A method for fault location and ranging in distribution networks based on the basis pursuit algorithm

Abstract

This invention discloses a method for fault location and ranging in distribution networks based on the basis pursuit algorithm, comprising: collecting data such as the topology and branch admittance of the distribution network and numbering the nodes to construct a matrix of impedance magnitudes of the distribution network nodes; determining the location and number of voltage measurement nodes and judging whether a fault has occurred in the distribution network based on the changes in the voltage of the measured nodes; when a short-circuit fault occurs, constructing an underdetermined node voltage equation for solving the magnitude of the positive sequence current change of the nodes, solving it using the basis pursuit algorithm and validating it; and judging the location of the fault node based on the magnitude of the node current change. This method can solve the problem of short-circuit fault location in distribution networks when there are insufficient effective measurement points.

Description

Technical Field

[0001] This invention relates to the field of power system relay protection, specifically to a method for locating and measuring fault intervals in distribution networks based on a base pursuit algorithm. Background Technology

[0002] Rapid and accurate fault location in distribution networks is a prerequisite for timely isolation of faulty areas and restoration of power to non-faulty areas, and is of great significance for improving system reliability. Statistics show that over 80% of power grid faults occur on the distribution network side. With the integration of numerous distributed power sources into the distribution network, creating an active network with bidirectional flow of normal operating power and fault current, fault location has become more complex, rendering traditional location algorithms inapplicable. Furthermore, traditional fault location methods require strict data synchronization and high sampling frequencies; devices meeting these conditions are expensive, making many fault location methods impractical. Existing wide-area communication-based distribution network fault location methods can only pinpoint the minimum fault area between two measurement points. When the number of measurement points in the distribution network is limited, the located fault area is large, requiring a considerable amount of time to troubleshoot. Therefore, researching new technologies for accurate distribution network fault location that meet the requirements of insufficient measurement points is an urgent technical challenge. Summary of the Invention

[0003] The purpose of this invention is to provide a method for locating and measuring fault intervals in a distribution network based on a base-tracking algorithm. This method can accurately locate and measure the intervals of short-circuit faults based on the magnitude of the reconstructed node current change magnitude when a short-circuit fault occurs in the distribution network.

[0004] To achieve the above functions, this invention designs a method for fault location and ranging in distribution networks based on the basis pursuit algorithm, comprising the following steps:

[0005] Step 1: Collect the topology of the distribution network, collect relevant data, including branch admittance between each node, admittance between each node and the zero potential point, total number of nodes N, and number all nodes in the topology.

[0006] Step 2: Construct the node admittance matrix Y of the distribution network based on the branch admittances between each node and the admittances between each node and the zero potential point. N×N Through Y N×N The inverse matrix is ​​used to obtain the nodal impedance matrix Z. N×N and to Z N×N The nodal impedance magnitude matrix Z′ is obtained by taking the modulus of all elements in the matrix. N×N ;

[0007] Step 3: Determine the location and number M of voltage measurement nodes in the distribution network according to preset rules;

[0008] Step 4: Measure the voltage at each voltage measurement node to determine if a short circuit fault has occurred in the distribution network; if a short circuit fault is detected, proceed to Step 5; otherwise, repeat this step at a preset cycle.

[0009] Step 5: When a short-circuit fault occurs in the distribution network, calculate the positive sequence voltage change magnitude vector ΔU before and after the short-circuit fault at each voltage measurement node. M×1 ;

[0010] Step 6: Based on the nodal impedance magnitude matrix Z′ N×N Obtain the impedance magnitude matrix Z′ between each voltage measurement node and all nodes in the topology. M×N Based on the positive sequence voltage change magnitude vector ΔU before and after the short-circuit fault at each voltage measurement node M×1 The vector of positive sequence current change magnitude ΔI at each node N×1 Impedance magnitude matrix Z′ M×N Construct the underdetermined node voltage equations, where the magnitude vector of the positive sequence current change at each node is ΔI. N×1 The variable to be solved;

[0011] Step 7: For the underdetermined nodal voltage equations, transform them into an l1 norm optimization problem using the basis pursuit method;

[0012] Step 8: Solve for the vector of positive sequence current magnitude change ΔI at each node using the l1 norm optimization problem. N×1 The solution steps are as follows: First, transform the absolute value function in the l1 norm optimization problem into a function defined by two non-negative column vectors u. N×1 With v N×1 The problem is first expressed as a linear function; then, based on the linear function obtained by the transformation, the nonlinear l1 norm optimization problem is transformed into a linear programming problem; finally, the linear programming problem solution method is used to solve for the positive sequence current change magnitude vector ΔI of each node. N×1 ;

[0013] Step 9: Obtain the vector of positive sequence current change magnitude ΔI at each node. N×1 The magnitude values ​​of the positive sequence current changes at all nodes are processed to obtain the vector ΔI′ of the magnitude values ​​of the positive sequence current changes at each node. N×1 ;

[0014] According to ΔI′ N×1 To determine the magnitude of the positive sequence current change at each node, proceed to step 10, step 11, or step 12.

[0015] Step 10: ΔI′ N×1 If only one node has a non-zero positive sequence current change magnitude, then the location of that non-zero node is the fault location point, and the fault location judgment ends.

[0016] Step 11: ΔI′ N×1 If only two nodes have positive sequence current change magnitudes that are not zero, then the fault point is determined to be on the line between the two nodes, and the location of the fault point in the line section is calculated, thus ending the fault location judgment.

[0017] Step 12: ΔI′ N×1 When multiple nodes exhibit non-zero positive sequence current magnitudes, ΔI′ is selected. N×1 The node with the largest positive sequence current change magnitude is taken as the dominant node. The positive sequence current change magnitude of its upstream node is set to 0. Among all nodes downstream of the dominant node, the value of the node with the largest positive sequence current change magnitude remains unchanged, while the magnitudes of other nodes are 0. Then, step 11 is executed to calculate the fault location.

[0018] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0019] This invention designs a method for locating and measuring fault intervals in distribution networks based on a base-pursuit algorithm. It effectively solves the problem of locating short-circuit fault intervals in distribution networks when measurement points are insufficient. Furthermore, this invention is computationally simple, requiring only steady-state voltage values, avoiding the need for strict data synchronization and high sampling frequencies. It has wide applicability, requires fewer measurement points, is economical, and is unaffected by false fault points. This invention can accurately locate and measure fault intervals in distribution networks, effectively reducing the manpower and material resources needed for fault diagnosis and improving the level of distribution automation. Attached Figure Description

[0020] Figure 1 This is a flowchart of a method for locating and measuring fault sections in a distribution network based on a base pursuit algorithm, provided by an embodiment of the present invention.

[0021] Figure 2 This is a schematic diagram of the IEEE 33-node topology provided according to an embodiment of the present invention;

[0022] Figure 3(a) is a schematic diagram of the changes in positive sequence current at each node when a two-phase AB short circuit occurs at node 2 according to an embodiment of the present invention.

[0023] Figure 3(b) is a schematic diagram of the changes in positive sequence current at each node when a two-phase AB short circuit occurs at node 5 according to an embodiment of the present invention.

[0024] Figure 4 This is a schematic diagram of the positive sequence current changes at each node when a three-phase short circuit occurs at 20% of section 3-4 according to an embodiment of the present invention.

[0025] Figure 5This is a schematic diagram of the changes in positive sequence current at each node when a two-phase A / B short circuit occurs at 20% of section 5-25 according to an embodiment of the present invention. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0027] Reference Figure 1 This invention provides a method for fault location and ranging in distribution networks based on the base pursuit algorithm, referring to... Figure 1 It includes the following steps:

[0028] Step 1: Collect the topology of the distribution network, collect relevant data, including branch admittance between each node, admittance between each node and the zero potential point, total number of nodes N, and number all nodes in the topology.

[0029] Step 2: Construct the node admittance matrix Y of the distribution network based on the branch admittances between each node and the admittances between each node and the zero potential point. N×N Through Y N×N The inverse matrix is ​​used to obtain the nodal impedance matrix Z. N×N and to Z N×N The nodal impedance magnitude matrix Z′ is obtained by taking the modulus of all elements in the matrix. N×N .

[0030] In step 2, the nodal admittance matrix Y of the distribution network N×N Through Y N×N The nodal impedance matrix Z obtained by taking the inverse matrix N×N , to Z N×N The nodal impedance magnitude matrix Z′ is obtained by taking the modulus values ​​of all elements in the matrix. N×N As shown in the following formula:

[0031]

[0032] Where: N is the total number of nodes in the distribution network topology, Y i·i Y is the self-admittance of the i-th node. i·j Z is the mutual admittance between the i-th node and the j-th node. j·j Z is the self-impedance of the j-th node. i·j Z′ is the mutual impedance between the i-th node and the j-th node. j·j Let Z′ be the self-impedance magnitude of the j-th node. i·j Let y be the magnitude of the mutual impedance between the i-th node and the j-th node. i·0 Let y be the branch admittance between the i-th node and the zero potential point. i·jLet be the branch admittance between the i-th node and the j-th node.

[0033] Step 3: Determine the location and number M of voltage measurement nodes in the distribution network according to preset rules;

[0034] In step 3, the voltage measurement nodes of the distribution network are divided into mandatory nodes and optional nodes. The locations of mandatory nodes are: nodes at the output of the distribution network reference power source; nodes with 3 or more branches; and the end nodes in the distribution network topology.

[0035] The location of the optional node is: the connection node between the branch or cable line and the overhead line whose length is less than the preset threshold.

[0036] The method for determining the number of voltage measurement nodes in a distribution network is as follows:

[0037]

[0038] In the formula: M is the number of voltage measurement nodes in the distribution network, P is 2 when judging a single fault and 4 when judging multiple faults; when the total number of mandatory nodes satisfies formula (2), M is the total number of mandatory nodes; when the total number of mandatory nodes does not satisfy formula (2), M is the total number of mandatory nodes plus some optional nodes until formula (2) is satisfied; when adding optional nodes also does not satisfy formula (2), nodes can be added arbitrarily until formula (2) is satisfied.

[0039] Step 4: Measure the voltage at each voltage measurement node, and determine whether a short circuit fault has occurred in the distribution network according to the following formula (3); if a short circuit fault has occurred in the distribution network, proceed to step 5; otherwise, repeat this step at a preset cycle.

[0040] U j·min ≤U z·d (3)

[0041] In the formula: U j·min Let U be the minimum line voltage at the j-th node, where U z·d For the setpoint, take U. z·d = (0.5~0.8)U N U N This is the system's rated line voltage.

[0042] Step 5: When a short-circuit fault occurs in the distribution network, calculate the positive sequence voltage change magnitude vector ΔU before and after the short-circuit fault at each voltage measurement node. M×1 The calculation method for the positive sequence voltage change magnitude of the j-th node is shown in equation (4):

[0043]

[0044] In the formula: The positive sequence measured voltage before the fault at the j-th node. The positive sequence measured voltage is the voltage after the j-th node fails.

[0045] Step 6: Based on the nodal impedance magnitude matrix Z′ N×N Obtain the impedance magnitude matrix Z′ between each voltage measurement node and all nodes in the topology. M×N Based on the positive sequence voltage change magnitude vector ΔU before and after the short-circuit fault at each voltage measurement node M×1 The vector of positive sequence current change magnitude ΔI at each node N×1 Impedance magnitude matrix Z′ M×N Construct the underdetermined node voltage equations, where the magnitude vector of the positive sequence current change at each node is ΔI. N×1 The variable to be solved.

[0046] The underdetermined node voltage equation constructed in step 6 is as follows:

[0047]

[0048] In the formula, ΔI j ΔU is the magnitude of the positive sequence current change at the j-th node; k Z′ represents the magnitude of the positive sequence voltage change before and after a short-circuit fault at the k-th voltage measurement node. k·j The mutual impedance magnitude between node j and voltage measurement node k is given.

[0049] Step 7: Since there are M known quantities in equation (5) and N quantities to be solved (N>M), ΔI cannot be obtained directly. j Therefore, for the underdetermined node voltage equation (5), it is transformed into an l1 norm optimization problem by using the basis pursuit method;

[0050] Step 7: For the underdetermined node voltage equation (5), the basis pursuit method is used to transform it into an l1 norm optimization problem as follows:

[0051]

[0052] In the formula: ||ΔI N×1 ||1 is ΔI N×1 The 1 norm, i.e., ΔI N×1 The sum of the absolute values ​​of all elements in the matrix; min‖ΔI N×1 ||1 is the objective function, i.e., ΔI N×1 Minimum of the 1-norm; stΔU M×1 =Z′ M×N ·ΔI N×1 Here are the constraints; ΔU M×1 Z′ is the vector of positive sequence voltage change magnitudes for all measurement nodes. M×NZ′ N×N The impedance magnitude matrix selected from the rows corresponding to the measurement nodes; ΔI N×1 Let be the vector of positive sequence current change magnitudes for all nodes to be solved.

[0053] Step 8: Solve for the vector of positive sequence current magnitude change ΔI at each node using the l1 norm optimization problem. N×1 The solution steps are as follows: First, transform the absolute value function in the l1 norm optimization problem into a function defined by two non-negative column vectors u. N×1 With v N×1 The problem is first expressed as a linear function; then, based on the linear function obtained by the transformation, the nonlinear l1 norm optimization problem is transformed into a linear programming problem; finally, the linear programming problem solution method is used to solve for the positive sequence current change magnitude vector ΔI of each node. N×1 .

[0054] In step 8, the positive sequence current magnitude vector ΔI at each node is solved using the l1 norm optimization problem. N×1 The specific methods are as follows:

[0055] Using the following formula, ||ΔI| N×1 The absolute value function in ||1 ​​is transformed into two non-negative column vectors u N×1 With v N×1 Linear functions represented by ;

[0056]

[0057] In the formula, |ΔI N×1 |for ΔI N×1 The vector c obtained by taking the absolute value of all its elements T It is a row vector of order 2N, with all elements being 1;

[0058] Based on the transformation of equation (7), the nonlinear l1 norm optimization problem of equation (6) can be transformed into a linear programming problem using the following equation (8):

[0059]

[0060] Using the simplex method in linear programming problem solving, we can solve equation (8) to obtain u. N×1 and v N×1 And calculate ΔI N×1 .

[0061] Step 9: Obtain the vector of positive sequence current change magnitude ΔI at each node. N×1 The magnitude values ​​of the positive sequence current changes at all nodes are processed to obtain the vector ΔI′ of the magnitude values ​​of the positive sequence current changes at each node. N×1 ;

[0062] According to ΔI′N×1 To determine the magnitude of the positive sequence current change at each node, proceed to step 10, step 11, or step 12.

[0063] Step 9 will solve for the vector of positive sequence current change magnitude ΔI at each node. N×1 The magnitude values ​​of the positive sequence current changes at all nodes are processed to be effective, where ΔI N×1 The effective processing method for the magnitude of the positive sequence current change at the j-th node is as follows (9):

[0064]

[0065] In the formula: ε is the allowable error value, ε=0.05I l·max I l·max ΔI is the maximum load current during normal operation of the distribution network. j Let ΔI be the magnitude of the positive sequence current change at the j-th node. j ′ is ΔI j The magnitude of the positive sequence current change at the j-th node after effective processing.

[0066] Step 10: ΔI′ N×1 If only one node has a non-zero positive sequence current change magnitude, then the location of that non-zero node is the fault location point, and the fault location judgment ends.

[0067] Step 11: ΔI′ N×1 If only two nodes have positive sequence current change magnitudes that are not zero, then the fault point is determined to be on the line between the two nodes, and the location of the fault point in the line section is calculated according to the following formula (10), thus ending the fault location judgment:

[0068]

[0069] Where: ΔI p ′ and ΔI q ′ is ΔI j The non-zero elements in ' are α, which is the ratio of the impedance of the fault point and the upstream measurement point to the line impedance of the measurement point adjacent to the fault point.

[0070] Step 12: ΔI′ N×1 When multiple nodes exhibit non-zero positive sequence current magnitudes, ΔI′ is selected. N×1 The node with the largest positive sequence current change magnitude is taken as the dominant node. The positive sequence current change magnitude of its upstream node is set to 0. Among all nodes downstream of the dominant node, the value of the node with the largest positive sequence current change magnitude remains unchanged, while the magnitudes of other nodes are 0. Then, step 11 is executed to calculate the fault location.

[0071] In step 12, ΔI′ N×1Each ΔI j If the magnitude of the positive sequence current change at multiple nodes is not zero, select ΔI′. N×1 The node with the largest positive sequence current change magnitude is taken as the dominant node, and the positive sequence current change magnitude of its upstream nodes is set to 0. Among all nodes downstream of the dominant node, the value of the node with the largest positive sequence current change magnitude remains unchanged, and the magnitudes of other nodes are 0, as shown in the following formula (11):

[0072]

[0073] Then continue with step 11 to calculate the location of the fault.

[0074] The following is a specific embodiment of the present invention:

[0075] A simulation diagram of the IEEE 33-node circuit was built using MATLAB / SIMULINK, with the circuit topology as follows: Figure 2 As shown. The sampling frequency of the simulation is 4kHz. The reference voltage at the beginning of the power network in the simulation is 12.66kV. The neutral point is not grounded and the total network load is 5084.26 + j2547.32 kVA. There are a total of 33 nodes, 32 branches, and 5 tie switch branches in the system. For the area between nodes 0 and 1, the line impedance is very small and can be regarded as the equivalent impedance of the power supply. Measurement points are installed at nodes 1, 2, 5, 17, 21, 24, and 32, a total of 7 locations. When generating the node admittance matrix, the reference node 0 needs to be removed. Therefore, the power saving admittance matrix is ​​of order 32, and the area that can be located is the 32 areas contained in nodes 1 to 32 in the distribution network.

[0076] (1) As shown in Figures 3(a) and 3(b), two fault points are set at nodes 2 and 5 in the example of this invention. The fault type is a two-phase short circuit of phases A and B. The location effect when the magnitude of the positive sequence current change at one node is not zero is discussed. As can be seen from Figure 3, when the fault occurs at node 2, after the positive sequence current change of each node is effectively processed, ΔI j Of the nodes, only ΔI2′ = 5611.66, while the magnitudes of the positive sequence current changes at the other nodes are all 0. Therefore, the fault location is node 2. When the fault occurs at node 5, there is a significant non-zero value among the positive sequence current changes at each node, corresponding to node 5. After validating the positive sequence current changes at each node, ΔI... j In the fault location analysis, only ΔI5′ = 1419.16, while the magnitude of the positive sequence current change at all other nodes is 0. The fault location result is node 5. The results after the above optimization process demonstrate that the fault location method is effective.

[0077] (2) Figure 4As shown, a fault point is set at 20% of section 3-4 in the example of this invention. The fault type is a three-phase short circuit. The positioning effect is discussed when the magnitude of the positive sequence current change at the two nodes is not zero. Figure 4 It can be seen that ΔI j There are two non-zero values, ΔI2′=4732.52 and ΔI5′=1645.10. Calculate α=0.2579. Based on the line impedance relationship, the location result is section 3-4, and the relative distance measurement error is 0.21%.

[0078] (3) Figure 5 As shown, a fault point is set at 20% of section 5-25 in the example of this invention. The fault type is a two-phase short circuit (AB phase). The positioning effect is discussed when the magnitude of the positive sequence current change at multiple nodes is not zero. Figure 4 It can be seen that ΔI j ΔI' has two non-zero values: ΔI2' = 20.39 and ΔI5' = 1956.04. 32 =14.43. At this time, node 5 is the dominant node, node 2 is its upstream node, and node 32 is its downstream node with the largest positive sequence current change magnitude. After setting the positive sequence current change magnitude of node 2 to 0, α = 0.0073 is calculated again. According to the line impedance relationship, the positioning result is section 5-25, and the relative distance measurement error is 0.47%.

[0079] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for locating and measuring fault intervals in a distribution network based on the basis pursuit algorithm, characterized in that: Includes the following steps: Step 1: Collect the topology of the distribution network, collect relevant data, including branch admittance between each node, admittance between each node and the zero potential point, total number of nodes N, and number all nodes in the topology. Step 2: Construct the node admittance matrix Y of the distribution network based on the branch admittances between each node and the admittances between each node and the zero potential point. N×N Through Y N×N The inverse matrix is ​​used to obtain the nodal impedance matrix Z. N×N and to Z N×N The nodal impedance magnitude matrix Z′ is obtained by taking the modulus of all elements in the matrix. N×N ; Step 3: Determine the location and number M of voltage measurement nodes in the distribution network according to preset rules; Step 4: Measure the voltage at each voltage measurement node to determine if a short circuit fault has occurred in the distribution network; if a short circuit fault is detected, proceed to Step 5; otherwise, repeat this step at a preset cycle. Step 5: When a short-circuit fault occurs in the distribution network, calculate the positive sequence voltage change magnitude vector ΔU before and after the short-circuit fault at each voltage measurement node. M×1 ; Step 6: Based on the nodal impedance magnitude matrix Z′ N×N Obtain the impedance magnitude matrix Z′ between each voltage measurement node and all nodes in the topology. M×N Based on the positive sequence voltage change magnitude vector ΔU before and after the short-circuit fault at each voltage measurement node M×1 The vector of positive sequence current change magnitude ΔI at each node N×1 Impedance magnitude matrix Z′ M×N Construct the underdetermined node voltage equations, where the magnitude vector of the positive sequence current change at each node is ΔI. N×1 The variable to be solved; Step 7: For the underdetermined node voltage equations, transform them into the basis pursuit method. Norm optimization problem; Step 8: Utilize Norm optimization problem: Solving the vector of positive sequence current magnitudes ΔI at each node. N×1 The solution steps are as follows: First, [the following steps are taken] The absolute value function in the norm optimization problem is transformed into two non-negative column vectors u N×1 With v N×1 The linear function is represented by [the transforming function]; secondly, based on the linear function obtained by the transformation, the nonlinear function is [transformed / represent ... The norm optimization problem is transformed into a linear programming problem; finally, the positive sequence current change magnitude vector ΔI at each node is obtained using the linear programming problem-solving method. N×1 ; Step 9: Obtain the vector of positive sequence current change magnitude ΔI at each node. N×1 The magnitude values ​​of the positive sequence current changes at all nodes are processed to obtain the vector ΔI′ of the magnitude values ​​of the positive sequence current changes at each node. N×1 ; According to ΔI′ N×1 To determine the magnitude of the positive sequence current change at each node, proceed to step 10, step 11, or step 12. Step 10: ΔI′ N×1 If only one node has a non-zero positive sequence current change magnitude, then the location of that non-zero node is the fault location point, and the fault location judgment ends. Step 11: ΔI′ N×1 If only two nodes have positive sequence current change magnitudes that are not zero, then the fault point is determined to be on the line between the two nodes, and the location of the fault point in the line section is calculated, thus ending the fault location judgment. Step 12: ΔI′ N×1 When multiple nodes exhibit non-zero positive sequence current magnitudes, ΔI′ is selected. N×1 The node with the largest positive sequence current change magnitude is taken as the dominant node. The positive sequence current change magnitude of its upstream node is set to 0. Among all nodes downstream of the dominant node, the value of the node with the largest positive sequence current change magnitude remains unchanged, while the magnitudes of other nodes are 0. Then, step 11 is executed to calculate the fault location.

2. The method for fault location and ranging in a distribution network based on the basis pursuit algorithm according to claim 1, characterized in that: In step 2, the nodal admittance matrix Y of the distribution network N×N Through Y N×N The nodal impedance matrix Z obtained by taking the inverse matrix N×N , to Z N×N The nodal impedance magnitude matrix Z′ is obtained by taking the modulus values ​​of all elements in the matrix. N×N As shown in the following formula: Where: N is the total number of nodes in the distribution network topology, Y i·i Y is the self-admittance of the i-th node. i·j Z is the mutual admittance between the i-th node and the j-th node. j·j Z is the self-impedance of the j-th node. i·j Z′ is the mutual impedance between the i-th node and the j-th node. j·j Let Z′ be the self-impedance magnitude of the j-th node. i·j Let y be the magnitude of the mutual impedance between the i-th node and the j-th node. i·0 Let y be the branch admittance between the i-th node and the zero potential point. i·j Let be the branch admittance between the i-th node and the j-th node.

3. The method for fault location and ranging in a distribution network based on the basis pursuit algorithm according to claim 2, characterized in that: In step 3, the voltage measurement nodes of the distribution network are divided into mandatory nodes and optional nodes. The locations of mandatory nodes are: nodes at the output of the distribution network reference power source; nodes with 3 or more branches; and the end nodes in the distribution network topology. The location of the optional node is: the connection node between the branch or cable line and the overhead line whose length is less than the preset threshold. The method for determining the number of voltage measurement nodes in a distribution network is as follows: In the formula: M is the number of voltage measurement nodes in the distribution network, P is 2 when judging a single fault and 4 when judging multiple faults; when the total number of mandatory nodes satisfies formula (2), M is the total number of mandatory nodes; when the total number of mandatory nodes does not satisfy formula (2), M is the total number of mandatory nodes plus some optional nodes until formula (2) is satisfied; when adding optional nodes also does not satisfy formula (2), nodes are added arbitrarily until formula (2) is satisfied.

4. The method for fault location and ranging in a distribution network based on the basis pursuit algorithm according to claim 3, characterized in that: The underdetermined node voltage equation constructed in step 6 is as follows: In the formula, ΔI j ΔU is the magnitude of the positive sequence current change at the j-th node; k Z′ represents the magnitude of the positive sequence voltage change before and after a short-circuit fault at the k-th voltage measurement node. k·j The mutual impedance magnitude between node j and voltage measurement node k is given.

5. The method for fault location and ranging in a distribution network based on the basis pursuit algorithm according to claim 4, characterized in that: Step 7 transforms the underdetermined node voltage equations into a basis pursuit method. The norm optimization problem is as follows: In the formula: ||ΔI N×1 ||1 is ΔI N×1 The 1 norm, i.e., ΔI N×1 The sum of the absolute values ​​of all elements in the array; min‖ΔI N×1 ||1 is the objective function, i.e., ΔI N×1 The minimum value of the 1-norm; stΔU M×1 =Z′ M×N ·ΔI N×1 These are constraints; ΔU M×1 Z′ is the vector of positive sequence voltage change magnitudes for all measurement nodes. M×N Z′ N×N The impedance magnitude matrix selected from the rows corresponding to the measurement nodes in the middle; ΔI N×1 Let be the vector of positive sequence current change magnitudes for all nodes to be solved.

6. The method for fault location and ranging in a distribution network based on the basis pursuit algorithm according to claim 5, characterized in that: Step 8 utilizes Norm optimization problem: Solving the vector of positive sequence current magnitudes ΔI at each node. N×1 The specific methods are as follows: Using the following formula, ||ΔI| N×1 The absolute value function in ||1 ​​is transformed into two non-negative column vectors u N×1 With v N×1 Linear functions represented by ; In the formula, |ΔI N×1 |for ΔI N×1 The vector obtained by taking the absolute value of all elements in c T It is a row vector of order 2N, with all elements being 1; Based on the transformation of equation (7), the nonlinear transformation of equation (6) is achieved using the following equation (8). The norm optimization problem is transformed into a linear programming problem: Using the simplex method in linear programming problem solving, we can solve equation (8) to obtain u. N×1 and v N×1 And calculate ΔI N×1 .

7. The method for fault location and ranging in a distribution network based on the basis pursuit algorithm according to claim 6, characterized in that: Step 9 will solve for the vector of positive sequence current change magnitude ΔI at each node. N×1 The magnitude values ​​of the positive sequence current changes at all nodes are processed to be effective, where ΔI N×1 The effective processing method for the magnitude of the positive sequence current change at the j-th node is as follows (9): In the formula: ε is the allowable error value, ε=0.05I l·max I l·max ΔI is the maximum load current during normal operation of the distribution network. j Let ΔI be the magnitude of the positive sequence current change at the j-th node. j ′ is ΔI j The magnitude of the positive sequence current change at the j-th node after effective processing.

8. The method for fault location and ranging in a distribution network based on the basis pursuit algorithm according to claim 7, characterized in that: In step 10, ΔI′ N×1 Each ΔI j If only one node has a non-zero positive sequence current change magnitude, then the location of that non-zero node is the fault location point, and the fault location judgment ends.

9. A method for locating and measuring fault intervals in a distribution network based on a base pursuit algorithm, as described in claim 7, characterized in that: In step 11, ΔI′ N×1 Each ΔI j If only two nodes have positive sequence current change magnitudes that are not zero, then the fault point is determined to be on the line between the two nodes, and the location of the fault point in the line section is calculated according to the following formula (10), thus ending the fault location judgment: Where: ΔI p ′ and ΔI q ′ is ΔI j The non-zero elements in ' are α, which is the ratio of the impedance of the fault point and the upstream measurement point to the line impedance of the measurement point adjacent to the fault point.

10. A method for locating and measuring fault intervals in a distribution network based on a base pursuit algorithm, as described in claim 7, characterized in that: In step 12, ΔI′ N×1 Each ΔI j If the magnitude of the positive sequence current change at multiple nodes is not zero, select ΔI′. N×1 The node with the largest positive sequence current change magnitude is taken as the dominant node, and the positive sequence current change magnitude of its upstream nodes is set to 0. Among all nodes downstream of the dominant node, the value of the node with the largest positive sequence current change magnitude remains unchanged, and the magnitudes of other nodes are 0, as shown in the following formula (11): Then continue with step 11 to calculate the location of the fault.

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