Fault feeder detection method utilized steady state and transient components based on FFT backstepping in distribution networks

Electrical Power and Energy Systems 114 (2020) 105391

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Fault feeder detection method utilized steady state and transient components based on FFT backstepping in distribution networks☆

T

⁎

Wang Xiaoweia,b, Wei Xiangxiangc, , Yang Dechangd, Song Guobinga, Gao Jiee, Wei Yanfangb, Zeng Zhihuib, Peng Wangf a

School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China c Electrical Engineering and Computer Science, Technische Universität Berlin, Berlin 10623, Germany d College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, China e Wenzhou Power Supply Company, Zhejiang Electric Power Company of State Grid, 325000, China f Electric Power Research Institute, Henan Electric Power Company of State Grid, 450052, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Fault feeder detection Steady-state components Transient components Fast Fourier transform Bubble sort method

A novel cut-in point for fault detection issue is introduced by dividing the transient zero sequence current (TZSC) into the steady-state components (SSCs) and transient components (TCs), a comprehensive detection method based on the coordinated SSCs and TCs is presented. For the SSCs criterion, the TZSCs within the second power cycle are used as the research objects, the local SSCs are obtained based on Fast Fourier transformation (FFT), if there is unique phase difference of the local SSCs is larger than Π/4, the correlation coefficients of SSCs are used to detect the fault feeder; Otherwise goes into the TCs criterion stage, the global SSCs based on the backstepping method is calculated, accordingly, the TCs can be obtained by subtracting SSCs, the difference between fault feeder and healthy feeders are enhanced by using the extremum of TCs and bubble sort method, lastly, the crosscorrelation distance (CCD) is introduced to detect the fault feeder. The proposed method not only has high detection accuracy but also needs least time length, the correctness and extensive applicability have been verified by the results from the radial distribution network simulation model, arc fault model, improved IEEE-13 node system and field test.

1. Introduction The ratio of single phase to ground (SPG) fault occupies almost 80% for all the fault types in distribution networks, detecting SPG fault has become an important topic to ensure the stability and reliability of power grids. The middle or low voltage systems (10 kV, 35 kV and 66 kV) are widely operated with neutral grounding via arc suppression coil. When the SPG fault occurs, the existing methods cannot efficiently detect fault lines because of the weak fault features [1–3]. 1.1. Related research works The existing SPG fault detection methods can be concluded as:

steady-state methods [4,5], artificial injection methods [6] and transient methods [7–21]. The steady-state methods use the steady-state fault features to detect the fault feeders, such as phases comparison methods, 5th harmonic methods, etc. The principles of artificial injection methods can be described as the fault feeders can be selected by detecting specific injection signals. The steady state methods and injection signal methods in Ref. [4,5] are convenient to implement and the detection theories are also simple, while the limitations of applications still exist because of complex fault conditions and different network structures, the detection accuracy cannot be ensured. To improve detection accuracy, many methods are based on the transient fault features, such as transient energy methods [7,8], wavelet transform (WT) methods [9–12], S transform methods [13–15], Hilbert-

Abbreviations: SPG, single phase to ground; TZSC, transient zero sequence current; SSCs, steady-state components; TCs, transient components; FFT, fast Fourier transformation; CCD, cross-correlation distance; CCCD, comprehensive CCD; CCCM, comprehensive correlation coefficient matrix; HHT, Hilbert-Huang transform; IMF, intrinsic mode function; WT, wavelet transform; SNR, signal-to-noise ratio ☆ This work was supported in part by the National Natural Science Foundation of China under Grants 61403127 and 61703144, and in part by the Tackling Key Project of Henan Science and Technology (182102210051). ⁎ Corresponding author. E-mail addresses: [email protected] (W. Xiangxiang), [email protected] (Y. Dechang), [email protected] (Z. Zhihui). https://doi.org/10.1016/j.ijepes.2019.105391 Received 13 January 2019; Received in revised form 26 May 2019; Accepted 30 June 2019 Available online 04 July 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

Electrical Power and Energy Systems 114 (2020) 105391

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Ucap Lp iL(t) Rp

i01

i0f(t)

C01

i02

Rg

C02 i0n

i0f(t)

Rg

Ug(t)

C0n

i01

i02

i0n

C01

C02

C0n

Rp iL(t) U cap Lp i0C(t)

Ug(t) (a) Simplified equivalent circuit of zero-sequence current

(b) Equivalent circuit of TZSC

Fig. 1. Transient equivalent circuit of simplified multi-feeder substation circuits.

improve the detection accuracy, the theories are simple and easy to implement in practical engineering. The main contributions of proposed method are listed as follow:

Huang transform (HHT) methods [16,17], clustering methods [18,19], optimized bistable system [20] and sparse decomposition method [21]. The details can be summarized as follow. By using the discrete WT, paper [7] presents a novel wavelet-based methodology for real-time detection of fault-induced transients in transmission lines. Based on the good frequency splitting ability of WT, the wavelet entropy is utilized to identify fault effectively [8]. Shannon entropy was calculated to detect fault feeder by introducing WT and singular value decomposition in [9], the availability of proposed method has been proved for fault feeder detection issue. Dong used WT to extract the initial traveling wave, the fault line was identified by comparing the magnitudes and polarities of feeders [10]. A novel fault location method was proposed based on WT [11]. Guo applied a continuous WT to acquire time-frequency fault features to detect the fault line [12]. The accuracy of detection methods using WT is higher than the steady state methods, different wavelet functions can significantly affect the fault detection results, while it is a very knotty problem about how to select or construct the suitable wavelet functions. S-transform algorithm was introduced to detect fault feeder in [13]. Shu used S-transform algorithm to obtain the amplitude matrix, the fault feeder can be identified by calculating the amplitude difference values [14]. S-transform and WT methods are used to solve the fault location issue in paper [15]. Cui adopted the HHT algorithm to extract the instantaneous energy, the high-frequency components were utilized to detect fault feeder [16]. Paper [17] used HHT to calculate the intrinsic mode functions (IMFs), the amplitudes were used to detect the fault line. While the detection results using HHT method may be incorrect because of mode mixing and end effects. Using the improved singular value decomposition algorithm and the ideal clustering algorithm, the fault feeder can be detected accurately [18]. Through collecting the fault features of voltage and current, the fault line can be identified in [19]. The detection precision in Ref. [18,19] heavily depends on the abundant training sample data, if we can achieve the enough fault sample data, the detection accuracy will be high. While it is difficult or unrealistic to collect all the sample data under different fault conditions. Besides, the classification algorithms are time consuming. Wang proposed an optimized bistable system to detect the weak fault situations [20]. Through constructing a mixed atom dictionary, the fault feeder can be selected by calculating the atoms’ energy spectrum in [21]. The simulation results show that the detection methods mentioned in [20,21] own high accuracy, while whose theories are complex and time consuming, the applicability of proposed methods need to be verified further.

(1) FFT backstepping method is firstly introduced to calculate the SSCs for fault feeder detection issue, the correctness and effectiveness of the proposed extracting SSCs method has been verified by the theoretical analysis, simulation results and practical test results. (2) The bubble sort method is used to rearrange the TCs, the difference between the fault feeder and healthy feeders can be enhanced, which helps to improve the detecting accuracy. (3) The relevant techniques or algorithms used in proposed method are simple and have been maturely applied to the practical application, which means the proposed method are more easily to implement in practical use. In addition, compared with the existing detection methods, the proposed method is less time assuming. The remaining of this paper is organized as follow. In Section 2, the fault characteristics of SPG are analyzed. In Section 3, the basic theories of fault detection methods are given. In Section 4, we utilize FFT algorithm and backstepping method to extract the global SSCs. In Section 5, the coordinated fault detection criteria are proposed. In Section 6, simulation results are verified. In Section 7, the applicability analysis of proposed method is presented, including simulation results under different fault conditions, arc fault results and unbalanced load test results. In Section 8, we compare the proposed method with the other existing methods. In Section 9, the field test results are given to verified the practicality and effectiveness of our fault detection method. In Section 10, we get the conclusions. 2. Analysis of TZSC equivalent circuit As shown in Fig. 1, a zero-sequence equivalent network when the nth feeder occurs the SPG fault [1,22,23]. Where i0j is TZSC of line j for healthy lines. C0j is the zero-sequence equivalent capacitance of line j, Rg is the grounding resistance, Rp and Lp are the equivalent resistance and inductance of arc-suppression coil, Ug(t) is the equivalent zero-sequence voltage, iL(t) is the inductor current, i0C(t) is the sum of each capacitance current, i0f(t) is the grounding current, Ucap is the capacitor voltage of parallel branch lines. From Fig. 1, it can be concluded that: (1) The flow directions of TZSCs between healthy feeders and fault feeder are opposite. The currents in the healthy lines flow from bus to feeders, while the current of fault line flows from fault location to bus. Additionally, if Ucap can be measured beforehand, regardless of the small inductor current, the SSCs’ phases are equal for healthy feeders, as shown in Eq. (1):

1.2. Contributions of proposed detection method This paper proposes a novel feeder detection method based on SSCs and TCs for SPG issues, FFT and bubble sort method are introduced to 2

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i 0j (t ) = jωCj Uc ap

(1)

WFFT (ω) =

∫t

T + tdecay

decay

iSSC, local (t ) e−jωt dt

(7)

Here i0j(t) is the TZSC of line j, j = 1, 2⋯,n . The inverse transform of FFT is shown in (8). (2) i0j(t) can be divided into two parts, one is steady state complements (SSCs) iSSC(t), another one is transient complements (TCs) iTC(t). Finally, i0j(t) can be expressed as:

i 0j (t ) = iTCj (t ) + iSSCj (t )

(2)

iSSCj (t ) = (ICmj − ILmj ) cos(ωt + φ)

(3)

ωf

iTCj (t ) = ICmj ⎛ sin φ sin ωt − cos φ cos ωf t ⎞ e ⎝ω ⎠

− τt

Cj

+

t ILmj cos φe− τL

iSSC, local (t ) =

ωLp ⎛ ⎞ ⎜ Rg (1 − ω2Lp ∑n C0j ) ⎟ j=1 ⎝ ⎠

(4)

i 0j [1] ⩾ (5)

i 0j [3] ⩾ ....... ⩾i 0j [r ]

(9)

i 0j [3] ⩽ ....... ⩽i 0j [r ]

(10)

4. Extracting SSCS with FFT and backstepping method When SPG fault occurs the decay time constant δ is related to the grounding resistance, fault distance and inductance. When the grounding resistance is small, according to paper [24], the decay time constant δ can be written as:

δ=

(Ru0 + 2Ru1) H + 2RT 1 + 3Rg (11)

2(Lu0 H + 2Lu1 H + 2LT 1)

where Ru0, Lu0, Ru1 and Lu1 are the lines’ zero-sequence resistance, positive-sequence resistance, zero-sequence inductance and positivesequence inductance for per unit length, respectively; RT1 and LT1 are the positive-sequence resistance and positive-sequence inductance, H means the fault distance, Rg is the grounding resistance. Some calculation results have been carried out in [24], as shown in Table 1. It can be seen from Table 1 all the decay time values are less than 10 ms, which is to say the attenuation behaviors are mainly in the first half power cycle. Besides, lager grounding resistance Rg corresponds to shorter decay time, for instance, when the resistance Rg increases from

(6)

Amplitude/A

The conditions described in Eq. (6) are met, therefore iSSC,local(t) can be decomposed by FFT to get the local SSCs WFFT(ω), it can be written in (7).

Table 1 Decay time with variable Rg and H.

TCs are of interest 0

(8)

Actually, γj represents the current flow directions as SPG fault occurs, which is to say, the sign of γj for fault line are the opposite to the sign of γj for healthy line. Therefore, the difference between fault line and healthy lines can be enhanced using Eqs. (9) and (10), the fault feeder can be identified more easily. The accurate signs cannot be always obtained because of the complex fault conditions, therefore, in order to avoid heavily depending on the signs of initial extreme value γj and improve the detection accuracy, a more comprehensive and coordinated detection method using TCs and SSCs will be introduced in the follow-up contents.

According to Eqs. (3) and (4), we can know that TZSCs are consisted of SSCs and TCs. If there is a time point tdecay, the TCs are of interest before tdecay and the SSCs are of interest after tdecay, as shown in Fig. 2. Where T is the time length of one natural frequency. Since the transient components are very small after tdecay, to simplified fault detection theories and easily implementation in practical scene, FFT is introduced to extract the local SSCs between tdecay and tdecay+T. The steady state angel φ can also be obtained, considering the angles φ are near among healthy lines and larger difference between fault feeders and healthy feeders, therefore, the angles φ can be used as foundation to construct fault detection criterion. In order to verify the ability of extracting SSCs by FFT, the simulation results are introduced. Here, we denominate the SSC after tdecay as iSSC,local(t), FFT can transform iSSC,local(t) from the time domain to the frequency domain, whose physic essence can be described as iSSC,local(t) is the summation of several sinusoidal functions. Since iSSC,local(t) is the periodic signal, iSSC,local(t) meets the Dirichlet conditions, which are integrable, limited number of discontinuities and extreme values. Therefore, there is:

|iSSC, local (t )| dt < ∞

i 0j [2] ⩾

i 0j [1] ⩽ i 0j [2] ⩽

3.1. FFT and its application for fault detection

T + tdecay

W (ω) e jωt dω

Here, r is the number of sampling points. When γj < 0, there is:

3. Basic theories of fault detection method

decay

T + tdecay

decay

In order to enhance the difference between healthy feeders and fault feeder, the bubble sort method is introduced based on the polarity of fault signals. The applications of bubble sort method can be described as follow. When SPG fault occurs, if the initial extreme values γj of TZSC i0j(t) are obtained, i0j(t) can be rearranged based on the sign of γj, the principles of re-sequencing can be written as: When γj > 0, there is:

Here, ϕ represents the initial angle of healthy feeders when fault occurs. It can be known that φ can be calculated by ϕ , the variables Rg and Lp.

∫t

∫t

3.2. Bubble sort method and its application

where ILmj and ICmj are the initial current values of inductor and capacitors, ω is angular velocity, τcj and τLj are the decay time constant of inductor current and capacitor current, φ is initial angel of n-th feeder, the equation is shown in Eq. (5).

φ = ϕ - arctan

1 2π

SSCs are of interest

tdecay

T+tdecay

t/s

Line type

Rg (Ω)

H (km)

Decay time (ms)

Overhead line

5

1 10

1.30 7.86

Cable line

1

1 10 1 10

1.97 2.82 0.49 1.47

5

Fig. 2. TCs and SSCs contained in TZSC. 3

Electrical Power and Energy Systems 114 (2020) 105391

200

Amplitude/A

100

0

-100

Amplitude/A

Local SSC

0

0.01

50

0.02 0.03 (a) Line 1

Local SSC 0.01 0.02 0.03 0.04 t/s (c) Line 3

0

0 -10

Local SSC 0

0 -50

10

0.04 t/s

Amplitude/A

Amplitude/A

W. Xiaowei, et al.

0.01 0.02 0.03 (b) Line 2

0.04 t/s

100 0

-100

Local SSC 0

0.01

0.02 0.03 (d) Line 4

0.04 t/s

Fig. 3. Global SSCs and TZSCs (Red line means global SSCs, blue line means TZSCs).

1 Ω to 5 Ω, H = 10 km, the decay time reduces from 2.82 ms to 1.47 ms. It can be easily extrapolated the decay time will be shorter with increasing Rg. Therefore, FFT can be used to extract SSCs of TZSC in the second cycle (20–40 ms). To further verify the ability of extracting the SSCs using FFT and proposed backstepping method, the simulation TZSCs i0j(t) (j = 1,2,3,4) within 2 cycles are carried out. Here, line 1 is a fault feeder, using FFT to decompose i0j(t) within 0.02–0.04 s, the local SSCs Wj,local(t) can be obtained, it is shown in (12).

⎧ W1, local (t ) = 6.93 cos(100πt − 1.3186) ⎪ W2, local (t ) = 1.98 cos(100πt − 2.1260) ⎨ W3, local (t ) = 10.8 cos(100πt − 2.1302) ⎪ ⎩W4, local (t ) = 19.63 cos(100πt − 2.1312)

In conclusion, the calculation results of simulation TZSCs prove that the SSCs and TCs contained in TZSCs can be extracted accurately by using FFT and backstepping method. to improve the accuracy of fault detection, based on the calculated SSCs and TCs, a novel and coordinated fault detection method will be proposed in the further steps. 5. Coordinated fault detection criteria 5.1. Criterion 1-correlation analysis based on SSCs After decomposing TZSC i0j(t) by FFT, the local SSCs Wp,local(t) and Wj,local (t) of p-th feeder and j-th feeder can be obtained, the phase difference |θpj| between Wp,local(t) and Wj,local (t) can be calculated as follow:

(12)

Global SSCs Wj,global(t) within 0–0.04 s can be obtained through using the backstepping method. The results of Wj,global(t) and i0j(t) are shown in Fig. 3. From Eq. (12) and Fig. 3, two conclusions can be obtained. The details are as follow:

|θpj| = |θp − θj|

(14)

If the correlation coefficient of Wp,local(t) and Wj,local (t) is larger than 0.7, a strong correlation exists between the two signals. Considering cos(π /4) ≈ 0.7 , to ensure the detection accuracy, we set a threshold |θpj| = π/4 . Therefore, it can be known that Wp,local(t) and Wj,local(t) will have a strong correlation when |θpj| ≥ π/4 , otherwise they have a low correlation. Besides, many simulation results and practical test results also reveal that the threshold |θpj| = 45° is acceptable. If there is unique |θpj| meets |θpj| ≥ 45°, we calculate the correlation coefficient matrix ρpj (whose size is n × n ) of all global Wj,global(t), after removing the maximum ρpjmax and minimum values ρpjmin of each row in ρpj. Then, the comprehensive correlation coefficient matrix (CCCM) ρj (whose size is1 × n ) can be defined as:

(1) The calculated local SSCs Wj,local(t) can fit the actual simulation results well during 0.02–0.04 s, the correctness of extracting local SSCs in the second power cycle using FFT can be verified. (2) The global variation trends of SSCs of TZSCs in Eq. (3) can be represented. Considering the periodic characteristics of local SSCs (0–0.02 s), the SSCs (0–0.02 s) can be calculated by using the backstepping method, at last the global SSCs contained in TZSCs (0–0.04 s) can be obtained.

n−2

ρj =

To calculate TCs of TZSCs and verify the good performance of proposed method on removing SSCs, the TCs Zj(t) can be written as Eq. (13).

Zj (t ) = i 0j (t ) − Wj, global (t )

∑ ρpj /(n − 2) p=1

(15)

The minimum ρjmin corresponds to the fault feeder, then, output the detection results.

(13)

The TCs Zj(t) contained in original TZSCs can be obtained using Eq. (13), the results are shown in Fig. 4. Form Eq. (13) and Fig. 4, it can be concluded that:

5.2. Criterion 2-maximum cross-correlation distance The detection results using the criterion 1 may be incorrect because of the complex fault conditions, for instance, big noise interference, therefore, the criterion 2 based on the TCs is introduced. The details are as follow: If there is no unique |θpj| meets |θpj| ≥ 45°, based on the signs of extremums λj of Zj(t), Wj,global(t) can be rearranged to get Sj(t) by utilizing the bubble sort method, as shown in Eqs. (16)–(18).

(1) FFT and the backstepping method can accurately calculate the SSCs of TZSCs, the amplitudes of Zj(t) are approximately equal to 0 after 0.02 s, which is to say almost all the SSCs of TZSCs can be removed by using proposed backstepping method. (2) The transient characteristics of TZSC can be fully displayed. For instance, the initial signs of extremum of TZSCs can be expressed purely without the interference from SSCs.

Sj (t ) = Zj [1], Zj [2], Zj [3], ···,Zj [m], ···Zj [r ] 4

(16)

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Fig. 4. TCs of simulation model.

5.3. Advantages of coordinated criteria

Table 2 Amplitudes and phase difference of SSCs. Type

Phases difference

Amplitudes difference

W11 and W22 W11 and W33

π/3 π/8

5.0 5.0

Actually, many practical factors can affect the phases of SCCs, such as grounding resistance, the errors of transforms, etc, the unique fault detection criterion cannot apply all the fault conditions. To verify the advantages of coordination criteria, we assume 3 signals W11, W22 and W33. Here, W11 is the SSC of fault feeder, W22 and W33 are the SSCs of healthy lines, whose amplitudes are different. As shown in Table 2. It should be note that although both the SSCs W22 and W33 belong to the healthy line, while the two signals are obtained in different fault conditions, which is the reason that the phase angles of W22 and W33 are not close. When the fault conditions are the same, it can be easily known that the similarity coefficients between any two healthy lines are equal to 1. From Fig. 5 and Table 2, since the similarity coefficient is equal to 0.5 between fault W11 and healthy W33 in Fig. 5(a), it is easy to distinguish the fault feeder and healthy feeder based on the similarity coefficient. However, the similarity coefficient is equal to 0.92 between W11 and W22 in Fig. 5(b), which is to say the similarity coefficient between fault feeder and healthy feeder is close to the similarity coefficients among the healthy feeders, therefore, it is difficult to distinguish fault line and healthy lines only with the criterion 1. These are the main reasons that why the two coordinated criteria based on TCs and SSCs are introduced. To summarize, the advantages of proposed coordinated criteria can be concluded as: firstly, the theories of criterion 1 are simple and less time consuming, it is easily to implement. Secondly, because of the high impedance and the compensation of Petersen coil, the TZSC polarities are disturbed seriously. Through calculating TCs polarities, the interference of SSCs can be removed, therefore, λj can truly reflect the current flow direction. Furthermore, the CCCD can enhance the difference between healthy feeders and fault feeders. The detection

where r is the number of sampling points, 1 ⩽ m ⩽ r . When λj ⩾ 0 , the queuing discipline can be described as:

Zj [1] ⩾

Zj [2] ⩾

Zj [3] ⩾ ....... ⩾Zj [r ]

(17)

When λj < 0 , the queuing discipline is the opposite, as shown in [25].

Zj [1] ⩽ Zj [2] ⩽

Zj [3] ⩽ ....... ⩽Zj [r ]

(18)

Calculate the cross-correlation distance (CCD) Dij between Si(t) of ith feeder and Sj(t) of j-th feeder, 1 ⩽ i ⩽ n , 1 ⩽ j ⩽ n . r

Dij =

∑

(

(Si (m) − Sj (m))2)

m=1

(19)

It can be seen that Dij is a matrix withn × n , all the diagonal elements are equal to 0. At last, remove the maximum Dijmax and minimum Dijmin, the comprehensive CCD (CCCD) CDj can be calculated as: n

CDj =

∑ Dij /(n − 2) i=1

(20)

The maximum CDmax corresponds to the fault feeder.

Fig. 5. Phase differences. 5

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Start Processing the analog signals of voltage and current

Sampling module

Data acquisition (2 cycles)

Analog to digital conversion

Start-up module

U0(t)>0.15Un?

Does TV disconnect?

Y

TV alarm

N Is Petersen coil resonant?

Adjust the Petersen coil away from the resonance point

Y

N

Set the related parameters

Save TZSC i0j(t) in CPU

Fault detection module

Use FFT and backstepping method to extract SSCs

Y

N

Crterion 1

Crterion 2

Output detection results

Output module Show, store, print

End Fig. 6. Fault detection implementation scheme in the practical protection delays.

protection delays, the detail implementation scheme is described in Fig. 6. Where U0(t) is the zero-sequence voltage, U(n) is the rated voltage, TV represents the voltage transformer. As described in Fig. 6, the implementation detection scheme in the

accuracy can be improved. 5.4. Implementation scheme in the practical protection delays In order to clearly show the incorporation with the practical 6

Electrical Power and Energy Systems 114 (2020) 105391

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Source 110kV

Transformer Bus 110kV/10.5kV

Table 3 Cross-correlation coefficients of branch lines.

10kV/0.4kV

l1 =13.5km i1

10kV/0.4kV

Arc suppression coil

l2 =24km i2 Lp

l31 =5km i3

Rp

l32 =12km

l4=10km

10kV/0.4kV

l1

l2

l3

l4

l1 l2 l3 l4

1 0.49 0.49 0.49

0.49 1 1 1

0.49 1 1 1

0.49 1 1 1

Two main conclusions can be obtained in Fig. 8, the first one is the dynamic attenuation time are short (less than 0.01 s); the second one is that the TZSCs within 0.04–0.06 s is presented as the sinusoidal function. So FFT can be used to extract the local SSCs Wj,local(t) (0.04 s < t < 0.06 s) contained in TZSCs. Based on FFT, the SSCs Wj,local(t) (0.04 s < t < 0.06 s) can be obtained as in (21).

10kV/0.4kV

i4 Overhead line Cable line Zero sequence current transformer

Feeder

10kV/0.4kV

Fig. 7. Simulation model.

⎧W1, local (t ) = 4.89 cos(100πt + 0.5139) ⎪ W2, local (t ) = 1.94 cos(100πt − 0.546) ⎨ W3, local (t ) = 10.6 cos(100πt − 0.548) ⎪ ⎩ W4, local (t ) = 19.31 cos(100πt − 0.55)

practical protection delays is consisted of four modules, these are the sampling module, start-up module, fault detection model and output module. The main responsibility of sampling module is to sample the original TZSCs, the second module is responsible to judge whether the SPG fault occurs or not, and then the proposed fault detection method will be implemented in the fault detection module, and lastly output the detection results, the whole detection process is over.

(21)

It can be known from Eq. (21) that the phase angles for healthy lines are near, while the phase angles between fault line and healthy lines have large difference, which is to say the similarity coefficients among the healthy feeders are almost the same (equal to 1), the similarity coefficients between fault line and healthy lines are obviously smaller than 1. Besides, the maximum θpj in Eq. (21) is equal to 60.73°, which is larger than 45°. Based on the proposed criterion 1, the cross-correlation coefficients between any two feeders are shown in Table 3. As the theoretical analysis beforehand, the similarity coefficients between fault line 1 and other healthy lines are equal to 0.49, while the similarity coefficients between any two healthy lines are equal to 1, therefore it is easily to detect the fault feeder using the calculated similarity coefficients. Finally, according to Table 3 and the Eq. (15), CCCM ρj (whose size is 1 × 4) can be calculated. The results are: ρj = [0.49 1 1 1]. Because of ρ1 = ρmin = 0.49, l1 is judged as the fault feeder.

6. Simulation verification 6.1. ATP-EMTP simulation The simulation model with 4 feeders are listed in Fig. 7, the related parameters including overhead lines, cable lines, transform can be found in [23]. The Over compensation degree is 10%, LN = 1.2819H, Rp = 40.2517 Ω. The sampling frequency fs = 105 Hz, the fault occurs at 0.02 s, the simulation time is set to 0.04 s. 6.2. Fault line detection based on SSCs When overhead line l1 occurs the SPG fault, the fault initial phase β = 90°, fault distance H = 10 km, Rg = 100 Ω. The TZSCs i0j(t) with 0.02–0.06 s are shown in Fig. 8.

Fig. 8. TZSCS with the local SSCs ij,local(t). 7

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0 -20

100

Amplitude

Amplitude

20

50 0 -50

20 0 -20 -40

0.02 0.03 0.04 0.05 0.06 t/s (a) S 1 (t)

Amplitude

Amplitude

Fig. 9. TCs in TZSC.

50

0.02 0.03 0.04 0.05 0.06 t/s (b) S 2 (t)

0 -50 -100

0.02 0.03 0.04 0.05 0.06 t/s (c) S 3 (t)

0.02 0.03 0.04 0.05 0.06 t/s (d) S 4 (t)

Fig. 10. Components after rearranging. Table 4 Selection results with different fault conditions. Fault types

Fault line

H/km

β/°

Rg/Ω

max(|θp − θj )| < π /4 ?

Comprehensive criterion matrix

Results

Right ?

Different fault resistances

l1

9

90

1 50 200 500

No No No No

[0.26 [0.35 [0.65 [0.63

l1 l1 l1 l1

Yes Yes Yes Yes

Different fault phase angles

l3

9

0

9

60

9

90

5 500 5 500 5 500

Yes Yes Yes Yes Yes Yes

[907.58 897.52 2216.65 1714.0] [164.21 160.68 268.98 250.35] [924.6 923.83 2125.91 1757.32] [187.26 179.22 337.16 320.60] [729.6 725.42 1518.77 1209.35] [166.31 154.86 211.11 197.09]

l3 l3 l3 l3 l3 l3

Yes Yes Yes Yes Yes Yes

2

0

9

0

17

0

1 500 1 500 1 500

Yes Yes Yes Yes Yes Yes

[1907.21 1908.4 3918.5 3069.4] [143.97 133.83 273.68 232.72] [1270.4 1269.7 2649.7 2220.3] [164.21 160.68 268.98 250.35] [941.8 941.2 1977.2 1661] [174.78 156.78 265.23 245.13]

l3 l3 l3 l3 l3 l3

Yes Yes Yes Yes Yes Yes

6

30

5 100 500

Yes Yes Yes

[1048.78 1049 1771.55 2269.3] [302.23 300.51 512.56 653.19] [104.55 95.32 97.56 148.44]

l4 l4 l4

Yes Yes Yes

Different fault distance

Inject noise (SNR = 10 dB)

l3

l4

8

1 1 1 1

1 1 1 1

1] 1] 1] 1]

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3 2 Amplitude/kA

6.3. Fault line detection based on TCs

1 0 -1 1.021 1.023

1

When the line 3 occurs SPG fault, the conditions are β = 0°, H = 5 km, Rg = 100 Ω, based on FFT, the local SSCs Wj,local(t) can be calculated, the results are shown in (22).

0 -1

Current zero time

⎧ W1 (t ) = 1.09 cos(100πt − 2.0912) ⎪ W2 (t ) = 1.95 cos(100πt − 2.0916) ⎨ W3 (t ) = 13.46 cos(100πt − 1.8114) ⎪W (t ) = 19.36 cos(100πt − 2.0945) ⎩ 4

Current zero time

Current zero time

-2

-3

1

1.01

1.02

1.03

1.04

1.05

(22)

It can be seen that the phases of Wj,local(t) are −119.82°, −119.84°, −103.79° and −120°, respectively, the difference of phase angles between any two feeders are small, when a small disturbance is added, the detection method based on the similarity coefficients may not select the accurate fault line. Since the maximum θpj between Wp,local(t) and Wj,local(t) is less than 45°, criterion 2 is introduced to detect fault feeder. Firstly, the SSCs Wj,local(t) signals within 0 ≤ t ≤ 0.04 can be calculated using FFT and backstepping method, then the TCs contained in Zj(t) can be calculated by removing SSCs, as shown in Fig. 9. It can be seen from Fig. 9 the amplitudes of TCs attenuate to 0 in a very short time, the SSCs have been removed thoroughly, the polarities of TCs can represent the current flow directions accurately. Besides, the calculated results shown in Fig. 8 also verify the correctness and effectiveness of extracting TCs with FFT and backstepping method. According to the proposed arrangement principles of bubble sort method and the polarities of extremum values, TCs Zj(t) can be rearranged as Sj(t). the results are shown in Fig. 10. From Fig. 10, since the initial polarities between fault line and healthy lines are opposite, the difference between fault line and healthy lines can be enhanced after rearranging TCs Zj(t). Finally, based on the criterion 2 and Eq. (19), the cross-correlation distance matrix Dij can be easily calculated, then the comprehensive cross-correlation distance matrix CDj can be obtained based on Eq. (20), the results are CDj = [260.28 232.13 778.88 416.82], due to CDj = CDmax = 778.88, line 3 is detected as the fault line.

1.06 t/s

Fig. 11. Arc current.

Fig. 12. Arc voltage.

7. Applicability analysis To verify the applicability of proposed comprehensive fault detection method, different fault conditions are set to test the proposed method, such as: different fault lines, fault phase angles β, grounding resistance Rg and fault distance H, the noise signals are also injected, the detection results can be calculated using proposed detection method, limited to the space, parts of results are listed in Table 4. From the detection results in Table 4, we can know that when the fault conditions are different, the proposed method can still detect fault line accurately, especially for the high ground resistance situations, the robustness of proposed method is enhanced. What’s more, when different noises are added in TZSCs, the proposed method can detect fault feeder accurately, which reveals that the proposed method owns good anti-noise capability. In order to further test the applicability of proposed method, arc fault test and unbalanced load test are carried out here, the specifics are described as follows:

Fig. 13. Arc resistance.

7.1. Arc fault test High impedance faults often occur in distribution networks, and it is difficult to detect the high impedance faults using the common relay protection devices. Because high impedance fault can easily lead to the arc flash, which is easy to produce fire hazard and personal injury, therefore it is significant to detect arc fault accurately. Mayr arc model is one of the most common models, which is based on arc column energy balance theory [25], the ratios of arc real power

Fig. 14. TZSCs under arc fault occasions.

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Table 5 Calculation results with proposed method. Fault types

Fault line

H/Km

β/°

Arc length/cm

Criterion method

Criterion matrix

results

Right ?

Different fault phases

Line 1

8 8

0 60

400 400

1 1

[−1 1 1 1] [−0.99 0.98 0.96 0.98]

l1 l1

Yes Yes

Different fault distance

Line 3

4 7

0 0

300 300

2 1

[0.97 0.87 1.82 0.88] [0.98 0.99 −0.99 0.99]

l3 l3

Yes Yes

Different arc length

Line 4

12 12

60 60

300 400

2 1

[0.96 1.24 0.75 4.02] [0.8 0.78 0.91 −0.92]

l4 l4

Yes Yes

Fig. 15. Modified IEEE-13 node test system.

shown in Fig. 12 and Fig. 13, respectively. From the above Figures, two conclusions can be concluded: (1) The arc voltage changes rapidly during the current zero time period, shown in Fig. 12, the arc extinction voltage and re-striking voltage are obvious. (2) During the current zero time period, the arc resistance is very high, as shown in Fig. 13, the large resistance can quench the arc flesh. When SPG fault occurs with arc features, to verify the applicability of proposed detection method, the above arc model is introduced into the distribution networks. Line 2 occurs the SPG fault, the fault distance H = 15 km, initial phase angle is equal to 0°, the arc fault currents are shown in Fig. 14. It can be known that when arc fault occurs in Fig. 14, the amplitudes of fault currents are small, especially for line 1, 3 and 4, whose values are around or smaller than 10 A. Besides, all the transient zero sequence currents have the zero-current time when the arc currents cross 0. Similarly, when fault distance H, initial phase angles β and arc length lp change, the simulation results under different fault conditions are used to test the correctness of proposed detection method, the calculation results are shown in Table 5. From the detection results in Table 5, It can be known that the proposed method is not influenced by varied fault initial angles, fault distance and arc length, the detection results are accurate, besides, the proposed two criteria can also coordinate very well.

Table 6 Detection results for modified IEEE-13 node system. Fault feeder

Rg/Ω

Criteria matrix

Results

l2

10 100 1000

[3.85 5520.0 1.85 2.36 1.85] [2.81 218.05 1.70 2.04 1.23] [2.11 21.80 1.44 2.38 1.08]

l2 l2 l2

l3

10 100 1000

[1030.0 1020.0 2620.0 1830.0 1720.0] [151.37 151.52 343.72 277.66 229.69] [17.53 17.62 58.0 30.65 24.71]

l3 l3 l3

to arc dissipation power can be reflected in Eq. (23).

1 dg (t ) 1 ⎛ E (t ) iarc (t ) = − 1⎞ g (t ) dt τm ⎝ Pm ⎠ ⎜

⎟

(23)

Here, g(t) is the arc conductance, E(t) is the arc voltage per unit length, iarc(t) is the arc current, Pm is the column loss power per unit length, τm = αip/lp, τm is the time constant, ip is the peak arc current, and lp is the arc length. We assume the fault occurs from 1 s to 1.06 s, the arc length lp = 400 cm, τm = 2.85 × 10−5, the peak arc current ip = 5 kA, the arc voltage of per unit length E(t) = 15v/cm, the arc current is shown in Fig. 11. From Fig. 11, it can be seen that arc current behaviors like a sine function, while when currents cross 0, the phenomenon of zero-current time will appear within a very short time, as described by red dotted line. In addition, the corresponding arc voltage and arc resistance are

7.2. Unbalanced load test The IEEE-13 node system is a typical topology for the distribution 10

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Amplitude/A

0 0 -50 -100 -150

-200 -400

0

0.001 0.002

0.01

0.02 (a)TZSC

-200 -400

-500 -1000

-600

-1500

0 66

0

Amplitude

Amplitude

0

0

50

-100

-50

-200

6

12

19 198

132 (b)[40]

0

200 0

-400

-200 0

0

0

6

66

12

19

132 (d)[42]

0.04

-200

264

0

0

0.003 0.03

-600

Amplitude

Amplitude

0

198

264

6

12

66

132 (c)[41]

19 198

264

50 0 -50 -100 -150

-200 -400

0

0 0

6

66

12

19

132 (e)[43]

198

264

Fig. 16. Frequency bands based on WT.

Amplitude/A

100 0

100 50 0 -50

-100 -200

0

0.005

0 0.001 0.015

0.01

0.003 0.02

0.005 0.03

0.025

0.035

0.04

(a) TZSC 0

5 0

-5

-5 -10

0

0 0.001 0.01

0.003 0.02

(b) IMF 1

0.03

0.005 0.04

Amplitude

Amplitude

10

0

50 0 -50

-50

-100 -150

0

0 0.01

0.001 0.02

(d) IMF 3

0.003 0.03

Amplitude

Amplitude

50

0.005 0.04

0

5 0 -5 -10

-10 -20

20 0 -20 -40 -60 -80

0

0

0.01

20 0 -20

0

0 0.01

0.001

0.003

0.005

0.02

0.03

0.04

0.001 0.02

0.003 0.03

0.005 0.04

(c) IMF 2

(e) IMF 4

Fig. 17. IMFs of TZSC.

the space, the overhead line l2 and cable line l3 are selected as examples, when l2 and l3 occur the SPG fault, respectively, parts of selection results based on the proposed method are listed in Table 6. From Table 6, it can be concluded that the proposed detection method can accurately judge the faulted feeder in an unbalanced load system with the change of grounding resistance. What’s more, the proposed method is also applied for the high grounding resistance fault conditions.

network with short branch lines, it is also an imbalance system [26], the characteristics of IEEE-13 system is very similar to the practical distribution networks, so we use revised IEEE 13 nodes system to verified the practicability of proposed method. The details are shown in Fig. 15, the specific parameters can be found in [21]. As described in Fig. 15, the test system is an unbalanced system, the highest unbalanced degree is equal to 201.1%. This test system is utilized to test the effectiveness of proposed method under unbalanced conditions. In this system, when a SLG fault occurred at 0.1 s, some fault conditions are considered, such as: (1) Fault location: f1, f2, f3, f4 and f5; (2) Grounding resistance: 10 Ω, 100 Ω and 1000 Ω. Limited to 11

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empirical mode decomposition (CA-EMD) in [28], respectively. Wavelet method is adopted to decompose the TZSCs, db4 is selected as the wavelet mother function, and the decomposed layers are set to 4. The computed frequency bands [4 0], [4 1], [4 2] and [4 3] are listed in Fig. 16. Similarity, the results of intrinsic mode functions (IMFs) decomposed by EMD algorithm are shown in Fig. 17. When line 3 occurs the SPG fault, β = 60°, H = 14 km. TZSCs within the first 1/4 power cycle (5 ms) are selected as the research objectives, based on the above three detection methods, the detection accuracy and time consume are calculated and compared. The results are listed in Table 7 and Table 8. It can be concluded in Table 7 that EM-TZSCs and SE-WT in Table 7 have accurate fault detection results for low grounding resistance fault conditions, but when the grounding resistance is large (1000 Ω), the both detection results are incorrect. What’s more, it should be not that the detection method based on CA-EMD owns high detection accuracy, even for high impedance fault conditions. The different time lengths that every method needs when the whole detection process is completed are counted in Table 8. From Table 8, the most time-saving method is EM-TZSCs, whose total time is 0.01 s. although CA-EMD detection method has a high accuracy, CA-EMD is also the most time-consuming method, whose time length is 0.394 s. However, the total time of proposed method based on the criterion 1 and 2 are 0.076 s and 0.091 s, much less than 0.394 s, which is to say the proposed method has good performance both for detection results and calculation time length. To sum up, the EM-TZSCs can complete the detection procedure in a very short time, but whose accuracy rate is low. The correctness of detection results by using SE-WT can’t be ensured. Although CA-EMD has a high accuracy rate, while the calculation time takes longer (larger than 4 times). Therefore, the proposed detection method based on SSCs and TCs has the optimal detection results and time consume.

EM-TZSCs

1 100 1000

[1.1 × 10 4.4 × 10 2.4 × 10 2 × 10 ] [4.6 × 103 1.7 × 104 2.9 × 105 3.3 × 105] [9.3 × 102 1.7 × 103 1.4 × 104 1.6 × 104]

l3 l4 l4

SE-WT

20 2000

[1.04 1.09 0.98 1.03] [1.01 1.08 0.97 0.93]

l3 l4

CA-EMD

1 200 1000

[0.53 0.48 −0.64 0.57] [0.21 0.17 −0.39 0.24] [0.05 0.05 −0.31 0.09]

l3 l3 l3

Table 8 Time consume of different methods. Methods

Sampling duration (s)

Time consume of processing (s)

Total time (s)

EM-TZSCs SE-WT CA-EMD Proposed method

0.005 0.005 0.005 0.04

0.005 0.243 0.389 criterion 1: 0.036 criterion 2: 0.051

0.010 0.248 0.394 0.076 0.091

Note: the calculation time mentioned above are the average values of 10 computations.

8. Comparison with the existing methods To verify the advantages of proposed detection method, three common fault detection methods are selected as the comparative objectives, they are based on the energy method of transient zero sequence currents (EM-TZSCs) in [27], the singular entropy based on wavelet transform (SE-WT) in [9] and the correlation analysis based on

Power supply structure of field test

Luoqing company 80KVA

Qingshui Village 80KVA

Yinhui Branch

Yinxing Branch

Hengshan Street

North

Chicken Factory 50KVA

Hengqi Road

Overhead line Cable line Emergency line 10kV/0.4kV transformer

110kV/10kV transformer

Tiewang Village 80KVA

No.522

Wangjiacun Road

No.521

f2

No.512

No.514

Shengou Village 100KVA

Bus switch

f1

No.527

Xing Village

Machinery Factory 100KVA

Bus No.2

50KVA

f3

f4

Wangjia Village 100KVA

No.511

Road

Qingbao Village 50KVA

No.513

Bus

Qinglin Village 75KVA

No.515

70KVA

No.517

No.518

Bus No.1

No.516

No.519

Coal company Water Stataion 100KVA 50KVA

Shitou Village 70KVA

Bus No.2

6

No.526

Results 6

4

No.524

4

No.525

Criteria matrix

No.523

Rg/Ω

No.528

Method

No.529

Table 7 comparison of detection results.

Lijia Village 80KVA Lijia Village Road

Biantou Village 100KV A

Grounding transformer Fig. 18. Power supply structure of field test. 12

Baitong Road

Hospital 100KVA

Electrical Power and Energy Systems 114 (2020) 105391

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Fig. 19. Zero sequence current waveforms of the field test.

Fig. 20. Local SSCs of TZSCs. Table 9 Detection results of practical SPG fault test. Fault line

Rg/Ω

Method

Comprehensive matrix

Results

No.513 No.515 No.524

500

Criterion 1 Criterion 2 Criterion 1

[0.85 0.60 −0.87 0.67 0.64 0.87 0.88 0.84 0.81] [21.36 41.94 26.34 21.38 208.17 39.23 49.64 22.37 21.48] [0.82 0.85 0.85 −0.67 0.85 0.81 0.85 0.19 0.89]

No.513 No.515 No.524

9. Field test of SPG fault

10.5, rated capacity 800KVA, rated current 144.34 A, neutral current 115 A, transition resistance 7 Ω, no load regulator. Respectively, line No. 513, No. 515 and No.524 occur SPG fault, and it was shown in f1, f2 f3 and f4 in the Fig. 18, among them, the grounding resistance are 500 Ω, respectively. We use 4 times recorded data to verify the proposed method: feeder No. 513, No. 515 of No. 1 bus, feeder No. 524 of No. 2 bus, respectively. Due to space limitations, we only give zero-sequence current waveform, when SPG fault occurred at the feeder No.513, respectively, which is shown in Fig. 19. The description of recorded data: sampling 100 points per period, a total recorded data of 6 cycles. Here, TZSCs within the second power cycle in Fig. 19 are decomposed by FFT, the SSCs can be obtained in Fig. 20. It can be known from Fig. 20 that FFT can also be used to decompose the practical fault TZSCs. At the same time, other practical test

We carried out field test at the New City substation of Yinchuan in China with the sampling frequency 5 kHz, the specific power supply structure is shown in Fig. 18, of which, two main transformers are 110 kV/10 kV, the connection group for the Y/△, every neutral point through the grounding transformer by arc suppression coil grounding the land, a total of two bus lines: Bus No. 1, Bus No. 2, each bus line includes 9 feeders, and most of the feeders are mixed feeders, including cable and overhead line, the feeders of bus No.1 are named as from No.511 to No.519; the feeders of Bus No.2 are named as from No.521 to No.529. Arc suppression coil parameters: XHDC-700/10.5/ 3 , rated capacity 700kvar, on-load voltage regulation, variable ratio 120 A/5 A (current range 120 A). Grounding transformer parameters: DKSC-800/

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[5] Morais AP, Cardoso Júnior G. A morphological filtering algorithm for fault detection in transmission lines during power swings. Electr Power Syst Res 2015;122:10–8. [6] Pasdar AM, Sozer Y, Husain I. Detecting and locating faulty nodes in smart grids based on high frequency signal injection. IEEE Trans Smart Grid 2013;4(2):1067–75. [7] Costa FB. Fault-induced transient detection based on real-time analysis of the wavelet coefficient energy. IEEE Trans Power Delivery 2014;29(1):140–53. [8] Li R, et al. Fault diagnosis algorithm for distribution line based on wavelet singular entropy and wavelet energy entropy. In: 2017 IEEE 2nd advanced information technology, electronic and automation control conference (IAEAC), Chongqing; 2017. p. 2395–98. [9] He Z, Fu L. Fault detection and classification in EHV transmission line based on wavelet singular entropy. IEEE Trans Power Delivery 2010;25(4):2156–63. [10] Dong XZ, Shi SX. Identifying single-phase-to-ground fault feeder in neutral noneffectively grounded distribution system using wavelet transform. IEEE Trans Power Delivery 2008;23(4):1829–37. [11] Borghetti A, Bosetti M. Integrated use of time-frequency wavelet decompositions for fault location in distribution networks: theory and experimental validation. IEEE Trans Power Delivery 2010;25(4):3139–46. [12] Guo MF, Zeng XD. Deep-learning-based earth fault detection using continuous wavelet transform and convolutional neural network in resonant grounding distribution systems. IEEE Sens J 2018;18(3):1291–300. [13] Stockwell RG, Mansinha L. Localization of the complex spectrum: S transform. IEEE Trans Signal Process 1996;44(4):998–1001. [14] Shu HC, Sun SY. A new method to detect single-phase fault feeder in distribution network by using S-transform. In: 2010 IEEE 11th international conference on probabilistic methods applied to power systems; 2010. p. 277–82. [15] Hasanvand H, Parastar A. A comparison between S-transform and CWT for fault location in combined overhead line and cable distribution networks. In: 21st electrical power distribution conference, Karaj-Alborz-Iran; 2016. p. 70–4. [16] Cui T, Dong XZ. Hilbert-transform-based transient earth fault detection in non-effectively grounded distribution systems. IEEE Trans Power Delivery 2011;26(1):143–51. [17] Guo ZW, Yao JG. Hilbert-Huang transform-based transient busbar protection algorithm. IET Gener Transm Distrib 2015;9(14):2032–9. [18] Wei X, Wen B, Yang D, et al. Fault line detection method based on the improved SVD de-noising and ideal clustering curve for distribution networks. IET Sci Meas Technol 2018;12(2):262–70. [19] Chen K, Hu J, He J. Detection and classification of transmission line faults based on unsupervised feature learning and convolutional sparse autoencoder. IEEE Trans Smart Grid 2018;9(3):1748–58. [20] Wang X, Gao J, Chen M, Wei X, Wei Y, Zeng Z. Faulty line detection method based on optimized bistable system for distribution network. IEEE Trans Ind Inf 2018;14(4):1370–81. [21] Wang X, Song G, Chang Z, et al. Faulty feeder detection based on mixed atom dictionary and energy spectrum energy for distribution network. IET Gener Transm Distrib 2018;12(3):596–606. [22] Song G, Chu X, Cai X, et al. A fault-location method for VSC-HVDC transmission lines based on natural frequency of current. Int J Electr Power Energy Syst 2014;63:347–52. [23] Deng F, Li X, Zeng X. Single-ended travelling wave protection algorithm based on full waveform in the time and frequency domains. IET Gener Transm Distrib 2018;12(15):3680–91. [24] Xue Y, Chen X, Song H, Xu B. Resonance analysis and faulty feeder identification of high-impedance faults in a resonant grounding system. IEEE Trans Power Delivery 2017;32(3):1545–55. [25] Wu Z, Wu G, Dapino M, Pan L, Ni K. Model for variable-length electrical arc plasmas under AC conditions. IEEE Trans Plasma Sci 2015;43(8):2730–7. [26] Xiaowei W, et al. High impedance fault detection method based on variational mode decomposition and teager-kaiser energy operators for distribution network. IEEE Trans Smart Grid. doi: 10.1109/TSG.2019.2895634. [27] Yi F, Yong X, Hua S, Ting G, Fan Y, Bing X. Transient energy analysis and faulty feeder identification method of high impedance fault in the resonant grounding system. Proc CSEE 2018;38(19):5636–45. [28] Zhong K, Dan L, Xiao L. Fault line selection with non-power frequency transient components of distribution network. Electric Power Automat Equip 2011;31(4):1–6.

cases have been carried out to verify the effectiveness of proposed fault detection method, the final detection results are listed in Table 9. From Table 9, it can be seen that the proposed fault detection method can accurately detect the practical fault feeder, the practicality of proposed method can be confirmed. 10. Conclusions Due to the complex practical fault conditions, the single criterion owns low detection accuracy for SPG fault detection issue, through dividing TZSCs into SSCs and TCs, a comprehensive and coordinated fault feeder detection method is proposed, the applicability of proposed method under different fault conditions has been verified, the main conclusions are as follow: (1) A novel cut-in point for fault feeder detection issue is introduced. The global SSCs can be calculated based on FFT and backstepping method, the theoretical analysis, simulation results and practical test prove the correctness and effectiveness of proposed criterion 1. (2) Based on the extremum values of TCs, the bubble sort method is used in criterion 2 to compute CCCD, through removing the maximum and minimum values in the correlation coefficient matrix, the difference between fault feeder and healthy feeders can be enhanced. (3) The arc fault model and improved IEEE 13 node system have been developed, the field test has also been carried out, the detection results have verified the correctness and effectiveness of proposed method. Besides, compared with the common existing method, the proposed method not only owns the high detection accuracy but also is the most time-saving. The parallel computing can be also implemented to improve the computational efficiency. Declaration of Competing Interest The authors declare that there is no conflict of interests regarding the publication of this article. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijepes.2019.105391. References [1] Barik MA, Gargoom A, Mahmud MA. A decentralized fault detection technique for detecting single phase to ground faults in power distribution systems with resonant grounding. IEEE Trans Power Delivery 2018;33(5):2462–73. [2] Wang X, Gao J, Wei X, Zeng Z, Wei Y, Kheshti M. Single line to ground fault detection in a non-effectively grounded distribution network. IEEE Trans Power Delivery 2018;33(6):3173–86. [3] Liu P, Huang C. Detecting single-phase-to-ground fault event and identifying faulty feeder in neutral ineffectively grounded distribution system. IEEE Trans Power Delivery 2018;33(5):2265–73. [4] Zhixia Z, Xiao L. Fault line detection in neutral point ineffectively grounding power system based on phase-locked loop. IET Gener Transm Distrib 2014;8(2):273–80.

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