Expanded double-end power distribution network single-phase stable grounding fault distance measurement method and system

Abstract

The invention discloses an extended double-end power distribution network single-phase stable grounding fault distance measurement method and system, and the method comprises the steps: enabling a power distribution network line to be equivalent to a pi-type equivalent circuit, and obtaining line parameters; measuring points are arranged at the head and tail ends of each section of the power distribution network and are used for acquiring zero-sequence voltage and zero-sequence current signals at the head and tail ends of the section and judging whether a single-phase stable grounding fault occurs or not; if a single-phase stable grounding fault occurs in the power distribution network, positioning a fault section, taking the fault section as an initial section, and respectively expanding to the upstream and downstream of the fault section; and representing the zero-sequence voltage of the fault point by using the zero-sequence voltage and zero-sequence current measured at the head end and the tail end of the expanded section, simultaneously obtaining a distance equation and solving the distance equation to obtain the distance from the fault point to the head end of the fault section, and constructing a least square equation to solve the position of the fault point. The method has the advantages of good fault tolerance, high fault point positioning reliability and high positioning accuracy, and the system is simple and easy to implement.

Description

Technical Field

[0001] The invention belongs to the technical field of single-phase ground fault distance measurement in a distribution network, and specifically refers to a single-phase stable ground fault distance measurement method and system for an extended double-terminal distribution network. Background Art

[0002] The distribution network is the terminal link of the power system. It is responsible for delivering electricity from the transmission network to the end user and is an important bridge connecting power production and consumption. Single-phase grounding fault is the most common fault in the distribution network, and its frequency accounts for more than 70% of the distribution network faults. When a single-phase grounding fault occurs in the distribution network, if it is not handled in time, it will evolve into a more serious fault such as phase-to-phase short circuit. Therefore, reliable and accurate positioning of the fault point is the key to distribution network fault handling and maintenance.

[0003] The fault location methods of distribution networks mainly include traveling wave method, signal injection method, intelligent algorithm and impedance method. The traveling wave method is based on the voltage or current traveling wave generated when a fault occurs, and determines the fault point by detecting the signal arrival time difference. This method is easily interfered by noise during the propagation of the traveling wave signal, resulting in reduced positioning accuracy; the signal injection method determines the fault location by injecting a specific signal into the line and analyzing the response signal of the fault point. This method has high requirements for the operating conditions, load status and equipment health status of the power grid, and requires additional injection equipment and measurement devices, which increases the complexity of the system; intelligent algorithms include methods based on machine learning, artificial neural networks, support vector machines, fuzzy logic, etc. to analyze and predict the location of the fault point. This method requires a large number of samples for training, which is costly and complex. The impedance method is a fault distance measurement method based on the relationship between current, voltage and line impedance, including single-ended impedance method and double-ended impedance method. The existing single-ended impedance method is easily affected by the grounding resistance in the line and has poor accuracy, especially when the grounding resistance is large or the line is long and the line topology is complex. The positioning error may be large; although the double-ended impedance method is not affected by the grounding resistance and complex topology lines, in the case of damage to individual transformers, both the traditional single-ended impedance method and the double-ended impedance method may cause ranging failure, and the fault tolerance is not high, which in turn affects the accuracy of positioning. Summary of the invention

[0004] The object of the present invention is to provide a method and system for measuring the distance of a single-phase stable ground fault in an extended double-terminal distribution network. The method has good fault tolerance, high reliability and high positioning accuracy of the fault point, and the system is simple and easy to implement.

[0005] To achieve the above object, the present invention provides an extended double-terminal distribution network single-phase stable ground fault distance measurement method, which converts the distribution network line into a π-type equivalent circuit, comprising the following steps:

[0006] Step 1: Obtain zero-sequence voltage, zero-sequence current and line parameters at the beginning and end of each section of the fault line;

[0007] Step 2: judging whether a single-phase stable grounding fault occurs according to the zero-sequence voltage and zero-sequence current signals obtained in step 1;

[0008] Step 3: Take the fault section as the starting section, expand forward, the end of the fault section is used as the end of the forward expansion section, and the head end of each section upstream of the fault section is used as the head end of the forward expansion section; expand backward, the head end of the fault section is used as the head end of the backward expansion section, and the ends of each section downstream of the fault section are used as the ends of the backward expansion section; use the zero-sequence current and zero-sequence voltage at the head and end of the expansion section and the fault section to obtain the zero-sequence voltage at the fault point;

[0009] Step 4: Combine the zero-sequence voltage equation of the fault point obtained by the zero-sequence voltage and zero-sequence current at the beginning and end of each extended section and the fault section to obtain the distance X1, X2,…, X from the fault point to the beginning of the fault section. i ,…,X n ;

[0010] Step 5: Construct the least squares equation to solve the fault point location.

[0011] As a further solution of the present invention: the line parameters in step 1 include the line impedance per unit length Z0:

[0012] Z0=R0+jwL0(1)

[0013] Among them, R0 is the zero-sequence resistance of the line per unit length, j is the imaginary unit, w is the power frequency, and L0 is the zero-sequence inductance of the line per unit length.

[0014] As a further solution of the present invention: in step 2, if the obtained zero-sequence current signal is stable and continuous, it is determined that a single-phase stable grounding fault occurs in the distribution network, wherein the method for determining whether the zero-sequence current signal is stable and continuous is as follows:

[0015]

[0016] If I0(t) satisfies formula (2) three to five cycles after a single-phase grounding fault occurs in the distribution network, it is judged that a single-phase stable grounding fault occurs in the distribution network, where I0(t) is the zero-sequence current of the fault line, T is the system frequency cycle, ε is the stability error, and the ε value is 1%, which can be adjusted according to the actual situation of the distribution network.

[0017] As a further solution of the present invention: in step 3, define They are the zero-sequence voltages at the beginning and end of each extended section when expanding forward, are the zero-sequence voltages at the beginning and end of each extended section when expanding backwards, They are the zero-sequence currents at the beginning and end of each extended section when expanding forward, are the zero-sequence currents at the beginning and end of each extended section when expanding backwards, then are the zero-sequence voltages at the beginning and end of the fault section, are the zero-sequence currents at the beginning and end of the fault zone respectively;

[0018] When the end of the fault section is taken as the end of the extended section and the fault section is extended upstream, the zero-sequence voltage at the fault point derived from the head end of the extended section is:

[0019]

[0020] in, is the zero-sequence voltage at the fault point, x i is the distance from the head end of the extended section to the fault point, Y0 is the zero-sequence susceptance per unit length of the line, and its expression is:

[0021]

[0022] Where C0 is the zero-sequence capacitance per unit length of the line;

[0023] The zero-sequence voltage at the fault point derived from the end of the fault section is:

[0024]

[0025] Among them, L mn It indicates the length of the extended section when extending upstream of the fault section, that is, (L mn -x i ) represents the distance from the end of the fault section to the fault point;

[0026] Combining equation (4) with equation (5) yields the distance x from the head end of the extended section to the fault point: i ;

[0027] When the head end of the fault section is taken as the head end of the extended section and extended to the downstream of the fault section, the zero-sequence voltage of the fault point derived from the head end of the extended section is:

[0028]

[0029] Among them, x i ′ is the distance from the head end of the fault section to the fault point;

[0030] The zero-sequence voltage at the fault point derived from the end of the fault section is:

[0031]

[0032] Among them, L′ mnThe length of the extended section when extending downstream of the fault section;

[0033] Combining equation (6) and equation (7) we can get the distance x from the beginning of the fault section to the fault point: i ′;

[0034] When the fault section is taken as the original section, the zero-sequence voltage of the fault point derived from the head end of the fault section is:

[0035]

[0036] The zero-sequence voltage at the fault point derived from the end of the fault section is:

[0037]

[0038] Wherein, L is the length of the fault section;

[0039] Combining equations (8) and (9) we can get the distance x from the beginning of the fault section to the fault point: i ′.

[0040] As a further solution of the present invention: in the step 4, when the end of the faulty section is taken as the end of the extended section and the extension is performed upstream of the faulty section, the distance X from the head end of the faulty section to the fault point obtained by the combination is i for:

[0041] X i =x i -L s (10)

[0042] L s The distance from the beginning of the extended section to the beginning of the faulty section when the faulty section is extended forward;

[0043] When the fault section head end is taken as the head end of the extended section and extended to the downstream of the fault section, the distance X from the head end of the fault section to the fault point is obtained by combining i for:

[0044] X i =x i ′(11)

[0045] Because x i ′ is the distance from the beginning of the fault section to the fault point, so the fault location calculated by the fault section and the forward and backward expansion from the fault section can be expressed as:

[0046]

[0047] As a further solution of the present invention: in step 5, based on the obtained fault location X i , construct the following least squares equation:

[0048]

[0049] Where n is the number of expansion sections and fault sections, and the least squares equation is used to solve the fault point location X f , when f(X) reaches its minimum value, X=X f .

[0050] An extended double-terminal distribution network single-phase stable grounding fault distance measurement system, comprising an acquisition module, a fault judgment module, a fault location module and a calculation module;

[0051] The acquisition module is equipped with measuring devices at the beginning and end of each section of the distribution network to measure zero-sequence voltage and zero-sequence current;

[0052] The fault judgment module judges whether a single-phase stable grounding fault occurs according to the collected zero-sequence voltage and zero-sequence current;

[0053] The fault location module, if a single-phase stable grounding fault occurs, obtains the fault section and divides the upstream extension section and the downstream extension section based on the fault section;

[0054] The calculation module uses the collected zero-sequence voltage and zero-sequence current at the beginning and end of each extended section, substitutes them into the distance equation, and finally obtains the fault location X i Substitute into the least squares equation and calculate the fault point location X f .

[0055] As a further solution of the present invention: it also includes a computer device, which includes a memory and a processor, the memory stores a computer program that can be run on the processor, and the processor implements the steps of the above-mentioned extended two-terminal distribution network single-phase stable grounding fault distance measurement method when executing the computer program.

[0056] As a further solution of the present invention: it also includes a storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned extended double-terminal distribution network single-phase stable grounding fault distance measurement method are implemented.

[0057] Compared with the prior art, the present invention proposes a single-phase stable grounding fault ranging method and system for an extended double-terminal distribution network. Based on the impedance ranging technology, the zero-sequence voltage and zero-sequence current information of the fault section and the head and end of the extended section are used to construct a ranging equation from the head and end of the extended section to the fault point position, and the least square method is used to calculate the final fault point position. The proposed method has good fault tolerance. When a single transformer fails, other extended sections can still be used to accurately locate the fault point, thereby avoiding ranging failure caused by damage to a single transformer. The method is independent of the topological structure of the distribution network, can be well adapted to the distribution automation system, accurately locate the fault point, reduce power outage time, have high positioning accuracy, and high anti-interference performance. The system is simple and easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The present invention is a flow chart of a method for measuring single-phase stable ground fault in a distribution network with an extended double terminal.

[0059] Figure 2 is the zero-sequence equivalent circuit diagram of the fault line in the present invention; wherein, Figure 2 a is a zero-sequence equivalent circuit diagram of the fault line in the forward extension section of the present invention; Figure 2 b is a zero-sequence equivalent circuit diagram of the fault line in the backward expansion section of the present invention; Figure 2 c is the zero-sequence equivalent network diagram of the fault section in the present invention.

[0060] Figure 3 It is a schematic diagram of a simulation circuit in the present invention. DETAILED DESCRIPTION

[0061] The present invention is further described below in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0062] The invention discloses a method and system for measuring the distance of a single-phase stable grounding fault in a distribution network with an extended double end, comprising: converting a distribution network line into a π-type equivalent circuit to obtain line parameters; installing measuring devices at the head and the end of each section of the distribution network to collect zero-sequence voltage and zero-sequence current signals at the head and the end of the section and determine whether a single-phase stable grounding fault occurs; if a single-phase stable grounding fault occurs in the distribution network, locating the fault section, taking the fault section as the starting section, and respectively extending the fault section upstream and downstream; using the zero-sequence voltage and zero-sequence current measured at the head and the end of the extended section to represent the zero-sequence voltage of the fault point, jointly obtaining a distance equation and solving it, obtaining the distance from the fault point to the head end of the fault section, and constructing a least squares equation to solve the fault point position.

[0063] like Figure 1 As shown, a method for measuring the distance of a single-phase stable ground fault in a distribution network with an extended double terminal includes the following steps:

[0064] Step 1: Obtain zero-sequence voltage, zero-sequence current and line parameters at the beginning and end of each section of the fault line;

[0065] In this step, zero-sequence voltage transformers and zero-sequence current transformers are installed at the beginning and end of each section of the distribution network line to monitor and convert zero-sequence voltage and zero-sequence current into measurable electrical signals in real time. When a single-phase grounding fault occurs in the line, optical fiber communication or wireless communication is used to transmit the data in real time to the control center.

[0066] Line parameters include line impedance per unit length Z0:

[0067] Z0=R0+jwL0(1)

[0068] Where R0 is the zero-sequence resistance per unit length of the line, j is the imaginary unit, w is the power frequency, and L0 is the zero-sequence inductance per unit length of the line;

[0069] Step 2: judging whether a single-phase stable grounding fault occurs according to the zero-sequence voltage and zero-sequence current signals obtained in step 1;

[0070] In this step, if the obtained zero-sequence current signal is stable and continuous, it is determined that a single-phase stable grounding fault occurs in the distribution network. The method for determining whether the zero-sequence current signal is stable and continuous is as follows:

[0071]

[0072] If I0(t) satisfies formula (2) three to five cycles after a single-phase grounding fault occurs in the distribution network, it is judged that a single-phase stable grounding fault occurs in the distribution network, where I0(t) is the zero-sequence current of the fault line, T is the system frequency cycle, ε is the stability error, and the ε value is 1%, which can be adjusted according to the actual situation of the distribution network.

[0073] Step 3: Take the fault section as the starting section, expand forward, the end of the fault section as the end of the extended section, and the beginning of each section upstream of the fault section as the beginning of the extended section; expand backward, the beginning of the fault section as the beginning of the extended section, and the ends of each section downstream of the fault section as the ends of the extended section; use the zero-sequence current and zero-sequence voltage at the beginning and end of the extended section and the fault section to obtain the zero-sequence voltage at the fault point;

[0074] In this step, starting from the fault section, the extended section is divided into: taking the end of the fault section as the end of the extended section, extending forward, and the head ends of each section upstream of the fault section as the head end of the extended section; taking the head end of the fault section as the head end of the extended section, extending backward, and the ends of each section downstream of the fault section as the end of the extended section; the line is equivalent to a π-type equivalent circuit, and the zero-sequence voltage and zero-sequence current of the forward extended section, the backward extended section and the head and end of the fault section are used to calculate the zero-sequence voltage of the fault point in the line π-type equivalent circuit;

[0075] definition is the zero-sequence voltage at the beginning and end of each extended section when expanding forward, is the zero-sequence voltage at the beginning and end of each extended section when expanding backward, is the zero-sequence current at the beginning and end of each expansion section when expanding forward, is the zero-sequence current at the beginning and end of each extended section when expanding backward, then is the zero-sequence voltage at the beginning and end of the fault section, is the zero-sequence current at the beginning and end of the fault zone;

[0076] When the end of the fault section is taken as the end of the extended section and the fault section is extended upstream, the zero-sequence voltage at the fault point derived from the head end of the extended section is:

[0077]

[0078] in, is the zero-sequence voltage at the fault point, x i is the distance from the head end of the extended section to the fault point, Y0 is the zero-sequence susceptance per unit length of the line, and its expression is:

[0079]

[0080] Where C0 is the zero-sequence capacitance per unit length of the line;

[0081] The zero-sequence voltage at the fault point derived from the end of the fault section is:

[0082]

[0083] Among them, L mn It indicates the length of the extended section when extending upstream of the fault section, that is, (L mn -x i ) represents the distance from the end of the fault section to the fault point;

[0084] Combining equation (4) with equation (5) yields the distance x from the head end of the extended section to the fault point: i ;

[0085] It should be further explained that the zero-sequence equivalent network of the fault section is the starting section, the extended section and the fault section extending backward is as follows: Figure 2 As shown, it is stipulated that the direction of zero-sequence current flowing toward the fault point at the beginning and end of the section is the positive direction;

[0086] When the head end of the fault section is taken as the head end of the extended section and extended to the downstream of the fault section, the zero-sequence voltage of the fault point derived from the head end of the extended section is:

[0087]

[0088] Among them, x i ′ is the distance from the head end of the fault section to the fault point;

[0089] The zero-sequence voltage at the fault point derived from the end of the fault section is:

[0090]

[0091] Among them, L′ mn The length of the extended section when extending downstream of the fault section;

[0092] Combining equation (6) and equation (7) we can get the distance x from the beginning of the fault section to the fault point: i ′.

[0093] The fault section is the original section, and the zero-sequence voltage of the fault point derived from the head end of the fault section is:

[0094]

[0095] The zero-sequence voltage at the fault point derived from the end of the fault section is:

[0096]

[0097] Wherein, L is the length of the fault section;

[0098] Combining equations (8) and (9) we can get the distance x from the beginning of the fault section to the fault point: i ′.

[0099] Step 4: Combine the zero-sequence voltage equation of the fault point obtained by the zero-sequence voltage and zero-sequence current at the beginning and end of each extended section and the fault section to obtain the distance X1, X2, ..., X from the fault point to the beginning of the fault section. i ,…,X n ;

[0100] In this step, when the end of the faulty section is taken as the end of the extended section and the faulty section is extended upstream, the distance X from the head end of the faulty section to the fault point is obtained by combining i for:

[0101] Xi =x i -L s (10)

[0102] L s The distance from the beginning of the extended section to the beginning of the faulty section when the faulty section is extended forward;

[0103] When the fault section head end is taken as the head end of the extended section and extended to the downstream of the fault section, the distance X from the head end of the fault section to the fault point is obtained by combining i for:

[0104] X i =x i ′ (11)

[0105] Because x i ′ is the distance from the beginning of the fault section to the fault point, so the fault location calculated by the fault section and the forward and backward expansion from the fault section can be expressed as:

[0106]

[0107] Step 5: Construct the least squares equation to solve the fault point location;

[0108] In this step, based on the obtained fault location X i , construct the following least squares equation:

[0109]

[0110] Where n is the number of expansion sections and fault sections, and the least squares equation is used to solve the fault point location X f , when f(X) reaches its minimum value, X=X f .

[0111] The present invention proposes an extended double-terminal distribution network single-phase stable grounding fault distance measurement method. The distance measurement accuracy is not affected by the fault time and the initial phase angle of the fault, and the accuracy is high. Compared with the traditional impedance distance measurement method, the extended double-terminal impedance distance measurement method proposed by the present invention adopts current transformers and voltage transformers in multiple sections to collect data and calculate the fault position, avoiding the distance measurement failure caused by the failure of individual transformers to work due to damage. The algorithm is simple and easy to understand, and the distance measurement reliability is high, which has a wide range of practical application value.

[0112] The effectiveness and reliability of the present invention are verified below.

[0113] like Figure 3 As shown, the distribution network has four feeder lines, namely L1, L2, L3 and L4, all of which are overhead lines. Figure 3The small circles in the figure represent measuring devices. Zero-sequence current transformers and zero-sequence voltage transformers are installed at the beginning and end of each section of the distribution network. The single-phase stable grounding fault is set in the DE section on the L1 feeder. AE, BE, and CE are forward fault sections. DF, DG, and DH are backward extension sections. L1=20km, AB, BC, CD, EF, FG, and GH sections are all 2km, DE section is 8km, L2=10km, L3=10km, and L4=10km.

[0114] Taking the A-phase grounding fault in a single-phase stable grounding fault as an example, the A-phase grounding fault is set to occur at the DE end, the fault position and transition resistance are changed, and the A-phase grounding fault is set at 2km, 4km, and 6km away from the D end respectively, and the fault resistance R is set. f They are 100Ω, 500Ω, 1000Ω, and 3000Ω respectively, and the sampling frequency is 200KHz. The ranging results are shown in Table 1.

[0115] Table 1 Different fault locations and transition resistance R f The distance measurement results

[0116]

[0117]

[0118] It can be seen from Table 1 that when a single-phase grounding fault without transition resistance occurs at different fault locations, the distance measurement error of the present invention is within 1%, meeting the engineering measurement error requirement.

[0119] The above method is applied to the extended double-terminal distribution network single-phase stable ground fault distance measurement system, which includes an acquisition module, a fault judgment module, a fault location module and a calculation module;

[0120] The acquisition module installs measuring devices at the beginning and end of each section of the distribution network to measure zero-sequence voltage and zero-sequence current;

[0121] The fault judgment module judges whether a single-phase stable grounding fault occurs based on the collected zero-sequence voltage and zero-sequence current;

[0122] The fault location module obtains the fault section and divides it into an upstream extension section and a downstream extension section if a single-phase stable grounding fault occurs;

[0123] The calculation module uses the collected zero-sequence voltage and zero-sequence current at the beginning and end of each extended section to substitute into the distance equation, and finally obtains the fault location X i Substitute into the least squares equation and calculate the fault point location X f .

[0124] The system also includes a computer device, the computer device includes a memory and a processor, the memory stores a computer program that can be run on the processor, and the processor implements the steps of the above-mentioned extended double-terminal distribution network single-phase stable grounding fault distance measurement method when executing the computer program;

[0125] It also includes a storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned extended double-terminal distribution network single-phase stable grounding fault distance measurement method are implemented.

[0126] The above shows and describes the basic principle and main features of the present invention and the advantages of the present invention. The protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by technicians in the technical field on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for measuring the distance of a single-phase stable ground fault in a distribution network with an extended double terminal, characterized in that: The distribution network line is equivalent to a π-type equivalent circuit, including the following steps: Step 1: Obtain zero-sequence voltage, zero-sequence current and line parameters at the beginning and end of each section of the fault line; Step 2: judging whether a single-phase stable grounding fault occurs according to the zero-sequence voltage and zero-sequence current signals obtained in step 1; Step 3: Take the fault section as the starting section, expand forward, the end of the fault section is used as the end of the forward expansion section, and the head end of each section upstream of the fault section is used as the head end of the forward expansion section; expand backward, the head end of the fault section is used as the head end of the backward expansion section, and the ends of each section downstream of the fault section are used as the ends of the backward expansion section; use the zero-sequence current and zero-sequence voltage at the head and end of the expansion section and the fault section to obtain the zero-sequence voltage at the fault point; Step 4: Combine the zero-sequence voltage equation of the fault point obtained by the zero-sequence voltage and zero-sequence current at the beginning and end of each extended section and the fault section to obtain the distance X1, X2,…, X from the fault point to the beginning of the fault section. i ,…,X n ; Step 5: Construct the least squares equation to solve the fault point location.

2. The method for measuring the distance of a single-phase stable ground fault in a distribution network with an extended double terminal according to claim 1, characterized in that: The line parameters in step 1 include the line impedance per unit length Z0: Z0=R0+jwL0(1) Among them, R0 is the zero-sequence resistance of the line per unit length, j is the imaginary unit, w is the power frequency, and L0 is the zero-sequence inductance of the line per unit length.

3. The method for measuring the distance of a single-phase stable ground fault in a distribution network with an extended double terminal according to claim 1, characterized in that: In the step 2, if the obtained zero-sequence current signal is stable and continuous, it is determined that a single-phase stable grounding fault occurs in the distribution network, wherein the method for determining whether the zero-sequence current signal is stable and continuous is as follows: If I0(t) satisfies formula (2) three to five cycles after a single-phase grounding fault occurs in the distribution network, it is judged that a single-phase stable grounding fault occurs in the distribution network, where I0(t) is the zero-sequence current of the fault line, T is the system frequency cycle, ε is the stability error, and the ε value is 1%, which can be adjusted according to the actual situation of the distribution network.

4. The method for measuring the distance of a single-phase stable ground fault in a distribution network with an extended double terminal according to claim 1, characterized in that: In step 3, define are the zero-sequence voltages at the beginning and end of each extended section when expanding forward, are the zero-sequence voltages at the beginning and end of each extended section when expanding backwards, They are the zero-sequence currents at the beginning and end of each extended section when expanding forward, are the zero-sequence currents at the beginning and end of each extended section when expanding backwards, then are the zero-sequence voltages at the beginning and end of the fault section, are the zero-sequence currents at the beginning and end of the fault zone respectively; When the end of the fault section is taken as the end of the extended section and the fault section is extended upstream, the zero-sequence voltage at the fault point derived from the head end of the extended section is: in, is the zero-sequence voltage at the fault point, x i is the distance from the head end of the extended section to the fault point, Y0 is the zero-sequence susceptance per unit length of the line, and its expression is: Where C0 is the zero-sequence capacitance per unit length of the line; The zero-sequence voltage at the fault point derived from the end of the fault section is: Among them, L mn It indicates the length of the extended section when extending upstream of the fault section, that is, (L mn -x i ) represents the distance from the end of the fault section to the fault point; Combining equation (4) with equation (5) yields the distance x from the head end of the extended section to the fault point: i ; When the head end of the fault section is taken as the head end of the extended section and extended to the downstream of the fault section, the zero-sequence voltage of the fault point derived from the head end of the extended section is: Among them, x i ′ is the distance from the head end of the fault section to the fault point; The zero-sequence voltage at the fault point derived from the end of the fault section is: Among them, L′ mn The length of the extended section when extending downstream of the fault section; Combining equation (6) and equation (7) we can get the distance x from the beginning of the fault section to the fault point: i ′; When the fault section is taken as the original section, the zero-sequence voltage of the fault point derived from the head end of the fault section is: The zero-sequence voltage at the fault point derived from the end of the fault section is: Wherein, L is the length of the fault section; Combining equations (8) and (9) we can get the distance x from the beginning of the fault section to the fault point: i ′.

5. The method for measuring the distance of a single-phase stable ground fault in an extended double-terminal distribution network according to claim 1, characterized in that: In step 4, when the end of the faulty section is taken as the end of the extended section and the extension is made to the upstream of the faulty section, the distance X from the head end of the faulty section to the fault point is obtained by combining i for: X i =x i -L s (10) L s The distance from the beginning of the extended section to the beginning of the faulty section when the faulty section is extended forward; When the fault section head end is taken as the head end of the extended section and extended to the downstream of the fault section, the distance X from the head end of the fault section to the fault point is obtained by combining i for: X i =x i ′(11) Because x i ′ is the distance from the beginning of the fault section to the fault point, so the fault location calculated by the fault section and the forward and backward expansion from the fault section can be expressed as:

6. The method for measuring the distance of a single-phase stable ground fault in an extended double-terminal distribution network according to claim 1, characterized in that: In step 5, based on the obtained fault location X i , construct the following least squares equation: Where n is the number of expansion sections and fault sections, and the least squares equation is used to solve the fault point location X f , when f(X) reaches its minimum value, X=X f .

7. A system for extending a double-terminal distribution network single-phase stable ground fault distance measurement method according to any one of claims 1 to 6, characterized in that: It includes an acquisition module, a fault judgment module, a fault location module and a calculation module; The acquisition module is equipped with measuring devices at the beginning and end of each section of the distribution network to measure zero-sequence voltage and zero-sequence current; The fault judgment module judges whether a single-phase stable grounding fault occurs according to the collected zero-sequence voltage and zero-sequence current; The fault location module, if a single-phase stable grounding fault occurs, obtains the fault section and divides the upstream extension section and the downstream extension section based on the fault section; The calculation module uses the collected zero-sequence voltage and zero-sequence current at the beginning and end of each extended section, substitutes them into the distance equation, and finally obtains the fault location X i Substitute into the least squares equation and calculate the fault point location X f .

8. The extended double-terminal distribution network single-phase stable ground fault distance measurement system according to claim 7, characterized in that: It also includes a computer device, which includes a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and when the processor executes the computer program, the steps of the method described in any one of claims 1 to 6 are implemented.

9. The extended double-terminal distribution network single-phase stable ground fault distance measurement system according to claim 8, characterized in that: It also includes a storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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