a correlation coefficient based algorithm for faults...

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERINGIEEJ Trans 2018; 13: 1394–1403Published online in Wiley Online Library (wileyonlinelibrary.com). DOI:10.1002/tee.22705

Paper

A Correlation Coefficient-Based Algorithm for Fault Detection andClassification in a Power Transmission Line

Mohammed H. H. Musa*,**a, Non-member

Zhengyou He*, Non-member

Ling Fu*, Non-member

Yujia Deng*, Non-member

This paper presents a new algorithm for fault detection and classification in a power transmission line. The fundamental ideaof the proposed algorithm is the calculation of the correlation coefficient (CC) between the current signal of each phase of thethree-phase system and its reference value. The following rule makes the decision of detecting and classifying the fault condition:when the system is running under healthy condition, the correlation between the current signal of each phase and its referencevalue is very strong; when the system is in faulty condition, the correlation between the current signal of each phase and itsreference value is low compared to that in the healthy condition. The new algorithm is applied to a power transmission line modelestablished in PSCAD/EMTDC. Different fault circumstances such as different inception times, different fault resistances, anddifferent locations have been verified. Additionally, far-end faults with high resistance, faults occurring near a terminal, faultsconsidering variable loading angle, and faults in the presence of noise are easily detected by the proposed method. For eachpossible scenario of fault, the proposed algorithm requires only the three-phase current measurement of the local measurementunit. The results show satisfactory performance in most cases. © 2018 Institute of Electrical Engineers of Japan. Published byJohn Wiley & Sons, Inc.

Keywords: fault detection; fault classification; statistical measure; correlation coefficient; power system network.

Received 19 June 2017; Revised 14 February 2018

1. Introduction

Power system behaviors change continuously during operationbecause of faults in the transmission line, loss of generation units,switching of lines with heavy loading, and sudden change to heavyloads. Thus fault detection and classification need to be routinelyperformed by utility engineers [1,2].

Many different techniques for fault detection and classificationin power transmission line have been proposed. These techniquescan be classified into two categories: the first uses two-terminaldata, and the second uses one-terminal data [3]. Techniques suchas artificial neural network, fuzzy logic, and genetic algorithm(GA) are used widely in fault analysis of power transmissionlines. For example, methods that employ different ANN archi-tectures have been discussed 4, 5. A continuous GA has also beenused for fault section estimation 6. A novel method for classifyingdifferent types of transmission line faults by integrating wavelettransform and GA was discussed 7. It used a discrete wavelettransform (DWT) to extract the characteristic features from theinput current signals that collected at the source end, and thengave the data as an input to the GA for fault classification. Func-tional analysis and computational intelligence technique have beenapplied for fault detection and classification in power transmis-sion 8. It offers a novel stochastic illustration of the transmissionline, which enables faster detection of faults. Wavelet combinedwith neuro-fuzzy, fuzzy, adaptive neuro-fuzzy interference system

a Correspondence to: Mohammed Hussien Hassan Musa.E-mail: [email protected]

*Department of Electrical Engineering, Southwest Jiaotong University,Chengdu, Sichuan, China

**Sudanese Thermal Power Generating Company, Khartoum, Sudan

(ANFIS) approach, and adaptive neuro-fuzzy scheme have beenintroduced 9–11. The ANFIS-based method for fault classifica-tion is used in Ref. 12, and wavelet entropy and neural network arediscussed in Ref. 13. In addition to the fault analysis techniques,the pattern recognition approach has also been used [14, 15. Anovel method for high-impedance fault detection based on patternrecognition was discussed in Ref. 16. A new method for identifyingfaulty phases in a transmission system was presented in Ref. [17].It depends on readings the phase currents and obtains a fast estima-tion of phasor components in a relatively short data window [18].

However, some of the conventional techniques involve relativelycomplex mathematical operations, and some require line parame-ters such as the positive-, negative-, and zero-sequence impedances[19]. Additionally, techniques that are based on the signal pro-cessing are categorized into time, frequency, and time–frequencydomain analyses [20]. DWT techniques in some cases require cur-rent and voltage measurements to extract the fault features [21].Additionally, they require a multi-level filter, which is consid-ered an additional computational process [22]. Therefore, a simplealgorithm compared to the conventional ones is introduced toaccomplish a great task, namely fault detection and classificationin a power transmission line. It requires only the measurementof the three-phase current at the local measurement unit (MU).Additionally, few researchers have addressed the use of statisticalmeasures in power system fault analysis. Therefore, the main con-tribution of this paper is the application of statistical measures infault analysis.

The proposed algorithm computes the correlation coefficient(CC) and utilizes it as a tool for fault detection and classification ina power transmission line. Moreover, the processes are carried outby taking the current signals and dividing them into small samplesbased on the sampling rate of the signals. Then, the CC between

© 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

A CORRELATION COEFFICIENT-BASED ALGORITHM FOR FAULT DETECTION

the current signals and its reference values is calculated for thei th sample of each phase. A three-phase current at the healthystatus is captured and taken as the reference value. It is foundthat, in the normal condition, the correlation between the currentmeasurements and its reference value is very strong, and thereforethe CC gets a value greater than the threshold. On the contrary,there is a less correlation in the case of a faulty condition, andtherefore the CC gets a value less than the threshold.

This paper is organized into four major parts. The first part isan introduction to the theory of CC. The second part discussesthe basic theory of CC. The third part presents the fault detectionand classification concept based on the CC algorithm. The fourthpart is devoted to the results and discussion. Finally, we drawconclusions of the work.

2. Correlation Coefficient – Basic Theory

Correlation analysis in statistics is a measure that is used toestimate the continuous variable’s association (e.g. between twoindependent variables or between an independent and a dependentvariable). It used to describe the strength and direction of alinear relationship between two variables [23,24]. The correlationmeasure just tells us the existence of the association between x andy , but it does not show us the shape of the relationship or giveany chance to predict one variable from the other. The correlationbetween two variables x and y is defined as [25]

ρxy = cov(x , y)

σx σy(1)

In practice, (1) is used for obtaining the CC of the population.Therefore, the alternative is to use a sample CC, which can beobtained as follows:

r =

N∑j=1

(xj − x)(yj − y)

√N∑

j=1(xj − x)2

√N∑

j=1(yj − y)2

(2)

The symbolrdenotes the sample Pearson’s CC, which rangesbetween −1 and + 1 [2]. x j andyj are the j th variables. x and yrepresent the sample mean of the corresponding variables. Thesign of the CC indicates the direction of the association [25,26].Therefore, the CC’s sign can tell us the direction of the linearrelationship. If the sign of r is negative (less than zero), then thecorrelation is negative, and the slope of the line will be descending.If the sign of r is positive (>0), then the correlation is positive, andthe slope of the line will be ascending. In general, a CC of 0–0.2can be described as very weak or negligible; 0.2–0.4 as weak orlow; 0.4–0.7 as moderate; 0.7–0.9 as strong, high, or marked;and 0.9–1.0 as very strong or very high[27]. The limit 0.9–1describes the maximum linear relationship that can be obtainedbetween two variables. It is important to note that there may be anonlinear relationship between two continuous variables, but thecomputation of the CC does not sense this condition. Therefore, itis always important to evaluate the data carefully before resortingto compute the CC.

3. Fault Detection and Classification Concept Basedon the CC Algorithm

As mentioned in the previous section, the CC is used to quan-tify the strength of a direct relationship between two variables.Moreover, the current signal at normal condition can be likened toa harmonious statistical community. For example, Fig. 1(a) illus-trates the trajectories of the relationship between the current signals(I 1, I 2, and I 3) during normal operation and its reference values(I 1 ref., I 2 ref., and I 3 ref). It is observed that in the case ofthe system running in healthy status, the relationship between twovariables has a linear relationship. Figure 1(b) shows the trajecto-ries during a single-phase fault; the trajectory of the faulty phaseseems nonlinear, whereas in the healthy phase, the trajectoriesappear to be linear or semi-linear. Figure 2(a) and (b) illustratesthe current trajectories during a two-phase fault and a three-phasefault, respectively. Also, it is noted that the trajectories of thehealthy phases are found consistently, whereas the trajectories of

Current Signals Trajectories during the safe operation

(a)

Current signals trajectories during single phase fault

–0.5 0.0 0.5

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(b)

Fig. 1. Current signal trajectories during (a) normal operation (b) single-fault condition

1395 IEEJ Trans 13: 1394–1403 (2018)

M. H. H. MUSA ET AL.

Current signals trajectories during double-phase fault

Current signals trajectories during three-phase fault

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(a)

(b)

Fig. 2. Current signal trajectories during (a) a double-phase fault and (b) a three-phase fault

the faulty phases are nonlinear. Therefore, statistical measurementscan be very useful to study the linear and nonlinear relationshipbetween the current signals and their reference values. One of thesestatistical measures is the Pearson CC.

In order to apply the Pearson CC for detecting and classifyingfaults, let us define two variables whose CC we wish to obtain:

• The first variable is a reference value; it is selected to be thethree-phase current signal that is captured when the systemruns in healthy condition.

• The second variable is the three-phase current measuredduring ordinary operation, including when the system is inthe faulty state.

The reference value should be captured continuously overa specified time determined by the designers. This continuousmeasurement of the reference value is very important to guaranteethat the reference value dynamically changes if there are somechanges occurring to the power system parameters such as thevoltage level, frequency, network topology, etc. Additionally, thiscontinuous measurement will be blocked when a fault conditionis registered, and then it should reset after the fault conditionis cleared. This is because the proposed algorithm essentiallycomperes the current situation with the previous situation byfinding the CC.

The CC samples for one cycle can be modeled as

CC (k) =k∑

i=k−n+1

r(i ) (3)

where ncorresponds to the number of samples per cycle, i is theinstantaneous sample, and k is the sampling instant.

If the correlation between these two variables is very strong,this is an indication that the system is in the safe operation

mode. Opposite of that is the faulty condition, where the currentmeasurements and their reference values show less correlationcompared to that in a healthy condition. These are the ways inwhich the proposed algorithm achieves these goals. The process offault detection and classification is performed as shown in Fig. 3.It can be clarified in the following steps.

Step 1. Obtain the current measurements, where I 1, I 2, I 3, andI 0 denote the currents of phases A, B, C, and zero sequence.

Step 2. Calculate the CC for the i th sample of each phase, whereCC1, CC2, CC3, and CC0 indicate the CC for phase A, phase

B, phase C, and zero-sequence current with their reference values.Step 3. Achieve the fault detection process.After simulating several faults experiments under different

circumstances, it found that, when the system is running underhealthy condition, the CC of each phase with respect to itsreference value will be greater than the threshold. On the otherhand, when the system is in the faulty condition, the CC of eachphase with respect to its reference value will be lower than thethreshold.

Moreover, the threshold is selected to be 0.9, which indicatesthe lower limit that could describe the correlation degree of thevariables as being very strong. In other words, when the CCof the variables (current signals and their reference values) arevery strong (CC1, CC2, and CC3 > threshold), it indicates that thesystem is in the healthy state. Otherwise, the system is in the faultystate. This criterion also can be applied for the fault classificationprocess, which is the next step.

Step 4. Achieve the fault classification process. It can bestipulated as follows:

The faulty phase has a CC value less than the threshold.The healthy phase has a CC value greater than the threshold.CC0 for the earth fault (either single-phase to earth fault or

double-phase to earth fault) is found to be less 0.6.

1396 IEEJ Trans 13: 1394–1403 (2018)


Start

End

No fault

detected

No

Yes

(CC1,CC2,CC3)>threshold

Measure the three phase

currents and zero sequence

current signals (I1,I2,I3, and I0)

Fault condition

has been detected

Calculate CC value of the three phase (CC1,

CC2,CC3,and CC0)

Apply the faults classification rules:

The faulted phase will obtain a CC value less than

the threshold .

The health phase will obtain a CC value greater

than the threshold .

The CC0in case ofph-ph to earth fault is less

than 0.6.

0.6.

The CC0in case of ph-ph fault is greater than

Fig. 3. Flowchart of the proposed algorithm

4. Results and Discussion

Figure 4 shows the employed power system model, whichwas simulated in PSCAD/EMTDC. It is used to obtain thecurrent signals that would be used for performing the tests.The employed power system model consists of two powersources 300 MVA, 230 kV, 60 Hz, and the positive-sequenceimpedance (Z1 = 52.9 �/80

◦for the sending-end voltage source

and Z1 = 52.9 �/88◦

for the receiving-end voltage source). All the

sequence impedances of voltage source are equal. The overheadtransmission line impedances (ZL0 represents the zero-sequenceimpedance, ZL1 represents the positive-sequence impedance,and ZL2 represents the negative-sequence impedance) areZL1 = ZL2 = 0.0347 + 0.4234i �/km, and ZL0 = 0.3 + 1.1426i�/km.The voltage and current signals are sampled at a samplingrate of 4 kHz. Then the current signals that are generated usingPSCAD/EMTDC are exported to the MATLAB environment forthe construction of the fault detection and classification process.

This section is divided in two parts. The first part sheds lighton the fault identification results. The second part deals withdependability test of the proposed algorithm.

4.1. Fault identification results As mentioned in theprevious section, the proposed algorithm accomplishes its targetsbased on calculating the CC of the three-phase current signal andits reference values. Whenever the CC values of the phases aregreater than a threshold, it indicates the healthy state; otherwise itindicates a faulty condition. The ABCg fault is taken as an exampleto verify the fault detection and classification process. Figure 5(a)represents the current waveforms, and Fig. 5(b) illustrates the CCtrajectories. The faulty case is created at a point 100 km awayfrom bus 1 along section A. The fault was carried out with a faultresistance of 10 � and started at 0.5 s and continued for 100 msafter fault inception. As seen from Fig. 5(b), the CC values weremaintained higher than the threshold until the instant of the faultinception; then a slump occurred in the CC trajectories of the faultyphases, and it remained stable at its lower amplitude during theperiod of the fault. The instant at which the CC values droppedbelow the threshold was employed for computing the responsetime of detecting the faulty condition. In this case, only 1.6 mswas enough for the CC trajectories of the faulty phases to crossthe threshold, which means the fault condition could be detectedwithin 1.6 ms after the fault was registered.

4.2. Dependability test This part is concerned withtesting the algorithm under various faulty circumstances, such asmultiple fault locations, multiple fault resistances, and multiplefault inceptions time. Additionally, it involves testing the algorithmwhen the fault happened a short time after the fault inception,faults with low resistance, faults happening nearby the busbars,faults accompanied with noise, and faults during variable pre-faultloading conditions, as well as under generation and load changes.

B5 B4

B1

Z1 = 52.9Ω /_ 80.0 [deg]

230.0 [kV], 60Hz

300.0 [MVA]Z1 = 52.9Ω /_ 88.0 [deg]

230.0 [kV], 60Hz

300.0 [MVA]

BUS3230kV

BUS1230kV

BUS2230kV

B3

B7

BUS4230kV

SUBSTATION 3

SUBSTATION 1SUBSTATION 2

Section B -100km Section C - 50km

Load Feeder

Section A - 200km

ZL0=0.3000 + 1.1426i Ω/km

ZL1=ZL2=0.0347 + 0.4234i Ω/km

P+jQ

50 [MW

]

5[M

VA

R]

Section D-50km

VA

VA

VA

V

A

B2VA

B6VA

MU1

MU5 MU4

MU3

MU2

MU6

Fig. 4. Schematic diagram

1397 IEEJ Trans 13: 1394–1403 (2018)


0.49 0.50 0.51 0.52 0.53 0.54 0.55

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1 I

2 I

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X = 0.50169

Y = 0.89765CC

1CC

2CC

3 threshold

CC

Fig. 5. Currents waveforms and its CC trajectories during ABCgfault

Table I. CC values for faults at multiple inception times

Fault typeInceptiontime (s) CC1 CC2 CC3 CC0

0.50075 0.1758 0.9969 0.9984 0.2757Ag 0.50490 0.3741 0.9969 0.9984 0.2782

0.50920 0.1880 0.9969 0.9984 0.27550.51330 0.3696 0.9969 0.9983 0.27810.50075 0.0015 0.4981 0.9967 0.7036

AB 0.50490 0.0028 0.4414 0.9967 0.72110.50920 0.00027 0.5135 0.9967 0.69650.51330 0.0025 0.4326 0.9967 0.72770.50075 0.0885 0.2818 0.1737 0.1159

ABCg 0.50490 0.2616 0.0334 0.2238 0.01630.50920 0.1029 0.2862 0.1599 0.11500.51330 0.2579 0.0308 0.2272 0.0174

4.2.1. Test results of faults in Section A Different typesof faults with different circumstances were tested along thetransmission line Section A. The first test is done by applyingdifferent types of faults with different inception times of 0.50075,0.5049, 0.5092, and 0.5133 s. The selected faults took place 100 kmaway from bus 1 and continued for 100 ms after the fault inception.Ag fault and ABCg fault were tested with a fault resistance 50 �.Table I shows the corresponding CC values during such faults.The currents signals that measured at the MU in position 5 (MU5)were used for obtaining the CC values. The CC values of healthyphases are marked with bold font.

The second test is performed by applying different types of faultswith different fault resistances of 10, 30, and 100 �. The selectedfaults (Bg, BCg, and ABCg) took place 100 km away from bus 1,started at 0.3 s, and continued for 50 ms after the fault inception.Table II shows the corresponding CC values during such a fault.

The results indicate that the proposed algorithm has a goodimmunity against variations in the fault resistance and faultinception time.

The third test is performed by applying an ACg fault with faultresistance 200 � at points 50, 100, 150, and 200 km away frombus 1. The fault started at 0.5 s and continued for 50 ms afterthe fault inception. Table III shows the corresponding CC valuesduring such faults.

Table II. CC values for faults with multiple resistances

Fault type Resistance (�) CC1 CC2 CC3 CC0

10 0.9948 0.3580 0.9952 0.2448Bg 30 0.9958 0.4120 0.9962 0.2574

100 0.9978 0.2910 0.9979 0.206510 0.9945 0.3033 0.4476 0.1445

BCg 30 0.9960 0.2906 0.3608 0.1867100 0.9989 0.1498 0.2250 0.247310 0.0025 0.2662 0.2858 0.0696

ABCg 30 0.0059 0.3281 0.2493 0.1028100 0.0350 0.1591 0.1373 0.1333

Table III. CC values for faults at multiple locations

Locations (km) CC1 CC2 CC3 CC0

50 0.0378 0.9982 0.0982 0.1342100 0.2355 0.9989 0.2665 0.1310150 0.5071 0.9981 0.5020 0.1017200 0.8698 0.9955 0.8506 0.0198

Table IV. CC values for ACg at multiple fault zones

Fault locationCurrent

measured at CC1 CC2 CC3 CC0

Section A MU1 0.7108 0.9964 0.7794 0.0580MU2 0.7505 0.9983 0.8136 0.1999MU3 0.8324 0.9974 0.8796 0.0958MU4 0.0059 0.9960 0.1439 0.2794MU5 0.0042 0.9920 0.0899 0.3118MU6 0.9408 0.9698 0.9398 0.2560

Section B MU1 0.2554 0.9969 0.3398 0.0399MU2 0.0054 0.9994 0.0454 0.2986MU3 0.0785 0.9979 0.3552 0.2797MU4 0.9119 0.9965 0.9149 0.0290MU5 0.8966 0.9926 0.8991 0.3653MU6 0.9035 0.9693 0.9226 0.3049

Load Feeder MU1 0.6485 0.9967 0.5642 0.0288MU2 0.7290 0.9984 0.6384 0.3748MU3 0.0043 0.9990 0.2187 0.3004MU4 0.9760 0.9982 0.9668 0.7084MU5 0.9322 0.9951 0.8956 0.1720MU6 0.1372 0.9608 0.3121 0.0759

Results in Table III show that the degree of correlation of thefaulted phase with its reference value increases as the distance ofthe fault point from the measurement point increases. Therefore,this feature could very useful for distinguishing the fault zone.Here, fault zone means the faulty area where the current is moresevere than in the other zones, and where the current amplitudeis high due to its nearness from the fault point. Table IV givesthe CC values for the ACg fault created at 50 km away frombus 1 along section A, 50 km along section B, and at the loadfeeder, respectively. The fault case was carried out with 50 � andthe inception of 0.5 s. The faulty zone is highlighted with italicbold font.

It can be obviously seen that the CC values in the faulty zoneare very small compared to the CC values out of the faulty zone.This feature could be very useful for sectioning the faulty zoneand also used in power system protection.

As is known, very strong correlation is selected for indicating thehealthy condition, and weak correlation, moderate correlation, andstrong correlation are selected for indicating the faulty condition.

1398 IEEJ Trans 13: 1394–1403 (2018)


Table V. CC values for far-end earth faults with high resistance

Fault type Resistance (�) CC1 CC2 CC3 CC0

Ag 100 0.4585 0.9954 0.9873 0.0103250 0.7384 0.9989 0.9962 0.0011500 0.8792 0.9997 0.9990 0.0020

ABg 100 0.5439 0.4395 0.9970 0.0045250 0.7732 0.7340 0.9984 0.00059500 0.8689 0.8950 0.9993 0.0145

ABCg 100 0.4713 0.4900 0.4200 0.0017250 0.7461 0.7573 0.7308 0.00061500 0.8833 0.8885 0.8789 0.0096

In order to give further clarification that the degree of correlationcould be used for sectioning the faulty zone and also the timegradient, we proceed as as follows: if the CC value is categorizedas weak, it means the fault is more severe and should be clearedfaster than in the case of moderate and strong correlation. If thefault condition is categorized as strong, it means the fault pointis far away from the measurement point. Therefore, the faultclearance time should be low in order to give a chance for thefaults zones that have a moderate and weak correlation to trip fast.

4.2.2. Test results of faults in section D This test iscarried out by applying a far-end fault with high resistance onthe side of the load feeder (very close to C.B6). Far-end faultsaccompanied by high resistance are usually very difficult for manyalgorithms because the difference in the current amplitude betweenthe faulty phases and healthy phases is not large enough to berecognized. A high-resistance fault (HRF) may occur when theenergized conductor comes into contact with an insulating objectsuch as a tree or a transmission line structure, or when theconductor falls to the earth. Therefore, faults such as Ag, ABg,and ABCg with resistances 100, 250, and 500 � were selectedto perform the test. The current signals that were measured atMU6 were used for obtaining the CC values. Table V shows thecorresponding CC values during a far-end fault with HRF on theside of the load feeder. From the results, we see that the proposedalgorithm has good performance in detecting and classifying thefar-end and HRF faults that could occur in a feeding transmissionline such as load feeder.

4.2.3. Test results of faults happening near the terminalsThe faults that occur close to the terminal are more severe

because of prospective relays. It may increase the possibilityof the current transformer (CT) saturation, which enhances thepossibility of incorrect operation of the relays. Additionally,the current magnitude is very high, which requires a fast andreliable protection system to limit equipment damage. This testis performed by applying an ABg fault created near the terminals(bus 1, bus 2, and bus 3). The fault with a fault resistance of10 � started at 0.5 s and continued for 100 ms. Table VI showsthe CC values during such a fault. The CC values were provided forboth terminals (sending and receiving terminals), and each terminalused the current signals that were measured at the local MU forobtaining the CC values.

The purpose of obtaining the CC values for both terminals is toshow the reliability of the proposed algorithm. The fault occurringnear the first terminal meanwhile took place at far-end fault to theother terminal.

Obviously, the fault condition could be easily detected andclassified at both sides of the transmission line simultaneously byusing the CC algorithm. The CC values of phase A and B wereless than threshold, whereas the CC value of phase C was greaterthan the threshold.

Table VI. CC values for faults near the terminals

LocationCurrent


Narby MU 1 0.0074 0.2137 0.9665 0.00062C.B1 MU 2 0.00058 0.0024 0.9782 0.00058Nearby MU 1 0.1561 0.5387 0.9918 0.00024C.B2 MU 2 0.00013 0.0001 0.9982 0.0070Nearby MU 2 0.5249 0.7711 0.9888 0.00023C.B3 MU 3 0.00085 0.0051 0.9894 0.00002Nearby MU 4 0.0047 0.0015 0.9891 0.0031C.B4 MU 5 0.2729 0.6166 0.9681 0.0023Nearby MU 4 0.0025 0.0036 0.9734 0.00097C.B5 MU 5 0.0098 0.0237 0.9506 0.00028

Table VII. CC values for faults with low resistance

Fault typeCurrent


Ag MU 4 0.00045 0.9947 0.9972 0.1182MU 5 0.0098 0.9978 0.9989 0.0836

ABg MU 1 0.0032 0.3536 0.9916 0.1813MU 2 0.0215 0.0188 0.9988 0.2128

ABCg MU 6 0.00067 0.0106 0.00013 0.0630

4.2.4. Test results for faults with low resistance Thefault current amplitude can be larger when the fault resistanceis small compared to the fault occurring with high resistance.Therefore, this test is performed by applying the Ag, ABg, andABCg faults with a fault resistance of 1 m�. Whereas the Ag faultwas created in the middle of section A, the ABg fault was createdat the middle section B, and the ABCg fault was created at the endof load feeder. The fault started at 0.3 s and continued for 100 msafter the fault inception. Table VII shows the corresponding CCvalues during such faults.

4.2.5. Fault happening for a short time after fault incep-tion This test is performed by applying an Ag fault with a faultresistance of 10 � created 50 km away from the sending end. It isstarted at 0.506 s and continued for 4 ms after the fault inception.Figure 6(a) shows the current waveforms during the correspond-ing fault, and Fig. 6(b) shows the CC trajectories. Only 1.1 mswas enough for the CC trajectory of the faulted phase to cross thethreshold, which indicates that a reasonable response time could beachieved for detecting the faulty condition. Therefore, the resultsprove the dependability of the proposed algorithm against faultsthat can occur for a short time after the fault inception.

4.2.6. Noise test For further confidence, the proposedalgorithm was tested under noisy conditions. The signal that wasused for creating the distortion is called additive white Gaussiannoise. The signal-to-noise ratio per sample was set to 20 dB. Ag,ABg, and ABCg were selected to perform the noise test with a faultresistance of 50 �. The selected faults took place in the middle ofSection B.

Figure 7(a) shows the case of Ag fault, where phase A iscontaminated with noise while phase B and phase C remainedclear of the noise. Figure 7(b) shows the CC trajectories of suchfaults. The fault started at 0.3 s and continued for 100 ms.

Obviously, the CC trajectories of the healthy phases remainedstable at values higher than the threshold until the instant ofoccurrence of the faulty condition. Here, the CC trajectory of thefaulty phase (phase A) dropped below the threshold. The instantat which the CC trajectory crossed the threshold was 1.62 ms afterthe fault was registered.

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0.500 0.502 0.504 0.506 0.508 0.510 0.512 0.514

–0.5

0.0

0.5

1.0

1.5

Time (s)

(a)

(b)

Time (s)

I1

I2

I3

0.500 0.502 0.504 0.506 0.508 0.510 0.512 0.514

0.8

0.9

1.0X = 0.507101046Y = 0.899224606

CC1

CC2

CC3

threshold

I (k

A)

CC

Fig. 6. Fault happening for a short time after inception

0.29 0.30 0.31 0.32 0.33 0.34 0.35–4

–2

0

2

4 I1

I2

I3

0.29 0.30 0.31 0.32 0.33 0.34 0.35

0.0

0.3

0.6

0.9

1.2

X = 0.30162

Y = 0.89582 CC1

CC2

CC3

threshold

I (k

A)

CC

(a)Time (s)

(b)Time (s)

Fig. 7. Ag fault in presence of noise

Figure 8 shows the case of the ABg fault, in which Fig. 8(a)shows the current waveforms and Fig. 8(b) shows the CC trajec-tories during such a fault. In this case, phase A and phase B weresubjected to contamination with noise, while phase C remainedwithout contamination.

By comparing the CC value of phase C (noncontaminated phase)with the CC values of phase A and phase B (contaminated phases)during the period of pre-fault condition, we conclude that the noisecondition has an impact on CC trajectories of phase A and phaseB, where the CC value of noncontaminated phase is greater thanCC values of the contaminated phases. But its impact is limited,because of not exceeding the threshold value. It is observed thatat t = 0.30109 s, the trajectories of the faulted phases crossed thethreshold, which means that the fault case could be detected within1.09 ms after the fault was registered.

Figure 9 shows another performance test of the proposedalgorithm against the noise condition. Figures 9(a) and (b) showthe current waveforms and the CC trajectories during the ABCg

0.29 0.30 0.31 0.32 0.33 0.34 0.35–4

–2

0

2

4 I1

I2

I3

0.29 0.30 0.31 0.32 0.33 0.34 0.35

0.3

0.6

0.9

1.2

X = 0.30109

Y = 0.89450

CC1

CC2

CC3

threshold

I (k

A)

CC

(a)Time (s)

(b)Time (s)

Fig. 8. ABg fault in presence of noise

0.29 0.30 0.31 0.32 0.33 0.34 0.35–4

–2

0

2

4 I1

I2

I3

0.29 0.30 0.31 0.32 0.33 0.34 0.35

0.0

0.3

0.6

0.9

1.2

X = 0.3045, Y = 0.886386894

CC1

CC2

CC3

threshold X = 0.3025

Y = 0.8693

I (k

A)

CC

(a)Time (s)

(b)Time (s)

Fig. 9. ABCg fault in presence of noise

fault, respectively. Phase C was contaminated with noise, whilephase A and phase B remained clear of noise. It is noticed thatthe CC value of phase C crossed the threshold and again backto the threshold and then completed crossing the threshold within4.5 ms after the fault inception. The delay was due to the faultinception angle of phase C (which occurred at 0

◦approximately).

The rate of change of the current waveform at FIA 0◦

is slowcompared to other inception times. It is responsible for the swingin the CC value of phase C at the inception of the fault, whichled to the delay in the response time. The proof is that in therest of the fault period the CC trajectories of the faulted phases(including the contaminated phase) remained stable at their lowestvalues without any swing. Therefore, the proposed algorithm is abetter option for fault detection applications because it shows lesssensitivity to noise.

4.2.7. Faults with different load angles The flow ofpower on the line is controlled by changing the load angle between

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0.50 0.52 0.54 0.56 0.58 0.60–4

–2

0

2

4 I

1I

2 I

3

Time (s)

(a)

0.50 0.52 0.54 0.56 0.58 0.60

0.0

0.3

0.6

0.9

1.2

X = 0.551329508

CC1

Y = 0.888982623

CC2

CC3

CC1

CC2

CC3

threshold

Time (s)

(b)

0.50 0.52 0.54 0.56 0.58 0.60

0.0

0.3

0.6

0.9

1.2

X = 0.551099038Y = 0.89127227

threshold

Time (s)(c)

I (k

A)

CC

CC

Fig. 10. ABg fault during different loadings

the two terminals of the line. Therefore; this test is performed byapplying ABg faults through load angles 5◦ and 30◦. The faultswere simulated at a location 50 km away from bus 1 along sectionA. It started at 0.55 s and continued for 50 ms with a fault resistanceof 50 �. Figures 10(a)–(c) show the current waveform and thecorresponding CC trajectories when an ABg fault happened atthe loading angle 5◦and 30◦, respectively. The performance of theproposed algorithm has been verified successfully by applying pre-fault loading conditions including large loading variation as in caseof the loading angle of 30◦.

4.2.8. Effect of the load condition change The perfor-mance of the proposed algorithm during a sudden change in theload condition was verified in three stages as follow:

I Operating the system at normal loading condition, andthen at t = 0.55 s the loading of one generation side wasdecreased to 20%.

II Operating the system at normal loading condition, andthen at t = 0.55 s the loading of one generation side wasincreased to 50%.

III Operating the system at normal loading condition, and thenat t = 0.55 s an extra load at bus 2 (50 MW and 17 MVAR)was added.

Figures 11(a1), (b1), and (c1) show the current waveforms, andFigs. 11(a2), (b2), and (c2) show the corresponding CC trajectoriesduring the tests. In these cases, we can see that there are changesin the CC trajectories but they not enough to reach the thresholdvalue. Therefore, it is not possible to detect the fault condition dueto a sudden change in the load condition.

0.52 0.54 0.56 0.58

–2

0

2

Time (s)

(c2)

Time (s)

(b2)

Time (s)

(a2)

Time (s)

(c1)

Time (s)

(b1)

Time (s)

(a1)

I (k

A)

0.52 0.54 0.56 0.58–4

–2

0

2

4

0.52 0.54 0.56 0.58

–2

0

2

I1

I2

I3

0.52 0.54 0.56 0.58

0.90

0.99

CC

I (k

A)

CC

I (k

A)

CC

0.52 0.54 0.56

Threshold = 0.9

0.58

0.90

0.99

0.52 0.54

Threshold = 0.9

0.56 0.58

0.90

0.99

Threshold = 0.9

CC1

CC2

CC3

Fig. 11. Effect of sudden change in the load condition

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5. Conclusion

In this paper, a CC-based algorithm was applied successfully forfault detection and classification in a power transmission line. Theunderlying idea of the proposed algorithm is as follows: During thehealthy condition, the CC of the three-phase current with respectto its reference value reached a value greater than the threshold.During faulty conditions, the CC of the three-phase current withrespect to its reference value reached a value less than the thresh-old. The lower limit that could describe the correlation of variablesas very strong was selected to be the threshold. The proposedalgorithm was validated through various simulation circumstancessuch as different fault locations, different fault inception times,and different fault resistances. Additionally, the algorithm wastested under faults with low resistance (1 m�), faults with veryshort time after the fault inception, fault near the terminals, faultsmuddled with noise, and also under different pre-fault loading con-ditions. The proposed algorithm is characterized by its simplicityand practicality because it relies only on the local terminal currentmeasurement. Additionally, a simple mathematical model is used,reflecting the time response, whereby the fault condition can bedetected within a few milliseconds after the fault is registered.

Acknowledgment

This work was supported by National Natural Science Foundation ofChina (51777173, 51525702).

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Mohammed H. H. Musa (Non-member) was born in Kadugli,Sudan, on May 29, 1981. He received theB.Sc. and M.Sc. degrees in electrical engi-neering from Sudan University of Scienceand Technology in 2005 and 2010, respec-tively. Presently, he is he pursuing the Ph.D.degree at Southwest Jiaotong University,China. He worked with the National Elec-tricity Corporation (NEC), Sudan, from 2006

to 2010. Since 2010, he has been with the Thermal Power Gener-ating Company (STPG) as Electrical Protection Engineer.

Zhengyou He (Non-member) was born in Sichuan Province,China, in 1970. He received the B.Sc.and M.Sc. degrees from Chongqing Uni-versity, China, in 1992 and 1995, respec-tively, and the Ph.D. degree in electricalengineering from Southwest Jiaotong Uni-versity (SWJTU), Chengdu, China, in 2001.Since 2002, he has been a Professor with theCollege of Electrical Engineering, SWJTU.

His research interests include signal processing and information

1402 IEEJ Trans 13: 1394–1403 (2018)


theory, their application to electrical power systems, and wavelettransform applications in power systems.

Ling Fu (Non-member) received the Ph.D. degree fromthe Department of Electrical Engineering,Southwest Jiaotong University (SWJTU),China, in May 2010. She carried out post-doctoral research at the University of Ten-nessee, Knoxville, USA, in 2011. She iscurrently with the Department of ElectricalEngineering, SWJTU. Her research interestsinclude power system stability and control,

signal processing, and wide-area protection.

Yujia Deng (Non-member) is currently pursuing the Ph.D.degree in electrical engineering at South-west Jiaotong University. His research inter-ests include fault diagnosis of power trans-mission systems, signal processing, artificialintelligence applications to power systems,and wavelet transforms application in powersystems.

1403 IEEJ Trans 13: 1394–1403 (2018)

a correlation coefficient based algorithm for faults...

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