Single-phase grounding fault line location method for distribution network

Abstract

The present invention specifically relates to a method for locating single-phase grounding fault lines in a distribution network, belonging to the technical field of detecting faults in a distribution network. The present invention includes the following steps: collecting the zero-sequence voltage and arc suppression coil current of the distribution network, calculating and drawing a fault judgment curve based on the zero-sequence voltage and arc suppression coil current, and judging whether a single-phase grounding fault occurs in the distribution network by whether the fault judgment curve exceeds the first fault judgment threshold; after a single-phase grounding fault occurs in the distribution network, the zero-sequence current of n feeders of the distribution network is collected in real time and preprocessed, a fault line judgment curve is drawn through the preprocessed zero-sequence current, and the fault line of the distribution network is located through the fault line judgment curve. The present invention amplifies the difference between the faulty feeder and the normal feeder by means of signal preprocessing, thereby sensitively selecting the faulty line, and can quickly and accurately locate the line where the single-phase grounding fault occurs, greatly improving the safety of the distribution network.

Description

Technical Field

[0001] The present invention specifically relates to a method for locating single-phase grounding fault lines in a distribution network, belonging to the technical field of fault detection in a distribution network (G01R31 / 08). Background Art

[0002] Existing methods for locating single-phase grounding fault lines are mainly divided into active methods and passive methods. For active methods represented by the signal injection method, the injection of non-arc-suppression current will delay the input of the arc-suppression device and even increase the fault current, worsening the fault. Passive methods using steady-state signals all need to avoid a long transient process, lacking rapidity. Moreover, when there is a high-resistance fault, the change in the steady-state quantity is very small, making the line selection method prone to losing reliability. Therefore, passive line selection methods using transient characteristics have attracted more and more attention.

[0003] The Chinese invention patent with the application number CN202410979555.9 and the publication number CN118795277A, titled "Single-phase grounding fault line selection method for small current grounding system based on improved SVM", uses the VMD algorithm to extract transient zero-sequence current and the GOA-SVM to optimize the classifier for fault line selection. However, this method has the disadvantages of less training set data and vague physical meaning. The Chinese invention patent with the application number CN201911229871.X and the publication number CN110736900A, titled "A method for locating single-phase grounding faults in distribution lines based on direction traveling waves", uses the different directions of the initial traveling waves of the line for fault line selection. However, due to the short length and many branches of the distribution line, the traveling wave reflection is complex, and it is difficult to form obvious traveling waves in the case of high-resistance grounding faults. The traveling wave line selection method has certain limitations. Existing line selection technologies lack the ability to quickly and accurately detect within a few cycles after a fault occurs, and at the same time, they lack reliability in an asymmetric line system. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: how to quickly and accurately locate the fault line when a single-phase grounding fault occurs in the distribution network.

[0005] To solve the above technical problem, the technical solution proposed by the present invention is: a method for locating a single-phase grounding fault line in a distribution network, comprising the following steps:

[0006] Step 1: Set the judgment period T for single-phase grounding faults in the distribution network, and collect the zero-sequence voltage of the distribution network and the current flowing into the arc suppression coil once every sampling period within one judgment period T in real time, for a total of M times of collection, and collect the zero-sequence voltage of the distribution network and the current flowing into the arc suppression coil to respectively form the first zero-sequence voltage matrix U of the distribution network 01 and the arc suppression coil current matrix I L, as shown in the following formulas (1) and (2),

[0007] (1)

[0008] (2)

[0009] In formulas (1) and (2), are respectively the first zero-sequence voltage of the first distribution network, the first zero-sequence voltage of the second distribution network to the first zero-sequence voltage of the Mth distribution network, which are collected in real time at every other sampling period at the start time of the judgment period T of the distribution network, are respectively the first arc suppression coil current, the second arc suppression coil current to the Mth arc suppression coil current, which are collected in real time at every other sampling period at the start time of the judgment period T of the distribution network;

[0010] Substitute all the data in the first zero-sequence voltage matrix U of the distribution network 01 into the following formula (3) to calculate the first zero-sequence voltage change rate of the distribution network:

[0011] (3)

[0012] In formula (3), is the ath element in the first zero-sequence voltage matrix U of the distribution network 01 , is the change rate;

[0013] Form the first zero-sequence voltage change rate matrix of the distribution network with the M - 1 first zero-sequence voltage change rates calculated according to formula (3) , as shown in the following formula (4),

[0014] (4)

[0015] Step 2: Substitute the first zero-sequence voltage matrix U of the distribution network 01 , the arc suppression coil current matrix I L and the first zero-sequence voltage change rate matrix of the distribution network into the following formula (5) to calculate M - 1 fault judgment quantities,

[0016] (5)

[0017] In formula (5), and are respectively the total capacitance to ground and the total conductance to ground of the distribution network;

[0018] ​​Taking the M - 1 fault judgment quantities calculated by the formula (5) as the ordinate and the time corresponding to the M - 1 and the fault judgment force as the abscissa, a smooth curve is plotted and defined as the fault judgment curve;

[0019] If the fault judgment curve is entirely within the positive and negative first fault judgment thresholds, it indicates that no single - phase grounding fault occurs within the judgment period T, then return to step 1 to continue monitoring the distribution network;

[0020] If there is a part of the fault judgment curve that exceeds the positive and negative first fault judgment thresholds, it indicates that a single - phase grounding fault has occurred within the judgment period T. At this time, record the moment corresponding to the point where the fault judgment curve first exceeds the positive and negative first fault judgment thresholds, and define it as the start time t0 of the single - phase grounding fault, and continue with the following step 3;

[0021] Step 3: Starting from the start time of the single - phase grounding fault Start, every other sampling period Real - time collect the zero - sequence voltage of the distribution network and the zero - sequence currents of n feeders once, for a total of N times of collection, and collect the zero - sequence voltage of the distribution network and the zero - sequence currents of n feeders collected to form the second zero - sequence voltage matrix U 02 and the zero - sequence current matrix I0 of the distribution network, as shown in the following formulas (6) and (7) respectively:

[0022] (6)

[0023] In formula (6), are respectively the first second zero - sequence voltage, the second second zero - sequence voltage to the Nth second zero - sequence voltage of the distribution network collected in real - time starting from the start time of the single - phase grounding fault Start, every other sampling period of the distribution network;

[0024] (7)

[0025] In formula (7), are respectively the first zero - sequence current of the first feeder, the second zero - sequence current of the first feeder to the Nth zero - sequence current of the first feeder of the n feeders of the distribution network collected in real - time starting from the start time t0 of the single - phase grounding fault ; are respectively the first zero - sequence current of the second feeder, the second zero - sequence current of the second feeder to the Nth zero - sequence current of the second feeder of the n feeders of the distribution network collected in real - time starting from the start time t0 of the single - phase grounding fault ; 、 、… to respectively, starting from the single-phase grounding fault start time t0, every sampling period for the nth feeder among the n feeders of the distribution network the first zero-sequence current of the nth feeder, the second zero-sequence current of the nth feeder to the Nth zero-sequence current of the nth feeder collected in real time;

[0026] Step 4: Substitute all the data in the second zero-sequence voltage matrix U of the distribution network 02 into the following formula (8) to calculate the second zero-sequence voltage change rate of the distribution network:

[0027] (8)

[0028] In formula (8), is the jth element in the second zero-sequence voltage matrix U of the distribution network 02 , is the change rate;

[0029] Form the second zero-sequence voltage change rate matrix of the distribution network with the N-1 second zero-sequence voltage change rates calculated according to formula (8) , as shown in the following formula (9):

[0030] (9)

[0031] Step 5: Preprocess all the data in the first N-1 columns of the zero-sequence current matrix I0 through the second zero-sequence voltage matrix U of the distribution network 02 and the second zero-sequence voltage change rate matrix . The preprocessing formula is as shown in the following (10):

[0032] (10)

[0033] In formula (10), is the natural unbalanced current of the kth feeder among the n feeders of the distribution network when the jth zero-sequence current is collected in real time; and are respectively the grounding conductance and grounding capacitance of the kth feeder among the n feeders of the distribution network;

[0034] Collect the N-1 zero-sequence currents after preprocessing for each of the n feeders of the distribution network to form the preprocessed zero-sequence current sequence of the n feeders, as shown in the following formula (11):

[0035] (11)

[0036] Taking the N - 1 pre - processed zero - sequence currents in the pre - processed zero - sequence current sequence of n feeders in formula (11) as the ordinate, and taking the acquisition times corresponding to the N - 1 pre - processed zero - sequence currents in the pre - processed zero - sequence current sequence of n feeders as the abscissa, draw n smooth curves, which are defined as the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve in turn;

[0037] Substitute the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve into the following formula (12) for judgment,

[0038] (12)

[0039] In formula (12), is the vth fault line judgment curve among the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve; is the second fault judgment threshold;

[0040] The distribution network feeder corresponding to the fault line judgment curve that satisfies the above formula (12) is a normal line; the distribution network feeder corresponding to the fault line judgment curve that does not satisfy the above formula (12) is a fault line.

[0041] Advantages of the present invention: The present invention proposes a method for locating the line of single - phase grounding faults in a distribution network. By means of signal pre - processing, the difference between the fault feeder and the normal feeder is amplified, and then the fault line can be sensitively selected, and the line where the single - phase grounding fault occurs can be quickly and accurately located, greatly improving the safety of the distribution network. Brief Description of the Drawings

[0042] Figure 1 is the flowchart of a method for locating the line of single - phase grounding faults in a distribution network according to the present invention.

[0043] Figure 2 is the simulation model diagram of the distribution network feeder in the embodiment of the present invention.

[0044] Figure 3 is the schematic diagram of the drawn fault judgment curve in the embodiment of the present invention.

[0045] Figure 4 is the schematic diagram of the drawn fault line judgment curve in the embodiment of the present invention. Detailed Embodiment

[0046] The following further describes a method for locating the line of single - phase grounding faults in a distribution network according to the present invention in combination with the drawings and specific embodiments

[0047] Embodiment

[0048] In this embodiment, a method for locating a line with a single-phase grounding fault in a distribution network is as follows Figure 1 shown, including the following steps:

[0049] Step 1: Set the judgment period T for the single-phase grounding fault in the distribution network. During one judgment period T, collect the zero-sequence voltage of the distribution network and the current flowing into the arc suppression coil once every sampling period in real time, for a total of M times of collection. Collect the zero-sequence voltage of the distribution network and the current flowing into the arc suppression coil and form the first zero-sequence voltage matrix U of the distribution network 01 and the arc suppression coil current matrix I L respectively, as shown in the following formulas (1) and (2):

[0050] (1)

[0051] (2)

[0052] In formulas (1) and (2), are the first zero-sequence voltage of the first distribution network, the second zero-sequence voltage of the second distribution network to the Mth zero-sequence voltage of the Mth distribution network collected in real time every sampling period at the start moment of the judgment period T of the distribution network respectively, and are the first arc suppression coil current, the second arc suppression coil current to the Mth arc suppression coil current collected in real time every sampling period at the start moment of the judgment period T of the distribution network respectively;

[0053] Substitute all the data in the first zero-sequence voltage matrix U of the distribution network 01 into the following formula (3) to calculate the first zero-sequence voltage change rate of the distribution network:

[0054] (3)

[0055] In formula (3), is the ath element in the first zero-sequence voltage matrix U of the distribution network 01 , is the change rate of;

[0056] Form the first zero-sequence voltage change rate matrix of the distribution network with the M - 1 first zero-sequence voltage change rates calculated according to formula (3), as shown in the following formula (4):

[0057] (4)

[0058] Step 2: The first zero-sequence voltage matrix U of the distribution network 01 , the arc suppression coil current matrix IL and the first zero-sequence voltage change rate matrix of the distribution network Substitute into the following formula (5) to calculate M - 1 fault judgment quantities,

[0059] (5)

[0060] In formula (5), and are respectively the total capacitance to ground and the total conductance to ground of the distribution network;

[0061] Taking the M - 1 fault judgment quantities calculated by formula (5) as the ordinate and the time corresponding to M - 1 and the fault judgment force as the abscissa, draw a smooth curve, which is defined as the fault judgment curve;

[0062] If the fault judgment curve is entirely within the positive and negative first fault judgment thresholds, it indicates that no single-phase grounding fault occurs within the judgment period T, then return to step 1 to continue monitoring the distribution network;

[0063] If there is a part of the fault judgment curve that exceeds the positive and negative first fault judgment thresholds, it indicates that a single-phase grounding fault has occurred within the judgment period T. At this time, record the moment corresponding to the point where the fault judgment curve first exceeds the positive and negative first fault judgment thresholds, and define it as the starting time t0 of the single-phase grounding fault, and continue with the following step 3;

[0064] Step 3: Starting from the starting time of the single-phase grounding fault Start, and collect the zero-sequence voltage of the distribution network and the zero-sequence current of n feeders once every sampling period in real time, and perform N collections in total. Collect the zero-sequence voltage of the distribution network and the zero-sequence current of n feeders collected to form the second zero-sequence voltage matrix U 02 and the zero-sequence current matrix I0 of the distribution network, as shown in the following formulas (6) and (7) respectively:

[0065] (6)

[0066] In formula (6), are respectively the first second zero-sequence voltage, the second second zero-sequence voltage to the Nth second zero-sequence voltage of the distribution network collected in real time starting from the starting time of the single-phase grounding fault of the distribution network and once every sampling period ;

[0067] (7)

[0068] In formula (7), are respectively the first feeder among the n feeders of the distribution network starting from the starting time t0 of the single-phase grounding fault and once every sampling period The first zero-sequence current, the second zero-sequence current to the Nth zero-sequence current of the first feeder collected in real time; They are respectively the second feeder among the n feeders of the distribution network starting from the single-phase grounding fault start time t0 at every other sampling period The first zero-sequence current, the second zero-sequence current to the Nth zero-sequence current of the second feeder collected in real time; 、 、… to They are respectively the nth feeder among the n feeders of the distribution network starting from the single-phase grounding fault start time t0 at every other sampling period The first zero-sequence current, the second zero-sequence current to the Nth zero-sequence current of the nth feeder collected in real time;

[0069] Step 4: Substitute all the data in the second zero-sequence voltage matrix U of the distribution network 02 into the following formula (8) to calculate the change rate of the second zero-sequence voltage of the distribution network:

[0070] (8)

[0071] In formula (8), is the jth element in the second zero-sequence voltage matrix U of the distribution network 02 , is 's change rate;

[0072] Form the second zero-sequence voltage change rate matrix of the distribution network with the N-1 second zero-sequence voltage change rates calculated according to formula (8) , as shown in the following formula (9),

[0073] (9)

[0074] Step 5: Preprocess all the data in the first N-1 columns of the zero-sequence current matrix I0 through the second zero-sequence voltage matrix U of the distribution network 02 and the second zero-sequence voltage change rate matrix , and the preprocessing formula is as shown in the following (10):

[0075] (10)

[0076] In formula (10), is the natural unbalanced current of the kth feeder among the n feeders of the distribution network when collecting the jth zero-sequence current in real time; and are respectively the grounding conductance and grounding capacitance of the kth feeder among the n feeders of the distribution network;

[0077] Collect the N-1 zero-sequence currents after preprocessing for each of the n feeders in the distribution network to form the preprocessed zero-sequence current sequences for the n feeders, as shown in the following formula (11):

[0078] (11)

[0079] Taking the N-1 preprocessed zero-sequence currents in the preprocessed zero-sequence current sequences of the n feeders in formula (11) as the vertical coordinates, and the acquisition times corresponding to the N-1 preprocessed zero-sequence currents in the preprocessed zero-sequence current sequences of the n feeders as the horizontal coordinates, plot n smooth curves, which are successively defined as the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve;

[0080] Substitute the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve into the following formula (12) for judgment,

[0081] (12)

[0082] In formula (12), is the vth fault line judgment curve among the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve; is the second fault judgment threshold;

[0083] The distribution network feeder corresponding to the fault line judgment curve that satisfies the above formula (12) is a normal line; the distribution network feeder corresponding to the fault line judgment curve that does not satisfy the above formula (12) is a fault line.

[0084] Next, use MATLAB / Simulink simulation to verify the line selection method for single-phase grounding faults proposed by the present invention. The simulation model is a 10 kV medium-voltage power grid with 3 feeders, as Figure 2 shown. The zero-sequence parameters of each feeder are shown in Table 1. The arc suppression coil operates in an over-compensation state of 15%, with a size of 0.2196 H. A single-phase grounding fault with a grounding resistance of 8000 Ω is set for phase A of line 1 at 0.13 s.

[0085]

[0086] Table 1

[0087] Verification of the fault line selection method: Starting from 0 s, collect the zero-sequence voltage and the arc suppression coil current of the distribution network. The sampling time is 0.08 ms, and it is judged whether a single-phase grounding fault occurs in the system every 0.02 s. Using the collected zero-sequence voltage and the arc suppression coil current, calculate the waveform of the fault judgment curve, as Figure 3As shown, the system is judged to have no fault before 0.12 s. Between 0.12 s and 0.14 s, the curve exceeds the threshold, indicating that a single-phase grounding fault occurs in the system during this period. At the same time, the time when it first exceeds the threshold is 0.13 s, indicating that the fault time of the system is 0.13 s. During the period from 0.13 s to 0.18 s, the zero-sequence voltage of the system and the zero-sequence currents of three lines are collected. The sampling time is 0.08 ms. After the zero-sequence current is preprocessed, the preprocessed zero-sequence current waveform is obtained, as Figure 4 shown. Only the zero-sequence current of Line 1 after preprocessing exceeds the threshold, and it is the faulty line.

Claims

1. A line positioning method for single-phase grounding faults in a distribution network, characterized in that: Including the following steps: Step 1: Set the judgment period T for single-phase grounding faults in the distribution network. Every other sampling period T within one judgment period T c The zero-sequence voltage of the distribution network and the current flowing into the arc suppression coil are collected in real time once. A total of M collections are made, and the collected zero-sequence voltage of the distribution network and the current flowing into the arc suppression coil are collected respectively to form the first zero-sequence voltage matrix U of the distribution network 01 and the arc suppression coil current matrix I L , as shown in the following formulas (1) and (2), U 01 = [u 01 (1), u 01 (2),..., u 01 (M)] (1) I L = [i L (1), i L (2),..., i L (M)] (2) In formulas (1) and (2), u 01 (1), u 01 (2),... to u 01 (M) are respectively the first zero-sequence voltages of the first distribution network, the second zero-sequence voltages of the second distribution network to the first zero-sequence voltages of the Mth distribution network collected in real time at every other sampling period T starting from the start time of the judgment period T c ; i L (1), i L (2),... to i L (M) are respectively the first arc suppression coil currents, the second arc suppression coil currents to the Mth arc suppression coil currents collected in real time at every other sampling period T starting from the start time of the judgment period T c ; Substitute all the data in the first zero-sequence voltage matrix U of the distribution network 01 into the following formula (3) to calculate the first zero-sequence voltage change rate of the distribution network: In formula (3), u 01 (a) is the a-th element of the first zero-sequence voltage matrix U of the distribution network 01 in, Λu 01 (a) is the change rate of the said u 01 (a); The M - 1 first zero - sequence voltage change rates calculated according to formula (3) form the first zero - sequence voltage change rate matrix ΛU of the distribution network 01 , as shown in the following formula (4) ΛU 01 = [Λu 01 (1), Λu 01 (2),..., Λu 01 (M - 1)] (4) Step 2: Substitute the first zero-sequence voltage matrix U of the distribution network 01 , the arc suppression coil current matrix I L and the first zero-sequence voltage change rate matrix ΛU of the distribution network 01 into the following formula (5) to calculate M-1 fault judgment quantities A(a) = -G ∑ u 01 (a) - C ∑ Λu 01 (a) - i L (a), a = 1, 2,..., M - 1 (5) In formula (5), C ∑ and G ∑ are respectively the total capacitance to ground and the total conductance to ground of the distribution network; Taking the M-1 fault judgment quantities calculated by the formula (5) as the ordinate and the time corresponding to the M-1 and the fault judgment force as the abscissa, draw a smooth curve, which is defined as the fault judgment curve; If the fault judgment curve is entirely within the positive and negative first fault judgment thresholds, it indicates that there is no single-phase grounding fault in the judgment period T, and then return to step 1 to continue monitoring the distribution network; If there is a part of the fault judgment curve that exceeds the positive and negative first fault judgment thresholds, it indicates that a single-phase grounding fault has occurred in the judgment period T. At this time, record the moment corresponding to the point where the fault judgment curve first exceeds the positive and negative first fault judgment thresholds, and define it as the start time t0 of the single-phase grounding fault, and continue with the following step 3; Step 3: Starting from the single-phase ground fault starting time t0, every other sampling period T c The zero-sequence voltage of the distribution network and the zero-sequence currents of n feeders are collected in real time once. A total of N collections are performed, and the collected zero-sequence voltage of the distribution network and the zero-sequence currents of n feeders are collected to form a second zero-sequence voltage matrix U 02 and a zero-sequence current matrix I0, as shown in the following formulas (6) and (7) respectively: U 02 = [u 02 (1), u 02 (2),..., u 02 (N)] (6) In formula (6), u 02 (1), u 02 (2),... to u 02 (N) are respectively the second zero-sequence voltages of the first distribution network, the second zero-sequence voltages of the second distribution network to the second zero-sequence voltages of the Nth distribution network, which are collected in real time at every sampling period T starting from the single-phase grounding fault start time t0 of the distribution network c ; In formula (7), i 01 (1), i 01 (2),... to i 01 (N) are respectively the first zero-sequence current, the second zero-sequence current to the Nth zero-sequence current of the first feeder among the n feeders of the distribution network, which are collected in real time at intervals of one sampling period T starting from the single-phase grounding fault starting time t0 c ; i 02 (1), i 02 (2),... to i 02 (N) are respectively the first zero-sequence current, the second zero-sequence current to the Nth zero-sequence current of the second feeder among the n feeders of the distribution network, which are collected in real time at intervals of one sampling period T starting from the single-phase grounding fault starting time t0 c ; i 0n (1), i 0n (2), … to i 0n (N) are respectively the first zero-sequence current, the second zero-sequence current to the Nth zero-sequence current of the nth feeder among the n feeders of the distribution network, which are collected in real time at intervals of one sampling period T starting from the single-phase grounding fault starting time t0 c ; Step 4: Substitute all the data in the second zero-sequence voltage matrix U of the distribution network 02 into the following formula (8) to calculate the second zero-sequence voltage change rate of the distribution network: In Equation (8), u 02 (j) is the j-th element in the second zero-sequence voltage matrix U 02 of the distribution network, and ΛU 02 (j) is the change rate of the u 02 (j); The N - 1 second zero - sequence voltage change rates calculated according to formula (8) form the second zero - sequence voltage change rate matrix ΛU of the distribution network 02 , as shown in the following formula (9) ΛU 02 = [Λu 02 (1), Λu 02 (2),..., Λu 02 (N - 1)] (9) Step 5: Preprocess all data in the first N - 1 columns of the zero - sequence current matrix I0 through the second zero - sequence voltage matrix U of the distribution network 02 and the second zero - sequence voltage change rate matrix ΛU 02 The preprocessing formula is as shown in the following formula (10): Υi 0k (j) = i 0k (j) - i bdk (j) - G k u 02 (j) - C k Λu 02 (j), k = 1, 2,..., n, j = 1, 2,..., N - 1 (10) In formula (10), i bdk (j) is the natural unbalanced current of the k-th feeder among the n feeders of the distribution network when the j-th zero-sequence current is collected in real time; G k and C k are respectively the grounding conductance and grounding capacitance of the k-th feeder among the n feeders of the distribution network; Collect the N-1 preprocessed zero-sequence currents of each of the n feeders of the distribution network to form the preprocessed zero-sequence current sequences of the n feeders, as shown in the following formula (11): Taking the N-1 preprocessed zero-sequence currents in the preprocessed zero-sequence current sequences of the n feeders in the formula (11) as the ordinate and the acquisition time corresponding to the N-1 preprocessed zero-sequence currents in the preprocessed zero-sequence current sequences of the n feeders as the abscissa, draw n smooth curves, which are sequentially defined as the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve; Substitute the first fault line judgment curve, the second fault line judgment curve to the nth fault line judgment curve into the following formula (12) for judgment, -δ2≤f v (t)≤δ2, v = 1, 2, 3, ..., n (12) In formula (12), f v (t) is the v-th fault line judgment curve among the first fault line judgment curve, the second fault line judgment curve to the n-th fault line judgment curve; δ2 is the second fault judgment threshold; the distribution network feeder corresponding to the fault line judgment curve that satisfies the above formula (12) is a normal line; the distribution network feeder corresponding to the fault line judgment curve that does not satisfy the above formula (12) is a fault line.

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