A transformer winding deformation online detection method and system based on impedance spectrum scanning

Abstract

This invention belongs to the field of transformer technology, specifically relating to an online detection method and system for transformer winding deformation based on impedance spectrum scanning. The method includes the following steps: acquiring complex frequency domain impedance data of the transformer winding within a set frequency sweep interval, and constructing a joint sequence of real and imaginary parts in ascending frequency order; establishing a discrete integral mapping matrix between the impedance spectrum and the relaxation time distribution based on logarithmic relaxation time coordinates, and constructing frequency weights according to the frequency point distribution density to obtain a weighted inversion model; and reconstructing the discrete integral mapping matrix using a preset non-uniform relaxation time discrete step size. This invention deeply explores the microscopic variation laws of the impedance spectrum from multiple dimensions, improving the sensitivity and evaluation accuracy of detecting minute deformations in transformer windings, and reducing the risk of misjudgment caused by single feature discrimination.

Description

Technical Field

[0001] This invention belongs to the field of transformer technology, specifically relating to an online detection method and system for transformer winding deformation based on impedance spectrum scanning. Background Technology

[0002] Transformers are highly susceptible to winding deformation when subjected to short-circuit inrush currents, transportation collisions, or long-term electrodynamic forces, leading to insulation damage and severe short-circuit accidents. Broadband impedance spectroscopy is widely used for transformer winding deformation detection due to its high sensitivity. However, impedance spectroscopy analysis relies on manually comparing the resonant frequency shift of the impedance curve or using macroscopic statistical indicators such as correlation coefficients for evaluation. This method suffers from strong subjectivity and is extremely insensitive to minor winding deformations. Amplitude-frequency or phase-frequency analysis cannot decouple the complex internal structural changes of the winding, causing local anomalies caused by minute deformations to be easily masked by the overall macroscopic trend of the curve or ambient noise, making early warning and accurate location of deformation impossible.

[0003] Patent application CN111881781A discloses a transformer winding deformation classification method based on scanning impedance method and support vector machine. It obtains winding amplitude frequency / phase frequency data through wideband impedance scanning, extracts feature vectors, and classifies winding deformation through support vector machine. However, it only uses macroscopic frequency domain features and is not sensitive to small deformations. It lacks DRT decoupling and peak cluster quantitative analysis, and the inversion is prone to oscillating spurious peaks, resulting in low detection accuracy.

[0004] The relaxation time distribution (DRT) analysis technique can transform complex frequency domain impedance data to the time constant domain through integral mapping, decoupling coupled responses over a wide frequency range into independent relaxation time peak clusters. This allows for high-resolution separation and amplification of local anomalies caused by changes in winding physical parameters. The mapping inversion from the impedance spectrum to the relaxation time domain is an extremely ill-posed mathematical inverse problem. Conventional solution methods are highly sensitive to discrete step lengths and data noise, easily leading to divergent results, severe numerical oscillations, or spurious peaks when processing swept-frequency impedance data with uneven distribution density. Existing regularized inversion models lack collaborative constraint and adjustment mechanisms for multi-scale features, often resulting in over-broadening of true characteristic peaks or loss of weak peaks in the reconstructed relaxation time distribution. Current technology remains at the stage of qualitative observation of DRT curves, lacking systematic peak cluster identification, quantitative index calculation, and a discrimination threshold system for transformer winding characteristics. This limits the practical application of this method in high-precision intelligent detection of transformer winding deformation. Summary of the Invention

[0005] This invention provides an online detection method and system for transformer winding deformation based on impedance spectrum scanning, in order to solve the technical problems of strong subjectivity in detection, insensitivity to slight deformation, easy generation of oscillation spurious peaks during inversion, and inability to make quantitative and accurate judgments in the prior art.

[0006] In a first aspect, the present invention provides an online detection method for transformer winding deformation based on impedance spectral scanning, comprising the following steps: The complex frequency domain impedance data of the transformer winding within a set frequency sweep interval are collected, and a joint sequence of real and imaginary parts is constructed in ascending order of frequency. Based on the logarithmic relaxation time coordinate, a discrete integral mapping matrix between the impedance spectrum and the relaxation time distribution is established, and frequency weights are constructed according to the frequency point distribution density to obtain a weighted inversion model. The discrete integral mapping matrix is ​​reconstructed using a preset non-uniform relaxation time discrete step size; a composite regularization term consisting of zero-order amplitude constraint, first-order smoothness constraint, and second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted according to the current iteration residual and the solution result of the previous round; the non-negative relaxation time distribution is solved iteratively using a weighted inversion model and the composite regularization term, and the frequency weights are updated according to the iteration residual; The obtained relaxation time distribution is subjected to peak cluster identification and merging, and the peak position, peak width and peak intensity characteristic parameters are extracted. Based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum to be measured, the spectral distance, peak position offset and peak width ratio are calculated to construct the winding state discrimination vector. The discrimination vector is compared with the preset discrimination threshold. When the spectral distance and peak position offset of at least one relaxation time segment meet the abnormal conditions and the corresponding peak width ratio exceeds the set threshold, the transformer winding deformation detection result is output.

[0007] Its effects are as follows: by decoupling the complex frequency domain impedance into mutually independent relaxation time peak clusters, and introducing a non-uniform step size reconstruction and residual feedback adjustment mechanism, it solves the problems of traditional impedance spectrum analysis relying on macroscopic statistical indicators, which leads to insensitivity to small deformations and susceptibility to environmental noise masking. It achieves in-depth analysis of the physical state of transformer windings under complex electromagnetic environments, enabling the keen detection of early structural hazards and significantly reducing the subjective errors and false alarm rates of manual qualitative interpretation.

[0008] Furthermore, the discrete integral mapping matrix is ​​reconstructed using a preset non-uniform relaxation time discrete step size, including: Analyze the frequency distribution density in the frequency sweep interval. Use a smaller relaxation time step size in the frequency band with drastic impedance changes to improve resolution, and use a larger relaxation time step size in the frequency band with gentle impedance changes to reduce computational dimensionality. A new relaxation time node sequence is generated based on the assigned non-uniform discrete step size; Substituting the new relaxation time node sequence into the integral kernel function between the impedance spectrum and the relaxation time distribution, the reconstructed non-uniform discrete integral mapping matrix is ​​calculated.

[0009] Its effect is that by using refined discretization step size in the impedance-changing section and sparse sampling in the smooth section, it overcomes the contradiction between computational accuracy and dimensionality when dealing with non-uniform frequency-scanning density data in traditional uniform discretization. While maintaining low computational overhead, it greatly improves the resolution of the dense polarization response region, ensuring that the relaxation time distribution can faithfully reproduce the microscopic physical polarization characteristics of the winding.

[0010] Furthermore, a composite regularization term consisting of a zero-order amplitude constraint, a first-order smoothness constraint, and a second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted based on the current iteration residual and the solution results of the previous round, including: Construct an identity matrix as a zero-order magnitude constraint matrix to limit the overall magnitude of the relaxation time distribution; A first-order difference matrix is ​​constructed as a first-order smoothing constraint matrix to suppress drastic fluctuations between adjacent nodes; Construct a second-order difference matrix as a second-order curvature constraint matrix to ensure the continuity and smoothness of the distribution curve; The zero-order magnitude constraint matrix, the first-order smoothness constraint matrix, and the second-order curvature constraint matrix are left-multiplied by their respective transpose matrices to unify the dimensions. The matrices after unification are then multiplied by their respective regularization constraint coefficients and linearly superimposed to generate a composite regularization term matrix. After each iteration, the ratio of the residual of the current iteration to the residual of the previous iteration is calculated. When the residual ratio is less than the set convergence threshold, the first-order regularization constraint coefficient and the second-order regularization constraint coefficient are increased proportionally to suppress high-frequency oscillations and enhance the stability of the algorithm.

[0011] Its effectiveness lies in the fact that by employing a composite regularization matrix composed of zero-order, first-order, and second-order constraints, and dynamically optimizing the constraint strength based on iterative residuals, it solves the problems of spurious oscillations and excessive broadening of characteristic peaks that are easily caused by traditional regularization methods. This gives the inversion process extremely strong numerical stability and noise resistance, effectively removing background noise interference from the field and extracting a healthy fingerprint spectrum with clear physical meaning and contours.

[0012] Furthermore, peak cluster identification and merging are performed on the obtained relaxation time distribution to extract peak position, peak width, and peak intensity characteristic parameters, including: The first derivative of the obtained non-negative relaxation time distribution curve is calculated. The relaxation time point corresponding to the zero crossover point where the first derivative turns from positive to negative is identified as the initial peak position, and the amplitude corresponding to the zero crossover point is taken as the initial peak intensity. Calculate the distance between adjacent initial peak positions. When the distance is less than the set overlap threshold, merge the corresponding adjacent peak clusters into a merged peak. The peak position of the merged peak is the relaxation time point obtained by weighting the relaxation time points corresponding to the original adjacent initial peak positions with the original adjacent peak intensities as the weights, and the maximum value among the original adjacent peak intensities is taken as the merged peak intensity. Extend outwards from the original two adjacent initial peak positions to find the two outermost relaxation time points corresponding to the amplitude dropping to half of the combined peak intensity. Calculate the relaxation time difference between the two points as the peak width characteristic parameter.

[0013] Its effectiveness lies in the following: by using first-order derivative peak finding and a peak cluster merging algorithm based on physical distance, it effectively eliminates the pseudo-splitting phenomenon caused by fluctuations in numerical calculations. This method clusters dispersed polarization responses into response clusters with substantial meaning, and by quantitatively extracting feature parameters such as peak value and peak width, it transforms qualitative curve observation into quantitative index analysis, providing a concise and efficient feature set for subsequent automatic fault mode classification.

[0014] Furthermore, based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the spectral distance, peak position offset, and peak width ratio are calculated to construct a winding state discrimination vector, including: The relaxation time distribution under normal transformer condition is used as the reference distribution. After interpolating the relaxation time distribution to be measured and the reference distribution to a unified node, the Euclidean distance between the relaxation time distribution to be measured and the reference distribution in the same relaxation time interval is calculated as the spectral distance. Extract the merged peak position of the corresponding peak cluster in the relaxation time distribution to be measured and the reference distribution, and calculate the absolute difference between the position coordinates of the two as the peak position offset. Extract the peak widths of the corresponding peak clusters in the relaxation time distribution to be measured and the reference distribution, and calculate the quotient of the peak width to be measured and the reference peak width as the peak width ratio. By combining spectral distance, peak position offset, and peak width ratio according to relaxation time intervals, a multidimensional discrimination vector representing the state of transformer windings is constructed.

[0015] Its effect is that by using Wasserstein distance to calculate spectral distance and combining it with peak position offset, a multi-dimensional discrimination vector covering the entire frequency band is constructed. Compared with simple correlation coefficient discrimination, it can better reflect the physical displacement and distortion of the inductance and capacitance parameters inside the winding in the local frequency band. By aligning with historical reference data, it can achieve accurate tracking of the mechanical state evolution of the winding throughout the entire life cycle of the transformer.

[0016] Furthermore, the discrimination vector is compared with a preset discrimination threshold. When the spectral distance and peak position shift of at least one relaxation time segment meet the abnormal conditions, and the corresponding peak width ratio exceeds a set threshold, the transformer winding deformation detection result is output, including: A discrimination threshold matrix containing normal, slightly deformed and severely deformed states is pre-established. The discrimination threshold matrix includes the spectral distance threshold, offset threshold and threshold range for different states. The multidimensional discriminant vector is compared with the discriminant threshold matrix segment by segment; When the spectral distance, peak position shift, and peak width ratio within any relaxation time interval fall within the discrimination threshold range corresponding to the slight deformation state, the discrimination interval is considered to have slight deformation; when the discrimination threshold corresponding to the severe deformation state is reached or exceeded, the discrimination interval is considered to have severe deformation. The test results are based on the comprehensive deformation status level of each section, the severity of deformation of the transformer winding, and the corresponding frequency band position.

[0017] Secondly, the present invention provides an online detection system for transformer winding deformation based on impedance spectrum scanning, comprising: The acquisition module is used to acquire complex frequency domain impedance data of transformer windings within a set frequency sweep interval, and construct a joint sequence of real and imaginary parts in ascending order of frequency; based on the logarithmic relaxation time coordinate, a discrete integral mapping matrix between impedance spectrum and relaxation time distribution is established, and frequency weights are constructed according to frequency point distribution density to obtain a weighted inversion model. The update module is used to reconstruct the discrete integral mapping matrix using a preset non-uniform relaxation time discrete step size; apply a composite regularization term consisting of zero-order amplitude constraint, first-order smoothness constraint, and second-order curvature constraint to the relaxation time distribution, and adjust the coefficients of each regularization constraint according to the current iteration residual and the solution result of the previous round; iteratively solve the non-negative relaxation time distribution using a weighted inversion model and composite regularization term, and update the frequency weights according to the iteration residual; The output module is used to identify and merge peak clusters in the obtained relaxation time distribution, and extract peak position, peak width, and peak intensity characteristic parameters. Based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the module calculates the spectral distance, peak position offset, and peak width ratio to construct a winding state discrimination vector. The discrimination vector is compared with a preset discrimination threshold. When the spectral distance and peak position offset of at least one relaxation time segment meet the abnormal conditions, and the corresponding peak width ratio exceeds the set threshold, the module outputs the transformer winding deformation detection result.

[0018] Furthermore, the discrete integral mapping matrix is ​​reconstructed using a preset non-uniform relaxation time discrete step size, including: Analyze the frequency distribution density in the frequency sweep interval. Use a smaller relaxation time step size in the frequency band with drastic impedance changes to improve resolution, and use a larger relaxation time step size in the frequency band with gentle impedance changes to reduce computational dimensionality. A new relaxation time node sequence is generated based on the assigned non-uniform discrete step size; Substituting the new relaxation time node sequence into the integral kernel function between the impedance spectrum and the relaxation time distribution, the reconstructed non-uniform discrete integral mapping matrix is ​​calculated.

[0019] Furthermore, a composite regularization term consisting of a zero-order amplitude constraint, a first-order smoothness constraint, and a second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted based on the current iteration residual and the solution result of the previous round, including: Construct an identity matrix as a zero-order magnitude constraint matrix to limit the overall magnitude of the relaxation time distribution; A first-order difference matrix is ​​constructed as a first-order smoothing constraint matrix to suppress drastic fluctuations between adjacent nodes; Construct a second-order difference matrix as a second-order curvature constraint matrix to ensure the continuity and smoothness of the distribution curve; The zero-order magnitude constraint matrix, the first-order smoothness constraint matrix, and the second-order curvature constraint matrix are left-multiplied by their respective transpose matrices to unify the dimensions. The matrices after unification are then multiplied by their respective regularization constraint coefficients and linearly superimposed to generate a composite regularization term matrix. After each iteration, the ratio of the residual of the current iteration to the residual of the previous iteration is calculated. When the residual ratio is less than the set convergence threshold, the first-order regularization constraint coefficient and the second-order regularization constraint coefficient are increased proportionally to suppress high-frequency oscillations and enhance the stability of the algorithm.

[0020] Furthermore, peak cluster identification and merging are performed on the obtained relaxation time distribution to extract peak position, peak width, and peak intensity characteristic parameters, including: The first derivative of the obtained non-negative relaxation time distribution curve is calculated. The relaxation time point corresponding to the zero crossover point where the first derivative turns from positive to negative is identified as the initial peak position, and the amplitude corresponding to the zero crossover point is taken as the initial peak intensity. Calculate the distance between adjacent initial peak positions. When the distance is less than the set overlap threshold, merge the corresponding adjacent peak clusters into a merged peak. The peak position of the merged peak is the relaxation time point obtained by weighting the relaxation time points corresponding to the original adjacent initial peak positions with the original adjacent peak intensities as the weights, and the maximum value among the original adjacent peak intensities is taken as the merged peak intensity. Extend outwards from the original two adjacent initial peak positions to find the two outermost relaxation time points corresponding to the amplitude dropping to half of the combined peak intensity. Calculate the relaxation time difference between the two points as the peak width characteristic parameter.

[0021] The beneficial effects are as follows: This invention constructs a joint sequence of real and imaginary parts by collecting complex frequency domain impedance data, thus preserving the integrity of impedance information. By establishing a discrete integral mapping matrix and combining it with frequency weights to construct a weighted inversion model, the interference of uneven frequency distribution on inversion accuracy is reduced. In the model solution, a non-uniform discrete step size is used to reconstruct the mapping matrix, and a composite regularization term consisting of zero-order amplitude, first-order smoothing, and second-order curvature is applied. The regularization constraint coefficients and frequency weights are precisely adjusted based on the iterative residuals and the results of the previous round, enhancing the noise resistance and numerical stability of the inversion process, avoiding overfitting, and ensuring the high-fidelity non-negative relaxation time distribution is obtained. By extracting the peak cluster features of the relaxation time distribution, calculating the spectral distance, peak position shift, and peak width ratio to construct a multi-dimensional discrimination vector, and performing multi-condition cross-comparison judgment, this mechanism deeply explores the microscopic variation law of the impedance spectrum from multiple dimensions, improving the sensitivity and evaluation accuracy of detecting small deformations in transformer windings, and reducing the risk of misjudgment caused by single feature discrimination. Attached Figure Description

[0022] Figure 1 This is a flowchart of an online detection method for transformer winding deformation based on impedance spectrum scanning.

[0023] Figure 2 This is a schematic diagram of non-uniform discrete step size distribution.

[0024] Figure 3 This is a schematic diagram of the regularization process.

[0025] Figure 4 This is a schematic diagram showing the comparison of discriminant vector features. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] An embodiment of the online detection method for transformer winding deformation based on impedance spectrum scanning provided by this invention: like Figure 1 As shown, the online detection method for transformer winding deformation based on impedance spectroscopy scanning includes the following steps: S1: Collect impedance data and construct a joint sequence of real and imaginary parts by sorting them by frequency.

[0028] Collect complex frequency domain impedance data of transformer windings within a set frequency sweep interval, and construct a joint sequence of real and imaginary parts in ascending order of frequency.

[0029] A wideband impedance analyzer is used to apply sinusoidal excitation signals to the high and low voltage windings of the transformer, and the linear or logarithmic frequency sweep control function at the device's underlying level is invoked to perform frequency sweep. The impedance spectrum containing the real part of the resistance and the imaginary part of the reactance is obtained. The real and imaginary part arrays are then concatenated row by row using the concatenate function of the NumPy library in Python to form a one-dimensional joint sequence of real numbers with a dimension of twice the number of frequency points.

[0030] S2, construct the mapping matrix, and construct the weighted inversion model according to the frequency density.

[0031] Based on the logarithmic relaxation time coordinates, a discrete integral mapping matrix between the impedance spectrum and the relaxation time distribution is established, and frequency weights are constructed according to the frequency distribution density to obtain a weighted inversion model.

[0032] Logarithmic coordinate axes are defined based on the reciprocal relationship between angular frequency and relaxation time, and a mapping relationship is constructed based on the impedance kernel function of the generalized Maxwell model. A two-dimensional grid of frequency and relaxation time is generated using the `meshgrid` function from the NumPy library, and the real and imaginary parts of the kernel function are calculated and combined to form a discrete integral mapping matrix. The reciprocal of the logarithmic difference between adjacent frequency points is used as the input to the kernel density estimation function. The `gaussian_kde` function from the SciPy library is used to calculate the frequency distribution density, and the reciprocal of the density is used to construct a diagonal weighting matrix. Multiplying this matrix by the mapping matrix yields the weighted inversion model.

[0033] S3, reconstruct the mapping matrix by allocating non-uniform step sizes according to impedance changes.

[0034] The discrete integral mapping matrix is ​​reconstructed by using a preset non-uniform relaxation time discrete step size.

[0035] The singular value distribution of the discrete integral mapping matrix in the logarithmic relaxation time domain is calculated, and the svd singular value decomposition function from the linalg module of the SciPy library is used to extract principal component features. The non-uniform discrete step size is set according to the gradient rate of change of the feature vectors. Logarithmically evenly spaced dense sampling is used in polarization regions with rapid gradient changes, while sparse sampling is used in gentler regions. Based on an interpolation algorithm, the interp1d function from the SciPy library is used to resample and reconstruct the discrete integral mapping matrix according to the new step size, performing dimensionality reduction processing. Figure 2 As shown, in the mid-frequency range where impedance changes drastically, a smaller step size is used to ensure high resolution; in the low-frequency and high-frequency ranges where the changes are gradual, a larger step size is used to reduce the computational dimensionality. This strategy achieves a balance between high local accuracy and low overall computational cost.

[0036] In one embodiment, the discrete integral mapping matrix is ​​reconstructed using a preset non-uniform relaxation time discrete step size, including: Analyze the frequency distribution density in the frequency sweep interval. Use a smaller relaxation time step size in the frequency band with drastic impedance changes to improve resolution, and use a larger relaxation time step size in the frequency band with gentle impedance changes to reduce computational dimensionality. A new relaxation time node sequence is generated based on the assigned non-uniform discrete step size; Substituting the new relaxation time node sequence into the integral kernel function between the impedance spectrum and the relaxation time distribution, the reconstructed non-uniform discrete integral mapping matrix is ​​calculated.

[0037] The degree of impedance variation within the frequency sweep interval is evaluated by calculating the first-order difference of the impedance magnitudes between adjacent frequency points. A set of impedance difference thresholds is defined: frequencies with a relative rate of change exceeding the preferred range of 10%-15% are defined as drastically changing frequency bands; those with a relative rate of change between 2%-10% are considered moderately changing frequency bands; and those with a relative rate of change less than 2% are considered gently changing frequency bands. Based on this, a non-uniform relaxation time step size is allocated: a smaller logarithmic step size is used in drastically changing frequency bands. =0.05, using a step size in the medium frequency variation band. =0.1, a larger step size is used in the gradually changing frequency band. =0.2, thus establishing the relaxation time range (e.g. s to Within s, a new relaxation time node sequence is generated, consisting of N=120 unequally spaced nodes. The generated new node sequence is then substituted into the Debye integral kernel function of the relaxation time distribution, where the real part of the kernel function is... The imaginary kernel function is Angular frequency here For each measured frequency point Relaxation time nodes The discrete integral values ​​of the kernel function on the node interval are calculated respectively, and the integral results of each node are spliced ​​together to form a reconstructed non-uniform discrete integral mapping matrix A with a size of 2M×N, where M is the total number of measurement frequency points, for example, M=100, thus achieving a balance between local high resolution and overall low computational dimensionality.

[0038] S4, add a composite regularization term, and adjust the constraint coefficients according to the iterative residuals.

[0039] A composite regularization term consisting of zero-order amplitude constraint, first-order smoothness constraint and second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted according to the current iteration residual and the solution result of the previous round.

[0040] A composite regularization operator matrix is ​​constructed, comprising a zero-order identity matrix, a first-order forward difference matrix, and a second-order central difference matrix. In each iteration, the relaxation time distribution vector from the previous iteration is extracted. The mean square error residual between the current reconstructed impedance and the measured impedance is calculated using the `norm` function from the NumPy library. The constraint coefficients are updated using the L-curve method combined with the generalized cross-validation (GCV) algorithm. The `minimize` function is used to output the third-order regularized constraint coefficients required for the next iteration, guided by minimizing the GCV objective function.

[0041] In one embodiment, a composite regularization term consisting of a zero-order amplitude constraint, a first-order smoothness constraint, and a second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted according to the current iteration residual and the solution result of the previous round, including: Construct an identity matrix as a zero-order magnitude constraint matrix to limit the overall magnitude of the relaxation time distribution; A first-order difference matrix is ​​constructed as a first-order smoothing constraint matrix to suppress drastic fluctuations between adjacent nodes; Construct a second-order difference matrix as a second-order curvature constraint matrix to ensure the continuity and smoothness of the distribution curve; The zero-order magnitude constraint matrix, the first-order smoothness constraint matrix, and the second-order curvature constraint matrix are left-multiplied by their respective transpose matrices to unify the dimensions. The matrices after unification are then multiplied by their respective regularization constraint coefficients and linearly superimposed to generate a composite regularization term matrix. After each iteration, the ratio of the residual of the current iteration to the residual of the previous iteration is calculated. When the residual ratio is less than the set convergence threshold, the first-order regularization constraint coefficient and the second-order regularization constraint coefficient are increased proportionally to suppress high-frequency oscillations and enhance the stability of the algorithm.

[0042] To construct the composite regularization term, generate an identity matrix of size N×N. As the zero-order magnitude constraint matrix, construct an (N-1)×N first-order difference matrix containing elements of 1 on the main diagonal and elements of -1 on the secondary diagonal. And a (N-2)×N second-order difference matrix containing a main diagonal of 2 and two side diagonals of -1. Calculate the product of each matrix and its transpose, i.e. , and This transforms the three matrices into N×N positive semidefinite symmetric matrices, which are then multiplied by the initial regularization constraint coefficients. , , The linear superposition generates a composite regular term matrix. This is used to construct the objective function and solve it in the initial iteration using a non-negative least squares algorithm. During the iterative solution process, the residual ratio is utilized. As a feedback variable, The relaxation time distribution is obtained from the k-th iteration. The convergence threshold is preferably set to 0.95. When A value <0.95 indicates that the objective function's downward trend is gradual and it may be approaching the overfitting edge. According to the update formula... and Increase smoothness and curvature constraints, where the adjustment factor is preferably... =1.2 and =1.5; conversely, if If the coefficient is ≥0.95, the current coefficient remains unchanged or is slightly reduced, allowing the regularization strength to be adjusted as the iterative residual evolves, thus suppressing spurious high-frequency oscillations and false peaks in the inversion results. Figure 3 As shown, the black curve represents the residual ratio during the iteration process, which gradually converges with the increase of the number of iterations; the gray curve represents the adjusted constraint coefficient, which increases after the residual ratio tends to stabilize. By adjusting the regularization intensity through the residual feedback mechanism, spurious peaks in the inversion results are suppressed, and the stability of the relaxation time distribution solution is improved.

[0043] S5, iteratively solve the non-negative distribution, and update the frequency weights according to the residuals.

[0044] The non-negative relaxation time distribution is solved iteratively using a weighted inversion model and a composite regularization term, and the frequency weights are updated based on the iterative residuals.

[0045] The composite regularization term is incorporated into the quadratic objective function of the weighted inversion model, transforming it into a standard non-negative least squares problem. The `nnls` function from the `optimize` module of the SciPy library or the FISTA fast iterative threshold shrinkage algorithm is used for numerical optimization with non-negativity constraints. This yields the relaxation time distribution vector for the current iteration, calculates the absolute residuals at each frequency point, and uses the Huber loss function to calculate and update the penalty factor. The diagonal weighted matrix is ​​then regenerated using the `diag` function from the NumPy library, replacing the original frequency weights, and the process continues until the rate of change of the residuals between two consecutive iterations is less than a set tolerance.

[0046] S6 identifies and merges peak clusters, extracting peak value, peak width, and peak intensity parameters.

[0047] Peak clusters are identified and merged from the obtained relaxation time distribution, and peak position, peak width and peak intensity characteristic parameters are extracted.

[0048] The `find_peaks` function from the `signal` module of the SciPy library is used to search for extreme points on the converged relaxation time distribution curve. A Gaussian Mixture Model (GMM) clustering algorithm is then used to merge adjacent peaks whose distance is less than half the full width at half maximum (WWM). The x-coordinate corresponding to the highest point of each independent peak cluster is extracted as the peak position. The peak width is calculated based on the x-coordinate distance spanned by the curve as it descends to half the height of the highest point. Finally, the `trapz` trapezoidal integral function from the `integrate` module of the SciPy library is used to calculate the area enclosed by the peak cluster curve and the x-axis, which is used as the peak intensity feature parameter.

[0049] In one embodiment, the obtained relaxation time distribution is subjected to peak cluster identification and merging, and peak position, peak width, and peak intensity feature parameters are extracted, including: The first derivative of the obtained non-negative relaxation time distribution curve is calculated. The relaxation time point corresponding to the zero crossover point where the first derivative turns from positive to negative is identified as the initial peak position, and the amplitude corresponding to the zero crossover point is taken as the initial peak intensity. Calculate the distance between adjacent initial peak positions. When the distance is less than the set overlap threshold, merge the corresponding adjacent peak clusters into a merged peak. The peak position of the merged peak is the relaxation time point obtained by weighting the relaxation time points corresponding to the original adjacent initial peak positions with the original adjacent peak intensities as the weights, and the maximum value among the original adjacent peak intensities is taken as the merged peak intensity. Extend outwards from the original two adjacent initial peak positions to find the two outermost relaxation time points corresponding to the amplitude dropping to half of the combined peak intensity. Calculate the relaxation time difference between the two points as the peak width characteristic parameter.

[0050] The first derivative of the inverted nonnegative relaxation time distribution curve is estimated using the finite difference method, and the derivative sequence is detected point by point using a peak-finding algorithm. The noise removal threshold is reached when the first derivative changes from positive to negative and the absolute value of the difference before and after the zero-crossing point exceeds a preset noise removal threshold. At that time, record the coordinates of the relaxation time node corresponding to the zero-crossing point, and mark the time node coordinates as the initial peak position. The corresponding amplitude is denoted as the initial peak intensity. By calculating the distance between adjacent initial peak positions in logarithmic coordinates. The distance is then compared with an overlap threshold (preferred to be between 0.5 and 0.8 decimal places, e.g., 0.6 in this example). If the distance is less than 0.6, the adjacent double peaks are determined to be pseudo-split phenomena caused by the same physical polarization process. For adjacent peak clusters that meet the overlap condition, a peak cluster merging procedure is initiated, and the position of the merged peak is calculated using a weighted average method. And the maximum value among the original adjacent peak intensities As a merger of Peak Power After all merging is completed, for each merged peak cluster containing multiple initial peaks, scan interpolation is performed from the leftmost initial peak position towards the low-frequency side and from the rightmost initial peak position towards the high-frequency side to locate the leftmost half-peak point where the amplitude decays to 0.5 times the merged peak intensity. and the rightmost half-highest point And calculate the difference on a logarithmic scale. , which serves as a peak width characteristic parameter representing the response span of the current relaxation polarization process.

[0051] S7 calculates the ratio of spectral offset to form the winding state discrimination vector.

[0052] Based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the spectral distance, peak position offset and peak width ratio are calculated, and the winding state discrimination vector is constructed.

[0053] Aligning the historical normal state reference impedance spectrum characteristics with the current measured characteristics, the wasserstein_distance function in the stats module of the SciPy library is used to calculate the bulldozer distance between the relaxation time distribution curves of the two as the spectral distance. The absolute value of subtracting the reference peak position from the measured peak position is used as the peak position offset. The measured peak width is divided by the reference peak width as the peak width ratio. Using the array function of the NumPy library, the extracted spectral distance, peak position offset, and peak width ratio values ​​for each relaxation time segment are arranged and combined in sequence to form a multidimensional floating-point winding state discrimination vector.

[0054] In one embodiment, based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the spectral distance, peak position offset, and peak width ratio are calculated to construct a winding state discrimination vector, including: The relaxation time distribution under normal transformer condition is used as the reference distribution. After interpolating the relaxation time distribution to be measured and the reference distribution to a unified node, the Euclidean distance between the relaxation time distribution to be measured and the reference distribution in the same relaxation time interval is calculated as the spectral distance. Extract the merged peak position of the corresponding peak cluster in the relaxation time distribution to be measured and the reference distribution, and calculate the absolute difference between the position coordinates of the two as the peak position offset. Extract the peak widths of the corresponding peak clusters in the relaxation time distribution to be measured and the reference distribution, and calculate the quotient of the peak width to be measured and the reference peak width as the peak width ratio. By combining spectral distance, peak position offset, and peak width ratio according to relaxation time intervals, a multidimensional discrimination vector representing the state of transformer windings is constructed.

[0055] Using the impedance spectrum of the transformer at the time of manufacture or initial commissioning as a benchmark, the relaxation time distribution under normal conditions is extracted as a reference distribution. A cubic spline interpolation algorithm is then used to resample the measured relaxation time distribution and the reference distribution onto a standard coordinate system containing N=200 logarithmically equidistant nodes. Based on this, the distribution range is divided into low-frequency regions according to the main polarization response frequency range, such as... s to s, intermediate frequency region s to s and high frequency region s to Within each segment, the standard resampling nodes are aligned one by one, and the Euclidean distance Ed between the amplitudes of the measured distribution and the reference distribution is calculated. The result is used as the spectral distance parameter representing the overall distortion of the waveform. Feature-level representation comparisons are performed, and the reference merged peak position is extracted using the mid-frequency segment as an example. For example, the corresponding relaxation time s and the position of the combined peak value to be measured ,like s, calculate the absolute difference between the two in logarithmic coordinates. As the peak position offset, the corresponding peak width to be measured is extracted. Compared with reference peak width Calculate the dimensionless quotient =1.25 is used as the peak width ratio. The spectral distance, peak position shift, and peak width ratio extracted from each segment are concatenated in an ordered manner, such as combining them into a one-dimensional array with 9 elements. In this way, a multidimensional discriminant vector can be constructed that can comprehensively represent the evolution of the mechanical state of transformer windings.

[0056] S8 compares the threshold to determine anomalies and outputs the winding deformation results.

[0057] The discrimination vector is compared with the preset discrimination threshold. When the spectral distance and peak position offset of at least one relaxation time segment meet the abnormal conditions and the corresponding peak width ratio exceeds the set threshold, the transformer winding deformation detection result is output.

[0058] Pre-trained classification thresholds based on the Support Vector Machine (SVM) algorithm are loaded into the industrial control computer's memory. Python's built-in logical relational operators are used to iterate and compare the discrimination vector elements. When an exception is detected where the spectral distance corresponding to a specific time constant interval is greater than a preset distance threshold, the peak position offset is greater than a preset time constant offset threshold, and the peak width ratio is greater than a preset broadening coefficient threshold, an exception boolean variable is triggered. The alarm information, including the degree of deformation and the damaged frequency band, is output to the host computer's display interface via Python's standard input / output stream using the `print` function or the serial communication library `pyserial`.

[0059] In one embodiment, the discrimination vector is compared with a preset discrimination threshold. When the spectral distance and peak position shift of at least one relaxation time segment meet the abnormal conditions, and the corresponding peak width ratio exceeds a set threshold, the transformer winding deformation detection result is output, including: A discrimination threshold matrix containing normal, slightly deformed and severely deformed states is pre-established. The discrimination threshold matrix includes the spectral distance threshold, offset threshold and threshold range for different states. The multidimensional discriminant vector is compared with the discriminant threshold matrix segment by segment; When the spectral distance, peak position shift, and peak width ratio within any relaxation time interval fall within the discrimination threshold range corresponding to the slight deformation state, the discrimination interval is considered to have slight deformation; when the discrimination threshold corresponding to the severe deformation state is reached or exceeded, the discrimination interval is considered to have severe deformation. The test results are based on the comprehensive deformation status level of each section, the severity of deformation of the transformer winding, and the corresponding frequency band position.

[0060] Based on historical transformer winding deformation fault samples and simulation data, a 3×3 discrimination threshold matrix is ​​constructed. Rows represent three states: slight deformation, moderate deformation, and severe deformation, while columns represent the critical triggering indicators for each state. For the mid-frequency range, the preferred threshold range for the normal state is set as the upper limit of the spectral distance threshold. =0.15, upper limit of offset threshold =0.1 tenth harmonic, the normal threshold range for peak width ratio is [0.9, 1.1]; if the index exceeds the above normal threshold, the spectral distance threshold range for slight deformation is further defined as [0.15, 0.3], and the offset range as [0.1, 0.25]; the spectral distance threshold range for moderate deformation is (0.3, 0.5], and the offset range is (0.25, 0.4]; the spectral distance threshold for severe deformation is set to be greater than 0.5, and the offset threshold is set to be greater than 0.4. During detection and evaluation, each element in the online generated multidimensional discrimination vector is compared with the discrimination threshold matrix according to frequency segments. For example, if In the mid-frequency range, a measured spectral distance of 0.35, a peak offset of 0.3 decathlon, and a peak width ratio of 1.35 were detected. Since these indicators fall within the threshold range for moderate deformation, the winding in this range is determined to have moderate deformation. The number of relaxation time segments classified as various deformation states is statistically analyzed and matched against a fault mapping table. For example, if only a slight threshold exceedance occurs in the high-frequency range, it is identified as slight lead deformation. If both mid- and high-frequency indicators fall within the severe deformation threshold range (e.g., spectral distance greater than 0.5 and offset greater than 0.4 decathlon), the diagnostic result of severe axial / radial deformation of the winding is output, along with the specific frequency band where the offset occurred. Figure 4As shown, under normal conditions, the spectral distance of each frequency band remains at a low level; when there is slight deformation, the spectral distance of the low and mid frequency bands rises to the slight threshold range; when there is severe deformation, the spectral distance of the entire frequency band increases and exceeds the severe threshold limit, with the high frequency band showing the largest increase.

[0061] In terms of experimental conditions, ablation experiments were conducted based on a measured broadband impedance spectrum dataset of transformers. This dataset contains 120 samples covering normal, slightly deformed, and severely deformed states, with a frequency sweep range of 10 Hz to 1 MHz. The experiments used four dimensions as evaluation metrics: root mean square error of inversion, average time taken for a single inversion, average number of spurious peaks, and accuracy of winding deformation state detection. The comparison models were set as the baseline scheme (uniform discrete step size combined with a single fixed second-order regularization), ablation scheme one (non-uniform discrete step size combined with a single fixed regularization), ablation scheme two (uniform discrete step size combined with composite regularization), and the complete scheme proposed in this paper.

[0062] The specific data and results of the experiment show that the root mean square error (RMSE) of the baseline scheme is 4.6%, the single-session time is 1.35s, the average number of spurious peaks is 2.4, and the detection accuracy is only 78.5%. The RMSE of ablation scheme one slightly decreased to 3.9%, the single-session time was shortened to 0.42s, the average number of spurious peaks was 2.2, and the detection accuracy improved to 82.4%. The RMSE of ablation scheme two decreased to 2.1%, the single-session time increased to 1.58s, the number of spurious peaks plummeted to 0.3, and the detection accuracy reached 91.5%. The complete scheme performed best, with an RMSE of only 1.2%, a single-session time maintained at 0.48s, completely eliminating spurious peaks, and a detection accuracy as high as 98.5%.

[0063] Performance improvement analysis shows that by employing non-uniform relaxation time dispersion and densifying nodes in regions of drastic impedance changes and sparser nodes in regions of smooth impedance changes, a balance between local high resolution and low computational dimensionality is successfully achieved, improving the algorithm's running efficiency. Utilizing a composite regularization strategy and adjusting constraint coefficients based on iterative residuals overcomes the high-frequency oscillation problem when the objective function approaches the overfitting edge, fundamentally eliminating the pseudo-splitting phenomenon caused by the physical polarization process. The complete scheme integrates the advantages of mesh reconstruction and regularization, extracting high-precision peak position offset and spectral distance discrimination features while ensuring fast response, enabling transformer winding deformation detection to achieve both high real-time performance and high reliability.

[0064] An embodiment of the online transformer winding deformation detection system based on impedance spectrum scanning provided by this invention includes the following modules: The acquisition module is used to acquire complex frequency domain impedance data of transformer windings within a set frequency sweep interval, and construct a joint sequence of real and imaginary parts in ascending order of frequency; based on the logarithmic relaxation time coordinate, a discrete integral mapping matrix between impedance spectrum and relaxation time distribution is established, and frequency weights are constructed according to frequency point distribution density to obtain a weighted inversion model. The update module is used to reconstruct the discrete integral mapping matrix using a preset non-uniform relaxation time discrete step size; apply a composite regularization term consisting of zero-order amplitude constraint, first-order smoothness constraint, and second-order curvature constraint to the relaxation time distribution, and adjust the coefficients of each regularization constraint according to the current iteration residual and the solution result of the previous round; iteratively solve the non-negative relaxation time distribution using a weighted inversion model and composite regularization term, and update the frequency weights according to the iteration residual; The output module is used to identify and merge peak clusters in the obtained relaxation time distribution, and extract peak position, peak width, and peak intensity characteristic parameters. Based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the module calculates the spectral distance, peak position offset, and peak width ratio to construct a winding state discrimination vector. The discrimination vector is compared with a preset discrimination threshold. When the spectral distance and peak position offset of at least one relaxation time segment meet the abnormal conditions, and the corresponding peak width ratio exceeds the set threshold, the module outputs the transformer winding deformation detection result.

[0065] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for online detection of transformer winding deformation based on impedance spectral scanning, characterized in that, Includes the following steps: The complex frequency domain impedance data of the transformer winding within a set frequency sweep interval are collected, and a joint sequence of real and imaginary parts is constructed in ascending order of frequency. Based on the logarithmic relaxation time coordinate, a discrete integral mapping matrix between the impedance spectrum and the relaxation time distribution is established, and frequency weights are constructed according to the frequency point distribution density to obtain a weighted inversion model. The discrete integral mapping matrix is ​​reconstructed using a preset non-uniform relaxation time discrete step size; a composite regularization term consisting of zero-order amplitude constraint, first-order smoothness constraint, and second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted according to the current iteration residual and the solution result of the previous round; the non-negative relaxation time distribution is solved iteratively using a weighted inversion model and the composite regularization term, and the frequency weights are updated according to the iteration residual; Peak clusters are identified and merged in the obtained relaxation time distribution, and peak position, peak width and peak intensity characteristic parameters are extracted; Based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the spectral distance, peak position offset and peak width ratio are calculated to construct a winding state discrimination vector. The discrimination vector is compared with a preset discrimination threshold. When the spectral distance and peak position offset of at least one relaxation time segment meet the abnormal conditions and the corresponding peak width ratio exceeds the set threshold, the transformer winding deformation detection result is output.

2. The online detection method for transformer winding deformation based on impedance spectrum scanning according to claim 1, characterized in that, The discrete integral mapping matrix is ​​reconstructed using a preset non-uniform relaxation time discrete step size, including: Analyze the frequency distribution density in the frequency sweep interval. Use a smaller relaxation time step size in the frequency band with drastic impedance changes to improve resolution, and use a larger relaxation time step size in the frequency band with gentle impedance changes to reduce computational dimensionality. A new relaxation time node sequence is generated based on the assigned non-uniform discrete step size; Substituting the new relaxation time node sequence into the integral kernel function between the impedance spectrum and the relaxation time distribution, the reconstructed non-uniform discrete integral mapping matrix is ​​calculated.

3. The online detection method for transformer winding deformation based on impedance spectrum scanning according to claim 1, characterized in that, A composite regularization term consisting of a zero-order amplitude constraint, a first-order smoothness constraint, and a second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted based on the current iteration residual and the solution result of the previous round, including: Construct an identity matrix as a zero-order magnitude constraint matrix to limit the overall magnitude of the relaxation time distribution; A first-order difference matrix is ​​constructed as a first-order smoothing constraint matrix to suppress drastic fluctuations between adjacent nodes; Construct a second-order difference matrix as a second-order curvature constraint matrix to ensure the continuity and smoothness of the distribution curve; The zero-order magnitude constraint matrix, the first-order smoothness constraint matrix, and the second-order curvature constraint matrix are left-multiplied by their respective transpose matrices to unify the dimensions. The matrices after unification are then multiplied by their respective regularization constraint coefficients and linearly superimposed to generate a composite regularization term matrix. After each iteration, the ratio of the residual of the current iteration to the residual of the previous iteration is calculated. When the residual ratio is less than the set convergence threshold, the first-order regularization constraint coefficient and the second-order regularization constraint coefficient are increased proportionally to suppress high-frequency oscillations and enhance the stability of the algorithm.

4. The online detection method for transformer winding deformation based on impedance spectrum scanning according to claim 1, characterized in that, Peak clusters are identified and merged from the obtained relaxation time distribution, and peak position, peak width, and peak intensity feature parameters are extracted, including: The first derivative of the obtained non-negative relaxation time distribution curve is calculated. The relaxation time point corresponding to the zero crossover point where the first derivative turns from positive to negative is identified as the initial peak position, and the amplitude corresponding to the zero crossover point is taken as the initial peak intensity. Calculate the distance between adjacent initial peak positions. When the distance is less than the set overlap threshold, merge the corresponding adjacent peak clusters into a merged peak. The peak position of the merged peak is the relaxation time point obtained by weighting the relaxation time points corresponding to the original adjacent initial peak positions with the original adjacent peak intensities as the weights, and the maximum value among the original adjacent peak intensities is taken as the merged peak intensity. Extend outwards from the original two adjacent initial peak positions to find the two outermost relaxation time points corresponding to the amplitude dropping to half of the combined peak intensity. Calculate the relaxation time difference between the two points as the peak width characteristic parameter.

5. The online detection method for transformer winding deformation based on impedance spectrum scanning according to claim 1 or 4, characterized in that, Based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the spectral distance, peak position offset, and peak width ratio are calculated to construct a winding state discrimination vector, including: The relaxation time distribution under normal transformer condition is used as the reference distribution. After interpolating the relaxation time distribution to be measured and the reference distribution to a unified node, the Euclidean distance between the relaxation time distribution to be measured and the reference distribution in the same relaxation time interval is calculated as the spectral distance. Extract the merged peak position of the corresponding peak cluster in the relaxation time distribution to be measured and the reference distribution, and calculate the absolute difference between the two position coordinates as the peak position offset. Extract the peak widths of the corresponding peak clusters in the relaxation time distribution to be measured and the reference distribution, and calculate the quotient of the peak width to be measured and the reference peak width as the peak width ratio. By combining spectral distance, peak position offset, and peak width ratio according to relaxation time intervals, a multidimensional discrimination vector representing the state of transformer windings is constructed.

6. The online detection method for transformer winding deformation based on impedance spectrum scanning according to claim 1, characterized in that, The discrimination vector is compared with a preset discrimination threshold. When the spectral distance and peak position shift of at least one relaxation time segment meet the abnormal conditions, and the corresponding peak width ratio exceeds a set threshold, the transformer winding deformation detection result is output, including: A discrimination threshold matrix containing normal, slightly deformed and severely deformed states is pre-established. The discrimination threshold matrix includes the spectral distance threshold, offset threshold and threshold range for different states. The multidimensional discriminant vector is compared with the discriminant threshold matrix segment by segment; When the spectral distance, peak position shift, and peak width ratio within any relaxation time interval fall within the discrimination threshold range corresponding to the slight deformation state, the discrimination interval is considered to have slight deformation; when the discrimination threshold corresponding to the severe deformation state is reached or exceeded, the discrimination interval is considered to have severe deformation. The test results are based on the comprehensive deformation status level of each section, the severity of deformation of the transformer winding, and the corresponding frequency band position.

7. An online detection system for transformer winding deformation based on impedance spectral scanning, characterized in that, include: The acquisition module is used to acquire complex frequency domain impedance data of transformer windings within a set frequency sweep interval, and construct a joint sequence of real and imaginary parts in ascending order of frequency. Based on the logarithmic relaxation time coordinates, a discrete integral mapping matrix between the impedance spectrum and the relaxation time distribution is established, and frequency weights are constructed according to the frequency point distribution density to obtain a weighted inversion model. The update module is used to reconstruct the discrete integral mapping matrix using a preset non-uniform relaxation time discrete step size; apply a composite regularization term consisting of zero-order amplitude constraint, first-order smoothness constraint, and second-order curvature constraint to the relaxation time distribution, and adjust the coefficients of each regularization constraint according to the current iteration residual and the solution result of the previous round; iteratively solve the non-negative relaxation time distribution using a weighted inversion model and composite regularization term, and update the frequency weights according to the iteration residual; The output module is used to identify and merge peak clusters in the obtained relaxation time distribution, and extract peak position, peak width and peak intensity characteristic parameters; Based on the relaxation time distribution characteristic parameters corresponding to the reference impedance spectrum and the impedance spectrum under test, the spectral distance, peak position offset and peak width ratio are calculated to construct a winding state discrimination vector. The discrimination vector is compared with a preset discrimination threshold. When the spectral distance and peak position offset of at least one relaxation time segment meet the abnormal conditions and the corresponding peak width ratio exceeds the set threshold, the transformer winding deformation detection result is output.

8. The system according to claim 7, characterized in that, The discrete integral mapping matrix is ​​reconstructed using a preset non-uniform relaxation time discrete step size, including: Analyze the frequency distribution density in the frequency sweep interval. Use a smaller relaxation time step size in the frequency band with drastic impedance changes to improve resolution, and use a larger relaxation time step size in the frequency band with gentle impedance changes to reduce computational dimensionality. A new relaxation time node sequence is generated based on the assigned non-uniform discrete step size; Substituting the new relaxation time node sequence into the integral kernel function between the impedance spectrum and the relaxation time distribution, the reconstructed non-uniform discrete integral mapping matrix is ​​calculated.

9. The system according to claim 7, characterized in that, A composite regularization term consisting of a zero-order amplitude constraint, a first-order smoothness constraint, and a second-order curvature constraint is applied to the relaxation time distribution, and the coefficients of each regularization constraint are adjusted based on the current iteration residual and the solution result of the previous round, including: Construct an identity matrix as a zero-order magnitude constraint matrix to limit the overall magnitude of the relaxation time distribution; A first-order difference matrix is ​​constructed as a first-order smoothing constraint matrix to suppress drastic fluctuations between adjacent nodes; Construct a second-order difference matrix as a second-order curvature constraint matrix to ensure the continuity and smoothness of the distribution curve; The zero-order magnitude constraint matrix, the first-order smoothness constraint matrix, and the second-order curvature constraint matrix are left-multiplied by their respective transpose matrices to unify the dimensions. The matrices after unification are then multiplied by their respective regularization constraint coefficients and linearly superimposed to generate a composite regularization term matrix. After each iteration, the ratio of the residual of the current iteration to the residual of the previous iteration is calculated. When the residual ratio is less than the set convergence threshold, the first-order regularization constraint coefficient and the second-order regularization constraint coefficient are increased proportionally to suppress high-frequency oscillations and enhance the stability of the algorithm.

10. The system according to claim 7, characterized in that, Peak clusters are identified and merged from the obtained relaxation time distribution, and peak position, peak width, and peak intensity feature parameters are extracted, including: The first derivative of the obtained non-negative relaxation time distribution curve is calculated. The relaxation time point corresponding to the zero crossover point where the first derivative turns from positive to negative is identified as the initial peak position, and the amplitude corresponding to the zero crossover point is taken as the initial peak intensity. Calculate the distance between adjacent initial peak positions. When the distance is less than the set overlap threshold, merge the corresponding adjacent peak clusters into a merged peak. The peak position of the merged peak is the relaxation time point obtained by weighting the relaxation time points corresponding to the original adjacent initial peak positions with the original adjacent peak intensities as the weights, and the maximum value among the original adjacent peak intensities is taken as the merged peak intensity. Extend outwards from the original two adjacent initial peak positions to find the two outermost relaxation time points corresponding to the amplitude dropping to half of the combined peak intensity. Calculate the relaxation time difference between the two points as the peak width characteristic parameter.

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