New fault location scheme for three-terminal untransposed parallel transmission lines

Electric Power Systems Research 154 (2018) 266–275

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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

New fault location scheme for three-terminal untransposed parallel transmission lines Ahmed Saber ∗ , Ahmed Emam, Hany Elghazaly ElectricPowerandMachineDepartment,CairoUniversity,Cairo,EgyptEgypt

a r t i c l e

i n f o

Article history: Received 15 March 2017 Received in revised form 13 July 2017 Accepted 30 August 2017 Keywords: Cross-country faults Evolving faults Fault location Phasor Measurement Unit (PMU)

a b s t r a c t This paper proposes a new fault location scheme in the phase-domain for three-terminal untransposed double-circuit transmission lines utilizing synchronized voltage and current measurements obtained by GPS technique. The proposed scheme is derived taking into consideration the distributed line model and the mutual couplings effect between the parallel lines to obtain accurate results. The proposed scheme is derived based on the transmission line theory and Taylor series expansion of the distributed line model parameters. All fault types including normal shunt faults, evolving faults, and cross-country faults can be discriminated from each other and the fault location can be obtained for all fault types. The evolving faults include earth faults occurring at the same location in two phases of one circuit or two phases of different circuits at different fault inception time. While cross-country faults include earth faults occurring at different locations in two phases of one circuit or two phases of different circuits at same or different fault inception time. The proposed scheme is tested under different fault locations, different fault resistances, different fault inception angles, and all fault types including cross-country and evolving faults. Also, the effect of different sampling rate, measurement and synchronization errors, earth resistivity variations, and transmission line parameters errors on the proposed scheme is considered. Simulations studies conducted by MATLAB software demonstrate that the maximum estimation error in fault location does not exceed 3.06%. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Transmission lines are very important for continuity of power supply. Since transmission lines are permanently exposed to different faults, the precise fault location is essential to repair the faulted line and minimize the outage time [1,2]. The transmission line faults include normal shunt faults (line to ground (LG), double line to ground (LLG), double line (LL), and three line (LLL)), evolving faults, and cross-country faults. Cross-country faults include earth faults occurring at different locations in two phases of one circuit or two phases of different circuits at same or different fault inception time. Cross-country faults which occur at same location between two different circuits are also defined as inter-circuit faults which appear in double-circuit transmission line. Inter-circuit faults are easily located because the inter-circuit faults occur at one location compared with the cross-country faults occurring at two different locations. Cross-country faults which include two phases in different locations at same or different fault inception time are very

∗ Corresponding author. E-mail address: a saber [email protected] (A. Saber). http://dx.doi.org/10.1016/j.epsr.2017.08.038 0378-7796/© 2017 Elsevier B.V. All rights reserved.

difficult to obtain their locations. While the evolving faults include earth faults occurring at the same location in two phases of one circuit or two phases of different circuits at different fault inception time. In other words, the evolving faults consist of primary earth fault which beginning in one line and secondary earth fault in another line at the same location. For single pole tripping function, the secondary faulted phase must be recognized. However, the faulty phase selector cannot easily recognize the secondary faulted phase because the evolving faults are more complex than normal shunt faults. Generally, conventional fault location techniques can be divided into four main categories. The first category uses the fundamental frequency components measurements [3–8]. The second one includes techniques based on the fault generated traveling waves [9–14]. The third category applied soft computing methods such as artificial neural network [15,16], genetic algorithm [17], combined wavelet-fuzzy [18,19], and adaptive neuro-fuzzy [20] for transmission line fault location. The last category is based on fault-induced transient analysis for high frequency signals [21,22]. Moreover, the use of synchrophasor measurements for multi-terminal parallel transmission lines has been presented in open literature [23–29].

A. Saber et al. / Electric Power Systems Research 154 (2018) 266–275

267

bus R, respectively. The A–D are 6 × 6 transmission line parameters matrices and they can be written in terms of infinite series as [40]:







(ZY)1 DR,m L

A DR,m L = 1 +



2



+

2!

(ZY)2 DR,m L

B DR,m L = Z(DR,m L) +

+ ...

4!





4

(ZY)1 Z DR,m L

3



(ZY)2 Z DR,m L

+

3!

(2)

5 + ...

5!

Fig. 1. Faulted two-terminal double-circuit transmission line.

(3)

However, in all these methods [3–29], the cross-country and evolving faults are not considered in power system simulation. Detection and classification of evolving faults and cross-country faults have been presented in Refs. [30–33] and [32–35], respectively. However none of these methods [30–35] discussed fault location estimation. Only few research papers discussed fault location estimation for cross country faults [36–38] and evolving faults [38,39]. First-zone distance relaying techniques for parallel transmission lines utilizing only one end measurements have been proposed for cross-country non-ground faults [36] and crosscountry ground faults [37]. In Ref. [38], discrete wavelet transform and back propagation neural network scheme have been incorporated to determine the fault location and identify the faulted phase of single-circuit transmission line during normal shunt faults and evolving faults, as well as cross-country faults. In this technique, neural network cannot be directly applied to new transmission line as manual retraining is required. In Ref. [39], a time-domain fault location scheme for evolving faults has been developed taking into account the influence of electric arc. In this paper, a new fault location scheme is derived based on the transmission line theory and the truncated Taylor series is used to model the line. The proposed scheme can discriminate normal shunt and evolving faults from cross-country faults and obtain accurately locations of all fault types including evolving and crosscountry faults. 2. Proposed fault location technique The proposed scheme is developed considering that the three-terminal synchronized measurements and communication channels are available.





Vm Im,r

 =

 







A DR,m L C DR,m L



 





B DR,m L

D DR,m L

VR −IR,S



−1

C DR,m L = Z −1

+

Z

 3

(ZY)

(ZY) (DR,m L) +

DR,m L

D DR,m L = 1 +

3

3!

+ ...

(4)





Z−1 (ZY)2 DR,m L

5

Z−1 (ZY)1 Z DR,m L 2!

2



Z−1 (ZY)2 Z DR,m L

+

4

4!

+ ... (5)

where Z and Y are the series impedance and shunt admittance matrices per unit length, respectively. Suppose that a transmission line fault occurred at point f which is Df in per unit apart from bus S. The voltage phasor at point f can be written from both ends of the line as: Vf = [ A(Df L)

B(Df L) ][

VS −IS,R

] = [ A((1 − Df )L)

B((1 − Df )L) ][

VR

] −IR,S (6)

T

where Vf = [ Vf,a1 Vf,b1 Vf,c1 Vf,a2 Vf,b2 Vf,c2 ] . If the voltage and current phasors are given at the two ends of the line, the unknown variable in Eq. (6) would only be the fault distance (Df ). A and B are only expanded to three terms because the simulation results confirm that the fault location accuracy will not increase by expansion of more terms. By substituting Eqs. (2)–(5) into Eq. (6), the following equation is obtained: (1 +

(ZY)1 L2 Df 2 (ZY)1 Z L3 Df 3 (ZY)2 L4 Df 4 + )VS − (ZLDf + 2 24 6

+

(ZY)2 Z L5 Df 5 (ZY)1 L2 (1 − Df )2 )IS,R − (1 + 120 2

+

(ZY)1 Z L3 (1 − Df )3 (ZY)2 L4 (1 − Df )4 )VR + (ZLDf + 24 6

+

(ZY)2 Z L5 (1 − Df )5 )IR,S = 0 120

(7)

Furthermore, Eq. (7) is rearranged and six polynomial equations are obtained: 1

(VS − [1 + 1

2

1

2

(ZY) L4 (ZY) ZL3 (ZY) ZL5 (ZY) L2 ZL + ] VR + [ + + ] IR,S )+ 2 24 1 6 120 2

1

2

([

4(ZY) L4 3(ZY) ZL3 5(ZY) ZL5 ZL 2(ZY) L2 + ]VR − ZLIS,R − [ + + ]IR,S )Df + 2 24 1 6 120

([

(ZY) L2 3(ZY) ZL3 (ZY) L2 6(ZY) L4 10(ZY) ZL5 ]VS − [ + ]VR + [ + ]IR,S ) Df 2 + 2 2 24 6 120

([

10(ZY) ZL5 (ZY) ZL3 (ZY) ZL3 4(ZY) L4 ]VR − [ ]IS,R − [ + ]IR,S ) Df 3 + 24 6 6 120

([

(ZY) L4 5(ZY) ZL5 (ZY) L4 ]VS − [ ]VR + [ ]IR,S ) Df 4 + 24 24 120

1

1

2

(1)

where Vm and VR are 6 × 1 voltage phasors at point m and bus R, respectively. Im,R and IR,S are 6 × 1current phasors at point m and

1

5!



2.1. Review of two-terminal untransposed parallel transmission line fault location algorithm The symmetrical components transformation is not applied for decoupling untransposed transmission lines due to the effect of mutual couplings. In Ref. [40], a fault location algorithm has been proposed for two-terminal single-circuit untransposed transmission line. Based on this work [40], the fault location scheme is extended to double-circuit untransposed transmission line and a new fault location scheme is proposed for evolving and crosscountry faults. Suppose that the parallel transmission line (S–R) depicted in Fig. 1 with length L. The voltage and current phasors in phasedomain at point m which is DR,m in per unit apart from bus R can be obtained as [41]:





2

1

1

1

2

2

(−[

2

2

2

(ZY) ZL5 (ZY) ZL5 ]IS,R − [ ]IR,S ) Df 5 = 0 120 120

2

2

(8)

268

A. Saber et al. / Electric Power Systems Research 154 (2018) 266–275

Fig. 3. Cross-country fault in phases a1 and c1 of line branch (S–G).

Fig. 2. Three-terminal untransposed parallel transmission line.

Therefore, the estimated fault distance (Df ) is calculated using Eq. (8). In addition, the fault current phasor at point f can be defined as: If = [C(Df L) D(Df L)][ where If = [ If,a1

VS IS,R

] + [C((1 − Df )L) D((1 − Df )L)][

If,b1

If,c1

If,a2

If,b2

VR

]

(9)

IR,S

T

If,c2 ] .

2.2. Fault branch identifier The first step in the suggested scheme is faulted branch identification. Let us consider the three-terminal parallel transmission line depicted in Fig. 2. Three PMUs are installed at buses S, R, and T so that the synchronized voltage phasors of buses S, R, and T and the synchronized current phasors of all lines connected to these buses are directly measured utilizing GPS technique. All measurements are sent to the central protection system using communication system. The lengths of line branches S–G, R–G, and T–G are respectively LS , LR , and LT where G is the tee-point. The voltage and all current phasors at tee-point G can be calculated using the available data at buses S, R, and T taking into account the line parameters of corresponding line branch. Thus, the voltage phasors (VGS , VGR , andVGT ) and the current phasors at tee-point G (IGS , IGR , and IGT ) are calculated as: [

VGS IGS

[

VGR IGR

[

VGT IGT

]=[

]=[

]=[

A(LS )

B(LS )

C(LS )

D(LS )

A(LR )

B(LR )

C(LR )

D(LR )

A(LT )

B(LT )

C(LT )

D(LT )

][

VS −IS

][

][

]

(10)

]

(11)

]

(12)

VR −IR VT −IT

Assume that: IG = abs(IGS + IGR + IGT )

(13)

The dimensions of IG are 6 × 1. Eqs. (10)–(12) will be applicable and consequently Eq. (13) will be applicable in normal conditions and external faults cases. Therefore, the values of IG ill be equal to zero according to Kirchhoff current law. In addition, one of the Eqs. (10)–(12) will not be applicable and consequently Eq. (13) will not be applicable in transmission lines faults cases. Therefore, the currents of faulted phases (IG ) will not be equal to zero. In practice, threshold value (ε) is defined and set at a small value higher than zero. The threshold value (ε) is equal to 0.1 per unit in this paper. As a result, the faulted phases are determined using the values of IG . The values of IG which are less than 0.1 per unit will be corresponding to the healthy phases and the values of IG which are greater than 0.1 per unit will be corresponding to the faulted phases.

Also, the voltage phasors (VGS , VGR , and VGT ) will be almost equal to each other in normal operating conditions and external faults cases. In case of transmission lines faults, only two voltage phasors from the three voltage phasors will be approximately equal and the third voltage phasor will be corresponding to the faulted branch because only two equations from Eqs. (10)–(12) will be applicable. Let’s consider that: VSR = max (abs (VGS − VGR ))

(14)

VRT = max (abs (VGR − VGT ))

(15)

VST = max (abs (VGS − VGT ))

(16)

The maximum absolute difference value between each two voltage phasors is calculated from Eqs. (14)–(16). Mathematically,   the common in the maximum two values of VSR , VRT , VST will be corresponding to the  faulted branch and the minimum value of VSR , VRT , VST will be corresponding to the two healthy branches. If the maximum two values are VSR and VRT , this means the faulted branch is R–G. Similarly, if the maximum two values are VSR and VST , this means the faulted branch is S–G. Also, if the maximum two values are VRT and VST , this means the faulted branch is T–G. 2.3. Proposed fault location scheme for different fault types As the faulted branch is determined, the following step is discriminating normal shunt and evolving faults from cross-country faults. As stated earlier, the evolving faults include earth faults occurring at the same location in two phases of one circuit or two phases of different circuits at different fault inception time. While cross-country faults include earth faults occurring at different locations in two phases of one circuit or two phases of different circuits at same or different fault inception time. Initially, the voltage and current phasors at both ends of the faulted line branch must be determined. Let the faulted branch is branch S–G. The voltage and current phasors at bus S are measured directly as a PMU is connected to this end. While the voltage phasor at tee-point G is equal to VGR or VGT and the current phasor at tee-point G in the direction of G–S can be obtained from: IGS = −( IGR + IGT )

(17)

As stated before, the faulted phases can be identified by employing Eq. (13). Consequently, for single-line to ground faults and three-line faults, the fault distance (Df ) is obtained by solving Eq. (8). For other faults including evolving and cross-country faults, the following proposed scheme in the next subsection is applied. 2.3.1. Proposed fault location scheme for double-line to ground, double-line, evolving, and cross-country faults Consider the circuit depicted in Fig. 3. It illustrates cross-country fault in line (S–G) at fault distance D1 and D2 in phase a1 and phase c1 , respectively. The voltage and current phasors in phase-domain

A. Saber et al. / Electric Power Systems Research 154 (2018) 266–275

at fault point f1 which is D1 in per unit away from bus S can be derived as: [

Vf1 If1,S

]=[

A(D1 LS )

B(D1 LS )

C(D1 LS )

D(D1 LS )

][

VS −IS,G

]

(18)

where Vf1 and If1,S are respectively voltage and current phasors at fault point  f1 . The current phasor in phase-domain at other fault point f2 If2,G which is D2 in per unit away from bus S can be derived as: [If2,G ] = [ C((1 − D2 )LS )

D((1 − D2 )LS ) ] [

VGR

]

−IGS

(19)

Also, the voltage phasor in phase-domain at fault point f2 (Vf2 ) can be obtained from: [Vf2 ] = [ A((1 − D2 )LS )

= [ A((D2 − D1 )LS )

B((1 − D2 )LS ) ] [

B((D2 − D1 )LS ) ] [

VGR −IGS Vf1

269

using full cycle Discrete Fourier Transform. The relative error in fault location is obtained from: Error(%) =

|estimated location − actual location| × 100% line branch length

(21)

The system is simulated using DIgSILENT Power Factory software [43] and the required computations are implemented using MATLAB [44] on a 2.1 GHz Core 2 Duo CPU with 2 GB of RAM. The estimated computational time is about 0.06 s to identify the faulted branch, discriminate normal shunt and evolving faults from crosscountry faults, and obtain the locations of all fault types including evolving and cross-country faults. Different faults are conducted in the following sections taking into account different fault resistances, different fault locations, different fault types, and different fault inception angles. In addition, the effect of different sampling rate, measurement errors, earth resistivity variations, and transmission line parameters errors is verified.

]

]

3.1. Testing of normal shunt and evolving faults (20)

If1,G

where If1,G is the current phasor at point f1 as shown in Fig. 3. The current phasor If1,G is equal to the current phasor If1,S excluding the value corresponding to phase a1 . If the stray shunt capacitance of transmission line (S–G) is neglected between the two fault points, this will lead to If1,G, a1 = −If2,G,a1 . Thus, T

If1,G = [− If2,G,a1 If1,S,b1 If1,S,c1 If1,S,a2 If1,S,b2 If1,S,c2 ] . This assumption is quite acceptable because it is only applied for one phase and for distance (D2 -D1 ) per unit. The only unknown variables in Eq. (20) are D1 and D2 . Consequently, Eq. (20) is rearranged and six polynomial equations are obtained. As a result, D1 and D2 can be obtained by solving Eq. (20). In our derivation above, it is assumed that D1 is less than D2 . However the above derivation is still valid mathematically if D1 is greater than D2 . If the difference between the two estimated fault distances is within 0.01 per unit [38], the fault type will be normal-shunt fault or evolving fault and the average value of obtained fault distances is accepted as the estimated fault location. Further, the fault current phasor at fault point is obtained by solving Eq. (9) to differentiate between double-line fault and double-line to ground fault. The current phasors of faulted phases will not be equal for double-line-to-ground fault while the magnitudes of faulted phases will be equal to each other with angle difference 180◦ for double-line fault. On the other hand, if the difference between the two fault distances is greater than 0.01 per unit [38], the fault type will be a cross-country fault and the obtained fault distances are the estimated fault locations. The proposed scheme flow chart is presented in Fig. 4. 3. Results and discussions The suggested scheme is applied to 220 kV three-terminal untransposed parallel transmission lines consisting of three line branches (S–G, R–G, and T–G) as depicted in Fig. 5. Loads with Wye connection are connected to buses S, R, and T and the value of each load is equal to 200 MVA and 0.8 power factor. The lengths of line branches and their lines parameters, as well as generator data are shown in Appendix A. Three PMUs are installed at buses S, R, and T and the current and voltage measurements are passed through a low pass second order Butterworth filter with cut-off frequency 400 Hz. After that, they are sampled at 2500 Hz and the dc component is removed using a digital mimic filter [42]. In addition, the data of modeled current and voltage transformer are provided in Appendix B. Finally, the power frequency component is extracted

In this subsection, the performance of suggested scheme is evaluated for normal shunt and evolving faults. Different fault cases are conducted on each line branch considering low and high resistance faults. The simulated results for normal shunt faults are shown in Table 1 for different line branches. The currents of faulted phases (IG ) are only shown in the table due to space restrictions. However, the values of IG corresponding to the healthy phases are less than 0.1 per unit in all simulated cases. The percentage fault location (F.L.) error is indicated in the last column. For example, case 2 in Table 1 is double-line fault (a1 c2 ) in branch S–G at fault point equal to 80% of line length with 100  fault resistance and 0◦ fault inception angle. To identify  the faulted branch, the common in the maximum two values of VSR , VRT , VST is corresponding to the faulted branch S–G. The values of IG do not exceed 0.1 per unit excluding the values corresponding to phase a1 and phase c2 . Therefore, the two phases are accepted as the faulted phases. Accordingly, the estimated fault distances corresponding to phase a1 and phase c2 are respectively equal to 0.7944 and 0.7944 per unit and they are approximately equal to each other. As a result, the fault type is normal shunt fault or evolving fault and the average fault distance is equal to 0.7944 per unit. In addition, the estimated value of current phasor at fault point is equal to [−1.6798 + 0.9917i 0.0003 − 0.0009i 0.0003 + 0.0011i −0.0007 − 0.0002i 0.0003−0.0007i 1.6794-0.9909i] per unit. It is obvious that the fault type is double-line fault as Ia1 = −Ic2 . Table 2 shows the effect of expansion of more terms on the accuracy of fault location and the proposed scheme is compared with previous proposed technique in Ref. [28]. As observed, the effect of expansion of more terms on the accuracy of fault location is very small. Therefore, the transmission line parameters matrices are only expanded to three terms to achieve less computational burden. In addition, the proposed scheme is more accurate than previous proposed technique in Ref. [28] since it rigorously considers the untransposed line parameters and the mutual coupling effect to formulate the problem. Also, the results for simulated evolving faults are indicated in Table 3 for different line branches. For example, case 5 is phase c2 to ground fault in branch R–G at fault point equal to 85% of line length with 100  fault resistance and 45◦ fault inception angle. Another fault in phase b2 at the same location is simulated with 0.1  fault resistance and 90◦ fault inception angle. To identify the faulted branch,  the common in the maximum two values of  VSR , VRT , VST is corresponding to the faulted branch R–G. The values of IG do not exceed 0.1 per unit excluding the values corresponding to phase b2 and phase c2 . Therefore, the two phases are accepted as the faulted phases. Accordingly, the estimated fault

270

A. Saber et al. / Electric Power Systems Research 154 (2018) 266–275

Fig. 4. The proposed scheme flow chart.

Fig. 5. Simulated three-terminal untransposed double-circuit transmission line.

Table 1 Results of different cases for normal shunt faults. Branch

S–G

R–G

T–G

Fault condition

 

(VSR ) (p.u.)

(VST ) (p.u.)

(VRT ) (p.u.)

IG for faulted phases (p.u.)

5.5660 0.1246 1.4526 0.1431 5.5192 0.4860 0.2851 0.1870 0.0034 0.0095 0.0009 0.0038

5.5665 0.1248 1.4518 0.1432 0.0023 0.0024 0.0057 0.0027 1.8337 0.4620 1.1576 2.3881

0.0005 0.0005 0.0060 0.0005 5.5204 0.4879 0.2884 0.1896 1.8360 0.4637 1.1579 2.3895

13.29 1.950 7.8350 1.190 7.643 1.966 4.486 1.177 2.606 4.118 1.063 4.446

Df for faulted phases (p.u.)

F.L. error%

0.0993 0.7944 0.3984 0.5944 0.1489 0.4994 0.9022 0.7013 0.4500 0.8532 0.2009 0.3495

0.07 0.56 0.16 0.56 0.11 0.06 0.15 0.13 0.00 0.31 0.08 0.05

◦

Type

Df (p.u.)

Rf 

␦f

a1 g a2 c2 b1 c1 g a2 b2 c2 b2 g a1 b1 a2 c2 g a1 b1 c1 c2 g b2 c2 a1 b1 g a2 b2 c2

0.1 0.8 0.4 0.6 0.15 0.5 0.9 0.7 0.45 0.85 0.2 0.35

0.1 100 0.1 100 0.1 100 0.1 100 0.1 0.1 100 0.1

180 0 45 90 180 135 0 45 90 0 45 180

distances corresponding to phase b2 and phase c2 are respectively equal to 0.8520 and 0.8525 per unit and they are approximately equal. As a result, the fault type is normal shunt fault or evolving fault and the average fault distance is equal to 0.8523 per unit. It can be seen from Table 1 and Table 3 that the fault location for normal shunt faults or evolving faults can be obtained accurately using the proposed scheme.

– 1.950 7.7933 1.224 – 1.967 4.919 1.223 – 4.118 1.252 5.025

– – – 1.238 – – – 1.242 – – – 4.591

– 0.7944 0.3984 – –0.4995 0.9008 – – 0.8530 0.2007 –

3.2. Testing of cross-country faults Several cross-country faults are conducted on each line branch considering low and high resistance faults. The results of proposed scheme are shown in Table 4 for different line branches. The currents of faulted phases (IG ) are only shown in the table due to space restrictions. However, the currents of healthy phases (IG ) are less

A. Saber et al. / Electric Power Systems Research 154 (2018) 266–275

271

Table 2 Comparing with previous technique and the effect of expansion of more terms on fault location accuracy. Branch

Three terms

S–G

R–G

T–G

Four terms

Previous technique [28]

Df for faulted phases (p.u.)

F.L. error%

Df for faulted phases (p.u.)

F.L. error%

Df (p.u.)

F.L. error%

0.0993 0.7944 0.3984 0.5944 0.1489 0.4994 0.9022 0.7013 0.4500 0.8532 0.2009 0.3495

0.07 0.56 0.16 0.56 0.11 0.06 0.15 0.13 0.00 0.31 0.08 0.05

0.0993 0.7944 0.3984 0.5944 0.1489 0.4994 0.9022 0.7013 0.4500 0.8532 0.2009 0.3495

0.07 0.56 0.16 0.56 0.11 0.06 0.15 0.13 0.00 0.31 0.08 0.05

0.1097 0.7656 0.4010 0.5750 0.1534 0.4968 0.9009 0.6961 0.4530 0.8535 0.2034 0.3498

0.97 3.44 0.10 2.5 0.34 0.32 0.09 0.39 0.30 0.35 0.34 0.02

– 0.7944 0.3984 – –0.4995 0.9008 – – 0.8530 0.2007 –

– 0.7944 0.3984 – –0.4995 0.9008 – – 0.8530 0.2007 –

The bold values signifies the maximum fault location error.

Table 3 Results of different fault cases for evolving faults. Branch

S–G

R–G

T–G

Df (p.u.)

0.25 0.55 0.7 0.9 0.85 0.4 0.2 0.6 0.05 0.9 0.75 0.5

Fault condition 1

 

Fault condition 2 ◦

 

VSR p.u.

VST p.u.

VRT p.u.

IG for faulted phases (p.u.)

Df for faulted phases (p.u.)

F.L. error%

2.677 0.972 0.588 0.184 0.419 1.941 4.147 1.092 0.001 0.009 0.005 0.003

2.679 0.972 0.587 0.184 0.005 0.005 0.003 0.006 14.58 0.380 0.810 1.606

0.003 0.007 0.005 0.006 0.424 1.945 4.150 1.097 14.58 0.385 0.813 1.608

7.412 1.475 4.171 1.378 3.260 3.639 5.868 3.042 1.440 1.352 2.449 1.296

0.2464 0.5476 0.69730 0.8989 0.8520 0.4015 0.1994 0.6033 0.0527 0.9091 0.7535 0.5014

0.24 0.23 0.29 0.21 0.23 0.09 0.05 0.22 0.10 0.65 0.32 0.09

◦

Type

Rf 

␦f

Type

Rf 

␦f

a1 g b2 g b1 g a1 g c2 g a1 g b1 g b2 g c1 g a2 g c1 g a1 g

0.1 100 0.1 100 100 0.1 0.1 100 0.1 100 0.1 100

90 0 0 45 45 90 0 0 0 45 90 135

b1 g c2 g b2 g c1 g b2 g a2 g c1 g a2 g b1 g c2 g c2 g c1 g

100 0.1 100 0.1 0.1 100 100 0.1 100 0.1 100 0.1

180 135 90 180 90 180 135 45 90 135 180 180

1.388 5.488 0.727 3.991 1.444 0.723 1.469 1.466 12.31 3.092 0.731 2.534

0.2488 0.5478 0.6969 0.8970 0.8525 0.4002 0.2015 0.6010 0.0493 0.9039 0.7528 0.5004

Table 4 Results of different fault cases for cross-country faults. Branch

S–G

R–G

T–G

Fault condition 1

Fault condition 2

 

◦

 

IG for faulted phases (p.u.) ◦

Type

Df (p.u.)

Rf 

␦f

Type

Df (p.u.)

Rf 

␦f

a1 g c2 g b1 g a2 g c1 g b2 g b1 g a2 g a1 g a2 g c1 g a2 g

0.15 0.2 0.10 0.50 0.25 0.40 0.60 0.30 0.40 0.30 0.10 0.15

0.1 100 0.1 100 100 0.1 100 0.1 0.1 100 0.1 100

0 90 90 45 90 45 0 135 0 90 135 45

b1 g b2 g c1 g c2 g a1 g a2 g c1 g b2 g b1 g b2 g b1 g c2 g

0.65 0.50 0.80 0.70 0.50 0.80 0.90 0.60 0.60 0.80 0.40 0.50

100 0.1 100 0.1 0.1 100 0.1 100 100 0.1 100 0.1

45 90 180 135 135 90 45 180 45 135 180 90

than 0.1 per unit in all simulated cases. For example, case 9 in Table 4 is phase a1 to ground fault in branch T–G at 40% of line length at ıf = 0◦ with Rf = 0.1  and another single phase b1 to ground fault in branch T–G at 60% of line length at ıf = 45◦ with Rf = 100 . To identify  the faulted branch,the common in the maximum two values of VSR , VRT , VST is corresponding to the faulted branch T–G. The values of IG elements do not exceed 0.1 per unit excluding the values corresponding to phase a1 and phase b1 so that the two phases are accepted as the faulted phases. Consequently, the estimated fault distances corresponding to phase a1 and phase b1 are respectively equal to 0.4000 and 0.6005 per unit. The two values are not equal to each other so that the fault type is a cross-country

10.39 5.000 13.44 1.315 3.687 1.310 1.304 3.000 2.576 1.224 1.268 1.191

1.221 1.292 1.165 4.341 1.326 3.465 10.79 1.317 1.281 2.847 7.426 2.461

Df for faulted phases

F.L. error%

D1 (p.u.)

D2 (p.u.)

D1

D2

0.1482 0.2014 0.0988 0.4937 0.2498 0.3991 0.6005 0.2968 0.4000 0.2995 0.0996 0.1479

0.6526 0.4987 0.8050 0.6988 0.4980 0.8000 0.9001 0.5998 0.6005 0.8004 0.3985 0.4992

0.18 0.14 0.12 0.63 0.02 0.09 0.05 0.32 0.00 0.05 0.04 0.21

0.26 0.13 0.50 0.12 0.20 0.00 0.01 0.02 0.05 0.04 0.15 0.08

fault and the percentage fault location errors are respectively equal to 0.00% and 0.05%. It can be concluded from Table 4 that the locations of cross-country faults can be estimated with high accuracy using the proposed scheme. To verify the effect of neglecting the shunt capacitance, Fig. 6 shows the effect of increasing the voltage level and the difference between D1 and D2 on the estimated fault location error for line branch (T–G) with Rf = 10  and ıf = 0◦ & 180◦ . As expected, the percentage error increases with increasing the voltage level and the difference between D1 and D2 due to neglecting the shunt capacitance. However, the maximum percentage error does not exceed 1.5%.

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Fig. 6. The effect of increasing the absolute distance (D2 –D1 ) on estimated error% in fault location for line branch (T–G).

Fig. 7. Average and maximum percentage errors considering transmission lines parameters errors.

3.3. Effect of line parameters errors The values of line parameters cannot be estimated accurately due to variation of conductor impedance. Therefore, variations of 1%, 2%, and 3% in impedances and admittances of all line branches have been considered to demonstrate the performance of suggested scheme against line parameters errors. The same cases in Tables 1, 3, and 4 are simulated. The average and maximum relative errors in fault location for different fault types are indicated in Fig. 7 considering variations of 1%, 2%, and 3% in all lines parameters. The maximum error% increases to 3.06% compared with 0.65% using exact line parameters values. In all tested cases, the faulted branch and all fault types are correctly determined. As expected, the fault location accuracy is affected by transmission lines parameters errors. However, the results of fault location are still acceptable from a practical point of view.

Fig. 8. Average and maximum percentage errors in fault location considering measurement errors.

3.4. Influence of measurement errors and different sampling rate To verify the influence of measurement errors in measuring instruments on accuracy of estimated fault location, 3% maximum error is considered in measurements in transient conditions according to IEEE standard [45]. The same cases in Tables 1, 3, and 4 are tested. The average and maximum relative errors in fault loca-

tion for different fault types are shown in Fig. 8. In all simulated cases, the faulted branch and all fault types are correctly identified. The maximum error% increases to 2.47% compared with 0.65% without considering measurement errors. It can be seen that the fault location accuracy is affected by measurement errors

A. Saber et al. / Electric Power Systems Research 154 (2018) 266–275

273

Fig. 9. Average and maximum percentage errors in fault location for different sampling rate.

Fig. 10. Average and maximum percentage errors considering variation of earth resistivity.

Fig. 11. Average and maximum percentage errors considering synchronization errors.

3.6. Influence of synchronization errors in measuring instruments. However, the obtained results are still acceptable practically. In addition, the same cases in Tables 1, 3, and 4 are simulated with different sampling rate 2.5, 5, and 10 kHz. The effect of varying the sampling rate is very small on the obtained results as shown in Fig. 9. As a result, one can conclude that the proposed scheme demonstrates good performance and the results are practically acceptable even with considering different sampling rate or measurement errors in measuring devices.

To verify the influence of synchronization errors on the accuracy of estimated fault location, ±31 ␮s maximum time error is considered according to IEEE standard [45]. The same cases in Tables 1, 3, and 4 are tested. The average and maximum relative errors in fault location for different fault types are shown in Fig. 11. In all simulated cases, the faulted branch and all fault types are correctly identified. The maximum error% increases to 1.290% compared with 0.650% without considering synchronization errors. It can be seen that the fault location accuracy is affected by synchronization errors. However, the obtained results are still acceptable practically.

3.5. Influence of earth resistivity variation 4. Conclusions The value of soil resistivity depends on weather conditions such as soil moisture content and soil temperature. Therefore, the value of earth resistivity varies continuously which affects on the estimated values of transmission line parameters. The value of earth resistivity that used to calculate the transmission line parameters in this paper is equal to 100 ohm m. The effect of earth resistivity variation on fault location accuracy is shown in Fig. 10. The same fault cases in Tables 1, 3, and 4 are simulated at the same conditions for different values of earth resistivity (100, 150, 200 ohm m). It can be concluded that the variation of earth resistivity has a small effect on fault location accuracy.

A fault location scheme for three-terminal untransposed parallel transmission lines has been presented in this paper. Synchronized voltage and current measurements in the phase domain are employed for faulted line branch identification and fault classification, as well as fault location. The proposed scheme is derived taking into account the effect of mutual couplings between the parallel lines. Simulation studies confirm the robustness of suggested scheme under different fault types, different fault inception angles, and different fault resistances. Furthermore, the proposed scheme shows acceptable performance against transmission line

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parameters errors, measurement and synchronization errors, earth resistivity variations, and different sampling rate. For all transmission lines faults, the faulted line branch is easily identified with high efficiency and all fault types including normal shunt faults, evolving faults, and cross-country faults are distinguished from each other. In addition, the maximum estimation error in fault location does not exceed 3.06%.

Line

Length (km)

Line branch LS

LR

LT

100

200

300

Appendix A. The series impedance and shunt admittance matrices of each line branch that calculated using MATLAB function [44] are as follows:

ZLS

0.090 + 0.597i0.0620 + 0.298i0.061 + 0.256i0.063 + 0.271i0.062 + 0.253i0.061 + 0.241i 0.062 + 0.298i0.0875 + 0.598i0.060 + 0.297i0.062 + 0.253i0.060 + 0.252i0.060 + 0.253i 0.061 + 0.256i0.0601 + 0.297i0.086 + 0.597i0.061 + 0.241i0.0600 + 0.253i0.059 + 0.271i ](/km) =[ 0.063 + 0.271i0.0620 + 0.253i0.061 + 0.241i0.090 + 0.597i0.062 + 0.298i0.061 + 0.256i 0.062 + 0.253i0.0607 + 0.252i0.060 + 0.253i0.062 + 0.298i0.087 + 0.598i0.060 + 0.297i 0.061 + 0.241i0.0600 + 0.253i0.059 + 0.271i0.061 + 0.256i0.060 + 0.297i0.086 + 0.598i

YLS

0.3079i − 0.0662i − 0.0221i − 0.0432i − 0.0224i − 0.0132i −0.0662i0.3199i − 0.0584i − 0.0224i − 0.0187i − 0.0176i −0.0221i − 0.0584i0.3247i − 0.0132i − 0.0176i − 0.0305i −5 ](S/km) = 10 x[ −0.0432i − 0.0224i − 0.0132i0.3079i − 0.0662i − 0.0221i −0.0224i − 0.0187i − 0.0176i − 0.0662i0.3199i − 0.0584i −0.0132i − 0.0176i − 0.0305i − 0.0221i − 0.0584i0.3247i

ZLR

0.045 + 0.552i0.023 + 0.227i0.023 + 0.188i0.022 + 0.155i0.023 + 0.157i0.023 + 0.153i 0.023 + 0.227i0.047 + 0.564i0.024 + 0.237i0.023 + 0.157i0.023 + 0.166i0.024 + 0.167i 0.023 + 0.188i0.024 + 0.237i0.048 + 0.572i0.023 + 0.153i0.024 + 0.167i0.025 + 0.175i ](/km) =[ 0.022 + 0.155i0.023 + 0.157i0.023 + 0.153i0.045 + 0.552i0.023 + 0.227i0.023 + 0.188i 0.023 + 0.157i0.023 + 0.166i0.024 + 0.167i0.023 + 0.227i0.047 + 0.564i0.024 + 0.237i 0.023 + 0.153i0.024 + 0.167i0.025 + 0.175i0.023 + 0.188i0.024 + 0.237i0.048 + 0.572i

YLR

0.2727i − 0.0609i − 0.0227i − 0.0204i − 0.0141i − 0.0086i −0.0609i0.2885i − 0.0539i − 0.0141i − 0.0128i − 0.0098i −0.0227i − 0.0539i0.2912i − 0.0086i − 0.0098i − 0.0099i = 10−5 x[ ](S/km) −0.0204i − 0.0141i − 0.0086i0.2727i − 0.0609i − 0.0227i −0.0141i − 0.0128i − 0.0098i − 0.0609i0.2885i − 0.0539i −0.0086i − 0.0098i − 0.0099i − 0.0227i − 0.0539i0.2912i

ZLT

0.083 + 0.635i0.057 + 0.303i0.057 + 0.259i0.058 + 0.260i0.057 + 0.253i0.057 + 0.238i 0.057 + 0.303i0.082 + 0.635i0.057 + 0.302i0.057 + 0.253i0.057 + 0.260i0.057 + 0.252i 0.057 + 0.260i0.057 + 0.302i0.081 + 0.635i0.057 + 0.238i0.057 + 0.252i0.056 + 0.259i =[ ](/km) 0.058 + 0.260i0.057 + 0.253i0.057 + 0.238i0.083 + 0.635i0.057 + 0.303i0.057 + 0.259i 0.057 + 0.253i0.057 + 0.260i0.057 + 0.252i0.057 + 0.303i0.082 + 0.635i0.057 + 0.302i 0.057 + 0.238i0.057 + 0.252i0.056 + 0.259i0.057 + 0.259i0.057 + 0.302i0.081 + 0.635i

YLT

0.2747i − 0.0588i − 0.0211i − 0.0307i − 0.0200i − 0.0107i −0.0588i0.2900i − 0.0517i − 0.0200i − 0.0206i − 0.0153i −0.0211i − 0.0517i0.2911i − 0.0107i − 0.0153i − 0.0187i −5 = 10 x[ ](S/km) −0.0307i − 0.0200i − 0.0107i0.2747i − 0.0588i − 0.0211i −0.0200i − 0.0206i − 0.0153i − 0.0588i0.2900i − 0.0517i −0.0107i − 0.0153i − 0.0187i − 0.0211i − 0.0517i0.2911i The generator data are given in the following table:

Generator

Base voltage (kV)

Power flow angle

Short circuit level (GVA)

X/R ratio

GS GR GT

220 220 220

20◦ 0◦ 10◦

20 20 20

15 15 15

The length of each line branch is shown in the following table:

A. Saber et al. / Electric Power Systems Research 154 (2018) 266–275

Appendix B. The following table provides the date of the modeled current and voltage transformers used in simulations. Current transformer Ratio:500/1 A Burden: 30 VA Class: 5P30

Voltage transformer √ √ Ratio:220000: 3/110: 3 V Burden: 100 VA Class: 3P

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