Abnormal Detection Line Method to Estimate Disconnection Points in Power Distribution Lines

Natural phenomena such as gale, rain, and lightning cause disconnections, which can disrupt power distribution. Therefore, a method that can estimate the disconnection point (DP) in power distribution lines is needed to ensure public safety and a stable power supply. A simple DP detection method using a common earthing conductor is applied to both residential and industrial areas with only two distribution lines with interconnection points at the ends. However, this method cannot be used in rural areas that have distribution lines without interconnection points. Therefore, we propose a novel DP estimation method for use in distribution lines in rural areas. To this end, an abnormal detection line was installed along a long distribution line with branch lines and ammeters placed at its starting and end points. DP estimation was realized by calculating the time difference between the zero-crossing points of the current flowing in the two ammeters. The DP estimation effectiveness of the proposed method was validated by simulating long distribution lines. Thus, the proposed method can be used to improve the performance of the distribution lines in rural areas.

primary cause of power disruptions. Methods such as wavelet analysis [2], fast Fourier transform analysis [3], methods based on common earthing conductors [4], and artificial neural networks [5] have been developed to estimate ground-fault points in distribution lines.
For short-circuit point estimation, methods such as pulse injection [6] and the method using anomaly-detection lines proposed by the author [7] have been studied.
In this study, we considered natural phenomena such as gale, rain, lightning, ice, snow, and tree contact as primary causes of disconnection. If a disconnected high-voltage line is connected to the grounding band at the time of disconnection, it develops into a ground fault and terminates the power supply to the distribution line. In contrast, the disconnection may not lead to a ground fault if the conductor of the high-voltage line is coated; the wire coating would cover the conductor after the disconnection. The protection relay of the distribution line does not operate under the disconnected state, and the power supply is not interrupted. If a person encounters a disconnected distribution line, there is a high risk of an electric shock. Thus, early detection of the disconnection point (DP) is necessary to ensure safety.
Various DP estimation methods have been reported using smart meters [8], artificial intelligence (AI) [9], and common earthing conductors [10], [11]. Moreover, extensive studies have been conducted to determine the voltage characteristics of the measuring equipment installed on a distribution line [12], [13], [14]. Further, several methods have been proposed to estimate the DPs in one branch of a distribution line by mining the system characteristics from the multisource data of distribution lines [15] and using machine learning with power, voltage, and current data [16]. Studies on the operation of relays depending on failure at the time of disconnection are underway [17]. DP estimation methods that employ smart meters are effective for urban and residential areas. In these methods, smart meters are installed across distribution lines; however, in rural areas, limited consumers are scattered across electricity-demand locations, and therefore it is difficult to identify the DP at the time of disconnection in the distribution line that connects the demand locations of users with no electricity.
In AI-based DP estimation methods, the DP is estimated considering the changes in the voltage and current waveforms generated at the time of disconnection. To determine the voltage This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ characteristics, the DP is specified by the number of voltage sensors installed. Further, a simple method is required to estimate the DP using data mining. Similarly, in the machine learning approach, a method that does not require a complex analysis of power, voltage, and current data is necessary. As described in [14], there are limited studies on the disconnection of distribution lines. Therefore, novel detection methods need to be developed to ensure public safety and a stable supply of electricity.
Current DP estimation methods focus on the trunk and branch lines of the distribution system [10], [11]. Ammeters are mounted at the starting point of a common earthing conductor installed on two adjacent distribution lines, and the DP is estimated by detecting the change in the phase of the current flowing through the ammeters at the time of disconnection. In this method, two adjacent distribution lines are considered in residential and urban areas. Unlike the method described in [10], [11], the DP must be identified within a narrow region using information from ammeters installed at the starting and end points of the common earthing conductor in rural areas. Therefore, there is a need for further improvement and validation of this method to apply it to distribution lines in rural areas.
In this study, we propose a DP estimation method considering a long distribution line that does not include interconnection points with other distribution lines common in rural areas. The proposed method involves installing an abnormal detection line (ADL) that detects the difference in the current flowing in the high-voltage line before and after a disconnection in the distribution line. In addition, grounding electrodes are installed at the starting and end points of the ADL. The proposed method estimates the DP based on the time difference between the zero-crossing points of the current flowing through the ammeters installed on the ADL during the disconnection.
The rest of this manuscript is organized as follows: Section II describes the current distribution line disconnection phenomenon, and Section III presents the proposed methodology and its theory. Section IV presents the simulation model and results, which are analyzed in further detail in Section V. Section VI discusses the validity of the theory of the proposed method, the advantages of the proposed method, and an application example where the proposed method is utilized at a real site. Finally, conclusions are provided in Section VII. Fig. 1 illustrates several distribution lines originating from one distribution substation with a grounding resistance (NGR) of 10 kΩ, which is equivalent to high-resistance grounding. Fig. 2 displays three high-voltage lines, the ADL, the transformer, and the switchgear located on the utility pole. The ground voltage of each phase of the high-voltage lines is 3.81 kV, and the lineto-line voltage is 6.6 kV. Fig. 3 shows the electricity supply to high-voltage consumers at 6.6 kV and to households at 6.6 kV to 100/200 V or 6.6 kV to 200 V for low-voltage consumers with large capacities.    During disconnection, the voltages of the two nondisconnected phases remain unchanged. The voltage of the disconnected phase after the disconnection is half of its original magnitude; its phase changes by 180°compared with that before the disconnection. Fig. 4 shows a vector diagram of the voltage characteristics before and after the disconnection.

II. CURRENT DISTRIBUTION LINE DISCONNECTION PHENOMENON
Currently, there is a difference in the disconnection detection process on the trunk and branch distribution lines because automatic switches are installed on the trunk, and no such switches are installed on the branch. For trunk line disconnection, the presence or absence of disconnection can be confirmed based on variations in the voltage phase before and after the disconnection using an automatic switch; however, the DP cannot be identified. Disconnection in the branch line is difficult to detect because the trunk line voltage remains unchanged following the disconnection.

A. Proposed Method
In the proposed method, ammeters are installed at the starting and end points of the ADL to measure the current before and after disconnection. The DP is estimated by detecting the time difference between the zero-crossing points of the currents flowing in the two ammeters before and after the disconnection. The distribution lines in rural areas are long and installed away from the substation to the scattered demand areas; therefore, the establishment of interconnection points with other distribution lines is difficult. In this study, we propose a DP estimation method for a single distribution line using an ADL.
The difference between the proposed and existing methods includes the use of an ADL instead of a common earthing conductor. The common earthing conductor is connected between adjacent poles and the grounding pole of each electrode, and it is subsequently connected to the adjacent distribution line at the end. Further, in existing methods, the frame of the switchgear, transformer, and grip of the high-voltage distribution lines are connected to the grounding electrode. However, in this study, the ADL was connected only to the grounding poles at the starting and end points of the distribution line.  [10], [11], which estimates the DP from the time difference between the zero-crossing points of the currents measured by ammeters CT1 and CT2 installed at the starting point of each common earthing conductor when a disconnection occurs in a distribution line where the common earthing conductors of two adjacent distribution lines are connected only at their ends. The proposed method estimates the DP based on the time difference between the zero-crossing points of the currents measured at the starting point of a common earthing conductor. Similar to previous studies [10], [11], the change in the synthetic resistance and synthetic inductance of the common earthing conductor related to the disconnection caused by the change in the high-voltage line current after the disconnection are identified as factors that cause the time difference at the zero-crossing point when a disconnection occurs.

B. Theoretical Consideration
In the present study, one distribution line in a rural area was considered under the condition that the ammeters are installed at the starting and end points of the distribution line. We assume that the induced voltage (caused by the product of the mutual  inductance of the high-voltage line and ADL, and the zero-phase current of the high-voltage line) in the ADL at the time of disconnection is V d = V dm cos(ωt+ϕ 1 ), where V dm is the peak value, ω = 2πf, and ϕ 1 is the phase; the current flowing on the power supply side is I d = I dm cos(ωt+ϕ 2 ), where I dm is the peak value, ω = 2πf, and ϕ 2 is the phase. The equivalent circuit when AC voltage is applied to the RLC circuit is shown in Fig. 6. The distribution substation that supplies power to the distribution line is shown on the left of the figure; the resistance of the distribution substation was set to 1 Ω. The ground resistance of the utility pole depicted in Fig. 2 at the end of the distribution line was set as 65 Ω based on the technical guidelines for lightning protection in Japan, as shown in Fig. 6. CT1 and CT2 were installed as shown in Fig. 6. Here, R d and X d represent the resistance and impedance of the ADL, respectively. Therefore, the current flowing into the ADL flows from the right side to the left side of the diagram when a disconnection occurs; the voltage source is shown on the right side of the diagram. In addition, I d is obtained by dividing V d by (R d +jX d ), where j represents an imaginary number. The time difference between these zero-crossing points is attributed to the changes in X d and R d of the ADL, depending on the DP; the time difference between the zero-crossing points of the currents flowing in CT1 and CT2 with respect to the current flowing in CT2 is expressed by [10], [11] However, to calculate (2), θ d must be obtained from (3), which is obtained by calculating electric power P d ; it is given by where T Ps and T Pf indicate the P d integration start and end time, respectively. P d represents the average value of one cycle. R d and X d can be obtained by solving (3) for θ d and substituting it into (2); Δt d can be calculated by substituting these values into (1).

C. Factors Causing Changes in X d
In previous studies [10], [11], the change in the impedance of the ADL X d shown in Fig. 6 was large compared to that in R d obtained from (2) when a disconnection occurred. Here, X d is calculated using where ω = 2πf. L a represents the acting inductance of the ADL considering the interaction with the high-voltage line, and C l represents the capacitance between the ADL and ground. C l should not be considered because the impedance of C l becomes large (approximately several microfarads per kilometer).
Factors that cause L a to change before and after the disconnection are examined as follows: L a is calculated by dividing the sum of the number of magnetic fluxes ϕ s of the ADL and the number of magnetic fluxes ϕ m attributed to the mutual inductance between the ADL and high-voltage line by I d ; this is calculated using where ϕ s represents the product of the self-inductance L s of ADL and I d . ϕ s is calculated using ϕ m represents the product of each phase of the mutual inductance between the high-voltage line and ADL and high-voltage The mutual inductances of the phases of the high-voltage line, R, S, and T, and the ADL are expressed as L m-R , L m-S , and L m-T , respectively; the corresponding currents are I h-R , I h-S , and I h-T , respectively. Here I h0 represents the zero-phase current of the high-voltage three-wire line. Table I summarizes the mutual inductance of each phase of the high-voltage line calculated using the line constant calculation program Alternative Transient Program (ATP). Table I indicates that the mutual inductance of each phase of the high-voltage line and the ADL is almost equal, and it can be expressed as L m . Equations (5)-(7) can be summarized as By using the maximum values of I h0m and I dm in the analysis, the nature of the simulation results for before and after disconnection can be easily understood. x i in (8) is obtained as follows: where I dm and I h0m represent the peak values of I d and I h0 , respectively; x i represents the ratio of I dm and I h0m multiplied by cosθ hd obtained from the phase difference between I h0 and I d , so that x i represents the average value of one cycle; and T is and T if are the start and end time for calculating (9), respectively. From the relationship between (1), (4), and (8), the time difference at the zero-crossing point before and after the disconnection is caused by the change in the magnitude and phase of the zerophase current in the high-voltage line and the current flowing in the ADL.    by T1 to T10 are located every 1 km from the feed point of the distribution line. Nodes B2-1-B2-5 are located every 1 km from the branch point of the branch line originating at 2 km from the feed point. Nodes B8-1-B8-5 are located every 1 km from the branch point of the branch line originating at 8 km from the feed point. The high-voltage line is a three-phase three-wire system that has loads on the trunk and branch lines every 1 km. Switchgear with built-in sensors, known as information technology switchgear (ITSW), of the high-voltage line was installed at the feed point of the distribution line. An ADL was grounded at the starting and end points of the trunk line and each branch line. Two ammeters (CT1 and CT2) were installed to measure the current flowing at the starting and end points of the ADL. The grounding of the ADL shared the grounding resistance value of 1 Ω with the distribution substation at the starting point of the ADL, and grounding resistance was 65 Ω at the end point of the branch line, according to the lightning protection standards. Fig. 8 depicts that the ADL is installed 1.9 m below the high-voltage line. Table II summarizes the specifications of the high-voltage lines and ADL. Fig. 8 illustrates that the load of the distribution line is arranged at R1, R2, and R3 to a high-voltage V-connected three-phase transformer in this study. Further, the load under the conditions presented in Table III is set such that the magnitude of the three-phase current is balanced and unbalanced for each phase. The load from P2 to P4 in Table III modifies the resistance value between each phase from 1 Ω to 0.5 Ω. Furthermore, the load is installed on the low-voltage line, which is transformed  We used ATP simulation to perform a transient analysis of the power system. In the ATP simulations, we considered the distribution-line model shown in Fig. 7, wherein the disconnection occurs in the trunk and branch lines. The disconnection condition was obtained by setting the disconnected phase as the S-phase (Fig. 8), and the DP was set at every 1 km for the trunk and branch lines. The ATP simulation was performed in the time range 0.0-0.1 s at intervals of 10 −6 s, with a disconnection occurring at t = 0.05 s. Fig. 9(a) and (b) show the voltage and current waveforms, respectively, considering T1 and T5 of the distribution-line model (Fig. 7) based on load condition P1 (Table III) and disconnection at T5. Waveforms at T1 and T5 are represented by solid and dotted lines, respectively. As indicated in Fig. 9(a), the voltage waveform at T1 remains the same before and after the disconnection because the DP is on the load side of T1. The voltage waveform at T5 confirms that the magnitude of the voltage of the disconnected phase approximately halved and had a phase change of 180°after disconnection. This result is consistent with those in Fig. 4(b), which shows the voltage characteristics at the time of disconnection. Fig. 9(b) illustrates that the current waveform at T1 decreases as the current flowing from the DP to the load side decreases during disconnection. For the current waveform at T5, the current does not flow between the phase associated with the disconnected phase. Consequently, the current flows only to the load connected to the two phases that are not the disconnected phases; this resulted in a single-phase load, and the current exhibited a phase difference of 180°. Fig. 10 shows the voltage and current waveforms of T1 and B2-3 in the distribution-line model (Fig. 7) at the time of disconnection considering B2-3 under condition P1 (Table III). Fig. 10(a) indicates that the voltage waveform at T1 is not affected by the disconnection. In the voltage waveform at the load side of B2-3, the voltage of the disconnected phase is approximately halved, and the phase changes by 180°. This result is consistent with Fig. 4(b), which shows the voltage characteristics at the time of disconnection. According to Fig. 10(b), the current supplied to the load side from the DP decreases after the disconnection, which decreases the current flow in the  disconnected phase at T1. The current through the disconnected phase at DP B2-3 reaches zero, and the load connected to the two phases that were not disconnected became a single-phase load. Consequently, the current flowing between the two phases exhibited a phase difference of 180°.

B. Simulation Results
In the case of condition P1 (Table III), the DPs were set to T1, T3, T5, T7, and T9. Fig. 11 shows the corresponding simulation results. To ensure that I CT1 and I CT2 had the same magnitude, I CT2 was set to a value 10 times that of the simulation. The phases of the currents I CT1 and I CT2 changed before and after the disconnection. The time difference between the zero-crossing points of I CT1 and I CT2 before and after the disconnection is referred to as Δt td ; the relationship between Δt td and DPs is illustrated in Fig. 12. For the load conditions summarized in Table III, P1 is −, P2 is −, P3 is −, and P4 is − for Δt td before disconnection, and P1 is •, P2 is •, P3 is •, and P4 is • for Δt td after disconnection. As shown in Fig. 12, Δt td decreases as the DP moves farther from the distribution substation.
Similarly, under condition P1 (Table III), the DPs were set to B2-1, B2-3, B8-1, and B8-3. The results of the current flowing through CT1 and CT2 calculated using the ATP simulation are shown in Fig. 13. The current phases of I CT1 and I CT2 changed   before and after the disconnection. Here, the time difference between the zero-crossing points of I CT1 and I CT2 before and after the disconnection is denoted as the relationship between Δt bd and the DPs is illustrated in Fig. 14. The symbols used for Δt bd are identical to those used for Δt td in Fig. 12. As in the previous case, I CT2 was set to a value 10 times that in the simulation. We observed that Δt bd decreased as the distance of the DP from the branch point increased.
Figs. 12 and 14 validate that the DP can be estimated by measuring Δt td and Δt bd , respectively, at the time of disconnection. As shown in Fig. 14, the values of Δt bd are nearly identical when the disconnection occurs in the branch line from B2 and B8, which implies that the DP cannot be accurately identified.
To address this problem, a voltage sensor (VS) was installed on the load side of the branch point at B2 and B8, and the voltage waveform was measured during disconnection to distinguish the disconnected areas at B2 and B8. Fig. 15 displays the recommended VS arrangement, wherein the range of different sensors is ITSW1 (from T1 and T2), VS2 (from the load side of  (2) at the time of disconnection in the trunk line with respect to the DP under the P1 load condition. Table V lists the values of X d and R d at the time of branch-line disconnection. Here, V d and I d required in (2) represent the voltage in CT2 and the current in CT1 obtained from the ATP simulation conducted on the equivalent circuit shown in Fig. 6, respectively. Table IV indicates that X d is approximately 15% larger at T9 than that at T1. Conversely, R d is approximately 109% larger when the DP is at T9 than that at T1. Similarly, Table V validates that the change in X d is larger than that in R d . Fig. 12 illustrates the relationship between Δt td-cal (shown as ) obtained from (1) using X d and R d (Table IV) and Δt td obtained from the ATP simulation. Similarly, Fig. 14 illustrates the relationship between Δt bd-cal (shown as ) obtained from (1) using X d and R d (Table V) and Δt bd obtained from the ATP simulation. Based on Figs. 12 and 14, we determine that the values of Δt td-cal and Δt td and those of Δt bd-cal and Δt bd are nearly identical. Thus, Δt td and Δt bd are generated based on the changes in X d and R d before and after the disconnection.
Tables IV and V indicate that the change in X d is large relative to the change in R d . This implies that the change in X d before and after the disconnection is related to the generation of Δt td and Δt bd . For before and after the disconnection in each section of Fig. 7, x i should be evaluated because the value of the current changes significantly on power-supply and load sides of the DP; therefore, each section in Fig. 7 is denoted by N in the following discussion.
From (8), x i is related to the change in L a. The value of x i before and after the trunk-line disconnection for each section shown in Fig. 7 is expressed as x tN_B and x tN_A , respectively. Similarly, the value of x i before and after the branch-line disconnection can be expressed as x bN_B and x bN_A , respectively. Further, N is represented as T01 when N indicates the interval between T0 and T1. If N indicates the distance between B2-1 and  B2-2 on the branch line from T2, N is represented as B2-12; it is the same for the branch line from T8. Table VI(a) summarizes I dNm , I h0Nm , and cosθ hDN of the trunk line at the time of the trunk line disconnection at DP T1 under P1 load conditions. I dNm , I h0Nx , and cosθ hDN of the branch line are presented in Table VI(b). Here, I dN and I h0N represent the values obtained from the ATP simulations. Fig. 16(a) illustrates the relationship between the x tN_B and x tN_A of a trunk line obtained from (8) and the DP at the time of the trunk-line disconnection. Fig. 16(b) shows the relationship between x tN_B and x tN_A of the branch line and the DP. Similarly, Fig. 17(a) illustrates the relationship between x tN_B and x tN_A of the trunk line obtained from (8) and the DP at the time of the branch-line disconnection. Fig. 17(b) illustrates the relationship between x bN_B and x bN_A of the branch line and DP.
We used the results shown in Fig. 16(a) to analyze the tendency of x tN_A to the DP at the time of the trunk-line disconnection. At DP T1, no current flowed in the disconnected phase on the load side from the DP, and therefore, I h0T01m increased in this section, which in turn increased x t01_A . Conversely, I h0T01m at the T01 of the DP T9 is smaller than that of DP T1 because the load current flows up to T9. These results suggest that the current imbalance in the T01 section decreases, which reduces I h0T01m . Consequently, x t01_A decreases because of (8). The current flowing in the disconnected phase of the high-voltage line in T01 increases and I h0T01m decreases because the DP becomes longer. From (8), x t01_A decreases as the DP becomes longer. These results are consistent with the tendency observed in Fig. 16(a). The change in x tN_B at the branch line after the trunk-line disconnection is considered in Fig. 16(b). At DP T1, no current flowed in the branch-line disconnected phase in B2 and B8, and the current imbalance on the starting side of the distribution line increased to a value higher than that on the terminal side. Consequently, both I h0Nm and x bN_B increased. At the time of the disconnection from T2 to T7, the branch line from B2 remained unchanged before and after the disconnection. In addition, the current imbalance increased in the branch line from B8 because no current flowed in the disconnected phase; this phenomenon increased the value of x bN_B . In DPs T9 and T10, the branch lines of B2 and B8 were not influenced by the disconnection. Therefore, x bN_B did not vary before and after their disconnection. Δt td of DP T1 with a large change in L aN (∼ x tN_A ) before and after the disconnection from Fig. 16(a) and (b) increases because L a represents the sum of the acting inductance of each section L aN in Fig. 7. Further, Δt td decreases because the DP becomes longer and the change in L a after disconnection decreases.
We analyzed the tendency of x bN_A in the trunk line at the time of the branch disconnection using Fig. 17(a). The range of the trunk-line current influenced by DP B2-1 was T01 and T12. At the time of the disconnection at DP B2, the current flowing in the disconnected phase from the branch point increased with an increase in the distance of the DP from the branch point. Therefore, the current imbalance flowing through T01 and T12 decreased with an increase in the distance of the DP from the branch point; the values of x b01_A and x b12_A decreased. In addition, we analyzed the tendency of x bN_A in the branch line at the time of the branch-line disconnection, as depicted in Fig. 17(b). At the time of the disconnection in DP B2-1, no current flowed in the disconnected phase. Therefore, the current imbalance increased, which in turn increased x b01_A . The current flowing through the disconnected phase increased with an increase in the distance from the branch point to the DP; this reduced the current imbalance of B2-01. Thus, x bN_A decreased with an increase in the distance of the DP. Because the branch line from B8 was not influenced by the disconnection at the branch line of B2, x bN_B and x bN_A remained unchanged before and after the disconnection. During the disconnection at the branch line from B8, the tendency remained identical to that observed for the disconnection that occurred at B2. For branchline disconnections, L a represents the sum of L aN (∼x bN_A ) in each section, and therefore, Δt bd is larger for B2-1 and B8-1 disconnections, as shown in Fig. 17(a) and (b). In addition, Δt bd decreases with an increase in the DP from the branch point and a decrease in the change in L a after the disconnection.
Therefore, the results indicated that the change in Δt td and Δt bd after the disconnection could be explained by the change in X d shown in (4).

A. Advantages of the Proposed Method
Currently, two methods are used to estimate DPs: (a) a method in which a detection device ITSW is installed on the distribution line to specify the DP [12], [13], [14], and (b) a method using a smart meter [8].
The advantages of the proposed method using an ADL are discussed and compared with the aforementioned methods. Fig. 18 illustrates the method using ITSWs as an example. As shown in Fig. 18, only a few ITSWs can acquire the voltage and current information in a distribution line. For instance, when a disconnection occurs between ITSW2 and ITSW3, the voltage information of ITSW2 on the power-supply side of the DP and ITSW3 after the DP reveals that the disconnected section is between them. The proposed ADL-based method, which can be used to estimate the DP of the trunk and branch line instead of the disconnected section from the time difference of the zero-crossing points, is illustrated in Figs. 12 and 14.
The method using smart meters is illustrated in Fig. 18. We assumed that smart meters are installed at different locations (load points). For example, if the DP occurs between T5 and T6, no abnormal voltage is generated in the smart meter at T3 on the power-supply side of the DP; however, an abnormal voltage is generated at the end side of the DP. This result indicates that the disconnected section is on the terminal side of T3. The proposed method can estimate DPs regardless of the presence of a smart meter, as shown in Figs. 12 and 14. The installation of the ITSW can be omitted if the voltage information obtained from the VS proposed in this method can be replaced by the information obtained from the smart meter. The disconnected section can be narrowed down by the smart meter, and the DP can be identified using the proposed method, thereby improving the cost-effectiveness.

B. Application of Proposed Method to Actual Equipment
To apply the proposed method in practice, a prior simulation is necessary to link the time difference between the zero-crossing and the DP. The management of distribution-line facilities is increasingly performed within systems such as servers, and therefore, highly accurate simulations are expected when using these facility data. The steps for the application of the proposed method to a real field are as follows: Step 1: The relationship between Δt td and Δt bd is determined with respect to DP by simulation using the load bias of the target distribution line as a parameter.
Step 2: The disconnected section is identified by obtaining voltage information from VS information.
Step 3: Δt td or Δt bd are calculated from the time difference between I CT1 and I CT2 at the time of the disconnection.
Step 4: Δt td or Δt bd obtained at the time of disconnection and the result obtained in Step 1 are compared to estimate the DP.
The DP can be estimated using this procedure. The current values in distribution lines change as the use of electricity changes during the day. This method is applicable even when the current flowing in the distribution line is approximately halved [10]. V d in Fig. 6 depends on the magnitude of I h0 , and as I h0 decreases, V d decreases, resulting in a relationship where I d also decreases. From (8), the reason for the occurrence of Δt td and Δt bd can be attributed to x i , which is an element of L a . I dm and I h0m both decrease with a decrease in the current flowing in the high-voltage line. Therefore, x i does not depend only on the magnitude of the high-voltage-line current.
We examined the time resolution of the ammeters (CT1 and CT2) required to construct the system. The distance between the utility poles was approximately 40 m, and based on our field experience, we determined that an estimation accuracy of approximately 100 m (two to three utility poles) would be required to reduce the time required to identify the DP. By comparing Figs. 12 and 14, the value of Δt td per km at the time of the trunk-line disconnection was found to be smaller than that at the time of the branch-line disconnection.
As the DP increased by 1 km, Δt td decreased by approximately 4 × 10 −5 s. The minimum time resolution required to estimate the DP with an accuracy of 100 m was 4 × 10 −6 s, which was 1/10 of 1 km. To improve the measurement accuracy, the time resolution was set to 1.0 × 10 −6 s, which was half of 2 × 10 −6 s truncated.
We developed a sensor switch that can realize time synchronization with a measurement frequency of several megahertz to ensure the time synchronization of CT1 and CT2. We used this switch to apply the method of using the time difference between the arriving ground-fault surge currents to the ground-fault point estimation of distribution lines. Furthermore, the time of the ammeters can be synchronized using a GPS.

VII. CONCLUSION
We developed an efficient DP estimation method using an ADL for long-distance distribution lines with branched lines. The proposed method requires the installation of ADL and VS equipment and two time-synchronized ammeters and estimates the point of disconnection from the time difference between the rise of the distribution line after the disconnection and the zerocrossing point of the current flowing through the two ammeters installed at the end of the line. Communication facilities must be constructed to transfer measurements of I CT1 and I CT2 . This method can be applied to general-purpose products that do not require the development of new equipment. Especially, in the case of distribution lines in rural areas over long distances, it takes significant time to determine the DP; therefore, it can be concluded that the proposed method, which can be constructed using general-purpose products, can effectively reduce the time required to identify the DP.
Furthermore, we investigated the factors that cause the time difference between the zero-crossing points before and after the disconnection. The procedure for applying the proposed method to the actual equipment and the time resolution required for the ammeters were analyzed. The proposed method can be used to achieve early DP detection, which can reduce power outage time and ensure public safety.
The proposed method should be validated in a facility close to the actual site to evaluate its field applicability in the future. To explore the applicability of the proposed method, the impact of load distribution in distribution lines needs to be evaluated, and the load magnitude should be varied at each point. The applicability of the proposed method in an event in which the load is randomly set also needs to be assessed.
We confirmed that the fault-point estimation method using the ADL could be applied to ground faults, short circuits, and the disconnection of distribution lines by ATP simulations; further, the proposed method can be considered an efficient maintenance method for distribution lines.