A Review of Techniques to Detect Downed Conductors in Overhead Distribution Systems

1. Introduction

The main reasons for power supply disturbances in distribution overhead lines are series, shunt, and series shunt faults. In both utility and public safety, fault detection is a crucial business. World or ground fault protection is an essential defence in electrical systems; it is necessary to preserve electrical networks and equipment. A cleaved conductor error (BCF) occurs when an overhead line is interrupted and may or may not contact the footing, depending on the upshot'south severity. The broken conductor on the source side with high impedance fault, broken conductor on the load side with any impedance mistake, or an open circuit with a conductor not touching the basis might all be responsible for the problem of undetected fault as illustrated and classified in Figure 1. The well-nigh mutual and dangerous type of BCF occurs when an heady mainline drops and contacts the earth. This condition is uncommonly harmful since in that location is a danger of electric stupor to people and a fire take a chance. As a result, detecting BCF is essential from human health and functioning efficiency standpoints. Protective relays and circuit breakers are major components of the big interconnected power system. Substations in power distribution systems involve numerous pre-programmed protection relays with multiple stages to protect the system from many types of faults. However, it is well known that current protection technology misses (xxx–l)% of BCF failures. This may lead to disquisitional and unsafe situations that threaten the lives of citizens and animals and reduce the lifetime of the utility equipment. A broken conductor represents an open up stage state on the electric excursion in a medium voltage distribution radial system. As shown in Figure 2, BCF might exist one of the post-obit causes: (1) Open line where usher does not touch the ground from two terminals. (2) Source side of the broken conductor with high ground resistance. (three) Load side broken conductor with whatever ground resistance. The load side broken conductor (LSBC) fault is a specific type of globe fault (single line to footing), which is challenging to detect since the conductor might remain suspended from the overhead line's source-side while touching the ground from the load side. The sparks of LSBC fault create a small mistake current that does not accomplish the pickup value of the earth mistake relay, so the protection relay volition not exist triggered, and the medium voltage (MV) feeder remains in the Close position [1]. Therefore, the LSBC faults are commonly undetectable by traditional over current and globe mistake protection relays equally well every bit no response of any activated protection relay. Explaining the substation feeder setting and the pickup values of protection relays is needed to analyze the practical problem in the protection of MV distribution feeders. The ground fault is prepare to 10% of the overcurrent setting; this is a minimum ratio to sense the low earth fault electric current. When the earth error setting value decreases, interference will occur, such as the leakage current results from the load unbalance.

Many studies have been done to enhance and observe the faults [2], where the detection technique example of open circuits and downed conductors shows: (1) A loss of phase-detection at pole-mounted switchgear. (2) Detection of blown high voltage (HV) fuses. (3) Using nether-voltage detection at transformer poles. Reference [3] offers disproportionate electric current methodology considering a relationship between the negative sequence and nil with the positive sequence during a BCF upshot.

According to [4], it is possible to locate a BCF using just the magnitudes of current and voltage phasors of a single final utilizing the group data treatment technique. The inputs and outputs of the interpolation role are the faulty phase's electric current and voltage, respectively, and the precise position of the fault. A method for early identification of faults in power lines by analyzing the symmetrical voltage components in real-time has been developed [v]. A new arroyo has been adult in [6] to detect surreptitious cable faults in radial distribution networks. The algorithm uses a radial line'southward end-measured phase-to-stage voltages as input signals. In [seven], the written report proposes an implementation of asymmetrical component logic that enhances traditional protection methods using a single-phase transformer. The authors in [8] present an approach based on the zero-sequence electric current's decreasing periodic components to locate a high impedance ground faulty line section. When a unmarried-phase high impedance fault (HIF) occurs in a resonant grounding system, it examines the parallel resonance procedure. A unique integrated approach has been proposed to detect and locate open up usher faults in HV transmission systems [9]. Decomposition of local current signals is performed utilizing a discrete wavelet transform with a unmarried-level corruption in the proposed scheme unit.

Appropriately, studying and analyzing LSBC fault is very important and requires identifying some concepts. In this paper, the proposed method solves the detection of LSBC fault depending on the human relationship between the negative and positive current sequence during LSBC error. The paper presents a new applicable study based on asymmetric electric current methodology as I₂/I_i during an LSBC fault. The other existing diagnosis methods are currently inapplicable to the existing traditional protection arrangement, as discussed in Section four. The contributions of this research paper are:

• Analyze the distribution system under faults.

• A new applicable method is proposed to detect LSBC faults.

• Protect the feeder 100% from LSBC fault.

The remainder of this newspaper is organized every bit follows: Department 2 introduces the methodology, which describes the proposed methods and introduces the mathematical analysis. Section iii describes the example study of existent distribution network. Department 4 presents the results and discusses them. Section 5 concludes the paper.

2. Methodology

2.i. Fault Incidents

The low voltage supply network experiences aberrant voltage in 2 or 3 phases. It occurs when a cleaved conductor or disconnected phase causes an open-circuit fault, such as blown HV fuses in an 11 kV radially fed overhead line. This has a significant impact on the supply of electricity to customers. Such problems are oft reported past customers who suffer abnormal energy supply or loss of power because of substation-based current detection techniques' inability to identify them. Short-circuit faults can be detected using phase overcurrent and earth mistake relays. Phase overcurrent and earth faults can be detected with (inverse definite minimum fourth dimension) or (definite time lag) protection.

It is impossible to start an overcurrent or earth fault if an open circuit causes it. Fault impedance tin be exceedingly loftier when a downed usher comes into touch with highly resistant substances, such as asphalt, sand, or boulders. Back-feed world fault current may not be detectable by overcurrent or earth mistake in the distribution power transformer in the case of a downed usher on the load side of a fault point, as shown in Figure 3.

ii.2. Mathematical Assay of LSBC Fault

It is possible to correspond the unbalanced power organization using the phase diagram; the phase representation is by applying analytical processes. The purpose is to dismantle this unbalanced system into balanced systems, each with phases equal to the number of phases of the original unbalanced system. These counterbalanced systems are then called symmetric compounds. Although this belittling method includes multi-stage systems, the chat will be limited to three-phase systems. The technique is beingness applied to obtain identical compounds by analyzing the iii unbalanced phases of the three-phase power organisation into three systems, each of which is 3-stage and counterbalanced. These groups of counterbalanced compounds are: (1) Compounds of the positive relay; these consist of three phases of equal size, shifted from each other past an bending of 120, and have the same sequence of phases equally the original system. (2) Compounds of the negative relay consist of three phases of equal magnitude, shifted from each other by an angle of 120, merely the phase sequence here is opposite to that of the original system. (three) Compounds of the zero sequence, which consist of three phases, equal in phases, and identical in management (that is, the value of the deportation angle between the 3 phases is equal to naught), so it was called the zero-sequence components [x]. Effigy 4 shows the representation of symmetrical components.

As depicted in Effigy 5, the LSBC concept is illustrated by a line that connects a supply-side to the load. The symmetric components transformation (SCT) can analyze LSBC faults, which is extensively applicative. Pseudo phasor algebra is practical to a sinusoidal situation using the SCT. A series impedance ZS represents the broken conductor to create a generic theory [11]. As shown in Figure half dozen, the shunt impedance Zg besides accounts for the conductor-to-ground contact.

When the total conductor interruption occurs, the series impedance tends to infinity (i.due east., Z_S → ∞) while the conductor to ground solid contact leads follow Zg → 0. The LSBC fault written report is performed by applying the SCT to the G and H sections, as shown in Figure iv, where:

$\overline{I}$

_a ,

$\overline{I}$

_b ,

$\overline{I}$

_c ,

$\overline{\mathrm{Five}}$

_a ,

$\overline{V}$

_b ,

$\overline{V}$

_c are phase currents and phase voltages earlier the error department.

$\stackrel{\overline{¯}}{I}$

_a ,

$\stackrel{\overline{¯}}{I}$

_b ,

$\stackrel{\overline{¯}}{I}$

_c ,

$\stackrel{\overline{¯}}{V}$

_a ,

$\stackrel{\overline{¯}}{5}$

_b ,

$\stackrel{\overline{¯}}{5}$

_c are phase currents and phase voltages afterward the fault section.

The line currents with symmetrical components in section G are given in Equation (ane).

$$\left[\begin{array}{c}{\overline{I}}_{c0}\\ {\overline{I}}_{c\mathrm{ane}}\\ {\overline{I}}_{c\mathrm{ii}}\end{array}\right]=\frac{\mathrm{i}}{3}\left[\begin{array}{ccc}1& \mathrm{ane}& 1\\ 1& a& a^2\\ \mathrm{i}& a^{\mathrm{ii}}& a\end{array}\right]\left[\begin{array}{c}{\overline{I}}_a\\ {\overline{I}}_b\\ {\overline{I}}_c\end{array}\right]$$

(1)

The subscripts 0, 1, and ii bespeak the zero, positive, and negative sequence components, respectively, where a = ane ∠ 120°, a² = 1 ∠ 240°. Equation (1) tin can be rewritten equally Equation (2).

$$\left[\begin{array}{c}{\overline{I}}_{{}_{c012}}\end{array}\right]={\left[F\right]}^{-\mathrm{ane}}\left[{\overline{I}}_{abc}\right]$$

(2)

In addition, department H, is rewritten equally Equation (three).

$$\left[\begin{array}{c}{\stackrel{\overline{¯}}{I}}_{\mathit{c}\mathbf{0}}\\ {\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{c}\mathbf{one}}\\ {\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{c}\mathbf{2}}\end{array}\right]=\frac{\mathbf{1}}{\mathbf{3}}\left[\begin{array}{ccc}\mathbf{ane}& \mathbf{1}& \mathbf{1}\\ \mathbf{1}& \mathit{a}& {\mathit{a}}^{\mathbf{2}}\\ \mathbf{one}& {\mathit{a}}^{\mathbf{2}}& \mathit{a}\end{array}\right]\left[\begin{array}{c}{\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{a}}\\ {\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{b}}\\ {\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{c}}\end{array}\right]$$

(three)

Applying Kirchhoff's current police force, the following expression in Equation (4) for the fault department tin can be written.

$$\left[\begin{array}{c}{\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{a}}\\ {\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{b}}\\ {\stackrel{\overline{¯}}{\mathit{I}}}_{\mathit{c}}\end{array}\right]=\left[\begin{array}{c}{\overline{I}}_a\\ {\overline{I}}_b\\ {\overline{I}}_c-I_m\end{array}\right]$$

(4)

Combining (one), (iii), and (four), the final formula is obtained as in Equation (five).

$$\left[\begin{array}{c}{I}_{\mathit{yard}}\\ {\mathit{I}}_{\mathit{g}}\\ {\mathit{I}}_{\mathit{g}}\end{array}\right]=\mathrm{three}\left[\begin{array}{c}{\overline{I}}_{c0}-{\stackrel{\overline{¯}}{I}}_{c0}\\ {\overline{I}}_{c\mathrm{ane}}-{\stackrel{\overline{¯}}{I}}_{c\mathrm{ane}}\\ {\overline{I}}_{c\mathrm{ii}}-{\stackrel{\overline{¯}}{I}}_{c\mathrm{ii}}\end{array}\right]$$

(five)

ii.3. Proposed Methodology

The protection engineer must understand the negative phase sequence (NPS) principle and utilise the necessary settings based on different fault situations when using NPS protection on each given feeder [12]. However, the values of I₂ can be sensitive to real load adjustments due to applied limitations in amalgam counterbalanced networks, where NPS protection is an excellent stage imbalance detector. Positive phase sequence (PPS) has traditionally been related to feeder loads and ofttimes indicates customer service quality. Overload of customer usage (or commonly asymmetrical three-phase fault) suggests that a line has besides much PPS flowing over it and that the current should be terminated to maintain the benefit [xiii].

The day load variations in utility supply may indicate college NPS, although this does non necessarily mean a conductor aperture. All the same, when ane or more of the lines are broken, typical overcurrent/earth error relays may fail to notice the output since the PPS does not necessarily increase. NPS protection is normally gear up at 30% of the overcurrent configuration. Therefore, it is safe to assume that a broken conductor will non exist recognized if it is practical to feeders. When the load current is less than 10A, a broken conductor can be identified with a high degree of certainty. This phenomenon is more than widespread at lower loads. For certain risks related to the failure of protection equipment, but NPS overcurrent protection tin can provide fill-in protection to solidly grounded Delta-Wye transformers [14]. Sequence components are present for a range of atmospheric condition, not only this type of faults as the open up pole, load and line unbalance, breaker pole scatters, and electric current transformer ratio errors and saturation [15].

Thus, the NPS to PPS ratio |I_two/I_ane| should exist compared, rather than each protective factor. This helps reduce the instability in NPS numbers across the range of energy distribution to customers while also detecting an open phase discontinuity. Figure 7 depicts the proposed process's flow chart. Figure 8 show the proposed methodology of this paper.

3. Case Report and Simulation Analysis

In this section, we consider the theoretical give-and-take. The implementation of a existent network as a instance study is presented. The Al-Abasia distribution substation located in the middle Euphrates region in Najaf governorate serves a large area of mixed residential, commercial, and agriculture loads and is taken as the study network. The secondary ability station consists of twelve feeders, whereas the F10 feeder consists of 15 overhead transformers with a rated line to line voltage of xi kV. The faux circuit of the unmarried-line diagram is presented in Figure ix. The screenshot of the MATLAB Simulink is given in Effigy x. The specification and parameters applied to this written report are given in Table 1. The load of 11 distribution transformers is balanced and distributed every bit in Tabular array two.

MATLAB software and its associated Simulink toolboxes are used to test the proposed methodology. The simulation program is performed 15 times for the load side broken conductor faults in the feeder, equally shown in Figure nine. The measurements were taken at the 33/11 kV substation and the end of the feeder for 15 cases of LSBC fault. The faults start from the beginning of the feeder, and the results are given in Table 3. It is noted that the fault current in the LSBC fault phase increases from zero up to a value that becomes approximately equal to the other two phases. It causes the percentage level between the faulted and the other two phases to change between 100% and 13%.

4. Results and Discussion

four.1. Mathematical Results

In the mathematical assay, Equation (five) was used to decide the ground current (I_g ) from the sequence currents (I ₀) measured by the Simulink plan in the substation when the fault occurs in phase C. Using Equation (6), the mathematical results were written in Table iv.

$$I_{\mathrm{chiliad}}=3\left({\overline{I}}_{c0}-{\stackrel{\overline{¯}}{I}}_{c0}\right)$$

(half-dozen)

In Tabular array 4, nosotros noted that there is an equal absolute value of the ground current resulting from the fault in the two cases of taking measurements using the MATLAB program and the results through mathematical assay every bit shown in Equation (7).

$${\left|I_{\mathrm{1000}}\right|}_{mathmatical}={\left|I_g\right|}_{simulatio\mathrm{due\; north}}$$

(7)

The results showed that the values of the phase shift to I_m between the mathematical and MATLAB results are approximately 180° for all fifteen cases of fault sites. The aforementioned results are formed using the other measurements to sequence currents I ₁ and I ₂ past Equations (8) and (9).

$$I_k=\mathrm{three}\left({\overline{I}}_{c1}-{\stackrel{\overline{¯}}{I}}_{c\mathrm{one}}\right)$$

(8)

$$I_g=3\left({\overline{I}}_{c2}-{\stackrel{\overline{¯}}{I}}_{c2}\right)$$

(9)

four.2. Unbalance Phases Current Results

When the location of the error is at the starting feeder, the measured values of the unfaulted lines' currents are 86 A to 76 A. At the same fourth dimension, the faulted line current in stage C is equal to zero. This is due to the presence of the LSBC fault, which is the main problem of this research paper. The protective devices are non sensitive to this type of error due to the decrease in the values of the three-phase fault currents, unlike other types of ability system faults in the Figure 1, in which the importance of the error currents is high. When the position of the LSBC fault is far from the substation, an increase in the current values occurs in the faulty stage C until the threshold value is reached. The threshold value is the significance that determines the change in the percentage value of the unbalance currents to be 10%. The permissible percentage in the distribution networks is less than x%. If it exceeds this value, it is considered a fault detection which the protection devices must protect the lines. In this case, 100% of the 11 kV feeder cannot exist protected through unbalanced protection. Increasing the loads to more than than loads of the case written report in this research newspaper volition inevitably decrease the unbalanced current table's percentage 1 to less than ten%. To calculate the percent ratio of the unbalance three-stage currents, we use Equation (10)

$$I_{unb}=\frac{\left(I_{\mathrm{thousand}ax}-I_{ki\mathrm{northward}}\right)}{I_{max}}\times 100\%$$

(10)

where I_max is the maximum current of iii-phase currents during the LSBC faults. I_min is the minimum current of iii-phase currents during the LSBC faults [16].

4.iii. Neutral Fault Current Results

The results showed in Table 3 that the earth error protection in a substation cannot detect neutral current because information technology was less than the permissible value 30 A in the case report (Al-Abasia substations). The electric current values through which the neutral protection operates vary from (30 to 150) amperes, where the earth fault current (Loftier) is determined by Equation (eleven), and the earth fault electric current (Depression) is determined past Equation (12).

$$I_{H\mathrm{Eastward}F}=I_{\mathrm{grand}ax}\times \mathrm{fifty}\%=300\times 50\%=150$$

(11)

$$I_{LEF}=I_{ma\mathrm{ten}}\times \mathrm{x}\%=300\times 10\%=30$$

(12)

The current value limits in Equations (10) and (eleven) utilize when the electric current transformer is 300/5, the range allowed in Iraqi substations. In Table 3, the electric current levels in neutral varied betwixt (7–29) A in the fifteen cases of LSBC fault, indicating that the protection devices are non responsive to the error. Due to decreasing the loads, the longer the altitude between the mistake and the substation, the less current flows. The currents resulting from the mistake in the neutral are the best possible state since the HIF is not taken, resulting from the usher's contact with more insulating materials similar grass, sand, soil, and others. The trouble will be increased considering the fault electric current is not detected.

iv.4. Negative to Positive Sequence Percentage Current Ratio Results

The ratio |I₂/I_one| was measured at 2 sites, first at the substation and the second at the feeder's end. It was observed that the ratio at the substation varied between (seven–79%). In comparing, information technology is fixed at fifty% at the feeder's finish, as shown in Figure 11. The relay setting of |I₂/I₁| should be less than 20% [17]. In other words, the relay does not operate past less than xx%. The ratio of |I₂/I₁| is (seven–eighteen%) measured at the substation side for the fault site number (11–xv). Then, information technology cannot be relied upon to detect the LSBC fault, which leads us to propose another style to measure |I₂/I_i| at the feeder end. It is noted that the ratio of currents |I₂/I_one| is proven to be 50% at the end of the feeder. This ratio is for all 15 cases of faults, which is the best solution to solve the research trouble. In the absence of a discontinuity, the |I_two/I₁| ratio is nearly constant for any variation in load demand on 3 phases. When a discontinuity emerges on one or more than lines, the |I₂/I_ane| ratio climbs above xx%, which is evident in a healthy line with |I₂/I_one| close to cipher. Impedance calculations are not necessary because the positive and negative sequence impedances are identical for most residential loads, as may be concluded by looking at the ratio between I₂ and I_ane. A comparing between the proposed method with recent literature is given in Table 5.

5. Conclusions

The electric faults in the power system atomic number 82 to a significant risk for public safety such as people, animals, crops, and forests. The LSBC fault is a specific type of fault that happens on the overhead line, which occurs on the load side since the faulted line is still energized via dorsum-feed from the distribution transformer. This type of fault has an entirely unlike upshot on current feeders than the traditional line-to-ground mistake. For the depression neutral current of LSBC mistake, the earth fault protection relay does not accomplish the pickup value, so it cannot detect the mistake. This paper presented the functioning analysis based on feeder electric current's NPS to PPS ratio |I₂/I₁|. The proposed approach is applied to a real distribution feeder in Republic of iraq that was simulated with the MATLAB platform. The results were compared with the mathematical analysis and other related works. It was observed that the proposed |I_ii/I_ane| at the substation side protects 67% of the feeder, while the proposed |I₂/I₁| at the feeder terminate protects 100% of the feeder from LSBC fault. This paper holds several advantages compared to the previous research. Firstly, the error is detected accurately without using distributed measurements. Secondly, the proposed method has high sensitivity on fault detection without depending on noise, power swing, transformer saturation, or harmonics. Thirdly, this method provided good analysis and found an applicable solution for the distribution utilities, which was previously missing in the literature of this field. The method can also be implemented to any other three-phase three-wire distribution feeder to get the same benefits.

For future work, we will consider analyzing other types of networks in the presence of distributed generation and evaluating the speed response of the relay. Additionally, nosotros will study the suitable techniques for transmitting the command from the feeder finish to the substation.

Author Contributions

Amidst those involved in the study'due south conception and execution were the authors A.K.A.-B., M.K.A. and F.Chiliad.F.F., besides as its analysis and newspaper writing. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Acknowledgments

We would similar to express gratitude to the section of electrical engineering, university of technology—Iraq. Special cheers to the state visitor of the north distribution electricity, ministry of electricity, Iraq for their cooperation.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Classification of ability system faults.

Figure one. Classification of power system faults.

Figure ii. The weather condition of normal country and broken usher faults.

Figure 2. The weather condition of normal state and broken conductor faults.

Figure 3. The back-feed from distribution transformers in load side broken usher fault.

Effigy iii. The dorsum-feed from distribution transformers in load side cleaved conductor mistake.

Figure 4. Representation of symmetrical components.

Figure 4. Representation of symmetrical components.

Figure 5. Clarification of a fault department.

Effigy 5. Description of a mistake department.

Figure half-dozen. Description of a fault section (including the shunt impedance Zg).

Effigy 6. Description of a fault section (including the shunt impedance Zg).

Effigy 7. The period chart of the proposed method.

Effigy 7. The flow chart of the proposed method.

Figure 8. The proposed methodology.

Figure viii. The proposed methodology.

Figure ix. Implement the LSBC fault on the distribution feeder.

Effigy 9. Implement the LSBC fault on the distribution feeder.

Figure ten. Simulation of the existent feeder.

Effigy 10. Simulation of the real feeder.

Figure eleven. Negative to positive sequence percentage current ratio.

Figure 11. Negative to positive sequence percentage electric current ratio.

Table 1. The parameters of the study network.

Table one. The parameters of the written report network.

Parameters	Value
Rated ability of ability transformers	(2 × 31.5) MVA
The voltage level of the ability transformer	(33/11) kV
Rated frequency	50 Hz
The voltage level of distribution transformers	(11/0.4) kV
Vector group of distribution transformers	Dyn11
Rated power of distribution transformers	(630, 400, 250, and 100) kVA
Blazon of usher	ACSR 120/20 mm2
Resistance of usher	0.246 ohm/km
Reactance of conductor	0.2899 ohm/km
Type of distribution feeder	three-stage 3-wire
Length of 11 kV feeder	iv km

Table 2. Distribution of the load for the case study.

Table 2. Distribution of the load for the case written report.

Transformer Capacity (kVA)	Continued Load (kW)	Bus No.
100	30	13
250	xc	11,12,14,15
	96	1,2,3,four,5,half-dozen,7,viii,9
400	150	x

Tabular array 3. The measurements at substation and feeder stop.

Table 3. The measurements at substation and feeder end.

Fault Location	Substation Side								Feeder Stop Side
	Ia (A)	Ib (A)	Ic (A)	Iunb%	In (A)	I1	Iii	I2: I1%	I1	I2	Iii: Ione%
No fault	86 ∠ 28	86 ∠ 28	86 ∠ 28	0	0	86 ∠ 28	0	0	8.2 ∠ 27	0	0
one	76 ∠ 47	76 ∠ −111	0	100	29 ∠ 148	48 ∠ 28	38 ∠ 88	79	5.5 ∠ 27	2.vii ∠ 87	l
ii	77 ∠ 46	76 ∠ −110	5 ∠ 149	93	27 ∠ 148	50 ∠ 28	36 ∠ 88	72	5.v ∠ 27	2.7 ∠ 87	l
3	77 ∠ 44	77 ∠ −109	xi ∠ 149	85	25 ∠ 148	53 ∠ 28	34 ∠ 88	64	5.v ∠ 27	2.7 ∠ 87	50
four	77 ∠ 43	77 ∠ −107	xvi ∠ 149	79	23 ∠ 148	55 ∠ 28	31 ∠ 88	56	v.5 ∠ 27	2.7 ∠ 87	50
5	78 ∠ 42	78 ∠ −106	21 ∠149	73	22 ∠ 148	57 ∠ 28	29 ∠ 88	51	5.5 ∠ 27	2.seven ∠ 87	50
6	78 ∠ 41	78 ∠ −105	27 ∠ 149	65	20 ∠ 148	60 ∠ 28	27 ∠ 87	45	five.5 ∠ 27	ii.7 ∠ 87	fifty
7	79 ∠ 39	79 ∠ −104	32 ∠ 148	59	18 ∠ 148	62 ∠ 28	24 ∠ 87	39	five.5 ∠ 27	ii.7 ∠ 87	50
8	80 ∠ 38	79 ∠ −102	37 ∠ 148	53	16 ∠ 148	64 ∠ 28	22 ∠ 87	34	5.5 ∠ 27	ii.7 ∠ 87	50
9	fourscore ∠ 37	80 ∠ −101	43 ∠ 148	46	fifteen ∠ 148	67 ∠ 28	xix ∠ 87	28	5.5 ∠ 27	ii.vii ∠ 87	l
10	81 ∠ 36	lxxx ∠ −100	48 ∠ 148	41	13 ∠ 148	69 ∠ 28	17 ∠ 87	25	5.5 ∠ 27	2.7 ∠ 87	50
11	82 ∠ 34	82 ∠ −98	56 ∠148	32	10 ∠ 148	73 ∠ 28	xiii ∠ 87	xviii	five.5 ∠ 27	2.vii ∠ 87	50
12	83 ∠ 33	82 ∠ −97	61 ∠ 148	27	viii ∠ 148	75 ∠ 28	11 ∠ 87	15	v.5 ∠ 27	2.seven ∠ 87	50
thirteen	83 ∠ 32	83 ∠ −96	66 ∠ 148	20	7 ∠ 148	77 ∠ 28	ix ∠ 87	12	five.5 ∠ 27	two.seven ∠ 87	50
xiv	83 ∠ 31	83 ∠ −95	68 ∠ 148	18	6 ∠ 148	78 ∠ 28	8 ∠ 87	10	5.5 ∠ 27	2.7 ∠ 87	50
xv	84 ∠ 30	84 ∠ −95	73 ∠ 148	13	4 ∠ 148	fourscore ∠ 28	6 ∠ 87	7	5.five ∠ 27	2.vii ∠ 87	50

Table 4. Comparison between simulation and mathematical issue.

Table 4. Comparison between simulation and mathematical result.

Fault Location	Source Side			Load Side			Simulation	Mathematical
	$\overline{\mathit{I}}$ c one (A)	$\overline{\mathit{I}}$ c 2 (A)	$\overline{\mathit{I}}$ c 0 (A)	$\stackrel{\overline{¯}}{\mathit{I}}{\mathit{c}}_1\left(\mathbf{A}\right)$	$\stackrel{\overline{¯}}{\mathit{I}}{\mathit{c}}_2\left(\mathbf{A}\right)$	$\stackrel{\overline{¯}}{\mathit{I}}{\mathit{c}}_0\left(\mathbf{A}\right)$	Ig (A)	Ig (A)
1	47.91 ∠ 27.86	38.33 ∠ 87.80	nine.584 ∠ −31.87	57.49 ∠ 27.88	28.74 ∠ 87.74	0.030 ∠ 59.46	28.75 ∠ 148.1	28.75 ∠ −32
2	44.95 ∠ 27.82	35.97 ∠ 87.76	eight.984 ∠ −31.95	53.94 ∠ 27.83	26.98 ∠ 87.72	0.025 ∠ 59.19	26.95 ∠ 148.one	26.95 ∠ −32
3	42.00 ∠ 27.lxxx	33.61 ∠ 87.74	eight.394 ∠ −31.98	fifty.40 ∠ 27.81	25.21 ∠ 87.70	0.024 ∠ 59.19	25.18 ∠ 148.0	25.xviii ∠ −32
iv	39.05 ∠ 27.77	31.25 ∠ 87.71	7.802 ∠ −32.03	46.85 ∠ 27.77	23.44 ∠ 87.68	0.022 ∠ 59.05	23.41 ∠ 148.0	23.41 ∠ −32
5	36.10 ∠ 27.74	28.89 ∠ 87.69	7.210 ∠ −32.08	43.31 ∠ 27.74	21.68 ∠ 87.67	0.019 ∠ 58.93	21.63 ∠ 147.ix	21.63 ∠ −32
6	33.14 ∠ 27.71	26.53 ∠ 87.67	half dozen.619 ∠ −32.12	39.76 ∠ 27.72	19.91 ∠ 87.65	0.016 ∠ 58.82	19.86 ∠ 147.9	19.86 ∠ −32
7	30.19 ∠ 27.69	24.xvi ∠ 87.66	half-dozen.029 ∠ −32.15	36.22 ∠ 27.70	18.fourteen ∠ 87.64	0.014 ∠ 58.76	18.09 ∠ 147.viii	18.09 ∠ −32
8	27.24 ∠ 27.68	21.eighty ∠ 87.65	5.441 ∠ −32.xvi	32.68 ∠ 27.68	16.36 ∠ 87.63	0.010 ∠ 58.75	16.32 ∠ 147.eight	xvi.32 ∠ −32
ix	24.29 ∠ 27.66	19.44 ∠ 87.63	four.852 ∠ −32.xix	29.fifteen ∠ 27.66	14.59 ∠ 87.62	0.013 ∠ 58.71	14.56 ∠ 147.8	14.56 ∠ −32
10	21.34 ∠ 27.64	17.08 ∠ 87.60	4.263 ∠ −32.22	25.61 ∠ 27.64	12.82 ∠87.60	0.011 ∠ 58.seventy	12.79 ∠ 147.8	12.79 ∠ −32
xi	16.77 ∠ 27.74	thirteen.42 ∠ 87.71	3.350 ∠ −32.11	20.12 ∠ 27.74	10.07 ∠ 87.71	0.011 ∠ 58.68	x.05 ∠ 147.9	x.05 ∠ −32
12	thirteen.82 ∠ 27.74	11.06 ∠ 87.70	two.761 ∠ −32.10	xvi.58 ∠ 27.73	viii.295 ∠ 87.70	0.010 ∠ 58.66	8.284 ∠ 147.9	8.284 ∠ −32
13	11.05 ∠ 27.72	viii.841 ∠ 87.67	2.208 ∠ −32.11	13.26 ∠ 27.70	half-dozen.633 ∠ 87.68	0.009 ∠ 58.65	half dozen.625 ∠ 147.9	half dozen.625 ∠ −32
fourteen	10.11 ∠ 27.65	8.091 ∠ 87.61	2.021 ∠ −32.17	12.xiii ∠ 27.64	6.070 ∠ 87.62	0.009 ∠ 58.64	6.063 ∠ 147.8	half dozen.063 ∠ −32
fifteen	7.343 ∠ 27.threescore	5.876 ∠ 87.55	1.468 ∠ −32.17	eight.812 ∠ 27.58	4.407 ∠ 87.57	0.009 ∠ 58.63	4.404 ∠ 147.8	iv.404 ∠ −32

Table 5. Comparison between the proposed method with contempo literature.

Table v. Comparing between the proposed method with contempo literature.

The Proposed Method	The Available Literature Methods
One measurement unit is needed at the feeder terminate.	The relays are needed in each bus of the grid [3]. Requires a voltage sensor to be placed at each end of the MV branch [5]. Fault indicating devices are needed [viii].
Detection does not depend on transformer connection (delta-star) or (star-delta).	Some drawbacks are mainly related to the delta transforms placed [3].
No need for collecting system historical data.	Need for collecting historical arrangement information [4].
Detection the faults in ungrounded and overhead lines.	Detecting the faults in ungrounded cables [half dozen].
Detect the faults when using single-phase and three-stage transformers.	Mainly detects the fault in a scenario with single-phase transformers [7].
No complicated communication is needed.	Feeder terminal units that are needed to install along the feeder with advanced communication links pb to additional hardware and software complexity [eight].
Applicable with the traditional overcurrent and earth fault protection.	Non applicable with the traditional protections [3,4,5,half-dozen,8].

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