kbytes. The execution time per sampleunder the unsaturated and saturated periods is different. Themaximum execution time per sample is almost 4200 DSP cy-cles which occurred at a saturated period. Since the DSP on theDSK board operated at 1 GHz, the maximum execution time persample was less than 4.2 s, which is significantly smaller thanthe fault measurements sample period ( s).Thus, the proposed algorithm has the potential to be applied forpractical applications.

V. CONCLUSION

In this paper, a new algorithm was proposed to detect and cor-rect the saturated CT measurements using the information con-tained in a decaying dc component. A great number of computersimulations have been performed on the MATLAB/SIMULINKsimulator to demonstrate the performance of the proposed algo-rithm under various fault and system conditions. The results ofthe performance studies indicate that the proposed algorithm hasthe following features.

1) The threshold values of the proposed detection index arepre-known. Thus, a level detection can be designed to de-tect CT saturation.

2) Even in a mild saturation case, smooth waveform distortioncan still be detected by the proposed algorithm.

3) In the case of large remanence, the proposed algorithm canwork properly.

4) Although the proposed detection algorithm is designedbased on the variations of a decaying factor, ac saturationcan still be detected using the proposed detection algo-rithm.

5) The proposed algorithm is effective under various fault andsystem conditions.

6) The proposed algorithm has been realized on a DSP toverify the real-time applicability.

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Correction of current transformer distorted secondary currents due tosaturation using artificial neural networks, IEEE Trans. Power Del.,vol. 16, no. 2, pp. 18919194, Apr. 2001.

[4] H. Khorashadi-Zadeh and M. Sanaye-Pasand, Correction of saturatedcurrent transformers secondary current using ANNs, IEEE Trans.Power Del., vol. 21, no. 1, pp. 7379, Jan. 2006.

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[11] Power System Blockset Users Guide. Natick, MA: The Math Works,Inc., 2002.

[12] R. Chassaing and D. Reay, Digital Signal Processing and ApplicationsWith the TMS320C6713 and TMS320C6416 DSK, 2nd ed. New York:Wiley, 2008.

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[16] W. J. DeCoursey, Statistics and Probability for Engineering Applica-tions. New York: Newnes, 2003.

[17] IEEE Recommended Practices and Requirements for Harmonic Con-trol in Electrical Power Systems, 519-1992, 1993, IEEE, New York.

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Chi-Shan Yu (M02) received the B.S. and M.S.degrees in electrical engineering from NationalTsing Hua University, Taipei, Taiwan, R.O.C., in1988 and 1990, respectively, and the Ph.D. degreein electrical engineering from National TaiwanUniversity in 2001.

From 2001 to 2006, he was with the National De-fense University. Currently, he is an Associate Pro-fessor of Electrical Engineering with the Departmentof Electrical Engineering, National Taipei Universityof Technology, Taipei. His research areas are com-

puter relay and digital signal processing.

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