Power distribution network cable fault positioning method based on limited DTU measuring point measurement data

Abstract

The invention relates to a power distribution network cable fault positioning method based on limited DTU measuring point measurement data, and the method comprises the steps: 1, enabling the positive-sequence injection current of a fault point to be equivalent to the virtual injection current of nodes at two ends of a fault region, and constructing a fault region judgment model; and 2, solving an underdetermined node voltage equation by using a compressed sensing theory to obtain virtual injection current and realize positioning of a fault area. According to the method, the fault area can be effectively positioned only through a small number of measuring points, the influence of fault types, transition resistance and load change factors is small, and the method has certain anti-noise capacity.

Description

Technical Field

[0001] The invention belongs to distribution network fault location, and in particular relates to a distribution network cable fault location method based on limited DTU measurement point measurement data. Background Art

[0002] The distribution network system has a complex structure and involves a large number of lines. Therefore, accurately locating the fault point after a fault has always been a challenge. At present, many distribution networks, especially cable lines, use terminal units (DTUs) in distribution automation to monitor fault currents and isolate fault areas. DTUs can collect and transmit data such as fault current, fault voltage, fault time, and switch status. The master station processes the data through this information and combines it with the corresponding fault location algorithm to quickly and accurately determine the fault location.

[0003] Existing fault location methods can be mainly divided into direct algorithms and indirect algorithms. Generally, both algorithms will first use DTU to determine whether the data in a certain area is faulty, and then further apply specific algorithms to locate the fault. The typical method of the direct algorithm is the matrix algorithm, which constructs a fault matrix based on the fault current information and distribution network topology provided by DTU, thereby calculating the minimized fault area. The recursive algorithm constructs a fitness function and optimizes the function using artificial intelligence algorithms (such as genetic algorithms, particle swarm optimization, ant colony algorithms, etc.) to achieve fault location. However, whether it is a direct algorithm or an indirect algorithm, the fault area it determines usually only involves the area covered by DTU. However, DTU cannot cover every node in the distribution network, so even if the fault area is isolated, a lot of manpower and material resources are still required for inspection. If the fault area can be further accurately narrowed, the troubleshooting time will be greatly reduced and the reliability of power supply will be improved. It is necessary to design a method that can achieve full-area fault location using only the measurement information of a small number of measurement points. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention proposes a method for locating cable faults in a distribution network based on measurement data of limited DTU measurement points.

[0005] The above-mentioned object of the present invention is achieved by the following technical solutions:

[0006] A method for locating cable faults in a distribution network based on limited DTU measurement point measurement data, comprising:

[0007] Step 1: Equivalent the positive sequence injection current of the fault point to the virtual injection current of the nodes at both ends of the fault area, and construct a model for fault area judgment;

[0008] Step 2: Then use the compressed sensing theory to solve the underdetermined node voltage equation, obtain the virtual injection current, and locate the fault area.

[0009] Furthermore, step 1 includes:

[0010] 1.1 The positive sequence fault voltage component is obtained by using the symmetrical component method, and the positive sequence fault voltage component of the node is calculated according to formula (1):

[0011]

[0012] In the formula, is the positive sequence fault voltage component at node i, is the voltage of node i before the fault, is the positive sequence voltage at node i after the fault, is the mutual impedance between node i and fault point f, is the positive sequence fault current; in the fault component positive sequence network, the fault current is only injected by the fault point, and there is no injection current in other nodes;

[0013] 1.2. Assume that there are N nodes in the distribution network and construct the node virtual injection current equation of the fault component positive sequence network I = Y·ΔU, see formula (2), where I is defined as the virtual injection current vector, Y is the node admittance matrix, and ΔU is the positive sequence fault voltage vector;

[0014]

[0015] 1.3. When the fault occurs on the line between nodes l and m, the value obtained by formula (2) is The actual injected current at node l is 0, and the following equation is obtained:

[0016]

[0017] Where: is the positive sequence fault voltage component of the fault point f, y is the ratio of the distance from the fault point f to the node l to the line, which is between 0 and 1;

[0018] 1.4 Comparing the two equations in equation (3), we can see that when y = 1, that is, when the fault point f is node m, is 0, and all other cases are not 0; when y=0, is 0, and is not 0 in other cases; at this time, the virtual injection currents of the remaining nodes are calculated, which are always 0; thus, a model for fault area judgment is obtained: if the virtual injection current between two nodes is not zero, then the area may be a fault area; if only one node has a non-zero virtual injection current, then the fault occurs at that node.

[0019] Furthermore, step 2 includes:

[0020] 2.1 Establish the connection between the compressive sensing mathematical model and the nodal voltage equation

[0021] The mathematical model of compressive sensing theory is as follows:

[0022] y = Φθ + e (4)

[0023] Where: y is an M×1 dimensional observation vector, Φ is an M×N dimensional sensing matrix, θ is an N×1 dimensional sparse vector to be reconstructed, e is an N×1 dimensional Gaussian white noise, and M << N. Equation (4) has an infinite number of solutions; taking the magnitude of the nodal impedance matrix Z M corresponds to the sensing matrix Φ, the virtual injection current vector I corresponds to the sparse vector θ to be reconstructed, and taking the magnitude of the positive sequence fault voltage ΔU M corresponds to the observed data y;

[0024] 2.2 Optimize the sparse vector θ to be reconstructed in step 2.1 using the sparse Bayesian learning algorithm

[0025] The conditions that the compressive sensing solution signal θ should satisfy are given by Equation (5), where |||| p denotes the l p norm, and the parameter ρ > 0 is the balance parameter.;

[0026]

[0027] From the Gaussian likelihood model of the observation vector y obtained by the sparse Bayesian learning algorithm, as shown in Equation (6), when y is known, estimate θ and σ 2 ;

[0028]

[0029] First, perform a prior estimate on the sparse vector θ to obtain the prior distribution form of θ. In Equation (7), a and b are hyperparameters in the parameter model, and α i is the precision of the Gaussian density function:

[0030]

[0031] From the observed data y and the prior distribution of θ, the posterior distribution is obtained as follows:

[0032] p(θ,α,σ 2 |y) = p(θ|y,α,σ 2 )p(α,σ 2 |y) (8)

[0033] The first term on the right side of Equation (8) is a multi-dimensional Gaussian distribution, and the mean and variance are as follows. Here, A = diag(α1,α2,…,α N ):

[0034] μ=σ -2 ΣΦ Τ y (9)

[0035] Σ=(σ -2 Φ Τ Φ+A) -1 (10)

[0036] The second term on the right side of equation (8) can be obtained by maximizing p(α,σ 2 |y) marginal likelihood function estimates α and σ -2 , and α and σ -2 Obeying the uniform distribution, using the expectation maximization algorithm, we get:

[0037]

[0038] Where: M is the length of observation data, γ i =1-α i Σ ii ,Σ ii is the i-th diagonal element in equation (10), μ i is the i-th element in formula (9); α i new and β new It is a function of μ and Σ, and μ and Σ are functions of α and β, so it can be solved iteratively, and finally the mean of the posterior estimate is used as the estimate of the sparse vector θ.

[0039] The advantages and positive effects of the present invention are:

[0040] The present invention is a distribution network cable fault location method based on limited DTU measurement point measurement data. The positive sequence injection current of the fault point is equivalent to the virtual injection current of the nodes at both ends of the fault area, and a model for fault area judgment is constructed; and the underdetermined node voltage equation is solved by using compressed sensing theory to obtain the virtual injection current to locate the fault area. This method only requires a small number of measurement points to effectively locate the fault area, and is less affected by the fault type, transition resistance and load change factors, and has a certain anti-noise ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Flow chart of the method for locating cable faults in a distribution network of the present invention;

[0042] Figure 2 Schematic diagram of virtual current injection of the present invention;

[0043] Figure 3 Schematic diagram of the multi-power distribution circuit and measurement point distribution of the present invention;

[0044] Figure 4The method of the present invention verifies the vector I when a BC-0Ω fault occurs between nodes 19 and 20 in the embodiment;

[0045] Figure 5 The method of the present invention verifies the reconstructed current vector I of each time period in the embodiment;

[0046] Figure 6 Schematic diagram of distribution network fault location results in the verification embodiment of the present invention, 6a, relative error of each position when ABG-10Ω fault occurs; 6b, relative error of each position under 1% noise; 6c, relative error of each position under load change. DETAILED DESCRIPTION

[0047] The structure of the present invention is further described below with reference to the accompanying drawings and by way of examples. It should be noted that the present examples are descriptive rather than restrictive.

[0048] A distribution network cable fault location method based on limited DTU measurement point measurement data is particularly suitable for multi-power distribution lines. The method includes equating the positive sequence injection current of the fault point to the virtual injection current of the nodes at both ends of the fault area, thereby proposing a model for fault area judgment; then using compressed sensing theory to solve the underdetermined node voltage equation to obtain the virtual injection current and realize the location of the fault area.

[0049] 1. Constructing a fault area judgment model

[0050] The present invention proposes an innovative fault area judgment method by making the positive sequence injection current of the fault point equivalent to the virtual injection current of the nodes at both ends of the fault area. After the fault occurs, the short circuit current is injected from the fault point into the distribution network, causing the voltage of each node in the entire network to change. Since different types of short circuit faults will cause changes in the positive sequence voltage, the fault location can be performed by analyzing the changes in the positive sequence voltage. The positive sequence fault voltage component is obtained using the symmetrical component method, and the positive sequence fault voltage component of the node is calculated using formula (1). The specific formula is as follows:

[0051]

[0052] is the positive sequence fault voltage component at node i, is the voltage of node i before the fault, is the positive sequence voltage at node i after the fault, is the mutual impedance between node i and fault point f, is the positive sequence fault current. In the fault component positive sequence network, the fault current is only injected by the fault point, and there is no injection current in the other nodes. Therefore, the fault area can be determined by calculating the virtual injection current.

[0053] Taking a distribution network with N nodes as an example, the node virtual injection current equation of the fault component positive sequence network is constructed: I = Y·ΔU, as shown in formula (2), where I is defined as the virtual injection current vector, Y is the node admittance matrix, and ΔU is the positive sequence fault voltage vector.

[0054]

[0055] like Figure 2 As shown, the fault occurs on the line between nodes l and m. The formula (2) gives The actual injected current at node l is 0, and the following equation is obtained:

[0056]

[0057] Where: is the positive sequence fault voltage component of the fault point f, y is the ratio of the distance from the fault point f to the node l to the line, which is between 0 and 1.

[0058] Comparing the two equations in equation (3), we can see that when y = 1, that is, when the fault point f is node m, is 0, and is not 0 in other cases. Similarly, when y=0, is 0, and is not 0 in other cases. Calculate the virtual injection current of the remaining nodes, which is always 0.

[0059] In summary: by calculating the virtual injection current, if the virtual injection current between two nodes is not zero, then this area may be the fault area. If only one node's virtual injection current is not zero, then the fault occurs at this node.

[0060] 2. Use the compressed sensing algorithm to solve the underdetermined node voltage equation and obtain the virtual injection current

[0061] In order to improve the accuracy of fault location, especially when there are only limited measurement points, the present invention adopts the theory of Compressive Sensing (CS) to solve the underdetermination problem of the node voltage equation, so as to accurately locate the fault area. Compressed sensing technology can restore the original signal through mathematical reconstruction methods under the conditions of few sampling points and sparse data, and is widely used in signal processing, image reconstruction, and power systems.

[0062] According to the fault area determination method mentioned above, the underdetermined node voltage equation is solved using compressed sensing theory to obtain the virtual injection current, and the fault area can be located. The specific scheme is as follows:

[0063] 1. Basic principles of compressed sensing theory

[0064] The theory of compressive sensing is based on the assumption of signal sparsity, that is, the signal is sparse in a certain basis, or most elements of the signal can be ignored. Therefore, by sparsely sampling the signal and combining with a reconstruction algorithm, the original signal can be effectively restored. The advantage of compressive sensing technology lies in its low sampling rate and high reconstruction accuracy, which makes it particularly suitable for fault location in power systems.

[0065] For the present invention, the target signal is the virtual injection current vector I, which represents the current changes at each node during a fault. By combining the measurement data with the theoretical model and using the compressive sensing theory to solve the relationship between the node voltage and current, the fault area can be accurately located.

[0066] 2. Mathematical Model and Application

[0067] The mathematical model description of the compressive sensing theory is usually expressed as:

[0068] y = Φθ + e (4)

[0069] Where: y is an M×1-dimensional observation vector, Φ is an M×N-dimensional sensing matrix, θ is an N×1-dimensional sparse vector to be reconstructed, e is an N×1-dimensional Gaussian white noise, and M << N. Equation (4) has an infinite number of solutions.

[0070] Through this model, the collected data can be combined with the theoretical model to recover the missing data and further calculate the fault location. In the fault location of the distribution network, there is a certain relationship between the node voltage change and the injection current. Connecting the compressive sensing mathematical model with the node voltage equation, the node impedance matrix Z M corresponds to the sensing matrix Φ, the virtual injection current vector I corresponds to the sparse vector θ to be reconstructed, and the positive-sequence fault voltage ΔU taking the amplitude M corresponds to the observed data y. Thus, we can use the compressive sensing algorithm, combined with the node voltage vector ΔU measured at finite measuring points M and the node impedance matrix Z M , to obtain the virtual injection current vector I, thereby realizing the location of the fault area.

[0071] 3. Optimization of Reconstruction Using Sparse Bayesian Learning (SBL)

[0072] The condition that the compressive sensing solution of the signal θ should satisfy is Equation (5), where |||| p represents the l p norm, and the parameter ρ > 0 is the balance parameter.

[0073]

[0074] At present, the Bayesian compressive sensing (BCS) algorithm based on sparse Bayesian learning (SBL) is the best method among many reconstruction algorithms. The SBL algorithm obtains the Gaussian likelihood model of the observation vector y (variance σ 2 Unknown) As shown in formula (6), when y is known, estimate θ and σ 2 .

[0075]

[0076] First, the sparse vector θ is estimated a priori, and the prior distribution form of θ is obtained, where a and b are hyperparameters in the parameter model, α i (inverse variance) is the Gaussian density function accuracy:

[0077]

[0078] From the observed data y and the prior distribution, the posterior distribution is obtained as follows:

[0079] p(θ,α,σ 2 |y)=p(θ|y,α,σ 2 )p(α,σ 2 |y) (8)

[0080] The first term on the right side of formula (8) is a multidimensional Gaussian distribution with the following mean and variance: N ):

[0081] μ=σ -2 ΣΦ Τ y (9)

[0082] Σ=(σ -2 Φ Τ Φ+A) -1 (10)

[0083] The second term on the right side of equation (8) can be obtained by maximizing p(α,σ 2 |y) marginal likelihood function estimates α and σ -2 , and α and σ -2 Obeying the uniform distribution, using the expectation maximization algorithm, we get:

[0084]

[0085]

[0086] Where: M is the length of observation data, γ i =1-α i Σii ,Σ ii is the i-th diagonal element in equation (10), μ i is the i-th element in formula (9). i new and β new is a function of μ and Σ, which are functions of α and β, so it can be solved iteratively, and finally the mean of the posterior estimate is used as the estimate of the sparse vector θ. i will approach infinity, and its corresponding θ i Approximately 0; a small amount of α i tends to a finite value, corresponding to θ i Not 0.

[0087] Therefore, the BCS algorithm can accurately reconstruct the sparse target, obtain the virtual injected current vector I, locate the fault area, and effectively solve the problem of pseudo fault points that are prone to occur in traditional algorithms.

[0088] 3. Simulation Verification and Fault Location Effect Analysis

[0089] In order to verify the effectiveness of the proposed distribution network fault location method, the present invention uses a modified IEEE33-node distribution network model as an example, and tests it in PSCAD / EMTDC simulation software. The sampling frequency of the simulation setting is 4kHz. Analysis shows that measurement devices need to be deployed at the nodes at the reference power outlet and the terminal nodes of the distribution network. According to the requirements of the compressed sensing theory on the number of measurement points, at least 6 measurement points should be configured to ensure sufficient fault location accuracy. In order to further improve the accuracy of fault location, one measurement point is added upstream and downstream of the node with lower impedance in the network. Therefore, 7 measurement nodes are finally configured, namely nodes 1, 8, 11, 17, 21, 24 and 32. The specific locations are as follows: Figure 3 In addition, to ensure the correctness of the multi-power distribution network structure, power sources are added at nodes 17 and 21 to form a three-source power distribution network. During the simulation, the voltage of each power line is set to 10 kV, the total network load is 5084.26+j2547.32 kVA, and the equivalent impedance of the power sources at nodes 17 and 21 is the same as the impedance between nodes 0 and 1, both of which are 0.092+j0.047Ω.

[0090] 1) Influence of fault type and transition resistance

[0091] A BC-0Ω fault occurs between nodes 19 and 20 and at a line length of 20% from node 19. This fault is used as an example to describe the fault location steps. The data of 7 measurement points from 0 to 20 ms after the fault is obtained, and the three-phase voltage is obtained by FFT transformation. Then the positive sequence voltage amplitude of the fault component is obtained as shown in the following table.

[0092] Table 1 Fault positive sequence voltage amplitude

[0093]

[0094] The virtual injection current vector I is obtained by using the BCS algorithm. Figure 4 As shown, the x-axis in the figure is the node number, and the y-axis represents the corresponding element in I.

[0095] Then, we take the data of 0.25-20.25ms to solve, and so on. Under the condition of sampling frequency of 4kHz, the data of 25ms window length can get 21 results, which is enough for data statistics and has certain reliability. Therefore, the time window length is selected as 25ms, and the virtual injection current vector I of each period is as follows: Figure 5 In the figure, the x-axis is the node number, the y-axis is the time window length (25ms in total, the initial period is 5ms), and the z-axis represents the corresponding element in I.

[0096] It can be determined that the fault occurs between nodes 19 and 20 .

[0097] 2) Impact of different situations on fault location results

[0098] In order to further verify the stability and reliability of the method in practical applications, the present invention also tests the influence of different factors on fault location, especially the influence of fault position change, transition resistance and noise on positioning accuracy. Figure 6 The figure is a schematic diagram of the distribution network fault location results under the influence of different factors. It can be seen from the figure that the location error of most fault locations is kept within 1%. For some fault locations, the location error is relatively large, with a maximum error of 3.67%, but it is still within an acceptable range, which fully proves the high accuracy and stability of the proposed method under different fault conditions. Further analysis shows that the location result error of this method is small when the fault location changes and factors such as transition resistance change, and it has strong anti-noise ability, which enables this method to maintain high accuracy and robustness in actual distribution networks, especially in the face of complex grid structures and uncertain factors.

[0099] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will appreciate that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for locating cable faults in a distribution network based on limited DTU measurement point measurement data, characterized in that: include: Step 1: Equivalent the positive sequence injection current of the fault point to the virtual injection current of the nodes at both ends of the fault area, and construct a model for fault area judgment; Step 2: Then use the compressed sensing theory to solve the underdetermined node voltage equation, obtain the virtual injection current, and locate the fault area.

2. The method for locating cable faults in a distribution network based on limited DTU measurement point measurement data according to claim 1, characterized in that: Step 1 includes: 1.1 The positive sequence fault voltage component is obtained by using the symmetrical component method, and the positive sequence fault voltage component of the node is calculated according to formula (1): In the formula, is the positive sequence fault voltage component at node i, is the voltage of node i before the fault, is the positive sequence voltage at node i after the fault, is the mutual impedance between node i and fault point f, is the positive sequence fault current; in the fault component positive sequence network, the fault current is only injected by the fault point, and there is no injection current in other nodes; 1.

2. Assume that there are N nodes in the distribution network and construct the node virtual injection current equation of the fault component positive sequence network I = Y·ΔU, see formula (2), where I is defined as the virtual injection current vector, Y is the node admittance matrix, and ΔU is the positive sequence fault voltage vector; 1.

3. The fault occurs on the line between nodes l and m (is this a set condition? Please explain). From formula (2), we get The actual injected current at node l is 0, and the following equation is obtained: Where: is the positive sequence fault voltage component of the fault point f, y is the ratio of the distance from the fault point f to the node l to the line, which is between 0 and 1; 1.4 Comparing the two equations in equation (3), we can obtain that when y=1, that is, when the fault point f is node m, is 0, and all other cases are not 0; when y=0, is 0, and is not 0 in other cases. Calculate the virtual injection current of the remaining nodes, which is always 0; By calculating the virtual injection current, if the virtual injection current between two nodes is not zero, then the area may be the fault area. If the virtual injection current of only one node is not zero, then the fault occurs at this node.

3. The method for locating cable faults in a distribution network based on limited DTU measurement point measurement data according to claim 1, characterized in that: Step 2 includes: 2.

1. Establishing the connection between the compressed sensing mathematical model and the node voltage equation The mathematical model of compressed sensing theory is: y=Φθ+e (4) where: y is an M×1 observation vector, Φ is an M×N sensing matrix, θ is an N×1 sparse vector to be reconstructed, e is an N×1 Gaussian white noise, and M << N. Equation (4) has an infinite number of solutions; the nodal impedance matrix Z taking the amplitude M corresponds to the sensing matrix Φ, the virtual injection current vector I corresponds to the sparse vector θ to be reconstructed, and the positive-sequence fault voltage ΔU taking the amplitude M corresponds to the observed data y; 2.2 Using the sparse Bayesian learning algorithm to optimize the reconstruction of the sparse vector θ to be reconstructed in step 2.1 The condition that the compressed sensing solution signal θ should satisfy is formula (5), where |||| p Indicates l p norm, parameter ρ>0 is the balance parameter; The Gaussian likelihood model of the observation vector y is obtained by the sparse Bayesian learning algorithm, as shown in Equation (6). When y is known, θ and σ are estimated 2 ; First, the sparse vector θ is estimated a priori to obtain the a priori distribution form of θ. In formula (7), a and b are hyperparameters in the parameter model, α i is the Gaussian density function accuracy: From the prior distribution of observed data y and θ, the posterior distribution is obtained as follows: p(θ,α,σ 2 |y)=p(θ|y,α,σ 2 )p(a,s 2 |y) (8) The first term on the right side of formula (8) is a multidimensional Gaussian distribution with the following mean and variance: N ): μ = σ -2 SF Τ y (9) S=(s -2 F Τ (F+A) -1 (10) The second term on the right side of equation (8) can be obtained by maximizing p(α,σ 2 |y) marginal likelihood function estimates α and σ -2 , and α and σ -2 Obeying the uniform distribution, using the expectation maximization algorithm, we get: Where: M is the length of observation data, γ i =1-α i Σ ii ,Σ ii is the i-th diagonal element in equation (10), μ i is the i-th element in formula (9); α i new and β new It is a function of μ and Σ, and μ and Σ are functions of α and β, so it can be solved iteratively, and finally the mean of the posterior estimate is used as the estimate of the sparse vector θ.

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