Transformer partial discharge positioning method based on multi-sensor elimination of abnormal time difference

Abstract

The application discloses a transformer partial discharge positioning method based on multi-sensor abnormal time difference elimination, S1: installing a sensor for receiving a partial discharge signal on the surface of a transformer, and extracting the time when the sensor receives the partial discharge signal; S2: establishing a spherical positioning equation set under a space rectangular coordinate system and linearizing; S3: solving the linearized equation set, and obtaining an initial solution set after screening; S4: using a DBSCAN clustering algorithm to perform clustering analysis on the initial solution set, and obtaining multiple clusters and outliers; S5: classifying the clusters according to residuals, counting the measurement time difference frequencies corresponding to the clusters and the outliers, and identifying good time differences, ordinary time differences and abnormal time differences; S6: eliminating the abnormal time differences, considering the measurement noise of the remaining time differences, and establishing a constrained total least squares model; S7: selecting an iterative initial solution, and using a Newton iteration method to calculate a final positioning solution. The application can eliminate abnormal time differences and reduce noise influence, and thus still has higher positioning precision in a higher noise environment.

Description

Technical Field

[0001] This invention relates to the field of transformer fault location, and in particular to a transformer partial discharge location method based on multi-sensor elimination of abnormal time difference. Background Technology

[0002] Transformers are among the most critical pieces of equipment in power systems, bearing the crucial responsibility of voltage level transformation. Their operating status directly impacts the safety and stability of the entire system. However, with long-term operation, transformers may develop insulation defects. Most catastrophic insulation breakdowns result from the cumulative effect of long-term partial discharge. Therefore, to ensure reliable transformer operation, rapid and accurate location of the discharge source is essential when partial discharge occurs.

[0003] Currently, partial discharge localization methods mainly rely on three techniques: Time Difference of Arrival (TDOA) localization, Direction of Arrival (DOA) localization, and Received Signal Strength Indication (RSSI) localization. Due to its simple principle and mature technology, TDOA is widely used in various passive localization problems, including the localization of transformer partial discharges. The key to solving for the source coordinates using TDOA technology lies in obtaining the time difference and calculating the nonlinear equations.

[0004] However, the positioning equations established based on this method are often highly nonlinear and cannot be solved directly. Currently, they are generally solved using traditional iterative algorithms and heuristic search algorithms. Newton's iteration method has the advantage of quadratic convergence, obtaining an accurate solution with fewer iterations. However, its disadvantages are also obvious: it only has one initial value and a single search path. Therefore, it is necessary to choose an initial value close to the true solution; otherwise, it may result in no solution or a large error in the solution. Compared with iterative algorithms, heuristic algorithms have the advantage of not requiring an initial value. However, heuristic algorithms often cannot consider the impact of measurement noise on the results during the optimization process.

[0005] On the other hand, the propagation speed of partial discharge signals is very fast, so this method requires high accuracy in time difference measurement. When the time difference measurement contains noise or even outliers, it often leads to large positioning errors. It is clear that the quality of the time difference measurement and the magnitude of noise directly affect positioning accuracy. However, existing solution methods, due to the limited number of measurements, generally do not identify or filter the quality of the time difference measurement, and even ignore the influence of measurement noise during the solution process. This results in larger positioning errors in scenarios with outliers and high measurement noise. Summary of the Invention

[0006] Based on the technical problems existing in the background technology, this invention proposes a transformer partial discharge localization method based on multiple sensors to eliminate abnormal time difference, which can eliminate abnormal time difference and reduce the impact of noise, thus maintaining high positioning accuracy even in high noise environments.

[0007] The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference proposed in this invention has the following steps:

[0008] S1: Install a sensor on the surface of the transformer to receive partial discharge signals, and extract the time when the sensor receives the partial discharge signal;

[0009] S2: Establish and linearize the system of equations for spherical positioning in a spatial rectangular coordinate system;

[0010] S3: Solve the linearized system of equations and obtain the initial solution set after filtering;

[0011] S4: Use the DBSCAN clustering algorithm to perform cluster analysis on the initial solution set to obtain multiple clusters and outliers;

[0012] S5: Classify clusters based on residuals, count the frequency of measurement time differences corresponding to clusters and outliers, and identify good time differences, normal time differences, and abnormal time differences;

[0013] S6: Eliminate abnormal time differences, consider the measurement noise of the remaining time differences, and establish a constrained overall least squares model;

[0014] S7: Select the initial solution for iteration and use Newton's iteration method to calculate the final localized solution.

[0015] Preferably, the sensor in S1 is an ultrasonic sensor or an ultra-high frequency sensor, and the number of sensors N > 6.

[0016] Preferably, in S2, a spatial rectangular coordinate system is established with one vertex of the transformer as the origin. Based on the TDOA principle, a set of spherical positioning equations for the local discharge source can be established:

[0017]

[0018] In the formula: N is the number of sensors, P(x,y,z) is the coordinate of the partial discharge source, (x i ,y i ,z i ) is sensor S i The coordinates are given, t1 is the time it takes for the partial discharge signal to travel from the partial discharge source to the reference sensor S1, and τ is the coordinates. i =T i -T1 represents the S values ​​of each sensor. i The measurement time difference between the reference sensor and the reference sensor (i = 2, 3, ..., N), where v is the constant wave velocity.

[0019] Preferably, in S3, any other spherical positioning equation can be selected and subtracted from the spherical positioning equation of the reference sensor to obtain a linear equation:

[0020]

[0021] In the formula: x i1 =x i –x1, y i1 =y i –y1, z i1 =z i –z1, V=v 2 K = v 2 t1, D i1 =(x i 2 +y i 2 +z i 2 )-(x1 2 +y1 2 +z1 2 ), (i = 2, 3, ..., N).

[0022] Preferably, the reference sensor, combined with any five other sensors, yields a solution for X = (x, y, z, V, K). T The system of linear equations, obtained from N sensors, yields a total of... A system of equations is solved using Gaussian elimination. A system of linear equations is obtained. We obtain an initial set of m coordinate solutions, discarding those whose equivalent wave velocity v significantly exceeds the normal wave velocity range or is an imaginary number. m}

[0023] Preferably, the steps of the DBSCAN clustering algorithm in S4 for clustering analysis of the initial solution set are as follows:

[0024] S41: Input the neighborhood search radius Eps, the minimum number of points in the neighborhood MinPts, and the initial coordinate solution set H;

[0025] S42: Randomly select a coordinate point P without a cluster label from the initial coordinate solution set H. i ;

[0026] S43: Find all points from point P i Regarding the points where the densities of Eps and MinPts are achievable;

[0027] S44: If P i It is the core point, namely point P.i If a neighborhood of point Eps contains no less than MinPts, a new cluster is formed, and a new cluster label is added to all points in the cluster. Then, the next core point in the cluster is processed, and core points with reachable density are collected and added to the cluster until no new core points are added. At this point, the cluster becomes a complete cluster.

[0028] S45: If P i It is a boundary point, that is, point P. i If the neighborhood of point P with radius Eps contains fewer points than MinPts, then P... i There are no density-reachable points; then select the next unlabeled point in the initial coordinate solution set H to search again;

[0029] S46: Repeat steps S42-S45 above until all points in the initial coordinate solution set H have been processed;

[0030] S47: After clustering, c clusters and l outliers are obtained.

[0031] Preferably, the method steps for classifying clusters based on residuals in S5 are as follows:

[0032] S51: Calculate the average of all initial solutions in each cluster.

[0033] S52: For measuring time difference τ i The absolute residual of the corresponding spherical equation is:

[0034] r i =|[(xx i ) 2 +(yy i ) 2 +(zz i ) 2 ]-v 2 (t i +τ i ) 2 |;

[0035] S53: Define the mean absolute residual of the h-th cluster as...

[0036] S54: Solve the average value of the h-th cluster. Substituting into the above formula, the mean absolute residual of each cluster can be obtained;

[0037] S55: Select the cluster with the smallest mean absolute residual as a good cluster, and solve its mean value X. g As the initial solution for iteration.

[0038] Preferably, the steps for identifying good jet lag, normal jet lag, and abnormal jet lag in S5 are as follows:

[0039] S56: Select the cluster with the smallest average residual as the good cluster, and the other clusters as ordinary clusters. Then, statistically analyze the measurement time difference τ. i The frequencies f of the corresponding initial coordinate solutions in good clusters and outliers, respectively. i and f i ';

[0040] S57: If the measurement time difference τ i The frequency satisfies: f i ′>f o / 2 and f i <f g / 2, then the measurement time difference τ is considered to be i This refers to outlier time difference measurements; where fo is the highest frequency of measurement time difference statistically obtained from outlier points, f g The highest frequency of measurement time difference obtained statistically from good clusters;

[0041] S58: If the measurement time difference τ i The frequency satisfies: f i >f g / 2 and f i ′<f o / 2, then the measurement time difference τ is considered to be i It's a good time difference;

[0042] S59: The remaining time differences are ordinary time differences.

[0043] Preferably, the steps for constructing the constrained global least squares model in S6 are as follows:

[0044] S61: Eliminate the equations corresponding to abnormal time differences, and combine the n-1 linear equations that do not contain abnormal time differences to obtain the linear equation system AX=b, where n is the number of remaining measurement time differences;

[0045] S62: The covariance matrix Q = E[η η] for time-difference noise η that follows a normal distribution. T Perform Cholesky decomposition Q = LL T The whitened noise vector u = L can be obtained. -1 η; thus, a constrained total least squares model can be established for the linear system of equations AX = b:

[0046]

[0047] In the formula: u is the whitened noise vector of the noise η of the measurement time difference; ΔA and Δb are the noise terms of matrix A and vector b, respectively.

[0048] Preferably, the Newton-Raphson iteration method is used to solve the constrained total least squares model, and the CTLS solution is the function. The iterative formula for finding the minimum value is:

[0049] X k+1 =X k -H(X k ) -1 G(X k )

[0050] In the formula: and These are the gradient matrix and the Hessian matrix of the function F(X), respectively.

[0051] The correction vector α is calculated at each iteration. k =H(X) k ) -1 G(X k Frobenius norm of ) When condition ||α k || F The iteration ends when ε is satisfied, where ε is the precision.

[0052] Beneficial technical effects of the present invention:

[0053] (1) The transformer partial discharge positioning method based on multi-sensor elimination of abnormal time difference of the present invention can eliminate abnormal time difference and reduce the influence of noise, so that it still has high positioning accuracy in high noise environment.

[0054] (2) This invention uses more sensors to obtain more sample sets, uses density-based clustering to process the sets, and calculates the magnitude of the mean absolute residual to determine the quality of the clusters, thereby identifying good and abnormal time differences.

[0055] (3) The present invention uses equations without abnormal time difference to re-establish the equation system, thereby eliminating the adverse effects of abnormal time difference on the positioning results; at the same time, considering the measurement noise of the remaining time difference, the influence of measurement noise is reduced by establishing a constrained overall least squares model, which further improves the positioning accuracy.

[0056] (4) The present invention uses the cluster center with the smallest average error as the initial solution for iteration. Compared with the random selection of the initial solution or the use of ordinary least squares solution as the initial solution in the traditional iterative method, the initial solution of the present invention is closer to the true solution, thereby effectively avoiding the situation that the traditional iterative method may not converge or has a long convergence time. Attached Figure Description

[0057] Figure 1This is a flowchart of the transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference proposed in this invention;

[0058] Figure 2 This is a clustering result diagram of the initial solution set.

[0059] Figure 3 This is a root mean square error diagram of localization under different Gaussian noise levels after outlier removal, as proposed in this invention. Detailed Implementation

[0060] The present invention will be further explained below with reference to specific embodiments.

[0061] The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference proposed in this invention includes the following steps:

[0062] Step 1: Install N=8 ultrasonic sensors on the transformer surface. The equivalent wave velocity v is typically in the range of 1200m / s ≤ v ≤ 1500m / s. In this embodiment, the equivalent sound velocity v is taken as 1500m / s. Measure the time it takes to receive the partial discharge (PD) signal; connect the sensors to an oscilloscope to receive the partial discharge signal, and then extract the S signal from each sensor. i Time difference τ of receiving PD signal i (i = 2, 3, ..., N); Set the transformer size as: x max ×y max ×z max =240×300×200, unit is cm; set the coordinates of the PD source as P(x r ,y r ,z r ) = (160, 120, 90), in cm; set the coordinates S of each sensor. i (x i ,y i ,z i As shown in Table 1; the theoretical propagation time is calculated based on the PD source coordinates and sensor coordinates:

[0063]

[0064] Next, the theoretical time difference τ is calculated. i =t i -t1;

[0065] Zero-mean Gaussian noise with a standard deviation of σ = 0.2 μs was added to the theoretical time difference to simulate measurement noise. Then, different percentage errors e were further added to the simulated time difference to simulate good or bad time difference performance. Where, when the theoretical time difference is τ... 0 When the simulation time difference is τ, the percentage error e is defined as follows:

[0066]

[0067] The coordinates and theoretical time differences of each sensor are shown in Table 1. A percentage error of e1∈(0,1%) is added to time difference 2 to simulate a good time difference, an error of e2∈(1%,5%) is added to time differences 3-7 to simulate a normal time difference, and a percentage error of e3=10% is added to time difference 8 to simulate an abnormal time difference.

[0068] Table 1 Sensor coordinates and theoretical time difference

[0069] Sensor number Sensor coordinates / cm Theoretical propagation time / μs Theoretical time difference / μs 1 (40,100,0) 1008.85 none 2 (40,200,0) 1133.33. 124.48 3 (90,120,200) 869.23 -139.62 4 (80,200,200) 1051.98 43.13 5 (160,100,0) 614.64 -394.21 6 (180,180,0) 733.33 -275.52 7 (200,100,200) 791.62 -217.23 8 (160,200,200) 906.76 -102.09

[0070] Step 2: Establish a system of spherical positioning equations in a spatial rectangular coordinate system and linearize it. The spatial rectangular coordinate system is established with one vertex of the transformer as the origin. Based on the TDOA principle, the system of spherical positioning equations for the PD source can be established as follows:

[0071]

[0072] In the formula, N is the number of sensors, (x r ,y r ,z r (x) represents the coordinates of the PD source. i ,y i ,z i ) is sensor S i The coordinates are given, t1 is the time it takes for the PD signal to travel from the PD source to the reference sensor S1, and τ is the time it takes for the PD signal to travel from the PD source to the reference sensor S1. i For each sensor S i The measurement time difference between the reference sensor and the reference sensor (i = 2, 3, ..., N), where v is the constant wave velocity.

[0073] Step 3: Solve the system of linear equations using Gaussian elimination. After filtering, obtain an initial solution set. Subtract the spherical positioning equation of the reference sensor from any other spherical positioning equation to obtain a linear equation:

[0074]

[0075] In the formula, x i1 =x i –x1, y i1 =y i –y1, z i1 =z i –z1, V=v 2 K = v 2 t1, D i1 =(x i 2 +y i 2 +z i2 )-(x1 2 +y1 2 +z1 2 ), (i = 2, 3, ..., N).

[0076] Combining the reference sensor with any five other sensors yields a solution for X = (x, y, z, V, K). T The linear equations can be obtained from the 8 sensors. A system of 21 equations was solved using Gaussian elimination, yielding 21 initial solutions. Initial positioning solutions where the equivalent wave velocity v significantly exceeded the normal wave velocity range or was an imaginary number were discarded. In this embodiment, an initial coordinate solution set H = {p1, p2, ..., p...} containing m = 20 samples was obtained. m}

[0077] Step 4: Use the DBSCAN clustering algorithm to perform cluster analysis on the initial coordinate solution set H containing m samples, obtaining 2 clusters and 8 outliers; the basic steps of the DBSCAN clustering algorithm are as follows:

[0078] S1: Input the neighborhood search radius Eps, the minimum number of points in the neighborhood MinPts, and the initial coordinate solution set H = {p1, p2, ..., p...} m}

[0079] S2: Where Eps is set to 0.1% to 2% of the transformer size; MinPts is set to βm (0 < β ≤ 1), and β can be 0.2 to 0.3; however, the specific values ​​of Eps and β should be adjusted according to the degree of clustering.

[0080] S3: Randomly select a coordinate point Pi without a cluster label from the initial coordinate solution set H;

[0081] S4: Find all points from point P i Regarding the points where the densities of Eps and MinPts are achievable;

[0082] S5: If P i It is the core point, namely point P. i If a neighborhood of point Eps contains no less than MinPts, a new cluster is formed, and a new cluster label is added to all points in the cluster. Then, the next core point in the cluster is processed, and core points with reachable density are collected and added to the cluster until no new core points are added. At this point, the cluster becomes a complete cluster.

[0083] S6: If P i It is a boundary point, that is, point P. i If the neighborhood of point P with radius Eps contains fewer points than MinPts, then P...i There are no density-reachable points; then select the next unlabeled point in the initial coordinate solution set H to search again;

[0084] S7: Repeat steps S2-S6 until all points in the initial coordinate solution set H have been processed.

[0085] S8: In this example, after clustering, a total of 2 clusters (with 7 points and 5 points respectively) and 8 outliers were obtained. The clustering results are as follows: Figure 2 As shown.

[0086] Step 5: Classify clusters based on residuals, count the frequency of measurement time differences corresponding to clusters and outliers, and identify good time differences, normal time differences, and abnormal time differences; where:

[0087] The method for classifying clusters based on residuals involves the following steps:

[0088] S1: Calculate the average of all initial solutions in each cluster.

[0089] S2: For the measurement time difference τ i The absolute residual of its corresponding spherical equation is

[0090] r i =|[(xx i ) 2 +(yy i ) 2 +(zz i ) 2 ]-v 2 (t i +τ i ) 2 |;

[0091] S3: Define the mean absolute residual of the h-th cluster as...

[0092]

[0093] S4: Solve for the average value of the h-th cluster. Substituting into the above formula, the mean absolute residual of each cluster can be obtained;

[0094] S5: According to the definition of residuals, the mean absolute residual (MAE) h This reflects the error between the fitted values ​​(calculated values) and the observed values. Therefore, the cluster with the smallest mean absolute residual is selected as the good cluster, and its mean value X is solved. g This will serve as the initial solution for the iterations described below.

[0095] The calculated average solutions for the two clusters are respectively and and The residual is the smallest, therefore the average solution of cluster 2 is chosen as the initial solution for subsequent iterations, i.e.

[0096] The steps for statistically measuring time difference frequency to filter the quality of time differences are as follows:

[0097] S1: Select the cluster with the smallest mean absolute residual as the good cluster, and the other clusters as ordinary clusters. Then, statistically measure the time difference τ. i The frequencies f of the corresponding initial coordinate solutions in good clusters and outliers, respectively. i and f i ';

[0098] S2: If a sensor measurement is abnormal, then the calculation of all the positioning equations combined with that sensor... All location results should be abnormal; therefore, the frequency of outliers should be considered. Measurement time difference τ i It was considered an abnormal measurement.

[0099] However, considering the impact of other small errors on the solution accuracy, and the influence of the selection of clustering parameters on the clustering results, the number of outliers in actual clustering is generally less than [a certain value]. In addition, there is still an extremely rare case that may affect the clustering results: an outlier combined with other outliers may be well located and become a point in a certain cluster. Therefore, the criteria for determining outliers are expanded to: if f i ′>f o / 2 and f i <f g / 2, then the measurement time difference τ is considered to be i It is an anomaly measurement; where f o f is the frequency of the measurement time difference obtained from the statistics of outliers. g The highest frequency of measurement time difference obtained statistically from good clusters;

[0100] S4: The frequency of measuring time difference i satisfies: f i >f g / 2 and f i ′<f o / 2, then the measurement time difference τ is considered to be i It is a good measurement;

[0101] S5: The remaining measurement time differences are considered as ordinary measurement time differences;

[0102] S6: In this example, the frequency statistics of time differences are shown in Table 2, where τ2 is the good time difference, τ3 to τ7 are the normal time differences, and τ8 is the abnormal time difference.

[0103] Table 2. Time Difference Frequency Statistics

[0104] jet lag Frequency of occurrence of good clusters Frequency of occurrence of ordinary clusters outlier frequency Good or bad time difference <![CDATA[τ2]]> 5 7 3 good <![CDATA[τ3]]> 3 3 8 ordinary <![CDATA[τ4]]> 4 4 6 ordinary <![CDATA[τ5]]> 4 4 7 ordinary <![CDATA[τ6]]> 5 3 6 ordinary <![CDATA[τ7]]> 3 4 7 ordinary <![CDATA[τ8]]> 1 7 6 abnormal

[0105] Step 6: Eliminate outlier time differences, consider measurement noise in the remaining time differences, and establish a constrained overall least squares model. The specific steps are as follows:

[0106] S1: Eliminate the equations corresponding to abnormal time differences, and combine the six linear equations that do not contain abnormal time differences to obtain the linear equation system AX = b;

[0107] in

[0108] S2: Considering that various errors will inevitably exist in the measured values ​​when the transformer partial discharge location problem is applied in practice, after eliminating abnormal time differences, a more reasonable constrained total least squares (CTLS) method is adopted to solve the problem in order to further improve the positioning accuracy.

[0109] S3: Among them, the measurement error of the sensor position on the transformer tank surface is always extremely small, so it can be ignored. That is, it is assumed that all sensor positions are noise-free, i.e., Δb = 0.

[0110] S4: Due to the influence of temperature on wave speed, refraction and diffraction of sound waves, and sensor sensitivity, the final measured time difference τ i Compared with the true value There will always be a certain degree of error η. i ,Right now It is generally assumed that the time difference noise η = [η1, η2, ..., η] n ,] T It follows a normal distribution with a mean of 0 and a standard deviation of σ, i.e., η ~ N(0,σ). 2 ); for the covariance matrix Q=E[ηη T Perform Cholesky decomposition Q = LL T The whitened noise vector u = L can be obtained. -1 η;

[0111] S5: Will and u=L -1 Substituting η into matrix A and ignoring the quadratic terms of noise, we can obtain...

[0112] ΔA=[0 0 0 2A1n 2A2n]=[0 0 0 Λ1u Λ2u];

[0113] in, Λ1 = 2A1L, Λ2 = 2A2L;

[0114] S6: At this point, for the true solution X of the system, we have

[0115] AX-b=(A o +ΔA)X-(b o +Δb)=A o Xb o +ΔAX-Δb=ΔAX-Δb;

[0116] Where A o and b o It is noiseless, therefore A o Xb o =0;

[0117] S7: Substituting ΔA=[0 0 0 Λ1u Λ2u] and Δb=0 into the above equation, we get...

[0118] AX-b=ΔAX-Δb=(VΛ1+KΛ2)u=W X u;

[0119]

[0120] Among them W X =VΛ1+KΛ2, W X The generalized inverse;

[0121] S8: From this, we can derive the CTLS model:

[0122]

[0123] Step 7: After constructing the CTLS model, it is necessary to select appropriate initial values ​​for iteration and solve the problem. The specific steps are as follows:

[0124] S1: The CTLS solution is the solution X that takes the minimum value of the following function:

[0125]

[0126] S2: Since F(X) is highly nonlinear and difficult to find a closed-form solution, Newton's iteration method is used to solve it. First, the gradient matrix G(X) and the Hessian matrix H(X) are calculated:

[0127]

[0128]

[0129] in Γ1=[0 0 0 Λ1 T pΛ2 T p],Γ2=[0 0 0 Λ1W X T pΛ2W X Tp];

[0130] The iterative formula can be obtained as follows:

[0131] X k+1 =X k -H(X k ) -1 G(X k );

[0132] Where k is the number of iterations;

[0133] For Newton's iteration method, the selection of the initial value is crucial. An initial value closer to the true solution can avoid non-convergence issues and achieve the required accuracy with fewer iterations. Generally, CTLS selects the ordinary least squares (LS) solution as the initial solution for iterative calculation. The LS solution for AX = b is...

[0134]

[0135] Furthermore, since cluster 1 is a good cluster, its average solution is... The smallest mean absolute residual indicates that It is very close to the true solution, so it is necessary to compare the error between the two and the true solution;

[0136] S3: The transformer size is x max ×y max ×z max The true coordinates of the PD source are (x r ,y r ,z r The algorithm in this paper solves for coordinates (x, y, z), and defines the absolute positioning error R and the relative positioning error. Used as a performance indicator for positioning error:

[0137]

[0138]

[0139] (7g) The errors between different initial solutions and the true solutions were calculated, as shown in Table 3. It can be seen that the average solution of the good cluster... To be closer to the true solution, therefore in this example... As the initial solution X0 for iteration, i.e.

[0140] Table 3 Errors for different initial solutions

[0141]

[0142] S4: Define the correction vector α k =H(X) k) -1 G(X k ), calculate α in each iteration k Frobenius norm

[0143] (7i) When the condition ||α k || F The iteration ends when ε is satisfied, where ε is the precision.

[0144] (7j) Since X0 = X g It closely approximates the true solution, so using it as the initial solution for iteration easily converges to a high-precision localization solution. The precision ε is generally set to a number much less than 1. When ε = 0.001, a satisfactory solution can usually be obtained after 3 to 5 iterations.

[0145] The localization results under different noise levels, with or without removing abnormal time differences, were calculated and are shown in Table 4.

[0146] Table 4. Localization results under different noise levels, with or without removing abnormal time differences.

[0147]

[0148] As shown in Table 4, under the same noise conditions, the positioning accuracy is significantly improved after eliminating abnormal time differences using the method proposed in this paper. Under noise conditions of σ = 0.2 μs and σ = 0.5 μs, the positioning accuracy improved by 4.19% and 4.29% respectively after eliminating abnormal time differences, indicating that the improvement effect is more significant when the noise level is higher, proving the effectiveness of the proposed algorithm in eliminating abnormal time differences. When the noise level is the same and abnormal time differences are removed, the calculation results of CTLS and LS, TLS (Total Least Squares), and TSWLS (Two-Step Weighted Least Squares) algorithms are compared, as shown in Table 4. Figure 3 As shown, after removing abnormal time differences, under the same noise conditions, the CTLS algorithm has the smallest positioning error. Furthermore, when the noise increases, the positioning error of the CTLS algorithm remains the smallest, proving that the proposed algorithm still has good positioning accuracy under high noise conditions.

Claims

1. A transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference, characterized in that, The steps are as follows: S1: Install a sensor on the surface of the transformer to receive partial discharge signals, and extract the time when the sensor receives the partial discharge signal; S2: Establish and linearize the system of equations for spherical positioning in a spatial rectangular coordinate system; S3: Solve the linearized system of equations and obtain the initial solution set after filtering; S4: Use the DBSCAN clustering algorithm to perform cluster analysis on the initial solution set to obtain multiple clusters and outliers; S5: Classify clusters based on residuals, count the frequency of measurement time differences corresponding to clusters and outliers, and identify good time differences, normal time differences, and abnormal time differences; S6: Eliminate abnormal time differences, consider the measurement noise of the remaining time differences, and establish a constrained overall least squares model; S7: Select the initial solution for iteration and use Newton's iteration method to calculate the final localization solution; The steps for classifying clusters based on residuals in S5 are as follows: S51: Calculate the average of all initial solutions in each cluster. , (h = 1, 2,...,c); S52: For measuring time difference 𝜏 i The absolute residual of the corresponding spherical equation is: ； S53: Define the mean absolute residual of the h-th cluster as... ; S54: Solve the average value of the h-th cluster. Substituting into the above formula, the mean absolute residual of each cluster can be obtained; S55: Select the cluster with the smallest mean absolute residual as a good cluster, and solve its mean value X. g As the initial solution for the iteration; The steps for identifying good, normal, and abnormal time zones in S5 are as follows: S56: Select the cluster with the smallest average residual as the good cluster, and the other clusters as ordinary clusters, then statistically measure the time difference 𝜏 i The frequencies f of the corresponding initial coordinate solutions in good clusters and outliers, respectively. i and f i '; S57: If the time difference is measured... i The frequency satisfies: and Then the measurement time difference is considered to be 𝜏 i It is an abnormal time difference measurement; where f o f is the frequency of the measurement time difference obtained from the statistics of outliers. g The highest frequency of measurement time difference obtained statistically from good clusters; S58: If the time difference is measured... i The frequency satisfies: and Then the measurement time difference is considered to be 𝜏 i It's a good time difference; S59: The remaining time differences are ordinary time differences; The steps for constructing a constrained global least squares model in S6 are as follows: S61: Eliminate the equations corresponding to abnormal time differences, and combine the n-1 linear equations that do not contain abnormal time differences to obtain the linear equation system AX=b, where n is the number of remaining measurement time differences; S62: Covariance matrix of time-difference noise η that follows a normal distribution Cholesky decomposition The whitened noise vector can be obtained. Therefore, a constrained total least squares model can be established for the linear system of equations AX=b: ； In the formula: u is the whitened noise vector of the noise η of the measurement time difference. and These are the noise terms for matrix A and vector b, respectively.

2. The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference according to claim 1, characterized in that, In S1, the sensor is an ultrasonic sensor or an ultra-high frequency sensor, and the number of sensors N > 6.

3. The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference according to claim 1, characterized in that, In S2, a spatial rectangular coordinate system is established with one vertex of the transformer as the origin. Based on the TDOA principle, a set of spherical positioning equations for the local discharge source can be established: ； In the formula: N is the number of sensors, P(x, y) , z) is the coordinate of the partial discharge source, (x) i , y i, z i ) is sensor S i The coordinates are given, where t1 is the time it takes for the partial discharge signal to travel from the partial discharge source to the reference sensor S1. For each sensor S i The measurement time difference between the reference sensor and the reference sensor (i=2,3,…,N), where v is the isotropic wave velocity.

4. The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference according to claim 1, characterized in that, By subtracting any other spherical positioning equation from the spherical positioning equation of the reference sensor in S3, a linear equation can be obtained: ； In the formula: , , , , , , (i = 2, 3,…,N).

5. The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference according to claim 4, characterized in that, The reference sensor, combined with any five other sensors, yields a solution. The system of linear equations, obtained from N sensors, yields a total of... A system of equations is solved using Gaussian elimination. A system of linear equations is obtained. We obtain an initial set of m coordinate solutions, discarding those whose equivalent wave velocity v significantly exceeds the normal wave velocity range or is an imaginary number. .

6. The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference according to claim 1, characterized in that, The steps of the DBSCAN clustering algorithm in S4 to perform cluster analysis on the initial solution set are as follows: S41: Input the neighborhood search radius Eps, the minimum number of points in the neighborhood MinPts, and the initial coordinate solution set H; S42: Randomly select a coordinate point P without a cluster label from the initial coordinate solution set H. i ; S43: Find all points from point P i Regarding the points where the densities of Eps and MinPts are achievable; S44: If P i It is the core point, namely point P. i If a neighborhood of point Eps contains no less than MinPts, a new cluster is formed, and a new cluster label is added to all points in the cluster. Then, the next core point in the cluster is processed, and core points with reachable density are collected and added to the cluster until no new core points are added. At this point, the cluster becomes a complete cluster. S45: If P i It is a boundary point, that is, point P. i If the neighborhood of point P with radius Eps contains fewer points than MinPts, then P... i There are no density-reachable points; then select the next unlabeled point in the initial coordinate solution set H to search again; S46: Repeat steps S42-S45 above until all points in the initial coordinate solution set H have been processed; S47: After clustering, c clusters and l outliers are obtained.

7. The transformer partial discharge localization method based on multi-sensor elimination of abnormal time difference according to claim 1, characterized in that, The constrained total least squares (CTLS) model is solved using Newton's iteration method; the CTLS solution is the function. The iterative formula for finding the minimum value is: ； In the formula: and These are the gradient matrix and the Hessian matrix of the function F(X), respectively. The correction vector is calculated at each iteration. Frobenius norm ; when condition The iteration ends when the condition is met, where ε is the precision.

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