Fault-Locator Scheme for Combined Taba-Aqaba Transmission System Based on New Faulted Segment Identification Method

In this paper, a new fault locator scheme is introduced to address the non-homogeneity of combined transmission lines (Taba-Aqaba Intertie transmission system). To achieve this goal, the faulted side is first determined using a new algorithm for identifying faulted segments. This identification algorithm relies on the voltage’s rate of change along the nonhomogeneous lines in the pure positive-sequence circuit, exploiting the inequality of positive-sequence impedances between power cables and overhead lines. The number of outputs generated by the algorithm is one less than the number of line segments being analyzed. For systems with two segments, the output directly identifies the faulted segment. However, for combined lines with three segments, a new voting system is utilized to determine the faulted segment. The fault distance is then calculated based on the identified faulted segment. To evaluate the proposed scheme, various fault scenarios are simulated on the Taba-Aqaba Intertie transmission system, which connects the Egyptian and Jordanian networks, using ATP-EMTP. These tests encompass different fault types and locations, including cases near the interconnection points between the segments. Additionally, the scheme is tested under nonlinear faults.


NOMENCLATURE x jun
The fault-side indicator.

L C
The cable length.

L
The total combined line length.

I A1
The positive-sequence current change value of Busbar A.
The associate editor coordinating the review of this manuscript and approving it for publication was Ali Raza .

I B1
The positive-sequence current change value of Busbar B.

Z C1
The cable positive-sequence impedance per unit length.Z OH 1 The overhead positive-sequence impedance per unit length.

x act
The actual distance.V f 1 The positive-sequence voltage change value of fault point.A OH2 , B OH2 , C OH2 , and D OH2 The constants of overhead line connected to busbar B considering the distributed line model.γ c1 The propagation constant of cable within positive-sequence circuit.
Zc c 1 The positive-sequence characteristic impedance of cable.γ OH1 The propagation constant of overhead line within positive-sequence circuit.Zc OH 1 The positive-sequence characteristic impedance of overhead line.
The calculated distance by considering an artificial fault at the first junction point jun1.
The calculated distance by considering an artificial fault at the second junction point jun2.V jun2 1 The positive-sequence voltage change value of jun2.I jun2 1 The positive-sequence current change value of jun2.
The length of first overhead line section.
The length of second overhead line section.V jun1 1 The positive-sequence voltage change value of jun1.I jun1 1 The positive-sequence current change value of jun1.A OH1 ,B OH1 , C OH1 , and D OH1 The constants of overhead line connected to busbar A considering the distributed line model.

List of abbreviations ANFIS
Adaptive network-based fuzzy inference system.FDOST Fast-discrete orthogonal Stransform.SVM Support vector machine.SVR Support vector regression.

I. INTRODUCTION
Electrical power is typically transmitted from power stations to substations near loads through overhead transmission lines.However, due to environmental requirements, modern construction often utilizes underground cables for power transfer.Additionally, power is transferred between countries through DC or AC submarine cables.As a result, combined power cables with overhead transmission lines are created [1], [2].The characteristics of overhead lines differ significantly from those of power cables.The cable's impedance is low due to the small space between the conductors.However, the cable capacitance is greater than that of overhead lines due to higher dielectric constants of the insulation materials used and the shorter distance between the sheath and the cable conductors.Consequently, the cable surge impedance is approximately 10% of that of an overhead line (ranging from 40 to 60 for underground cables and 400 to 600 for overhead lines) [2].Transmission systems are prone to various fault occurrences, with both overhead lines and power cables being susceptible to shunt faults [3].Therefore, a variety of protective devices are employed to detect and isolate faults on the transmission lines.Moreover, accurately determining the fault location is crucial for quickly initiating the necessary repair processes and reducing costs [4], [5].
Fault-distance estimation for combined lines presents a challenge due to the unequal impedances per unit length of the cable and the overhead line.Fault locator algorithms based on artificial neural networks require higher training effort compared to conventional methods to mitigate the potential interference that can lead to erroneous identification of the faulted section.On the other hand, traveling wave-based fault locator algorithms necessitate a single value for the propagation velocity.The fundamental phasor components-based fault locator algorithms typically require a single value for both positive-and zero-sequence line impedances.Additionally, the problem becomes more complex when the combined transmission system contains three different segments, such as the actual transmission line connecting the Egyptian and Jordan electricity networks.
The application of artificial neural network for fault distance estimation in combined transmission line is introduced in [6], [7], and [8].These approaches typically involve two stages.In the first stage, the faulted side is determined whereas in the second stage, the fault distance is estimated.In [6], the support vector machine is employed to identify the faulted section.In [7], an adaptive network-based fuzzy inference system (ANFIS) with four inputs is employed for the training process to locate the fault.In [8], a new scheme that can detect, classify, and locate the faults for two-and multi-terminal transmission lines is proposed.This scheme is based on the fast-discrete orthogonal S-transform (FDOST) in conjunction with the support vector machine (SVM).The signals of the three-phase currents are measured at a line end to obtain the entropy of FDOST coefficients, and then these coefficients are fed to support vector regression (SVR) to detect the fault location.However, in [6], [7], and [8], the retraining process is again required when significant changes occur in the system configuration.
Travelling waves are utilized to locate faults in combined transmission lines, as described in [9].However, this method requires a high sampling frequency.Dynamic load conditions, such as abrupt connections of industrial loads, affect fault current levels in a power system.Load increases lead to higher fault currents, while load decreases result in reduced fault currents.Considering dynamic loading's influence is critical in power system design, including protective scheme development, current transformer selection, and choosing protective devices, to ensure safe fault handling and prevent equipment damage [10].The dynamic loading affects fault location techniques based on traveling waves.Fluctuations in transmission line impedance due to dynamic loading affect the reflection and transmission of fault-generated transient signals [10], making accurate fault location estimation challenging in the time domain.Additionally, dynamic loading causes variations in the line charging current [10], influenced by line capacitance and length, which can interfere with transient signal detection and interpretation, potentially complicating the fault location process.On the other hand, the dynamic loading affects the accuracy of fault location techniques based on the fundamental phasor components using single-end measurements by introducing uncertainties in the estimation of fault resistance, crucial for the accuracy of these techniques.This negative effect can be mitigated through accurate load modeling, which aids in predicting the dynamic behavior of the system and enables more precise fault location estimation.Additionally, fault location techniques using Phasor Measurement Units (PMUs), which are devices that measure the phasors of voltage and current at high-speed, provide synchronized real-time data from various locations in the power system.By using PMU data, the impact of dynamic loading on the fundamental phasor components-based fault location using two-end measurements can be minimized since the measurements remain unaffected by data latency.
The fault location determination by utilizing the fundamental phasor components is introduced in [11], [12], [13], and [14].In [11] and [12], the fault location for cascaded overhead cable transmission line is obtained by equating the voltage equation at fault point as a function of measured electrical quantities at one terminal and quantities at the junction point computed from another terminal using modal components based on DFT.This approach yields two solutions: The correct solution is less than the considered faulted section length whereas the improper solution is more than the considered healthy section length.This idea is further developed in [13] to be applicable to two-terminal multi-section nonhomogeneous transmission lines using synchronized phasor measurements.In this case, a selector is introduced to discriminate the faulted zone, and then fault distance estimation can be performed.The authors in [13] extend their work to three-terminal nonhomogeneous transmission lines by introducing an indicator that identifies both the faulted branch and the specific zone (cable/overhead) within the branch, as demonstrated in [14].Additionally, [15] presents a technique consisting of two steps: the first step involves converting the system of nonlinear equations into an optimization problem, and the second step involves solving the problem using a modified Newton method.
A technique based on prior morphological spectrum and forward and backward traveling waves, suitable for nonhomogeneous distribution systems using measurements at one end, is proposed in [16].Similarly, a work locating a fault on combined transmission lines (an overhead line combined with an underground cable) by extracting the traveling wave arrival times of the measured voltages using two consecutive sliding windows and curve fitting is developed in FIGURE 1.A cascaded overhead transmission line with cable connections, experiencing a fault at the junction point.[17].Both [16] and [17] require a high sampling frequency for accurate results.It is important to note that traveling wave-based techniques necessitate substantial computational burden and specially designed transducers.To introduce an additional faulted section identifier independent of the fault location calculations, a new approach in this paper is presented concentrating on an actual combined transmission line connecting between Egyptian and Jordan electricity networks (Taba-Aqaba Inter-Tie transmission system).
The primary objective of this paper is to introduce a novel faulted-section identification scheme for a practical transmission system consisting of overhead lines, submarine cables, and overhead lines, specifically the Taba-Aqaba Inter-Tie transmission system.Importantly, the calculation process of the presented identification method is independent of fault distance calculations.The output of this faulted segment indicator directly indicates the faulted segment when the transmission line has two segments.However, in the case of the Taba-Aqaba Inter-Tie transmission system with three different segments, the identification method produces two outputs.To determine the faulted segment, a comparator or voting system is employed.Subsequently, the fault location is computed based on the identified faulted segment.Notably, the presented scheme is robust against variations in source impedance, fault type, and zero-sequence circuit parameters, making it applicable for submarine cables.To validate the reliability of the scheme, extensive simulation cases were conducted using ATP-EMTP.The results demonstrate that the proposed identification method is reliable under various fault conditions.

II. INTRODUCED FAULT-LOCATOR ALGORITHM FOR COMBINED TRANSMISSION LINES
The non-homogeneity of the combined transmission lines poses a problem for both single-and two-ended fault location techniques.In one-ended techniques, the issue arises from the changing positive-sequence impedance per unit length, which is a crucial input for algorithms, depending on the fault location.As a result, the accuracy of conventional algorithms varies significantly with changes in the fault distance.In two-terminal techniques, the challenge lies in identifying the faulted side of the transmission line.This paper introduces a new algorithm for identifying the faulted side in two-terminal combined lines with three different segments, such as the Taba-Aqaba Inter-Tie transmission system.The introduced identification method is initially demonstrated using a cascaded overhead-cable transmission line with only two segments.
A. FAULTED SEGMENT IDENTIFICATION

1) COMBINED LINE HAVING TWO SEGMENTS
A transmission line, shown in Fig. 1, consists of an underground cable combined with an overhead line.At the junction point, a shunt fault occurs.This combined transmission line connects two substations, A and B. To locate the fault on the combined line, the faulted side must be determined first, and then the fault location is computed.In other words, for faults on either the cable or overhead line segment, the difficulty arises from the presence of an unknown length on this segment, which has a different rate of voltage change compared to the cascaded nonhomogeneous segment.Fig. 2 provides an illustration of this scenario.
The identification of the faulted side is accomplished by introducing a formula for identifying the faulted side (x jun ).The fault-side indicator (x jun ) is a calculated distance under considering an artificial fault at the junction point regardless of the actual fault point.This obtained distance (x jun ) precisely identifies the faulted side whether the fault is on the cable or overhead side.If x jun is less than the cable length (L C ) then the fault must be on the cable section and vice versa.This is illustrated in detail as follows: The fundamental concept behind the fault-side indicator (x jun ) is illustrated in Fig. 2, where the capacitor current is neglected to simplify the illustration.This allows for a linear representation of the voltage magnitude variation along the length of each segment of the combined line.The formula of x jun is derived by equating the formulas of the change in positive-sequence voltage at the junction point ( V jun1 ) from both ends of the combined line using the short model representation, irrespective of the actual fault position as shown in (1).
where, V SA1 and V SB1 represent the changes in positive-sequence voltage components at Busbars A and B, respectively.I A1 and I B1 represent the changes in positive-sequence current components at Busbars A and B, respectively.The positive sequence components are chosen to be suitable for all types of faults, while the change values are used to mitigate the impact of the capacitive charging current and pre-fault current.These components are estimated using the measured three-phase voltages and currents.
x jun is the fault-side indicator.Z C1 and Z OH 1 represent the positive-sequence impedances per unit length of cable and overhead line, respectively.These parameters are known, and their values remain unchanged regardless of the fault point.L denotes the total combined line length, which is equal to the sum of cable length (L C ) and overhead line length (L OH ) as depicted in Figs. 1 and 2.
This obtained distance (x jun ) accurately identifies the faulted side whether the fault is on the cable or overhead side.This is proved as follows: The evidence supporting the authenticity of the introduced indicator (x jun ) is demonstrated by substituting with the actual difference between the changes in positive-sequence voltages at terminals A and B due to the occurrence of a fault ( V SA1 -V SB1 ) as in (1).This voltage difference ( V SA1 -V SB1 ) under the three possible fault conditions -a fault at the junction point, cable side, or overhead side, as illustrated in Figs.2.a, 2.b, and 2.c respectively -is expressed as (2), (3), or (4) respectively. (2) Then, the output of the introduced formula of x jun is expected to be as shown in ( 5), (6), and (7) by substituting (2), (3), and ( 4) into (1) and performing some mathematical simplifications for a fault at junction point, cable side, and overhead side, respectively. (5) One can observe the following points.Under faults at junction point, the obtained fault distance equals the actual fault distance, as shown in (5).under cable side faults, assuming that the rate of change of the selected voltage component through the unknown cable partition length (L c -x act ) equals Z OH 1 .I B1 instead of the actual value Z C1 .I B1 , the actual fault distance (x act ) is less than the obtained output value of x jun by a correction factor.This factor is directly proportional to the difference between the actual and assumed rates of change of the considered voltage component, expressed as a ratio of the sum of the two actual rates of change, as shown in (6).This factor is less than 1.Therefore, if the fault is on cable side, x jun must be more than the actual distance (x act ), but it must also be less than the cable length (L C ).This is further supported by the voltage magnitude profile of the pure positive-sequence circuit depicted in Fig. 2.b, where the Z OH 1 is higher than the Z C1 .The decreasing rate of the selected voltage component in the region between the junction and fault points, illustrated by dashed line in Fig. 2.b, is higher than the actual decreasing rate depicted by dotted line.Consequently, the calculated positive-sequence voltage reaches the intersection point at a distance (x jun ) that is more than x act .However, x jun is less than L C because the voltage calculation from the direction of Busbar B is accurate until the junction point.Therefore, the value of V jun1 calculated from this direction is more than the actual value of the change in positive-sequence voltage at the fault point V f 1 , as illustrated in Fig. 2.b.
Similarly, in the case of overhead side faults, assuming that the rate of change of the voltage through the unknown overhead partition length (x act -L c ) equals Z C1 .I A1 instead of the actual value Z OH 1 .I A1 , the actual fault distance (x act ) is less than the obtained output value of x jun by a similar correction term as shown in (7).Thus, if the fault is on overhead side, x jun must be more than x act and then more than L C .This is further supported by the voltage magnitude profile shown in Fig. 2.c where Z C1 is lower than Z OH 1 .The decreasing rate of the calculated positive-sequence voltage in the region between the junction and fault points, illustrated by the dashed line in Fig. 2.c, is lower than the actual decreasing illustrated by the dotted line.Consequently, the positive-sequence voltage calculated from the direction of Busbar A reaches the intersection point at a distance (x jun ) that is more than x act .Finally, the obtained value of the x jun successfully identifies the faulted section for combined lines with two segments.However, the capacitive charging current should be taken into consideration.
To account for the effect of capacitive charging current, the formula is derived by equating the calculated change in positive-sequence voltage at the junction point (V jun1 ) from both ends of the combined line, using the distributed line model representation regardless of the actual fault location, as shown in (8).
The formula given in (8) can be expressed as follows: Using the following identities: The formula given in ( 9) can be expressed as follows: According to Taylor's expansion, the hyperbolic functions can be expanded as follows: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Then, the formula given in (10) can be rewritten as follows: The formula in (11) can be rewritten as follows: For the 5 th degree of expansion and by converting formula in (12) to a zero equation, it can be written in the following form: where these constants (a, b, c, d, e, and g) are as follows: By using the initial guess for (x) as in [18], the roots of the formula given in (13) can be obtained numerically.The introduced identification method is also applicable to the combined transmission lines that consist of three segments, as in the following subsection.

2) COMBINED LINE HAVING THREE SEGMENTS
The proposed concept is also applicable for combined transmission systems composed of three segments, such as line-cable-line combined networks.Fig. 3 shows a single-line diagram of a line-cable-line combined transmission system, such as the Taba-Aqaba Intertie transmission system.The identification of the faulted side is accomplished by applying the proposed concept twice at the two junction points (jun1 and jun2) between the adjacent sections, as illustrated in Figs. 4 and 5, and obtaining two distances (x jun1 and x jun2 ), respectively.The two distances, x jun1 and x jun2 , are obtained by considering an artificial fault at either junction point, jun1 or jun2, irrespective of the actual fault point.Subsequently, the faulted side is determined by utilizing an introduced voting system (comparator) as follows: If both values (x jun1 and x jun2 ) indicate a fault on the cable section, then the faulted side is determined to be the cable section.This is illustrated in detail in Fig. 4 for a fault on the cable section.On the other hand, if both values (x jun1 and x jun2 ) indicate a fault on an overhead section, then the faulted side is determined to be that overhead section.If one of the values indicates a fault on an overhead section and the other indicates a fault on the cable section, then the faulted side is determined to be the overhead section.The basic concept of this condition is illustrated in detail in Fig. 5 for a fault on the first overhead section.In other words, the first fault-side indicator (x jun1 ) directly identifies faults occurring at the first overhead section, whereas the second indicator (x jun2 ) directly identifies faults occurring at the second overhead section.However, faults occurring at the cable section are recognized by both indicators as cable faults.The conditions of the introduced comparator are summarized in Table 1.The calculation of two indicators x jun1 and x jun2 is as follows: The calculation of x jun1 is performed by representing the combined transmission line as an overhead line combined with an underground cable, with terminals A and jun2.The change in positive-sequence voltage and current at jun2 is calculated based on the measured data at terminal B and the parameters of the overhead section II (OH2) connected to terminal B, as shown in (20).
where A OH2 , B OH2 , C OH2 , and D OH2 are the constants of the overhead line connected to busbar B considering the distributed line model representation.
The formula of x jun1 is derived by equating the two formulas that calculate the change in positive-sequence voltage  at the first junction point, considering both sides A and jun2.These formulas utilize the distributed line model representation regardless of the actual fault point as shown in (16).
Therefore, x jun1 is obtained by solving a 5 th degree equation, where the coefficients are presented in (17), similar to (14) with changes in symbols for line terminals and the 104276 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

considered line length (L
Similarly, under x jun2 calculation, the line can be represented as an underground cable combined with an overhead line where its terminals are jun1 and B. The change of positive-sequence voltage and current at jun1 is computed using the measured data at terminal A and the parameters of the overhead section connected to terminal A as shown in (18).
where A OH1 , B OH1 , C OH1 , and D OH1 represent the constants of overhead line connected to busbar A, considering the distributed line model.The positive-sequence voltage at the second junction point, calculated from both sides jun1 and B, is equated using the distributed line model representation, regardless of the actual fault position, as shown in (19).
Also, x jun2 is obtained by solving a similar 5 th degree equation where the coefficients are presented in (20), following a similar approach as in ( 14) but with changes in the symbols of line terminals and the considered line length (L C + L OH 2 ).Subsequently, the length of the overhead section I (L OH 1 ) is added to establish the reference of the obtained distance as Busbar A.
Finally, the faulted section is precisely identified by analyzing the two values of x jun1 and x jun2 , as shown in Table 1.Then, the actual fault distance is directly obtained as described in the following subsection.

B. FAULT-LOCATOR ALGORITHM
After gathering the measured data from the ends of the combined line, the symmetrical components of measured three-phase voltages and currents are computed.The identification of the faulted section, as presented in the above subsection, is then accomplished.Additionally, the positive-sequence data at the terminals of the obtained faulted section are prepared, as mentioned above.The fault location estimation is carried out based on the obtained faulted section.For example, let's consider a fault on the cable section of the combined line, which has three segments as illustrated in Fig. 4. The fault location is determined as follows: The two values of x jun1 and x jun2 indicate a fault on the cable section, and therefore the obtained faulted side is the cable section.Furthermore, the positive sequence voltage and current at the two junction points jun1 and jun2 (V jun11 , I jun11 , V jun21 , I jun21 ) are estimated as mentioned above.Then, the fault location is estimated by equating the positive sequence voltage of fault point as a function of the estimated data at the two junction points as; Hence, the fault distance (x) is estimated as in ( 22) and then adding the L OH 1 length to be referred to the Busbar A.
Similarly, the fault location is also obtained under faults on the overhead sections.For example, for faults on the overhead section II, a similar formula to that shown in ( 22) is utilized with some changes.These changes are replacing the cable parameters with these faulted overhead section parameters as well as using the data at Junction 2 and Busbar B instead of that at Junction 1 and Junction 2, respectively.To be the obtained distance referred to the Busbar A, the lengths of both L OH 1 and L c should be added.
Finally, the presented scheme can be implemented in the intertie combined transmission line by first identifying the faulted section and then locating the fault point.In combined transmission systems with two segments, the faulted section is identified by analyzing the value of the fault-side indicator (x jun ) obtained from (14), as illustrated in Fig. 6.For combined transmission systems with three segments, the faulted section is identified by analyzing the values of the two computed distances, x jun1 and x jun2 , as shown in both Table 1 and Fig. 7.These two computed distances (x jun1 and x jun2 ) are obtained by solving a 5th-degree equation, where their coefficients are presented in (17) and (20), respectively.
After identifying the faulted section, the positive-sequence voltages and currents at the two ends of the faulted section are calculated.The fault location is then determined using these calculated values and the parameters of the faulted section.For example, if the fault occurs on the cable section of the three-segment combined line, the fault distance is obtained as described in (22).

III. SIMULATION OF ACTUAL COMBINED TRANSMISSION LINE
To accomplish the aimed study, an actual nonhomogeneous transmission line connecting the Egyptian and Jordanian networks is studied.Fig. 8 illustrates the selected power system network from 500 kV Eyoun-Mousa station in Egypt to 400 kV Aqaba station in Jordan including the following parts: -500 kV, 244 km length, overhead transmission line starting from Eyoun-Mousa station to 500 kV Taba substation.-750 MVA, 500/400/22 kV three-phase autotransformer (consisting of three-single phase ones).-400 kV, 20 km overhead transmission line connecting between 500 kV Taba substation and Egyptian submarine cable side.-400 kV, 13.6 km three single core submarine cable linking Egyptian and Jordanian networks.-400 kV, 10 km overhead line linking the submarine cable with 400 kV Aqaba station.
As shown from these elements, Taba-Aqaba inter-tie transmission system represents an actual system for evaluating the associated problems with the fault-locator techniques for composite lines.The appendix includes the parameter data for simulated overhead sections and simulated underground section.ATP/EMTP package is used for simulating the considered actual system.

IV. THE PROPOSED SCHEME ASSESSMENT
Different fault cases were prepared in the ATP package using 32 samples per cycle at various points, covering the entire range of the line, including faults close to tie points between the different segments.The fundamental frequency components of the three-phase voltage and current phasors are calculated using the cosine filter.The cosine filter cancels exponentially decaying DC offsets, cancels all harmonics, approximates desirable bandpass filtering, and has a perfect transient response [19].The cosine filter outperforms the Fourier filter in the presence of DC offsets.Subsequently, the presented faulted section identification method and the fault-locator technique are carried out sequentially.Finally, the error is computed as a percentage of the length of the faulted segment.
The studied cases can be categorized as follows: Case 1: Different fault types, fault distances, and fault resistance effects.
Case 2: Effect of nonlinear fault resistance (arcing fault).Case 3: Effect of changing the source impedance.Case 4: Effect of changing the fault impedance.

A. SIMULATION RESULTS: CASE 1
The presented faulted-side identification method and the fault locator were tested for both line-to-ground, line-to-line, lineto-line-to-ground, and three-phase faults, as shown in Tables 2, 3, 4, and 5, respectively.The tests considered faults close to the junction point.
From the results, one can observe that, during faults on the cable section, the values of two obtained indicators (x jun1 and x jun2 ) fall within the range of 20 to 33.6 km for all fault types.Thus, the output of the presented comparator indicates a fault in the cable section, as listed in Tables 2, 3, 4, and 5. On the other hand, during faults on the first overhead section OH1, the value of x jun1 is less than 20 km, and xjun2 is also less than 33.6 km.This output of the comparator indicates a fault in the OH1 section.Similarly, for faults on the second overhead section OH2, the value of x jun1 is greater than 20 km, and x jun2 is greater than 33.6 km.The comparator's output indicates a fault in the OH2 section.The results prove that the presented faulted side identification method is successful even under faults close to the junction points (jun1 and jun2), as shown in the shaded rows in Table 6.Therefore, the fault location algorithm accurately pinpoints the fault location after identifying the faulted section, where the maximum error is 0.837% of the faulted segment only, as shown in the right-hand side column in Table 6.Finally, the results demonstrate the efficacy of the proposed algorithms.
Although the proposed scheme is accurate under faults close to the junction points connecting the cable section to the overhead lines' sections (demonstrated both theoretically in the paper, Section II, and through the obtained results), if the scheme's output indicates a fault within the 20 m threshold around a junction point, it signifies that the fault is around the corresponding junction point.

B. SIMULATION RESULTS: CASE 2
The previous results are with fixed fault resistance whatever its value.In this case, the performance of the presented protection scheme was investigated during an arcing fault, in which the fault resistance is nonlinear based on the arcing model presented in [20].The arcing model is depicted in Fig. 9.The model is based on energy balance in the arc [20] and is characterized by the following differential equation: where τ is the arc time constant.Gand gare the stationary and instantaneous arc conductance, respectively.The stationary arc conductance is defined as: where i is instantaneous arc current.U O and R are the constant voltage and the resistive component parameter per arc length, respectively.The values of parameters U O , R, and τ are 13.5 V/cm, 1 m /cm, and 0.8 ms, respectively.One example of an arcing fault occurring at 23.6 km from terminal A is carried out to test the proposed algorithm.Fig. 10 illustrates the simulated arc characteristic (arc voltage, arc resistance, and I-V characteristic).Fig. 11 shows the measured three-phase current and voltage under the simulated arcing fault and the response of the cosine filter.Fig. 12 shows the response of the presented algorithm under this arcing fault.Figs.12.a and 12.b show the output of the first and second fault-side indicators (x jun1 and x jun2 ) where the two values indicate that the fault is on the cable side.Then, the presented algorithm identifies the faulted section.Fig. 12.c shows the estimated fault distance and confirms the reliability  of the presented for the Taba-Aqaba Intertie transmission system under arcing faults (nonlinear faults).

C. SIMULATION RESULTS: CASE 3
The presented scheme was also investigated by varying the source impedance.In this test case, +/−10% range is utilized   in varying the source impedance with a line-to-ground fault at 25 km distance.Table 6 depicts the results obtained, which validate the efficacy of the presented scheme.

D. SIMULATION RESULTS: CASE 4
Testing of the proposed scheme was conducted by varying the fault impedance, specifically considering high impedance faults.To achieve this, we introduced different line-to-ground faults within the cable section located at a 30 km distance from terminal A, with fault impedances ranging from 0.1 to 1 k .The results of these tests, as illustrated in Fig. 13, which shows the outputs of the scheme versus the selected fault circumstances, confirmed that the proposed scheme remains effective and independent of the fault impedance variations.

V. CONCLUSION
A new fault location scheme for an actual overhead linesubmarine cable-overhead transmission system (Taba-Aqaba Inter-Tie transmission system) is introduced.The proposed algorithm depends on identifying the faulted section by introducing new fault-side indicators.The fault-side indicators (x jun1 and x jun2 ) are the calculated distances under considering an artificial fault at either the first or second junction point regardless of the actual fault point.Then, a new voting system is used to obtain the faulted zone.In other words, the first fault-side indicator (x jun1 ) directly refers to faults occurring at the first overhead section, whereas the second indicator (x jun2 ) directly refers to faults occurring at the second overhead section.However, the faults occurring at the cable section must be seen by the two indicators as cable faults.The introduced identification method depends on the rate of change of the voltage along the nonhomogeneous line in the pure positive-sequence circuit by exploiting the inequality of positive-sequence impedances of both power cable and overhead line.The proposed scheme is investigated under different simulation cases using ATP-EMTP.The results confirmed the high efficacy of the proposed faulted section determination.The proposed scheme is unaffected by variations in source impedance, fault types, and zero-sequence circuit parameters making it applicable for submarine cables.Additionally, the proposed algorithm is reliable under nonlinear faults.Consequently, the fault location can be determined straightforwardly by equating the formulae of positive-sequence voltage at the fault point, derived as a function of the data at the obtained faulted section terminals.An essential future prospect of this paper involves enhancing the presented scheme's applicability under unsynchronized data considering dynamic loading effect.
V jun1 The positive-sequence voltage change value of the junction point.V SA1 The positive-sequence voltage change value of Busbar A. V SB1 The positive-sequence voltage change value of Busbar B.

FIGURE 2 .
FIGURE 2. The pure positive-sequence circuit and its voltage magnitude profile to investigate the x jun value under a fault at: (a) the junction point (b) the cable side (c) the overhead side.

FIGURE 4 .
FIGURE 4. The pure positive-sequence circuit of a three-segment combined line under a fault on the cable side as in (a) , and its voltage magnitude profile obtain x jun1 as in (b) and x jun2 as in (c).

FIGURE 5 .
FIGURE 5.The pure positive-sequence circuit of a three-segment combined line under a fault on the first overhead section as in (a) , and its voltage magnitude profile to obtain x jun1 as in (b) and x jun2 as in (c).

FIGURE 6 .
FIGURE 6.The presented algorithm flowchart for a two segments transmission line.

FIGURE 7 .
FIGURE 7. The introduced flowchart for Taba-Aqaba transmission line.

FIGURE 10 .
FIGURE 10.The simulated arc characteristic illustrating the (a) arc voltage, (b) arc resistance, and (c) I-V characteristic.

FIGURE 11 .
FIGURE 11.The measured three-phase current and voltage under an arcing fault at 23.6 km distance from terminal A and the response of the cosine filter.

FIGURE 12 .
FIGURE 12.The response of the presented algorithm under non-linear fault resistance at 23.6 km fault distance where (a) Xjun1, (b) Xjun2, and (c) estimated distance.

FIGURE 13 .
FIGURE13.response of the presented algorithm under line-to-ground faults with varying the fault impedance.

FIGURE 14 .
FIGURE 14.The utilized tower configuration for the overhead transmission.

FIGURE 15 .
FIGURE 15.Cross-sectional area of the used single-core cable and its relevant parameters.

TABLE 1 .
The proposed comparator identifying the faulted section.

TABLE 2 .
The proposed scheme performance under L-to-G faults associated with 10 fault resistance.

TABLE 3 .
The proposed scheme performance under L-to-L faults associated with 20 fault resistance.

TABLE 4 .
The proposed scheme performance under L-to-L-to-G faults associated with 30 fault resistance.

TABLE 5 .
The proposed scheme performance under three phase faults associated with 50 fault resistance.

TABLE 6 .
The proposed scheme performance under variation of the source impedance.

TABLE 7 .
Dimensions of the utilized towers (in meters).

TABLE 8 .
Parameters of overhead line.

TABLE 9 .
Parameters of cable.