First-zone distance relaying algorithm of parallel transmission lines for single-phase to ground faults

Electrical Power and Energy Systems 80 (2016) 374–381

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First-zone distance relaying algorithm of parallel transmission lines for single-phase to ground faults Z.Y. Xu a,b,⇑, X. Zhang a, J. He a, A. Wen c, Y.Q. Liu d a

School of Electrical & Electronic Engineering, North China Electric Power University, Beijing 102206, China Beijing Sifang Automation Co. Ltd, Shangdi District, Beijing 100085, China c China Southern Electrical Power Grid Co., Ltd., Guangzhou 510003, China d Guangzhou Power Supply Bureau, Guangzhou 510620, China b

a r t i c l e

i n f o

Article history: Received 22 May 2014 Received in revised form 23 December 2015 Accepted 14 January 2016

Keywords: Distance relaying algorithm Parallel lines Single phase to ground faults Mutual coupling

a b s t r a c t A novel zone-one distance relaying algorithm for single phase to ground faults on parallel lines is proposed. The proposed algorithm only requires sampled current and voltage values at one end of the protected line to calculate the fault impedance. The adjacent circuit zero-sequence current can be calculated from the protected circuit zero-sequence current and without cross-connection. The algorithm can overcome the issues of overreach and under-reach. The study in this paper shows that the new algorithm has higher reliability than that of conventional distance relays with and without cross-connected zero-sequence current compensation. Therefore, the algorithm optimizes the performance of zone-one distance relaying for parallel transmission lines. The results are verified by the simulations using PSCAD software. Ó 2016 Elsevier Ltd. All rights reserved.

Introduction Step distance relays are widely used as the main or backup protection on parallel lines. Two issues require special consideration for first-zone distance relaying. These issues are the zero-sequence mutual coupling between the circuits, and crosscountry faults involving more than one lines. In the cross-country ungrounded faults, the two zero-sequence currents of parallel lines are equal in magnitude and opposite in phase [1]. In the crosscountry grounded faults, the two zero-sequence currents of parallel lines are same in magnitude but variational in phase [2]. The new schemes for first-zone distance relay have been presented according to those characteristics [1,2]. However, in the single phase to ground faults the characteristic of two zero-sequence current of parallel lines is completely different from cross-country faults, which makes it more difficult to resolve. The traditional distance relays without cross-connected zerosequence current compensation from adjacent line may result in under-reach or overreach due to errors in measured fault impedance [3–6]. The solutions based on cross-connected zerosequence current compensation for phase distance relaying have been proposed [7,9–13]. According to the references those methods can correctly measure the fault impedance for the solid faults ⇑ Corresponding author at: School of Electrical & Electronic Engineering, North China Electric Power University, Beijing 102206, China. E-mail address: [email protected] (Z.Y. Xu). http://dx.doi.org/10.1016/j.ijepes.2016.01.027 0142-0615/Ó 2016 Elsevier Ltd. All rights reserved.

on protected lines. However, the following two situations are inevitable for such kinds of cross-connected distance relays. Firstly, false tripping of adjacent healthy line may occur due to zerosequence currents between parallel lines inversion [8,12]. Secondly, as presented in this paper, the distance relay with crossconnection cannot avoid overreach in single phase to ground fault with arc resistance. Ref. [8] presents a new scheme to correct under-reach in twin circuit without residual current input from the parallel line, while this scheme has not involved overreach of distance relay on parallel lines. Therefore, it will be advantageous if this algorithm can overcome the problems of overreach and under-reach while it only needs data measured at one terminal of protected line. This paper presents such a new algorithm for first-zone distance relaying of parallel transmission lines. In order to verify the validation of proposed algorithm, firstly, the new algorithm is compared against the traditional algorithms under the condition of solid single phase to ground faults. The results indicate that the new algorithm satisfies the requirement of reach accuracy for first-zone distance relaying, while the traditional algorithm without cross-connection will under-reach. Secondly, the new algorithm and traditional algorithms are compared under the condition of single phase to ground faults with fault resistance. The simulation results show that the proposed algorithm has a better performance than the traditional algorithms with or without cross-connection under different ground resistances. The traditional algorithm with or without

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cross-connection cannot avoid over-reach for the faults on protected line with fault resistance or the solid faults on adjacent line. Finally, sources of the algorithm error, such as zero-sequence current ratio factors, load currents, fault resistances and shunt capacitance are analyzed. The required computations of proposed algorithm are simple and non-iterative. The proposed algorithm has significant potential for practical applications.

M D(Z0+3Z M 0 ) K (1-D)(Z0+3Z M 0) IK0T UK0T

2ZMS0

N 2ZNS0

(a) Forward component distribution network of zero-sequence Analysis for single phase to ground fault on parallel transmission lines

M

ð1Þ

When a solid single phase to ground fault occurs, Rf is equal to zero. According to Eq. (2) in Ref. [1], the zero-sequence currents flowing through parallel lines at the end M or N can be expressed as follows:




II0 ¼ I0T þ I0F ¼ C 0T IK0T þ C 0F IK0F

where C0T, C0F are the forward and reverse component distribution factors of zero-sequence current at end M or N, respectively. The zero-sequence current ratio factor k is defined as:

III0 ðC 0T  C 0F ÞIK0F C 0T  C 0F ¼ ¼ II0 ðC 0T þ C 0F ÞIK0F C 0T þ C 0F

ð3Þ

According to Fig. 2 the distribution factors of zero-sequence fault currents at end M and N can be obtained as follows:

8 > C ¼ ð1DÞðZ0 þ3ZM0 Þþ2ZNS0 > > M0T 2ZMS0 þZ0 þ3ZM0 þ2ZNS0 > C > N0T ¼ 2Z > MS0 þZ 0 þ3Z M0 þ2Z NS0 > : C N0F ¼ D

ZMS0

Magnitude

0.6

0.2275

0.4 0.2

0.85

0 0

0.2

0.4

0.6

0.8

1

D

(a) Magnitude 10 k

0.9201°

5 0 -5 0.85

-10 0

0.2

0.4

0.6

0.8

1

0.8

1.0

D

(b) Phase-angle

1 0.5

Kmax Kmin

0 -0.5 0

0.2

0.6

0.4 D

Fig. 3. k against the fault distance and operating states.

ð4Þ

N II

ZM0

I

k

(c) k with different operating states and fault distances

M S1

1 0.8

ð2Þ

III0 ¼ I0T  I0F ¼ C 0T IK0T  C 0F IK0F

k¼

Fig. 2. The zero-sequence distribution networks of fault component.

K

IK0T ¼ IK0F

UK ¼ Z K1T þ Z K2T þ Z K0T þ Z K1F þ Z K2F þ Z K0F þ 6Rf

N

(b) Reverse component distribution network of zero-sequence

Phase-angle/deg

Fig. 1 shows the system diagram of parallel lines for the analysis of single phase to ground fault, where ZMS0 and ZNS0 are zerosequence equivalent source impedances at end M and N, respectively. In the following description of this paper, ‘0’, ‘1’ and ‘2’ are used in the subscript of variables or parameters to indicate that they are zero-, positive- and negative-sequence components, respectively. K is fault point; Rf is fault resistor; Z0 and ZM0 denote total line zero-sequence impedance and mutual coupling impedance of parallel line, respectively. D is fault distance from relay location to fault (0 6 D 6 1). The new relations are derived based on the boundary conditions of IAG single phase to ground fault after analysis by symmetrical component method for parallel lines [1,2]. Fig. 2 shows the zerosequence distribution networks of fault component. IK0T and IK0F represent the forward and reverse component of zero-sequence current in fault point, respectively. More details can be found in Refs. [1,2]. According to the analysis in Appendix A, the following equation can be obtained. ZK0T, ZK1T, ZK2T, ZF0T, ZF1T and ZF2T represent the forward and reverse components of zero-, positive- and negativesequence impedances, respectively.

D(Z0 -3Z M 0) K (1-D)(Z0 - 3Z M 0) IK0F UK0F

K

Z NS0

S2

where CM0T, CN0T and CM0F, CN0F are the forward and reverse component distribution factors of zero-sequence currents at end M and N, respectively. According to Eq. (3) the relationship between II0 and III0 can be expressed as:

III0 ¼ kII0

ð5Þ

D Rf Fig. 1. Parallel transmission line for analysis.

where k is zero-sequence current ratio factor of parallel lines, which is determined by the fault distance D, and the zero-sequence impedances of parallel lines and systems at two ends. For some parallel transmission lines the zero-sequence impedance of line is a

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constant, while the system equivalent zero-sequence impedance may change in different operating states. Fig. 3(a) and (b) shows the typical magnitudes and phase-angles of factor k, which correspond to special operating states and different fault distances. When the fault point moves from the relay location to the remote end of protected lines the zero-sequence current ratio factor k increases gradually. The zero-sequence current ratio factor k will reach 1.0 when the fault point moves to the remote end of protected lines. The phase-angle of the zerosequence current ratio factor k is near to zero degree because the parallel lines and the systems have nearly the same zerosequence impedance angles, which means k is a real number. With varying operating states, the system zero-sequence impedances may change and the zero-sequence current ratio factor k may also change. For every special fault distance when ZMS0 reach minimum value and ZNS0 reach maximum value the maximum zero-sequence current ratio factor kmax at end M will be obtained; while the minimum zero-sequence current ratio factor kmin at end M will be obtained when ZMS0 reach maximum value and ZNS0 reach minimum value. The shaded area in Fig. 3(c) shows the different k values, with corresponding different fault distances and operating states of systems at two ends. It can also be found that the maximum and minimum k values tend to be 1.0 when the fault points move to the remote end of parallel lines for different system operating states. In other words, when the single phase to ground fault occurs at the remote end of parallel lines the zero-sequence currents on parallel lines are same. In actual power system, the zero-sequence equivalent impedances at two terminals may change in a very small region in different operating states. For instance, in case of zero-sequence circuits directly grounded through transformer neutral points at two buses, the zero-sequence equivalent impedances and the zero-sequence current ratio factor k will not change with different system operating states. New algorithm for first-zone distance relaying on parallel lines When a single phase to ground fault occurs, considering Eq. (5), for the phase voltage of fault phase u at relay location, the following Eq. (6) can be obtained.

U u ¼ DZ 1 ðIIu þ 3K 0 II0 Þ þ DZ M0 III0 ¼ DðZ 1 ðIIu þ 3K 0 II0 Þ þ kZ M0 II0 Þ

ð6Þ

where K 0 ¼ ðZ03ZZ1 1 Þ, and K 0 is the zero-sequence current compensation factor. The fault distance D can be obtained as Eq. (7).

D¼

Eð%Þ ¼ ðD  DaÞ=Da  100

ð8Þ

where D is the calculated fault distance with Eq. (7), and Da is the actual fault distance of a parallel line. A positive error means the calculated fault distance is larger than actual fault distance, while a negative error means the calculated fault distance is smaller than actual fault distance. As shown in Fig. 4 above, for different fault distances and system operating states, the k values are set as the maximum value kset, corresponding to the reach setting of first-zone distance relay. In practical, 85% line length is selected as protected coverage of zone-one distance relay. The fault distance can be expressed as Eq. (9).

D¼

Uu Z 1 ðIu þ 3K 0 II0 Þ þ kset Z M0 II0

ð9Þ

The fault impedance can be obtained as Eq. (10).

Z u ¼ Z 1 absðDÞ

ð10Þ

Note that u represents any phase a, b or c. Eqs. (9) and (10) are suitable for any single phase-ground faults on parallel transmission lines. As shown in Fig. 4 above, kset is larger than actual k value for the internal single-phase to earth fault, and the calculated fault distance D will be less than reach setting. It will cause negative errors and this will ensure that the distance relay will be reliable to operate for an in-zone fault. In case of external single-phase to earth fault kset is less than actual k, and the calculated fault distance D will be larger than the reach setting. It will cause positive errors and this will ensure the distance relay to stop operation for an out-zone fault. As shown in Fig. 4 the maximum positive error of calculated fault distance reaches to 12%, so that the reach setting of first-zone distance relay can be expanded to a length larger than 90% of the protected parallel line. Fig. 5 shows the actual protected coverage against different k values. As shown in Fig. 4, kset corresponds to the maximum kmax value in reach setting of first-zone distance relay. When system operating states change the actual k value, the calculated fault impedance with kset will decrease and resultantly actual protected coverage will be expanded, but the expanded coverage will never cover 100% line length. As shown in Fig. 5, with varying system operating states when the zero-sequence current ratio factor k reaches to the minimum value, the protected coverage will be 92.5% (370 km). Digital verification

Uu Z 1 ðIu þ 3K 0 II0 Þ þ kZ M0 II0

ð7Þ

Fig. 4 shows the calculated fault distance errors with a k value of 0.85 fault distance, the typical parameters of 500 kV parallel transmission lines and systems at two ends as shown in Ref. [1]. The error (%) is defined as:

The studied first-zone distance relay is set to protect 85% of the 400 km line (i.e. 340 km). The PSCAD and MATLAB are used for the simulations of power system and the new algorithm. Source S1 leads S2 by the angles between 0° (no load) and 30° (heavy load). Fault inception time is 0.5 s. The sampling rate of 2000 Hz is used, and FFT (Full Cycle Fourier Transform) is used to filter out the higher order harmonic components.

30 Proposed algorithm

0.378 0.300

10 0

K

E r ro r ( % )

20

reach setting

0.200

Protection Coverage

0.100

-10 -20 0.125

kmax

0.85 0.250

0.375

0.500 0.625 D

0.750

Fig. 4. Errors against the fault distance.

0.875

1.000

0.000 -0.051 0

0.925

kmin

0.125 0.25 0.375

0.5 D

0.625 0.75 0.875

Fig. 5. Actual protected coverage against k.

1

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The traditional algorithms [2] with and without the zerosequence current compensation from adjacent line are given in Eqs. (11) and (12), which are used for comparison with the proposed algorithm.

X ¼ imagðU u =ðIIu þ 3K 0 II0 þ K M0 III0 ÞÞ

ð11Þ

X ¼ imagðU u =ðIIu þ 3K 0 II0 ÞÞ

ð12Þ

where K M0 ¼ Z M0 =Z 1 . Fig. 6 shows the phase voltages, currents and fault distance loci measured at end M on the protected line for a solid IAG fault located at 360 km away, which is outside the reach of first-zone. As expressed in Eq. (5), the zero-sequence current components on both circuits directly appear in phase. For the new algorithm the stable fault impedance is obtained with a positive error within a cycle following the fault occurrence. Fig. 7 shows the phase voltages, currents and calculated fault distance loci when a single-line IAG solid grounding fault occurs at 320 km away from end N (receiving end), that is within the reach of first-zone of the distance relay at end N. As shown in Fig. 7(b) the proposed algorithm can obtain the stable fault impedance with a negative error within a cycle. As shown in Fig. 8, the errors with new algorithm are negative when the faults are behind the protected zone, while the errors are positive when the faults are beyond the protected zone, this will enhance the reliability of distance relay in this case. As shown in

Fig. 8(a) the relay with the traditional algorithm with crossconnection can also correctly measure the fault reactance for solid single phase to ground faults. As show in Fig. 8(a), when the adjacent circuit zero-sequence current is utilized directly in the traditional algorithm with cross-connection, this algorithm can accurately measure the fault distance for solid faults. However, in most practical engineering, the adjacent circuit zero-sequence current cannot be cross-connected, the traditional distance relay will overreach or under-reach for single-phase to ground faults. The proposed algorithm has negative errors for the internal faults, smaller fault impedance than the real fault point will be obtained and the distance relay can reliably operate. While it has positive errors for the external faults, larger fault impedance than the real fault point will be obtained and the distance relay can reliably inoperate. The proposed algorithm can fully overcome the issues of overreach and under-reach without any cross-connection from the adjacent line, and will increase the reliability of the distance relay. As shown in Fig. 8(b), the conventional distance relays with and without cross-connection have large negative errors for external fault and they may cause overreach for the single phase to ground faults with fault arc resistance. Fig. 9 shows estimated fault distance under IIAG solid grounding fault at different fault locations on adjacent line. As shown in Fig. 9(b) for traditional algorithms including the cross-connection algorithm, the calculated fault distance may overreach into the operating zone of first-zone distance relay while the fault distance

Voltage (kV)

500 Ua Ub Uc 3U0

0 Circuit I

-500 0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

Time (s) Current (kA)

5 Ia Ib Ic 3I0

0 Circuit I -5 0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.56

0.58

0.6

0.62

Time (s) 3I0 (kA)

5

0 Circuit I Circuit II -5 0.46

0.48

0.5

0.52

0.54

Time (s) (a) Fault waveform

Distance (km)

600 500 370.2 km 400 300 340 km m 200 0.5

0.52

0.54

0.56 0.58 Time (s) (b) Impedance loci

0.6

0.62

0.64

Fig. 6. Fault waveform and estimated fault impedance under IAG solid fault at 360 km from bus M.

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Z.Y. Xu et al. / Electrical Power and Energy Systems 80 (2016) 374–381

Voltage (kV)

500 Ua Ub Uc 3U0

0 Circuit I -500 0.46

0.48

0.5

0.52

0.54

5

Current (kA)

0.56

0.58

0.6

0.62

Time (s) Ia Ib Ic 3I0

0 Circuit I -5 0.46

0.48

0.5

0.52

0.54 Time (s)

0.56

0.58

0.6

0.62

0.62

0.64

(a) Fault waveform

Distance (km)

600 500 340 km m 400 300 315.8 km 200 0.5

0.52

0.54

0.56

0.58 Time (s)

0.6

(b) Impedance loci

Error (%)

Fig. 7. Fault waveform and estimated fault impedance under IAG solid fault at 320 km away from bus N.

25 20 15 10 5 0 -5 -10

Proposed algorithm Cross-connection Traditional algorithm

340km 50

100

150

200 250 Fault distance (km)

300

350

400

(a) Estimated fault reactance error for solid fault 20 Error (%)

10 0 -10

Proposed algorithm Cross-connection Traditional algorithm

-20 -30

50

100

150

340 k m 200 250 Fault distance (km)

300

350

400

(b) Estimated reactance error with 15ohm fault resistance Fig. 8. Estimated fault reactance errors under ICG single-phase fault with the condition of d ¼ 30° under different fault locations.

of new algorithm is larger than operating zone of first-zone distance relay that will avoid overreach.

fault occurs at the end of protected line the zero-sequence current in both lines will be in opposite direction and can be expressed in Eqs. (13) and (14).

One of parallel lines in maintenance

III0 ¼ k II0

The proposed algorithm is derived on the basis of assumption that the both lines are in service. As shown in Fig. 10(a), if one of the parallel lines is in maintenance and grounded at both ends, the impact of the zero-sequence current to the proposed algorithm is analyzed in this section. In this case when single phase to ground

0

0

k ¼

Z M0 Z0

ð13Þ ð14Þ

When one of parallel lines is in maintenance state, kset can be set as:

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Z.Y. Xu et al. / Electrical Power and Energy Systems 80 (2016) 374–381

protected line can be achieved. The application of the new algorithm can enhance the performance of the distance relays on parallel lines.

d

M

K

II

Z MS0

Z M0

S2

Z NS0

I

Sensitivity analysis

(a) Simulated faults in adjacent line

Impact of system operating states

1200

d ( k m)

800 400 0

Proposed algorithm Cross-connection

340km ( reach setting )

-400

50

100

Traditional algorithm

150 200 250 Fault distance (km)

300

350

400

(b) Estimated fault distance Fig. 9. Estimated fault distance under IIAG solid grounding fault at different fault locations on adjacent line d: fault distance from bus M to fault point K on adjacent line (km).

M S1

N II

ZMS0

ZM0

I

Z NS0

S2

K D

(a) System diagram

Impact of fault resistances and load currents

10

Error (%)

-3.71% 3.79%

0

-20

- 4.15%

Proposed algorithm Cross-connection Traditional algorithm

-10

50

100

150

340km 200

250

300

-12.75% 350

400

Fault distance (km)

(b) Estimated reactance error for solid faults Fig. 10. Parallel transmission lines in maintenance.

kset ¼

2 0 k 3

As described in Section ‘New algorithm for first-zone distance relaying on parallel lines’, with changing operating states zerosequence impedances of system may vary and the zero-sequence current ratio factor k may also change. The varying zerosequence current ratio factor k may impact the errors of calculated fault reactance of new algorithm. Fig. 11 shows estimated fault reactance errors under IAG solid grounding fault with minimum zero-sequence current ratio factor k. In new algorithm, kset is set at maximum k value when the fault is located at reach end of first-zone distance relay. As shown in Fig. 8(a) for the system operating state that corresponds to maximum k, the error of calculated fault distance is zero when the fault is located at reach end. In other words, it is the zero error point. For the internal faults the errors are negative, while for the external faults the errors are positive. As shown in Fig. 11 for the minimum value of k, the zero error point is expanded to 395 km and the actual protected coverage is expanded to 370 km (92.5%). Faults that are at 395–400 km have positive errors, this will ensure that the first-zone distance relay does not malfunction. The new algorithm has a better performance than the traditional algorithm.

ð15Þ

For the practical distance relay a digital input can be used to know whether the system is in normal operating state or in maintenance state. When the safety grounding points are located in the line side of CTs as shown in Fig. 10(a) the zero-sequence currents in maintenance line will be bypassed by the grounding points and this cannot be avoided in practical engineering. In this case the algorithm with cross-connection still causes over-reach as the traditional algorithm without cross-connection. Fig. 10(b) shows the simulation results using one of the parallel lines in maintenance state with the typical parameters in Ref. [1]. The errors of calculated fault reactance by proposed algorithm are quite small when the faults are located at the end of protected line, and it can avoid over-reach. The errors of traditional algorithm with and without cross-connection are much large when the faults located at the end of protected line, this will cause over-reach for first-zone distance relays. The improved performance for the distance protection of parallel lines offered by the new algorithm can be seen from these results. A good performance based on the signals only from the

It can be concluded that the reach of the new algorithm can be affected by the fault resistance according to the derived formulas (9). Figs. 6 and 7 show that the new algorithm has a good performance when a solid single phase to ground fault occurs. In practice the fault resistance for the single phase to ground fault may be large [14]. A simulation is given under the extreme conditions of d = 30° (heavy load) and Rf = 0–300 X. As shown in Fig. 12, the new algorithm has positive errors, while the traditional algorithms with and without cross-connection of zero-sequence current from adjacent line have negative errors, this will cause overreach of first-zone distance relays. As shown in Fig. 12, with the increment of the fault resistance the errors will reach negative 100% for traditional algorithms including cross-connection algorithm, the huge negative errors will cause overreach of zone-one distance relay that will mistakenly recognize an external resistive fault as an internal fault, while the new algorithm has positive errors that cannot cause overreach of first-zone distance relays, even though it reaches 150%. Impact of shunt capacitance and shunt reactor The proposed algorithm is derived by neglecting the shunt capacitance of parallel lines. As shown in Figs. 6–12, the 20

Error (%)

S1

N

Proposed algorithm Traditional algorithm

10 0 -10

Zero Error Point -20

50

100

150

200

250

300

350

Fault distance (km) Fig. 11. Estimated fault reactance errors under IAG solid grounding fault with minimum k values.

Z.Y. Xu et al. / Electrical Power and Energy Systems 80 (2016) 374–381

Error (%)

380

200 150 100 50 0 -50 -100

2

1 1 1 6 1 1 a2 6 6 61 1 a M¼6 6 1 1 1 6 6 4 1 1 a2

Proposed algorithm Cross-connection Traditional algorithm

0

50

100

150

200

250

1 1

300

Rf (ohm) Fig. 12. Estimated fault reactance errors under ICG faults with Rf 0–300 X at 320 km away from bus M.

a

1

1

a2 a

a a2

1

1

a2

a a2 a2

a

1

3

7 7 7 7 7 1 7 7 7 a 5

a a2

ðA3Þ

The coupled transmission equations are transformed into decoupled ones (A4) depending on the sequence-component.

3 2 3 2 Z 0T 0 U 0T 6U 7 6 0 7 6 0 7 6 6 0F 7 6 7 6 7 6 6 6 U 1T 7 6 U K 7 6 0 7 6 7¼6 6 6U 7 6 0 76 0 7 6 6 1F 7 6 7 6 7 6 6 4 U 2T 5 4 0 5 4 0 2

0

U 2F

0

0

0

0

0

Z 0F

0

0

0

0

0

Z 1T

0

0

0

0

0

Z 1F

0

0

0

0

0

Z 2T

0

3 I0T 76 I 7 76 0F 7 76 7 76 I1T 7 76 7 76 I 7 76 1F 7 76 7 54 I2T 5

0

0

0

0

Z 2F

I2F

0

32

ðA4Þ

In case of single phase to ground faults, the fault boundary condition of IAG is shown in Fig. 13. If the fault resistance can be seen as equivalent system parameters, marked as super-script ‘‘0 ”, following equation can be obtained.

Fig. 13. The boundary condition of IAG fault.

simulations are carried out using distributed parameter line models that include the shunt capacitance and the shunt reactor. The shunt reactor is set to compensate 60–80% distributed capacitance of the long transmission line. In this paper, the shunt reactors have been designed for compensating 70% of the distributed capacitance in all the simulations. The result shows that the impact of the distributed capacitance and the shunt reactor for the new algorithm is insignificant. If the series capacitors are considered, the algorithm will be quite different from the proposed algorithm in this paper, and the proper algorithm has been discussed in others papers [15].

Z 0Kij ¼ Z Kij þ Rf

ði ¼ 0; 1; 2; j ¼ T; FÞ

ðA5Þ

For IAG fault the boundary conditions can be described as Eqs. (A6) and (A7).

U_ 0KIA ¼ 0

ðA6Þ

IKIB ¼ IKIC ¼ IKIIA ¼ IKIIB ¼ IKIIC ¼ 0

ðA7Þ

Substituting Eq. (A6) into (A1), we have

U 0K0T

þ U 0K1T þ U 0K2T þ U 0K0F þ U 0K1F þ U 0K2F ¼ 0

ðA8Þ

Substituting Eq. (A7) into (A2), we have Conclusion

IK0T ¼ IK1T ¼ IK2T ¼ IK0F ¼ IK1F ¼ IK2F ¼ A novel algorithm of first-zone distance relaying for single phase to ground faults on parallel lines is presented. The new algorithm can satisfy the accuracy requirement for the first-zone distance relaying on parallel lines, while traditional algorithm may overreach or under-reach. The main advantage of the new algorithm over the distance relaying algorithm with crossconnected zero-sequence current is that only local data of protected line is required and overreach of first-zone distance relay is fully overcome. This makes the design, installation and operation of the new distance relay much simpler, hence improving its reliability. Acknowledgement This work is supported in part by Key Science and Technology Project of China Southern Power Grid (No. GZHKJ 00000101).

1 IKIA 6

ðA9Þ

Meanwhile, substituting the sequence voltage and current relationship of matrix (A4) into Eqs. (A8), (A10) can be obtained.

U K  IK1T Z 0K1T  IK2T Z 0K2T  IK0T Z 0K0T  IK0F Z 0K0F  IK1F Z 0K1F  IK2F Z 0K2F ¼0

ðA10Þ

Substituting (A9) into (A10), the fault currents of sequence components can be obtained as follows.

IK0T ¼ IK1T ¼ IK2T ¼ IK0F ¼ IK1F ¼ IK2F ¼

1 IKIA 6

¼

UK Z 0K1T þ Z 0K2T þ Z 0K0T þ Z 0K0F þ Z 0K1F þ Z 0K2F

¼

UK Z K1T þ Z K2T þ Z K0T þ Z K0F þ Z K1F þ Z K2F þ 6Rf

ðA11Þ

Appendix A The essence of the sequence-component algorithm for parallel lines is to eliminate mutual inductance. They are based on the well-known symmetrical components method of a single threephase circuit. It is easy to obtain the sequence-components of parallel lines from the phase-components as (A1) and (A2).

UT IT

F

F

¼ M 1 U I

¼ M1 II

II

II

The transforming matrix M is presented as follows:

ðA1Þ ðA2Þ

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