A method and system for correcting CVT broadband harmonic measurement error

Abstract

The application relates to the technical field of electric power, and provides a CVT wide-frequency harmonic error correction method and system, which comprises the following steps: performing multi-dimensional feature enhancement on the amplitude transfer ratio and the phase difference of a capacitive voltage transformer secondary side under low-order harmonics obtained through collection and calculation to generate a feature vector; constructing a CVT wide-frequency equivalent model, and adopting the feature vector to construct an identification target function of stray capacitance parameters; based on the physical constraints of the parameters, taking the minimization of the identification target function as a target, performing LSHADE algorithm parameter optimization for several rounds to obtain a candidate solution set of the stray capacitance parameters; and performing probability density statistical analysis on the candidate solution set to obtain optimal stray capacitance parameters, which are substituted into the wide-frequency equivalent model to inversely deduce primary side harmonic voltages after correction. The method can improve the accuracy of CVT wide-frequency harmonic measurement at low cost.

Description

Technical Field

[0001] This invention relates to the field of power technology, and specifically to a method and system for correcting wideband harmonic errors in CVT (Continuous Voltage Transmission). Background Technology

[0002] As a key device for voltage signal sensing in high-voltage power grids, capacitive voltage transformers have completely replaced traditional electromagnetic voltage transformers and are widely used in substations with voltage levels of 110kV and above, thanks to their outstanding advantages such as high insulation reliability, low manufacturing cost, simple operation and maintenance, and the ability to function as carrier communication coupling capacitors. Accurate measurement of primary-side harmonic voltage signals is the most critical parameter for evaluating the operating status of capacitive voltage transformers. Under low-frequency conditions, due to the large capacitive reactance of stray capacitors, their interference with voltage transfer characteristics is negligible, and the measurement results are almost unaffected. However, under high-frequency conditions, the coupling effect of internal stray capacitors is amplified dramatically, triggering internal series and parallel resonances. This leads to excessive harmonic measurement errors in the capacitive voltage transformer, nonlinear distortion of the transfer characteristics, and consequently, the secondary-side output cannot accurately reflect the primary-side harmonic content. Furthermore, the stray capacitance parameter of a capacitive voltage transformer is not a fixed constant; it is affected by multiple factors such as manufacturing process deviations, installation stress, operating temperature, and humidity, exhibiting random fluctuations within a certain range, further exacerbating the uncertainty of harmonic transfer characteristics.

[0003] In the prior art, Chinese invention patent application CN121234731A, entitled "A Harmonic Error Prediction Method for Capacitive Voltage Transformers Based on NRBO-BP," establishes a CVT harmonic impedance model and calculates the transfer function, analyzes harmonic transmission characteristics, adjusts stray capacitance numerically to simulate different operating environments and obtains harmonic error data through simulation, optimizes the initial weights and biases of the BP neural network using the NRBO algorithm, constructs a harmonic error prediction model, and finally predicts the 2nd to 60th harmonic errors using typical harmonic errors as characteristic parameters. However, this scheme is a purely data-driven black-box modeling method, with limited generalization ability and reliance on full-band training data that is difficult to obtain accurately. The training data generated by simulation has inherent deviations from actual operating conditions, making it difficult to guarantee prediction accuracy. Chinese invention patent application CN113189532A, entitled "An Online Correction Method and Device for Harmonic Measurement Errors of Capacitive Voltage Transformers," achieves online correction of harmonic voltage measurement errors in CVT devices by adding harmonic voltage amplitude and phase error compensation functions to the control system. However, this solution is only applicable to flexible DC transmission systems equipped with modular multilevel converters, requires extensive modification of the pole control system and may interfere with the power quality of the power grid, cannot achieve error compensation under transient operating conditions, and has poor economic efficiency. Summary of the Invention

[0004] The technical problem to be solved by this invention is how to improve the accuracy of CVT broadband harmonic measurement at low cost.

[0005] The present invention solves the above-mentioned technical problems through the following technical means: This invention provides a method for correcting wideband harmonic errors in CVTs, comprising: performing multi-dimensional feature enhancement on the amplitude transfer ratio and phase difference under low-order harmonics on the secondary side of a capacitive voltage transformer obtained by acquisition and calculation, generating feature vectors; constructing a wideband equivalent model of the CVT, and using the feature vectors to construct an identification objective function for stray capacitance parameters; under the physical value range constraints of the stray capacitance of the compensation reactor and the stray capacitance to ground on the primary side of the intermediate transformer, performing several rounds of parameter optimization using the LSHADE algorithm with the goal of minimizing the identification objective function, and obtaining a candidate solution set for stray capacitance parameters; performing probability density statistical analysis on the candidate solution set, and substituting the parameter with the highest clustering degree as the optimal stray capacitance parameter into the wideband equivalent model to back-calculate the corrected primary side harmonic voltage.

[0006] Furthermore, the amplitude transfer ratio and phase difference under the low harmonics of the secondary side of the capacitive voltage transformer, obtained by acquisition and calculation, specifically include the following steps: S11. A voltage acquisition device is used to synchronously acquire the voltage signals of the primary and secondary sides of the CVT; S12. Perform a fast Fourier transform on the acquired voltage signal to extract the amplitude and phase of the 2nd, 3rd and 4th harmonics respectively. S13. Calculate the voltage transfer ratio of the CVT relative to the fundamental wave and the phase difference relative to the fundamental wave under each harmonic.

[0007] Furthermore, the multi-dimensional feature enhancement and feature vector generation specifically includes the following steps: S21. Calculate the first-order slope and second-order curvature of the amplitude transfer ratio and phase difference as a function of frequency for each harmonic. S22. Concatenate the amplitude transfer ratio, phase difference, first-order slope of amplitude transfer ratio, second-order curvature of amplitude transfer ratio, first-order slope of phase difference, and second-order curvature of phase difference in sequence to generate a feature vector, as shown in the following formula:

[0008] in, and These are the amplitude transfer ratio and phase difference of the low-order harmonic amplitude and phase relative to the fundamental wave on the secondary side of the CVT, respectively. and This refers to the attenuation or shift trend of amplitude transfer ratio and phase difference as a function of frequency; and The degree of nonlinear distortion of the trend.

[0009] Furthermore, the identification target function is specifically as follows: Construct the identification objective function in the form of a weighted sum of squares, as follows:

[0010] in, For the actual feature vector, The parameters to be identified are the stray capacitance parameters in the two-dimensional parameter space. To compensate for the stray capacitance of the reactor, This refers to the stray capacitance to ground on the primary side of the intermediate transformer. The theoretical feature vector is generated by substituting the stray capacitance parameters to be identified into the CVT wideband equivalent model; For feature dimensions; Adaptive penalty weights for each dimension of features.

[0011] Furthermore, under the physical constraints of the stray capacitance of the compensating reactor and the stray capacitance to ground on the primary side of the intermediate transformer, the LSHADE algorithm is executed for several rounds of parameter optimization with the goal of minimizing the objective function, to obtain a candidate solution set for the stray capacitance parameters. This specifically includes the following steps: S31. Initialize the parameter memory and iteration counter to generate an initial population within the stray capacitance physical constraint range, as shown in the following equation:

[0012] in, For indexing individuals in the population, Index for variable dimensions, This represents a random number that follows a uniform distribution within the interval [0,1]. and For physical boundaries; S32. Using the identification objective function Calculate the fitness value of each individual in the initial population; then dynamically sample the scaling factor and crossover probability, using the current individual... A difference vector is constructed between the mutant individuals and the top 20% of the population in terms of fitness, thereby generating the mutant individuals. As shown in the following formula:

[0013] in, Individuals randomly selected from the top 20% of the current population in terms of fitness; For the first Individual adaptive scaling factor; and These represent two distinct random individuals randomly selected from the current population or an external historical archive, respectively. S33. Perform a binomial crossover experiment to generate individuals from the current individual and the variant individuals. ; test individuals The included parameters are then substituted back into the CVT wideband equivalent model and the identification objective function to calculate its theoretical eigenvector and obtain the fitness value of the experimental individuals. The next generation is selected by greedily choosing individuals with small feature matching errors, as shown in the following formula:

[0014] in, This represents the current fitness value of the individual. S34. Update the parameter memory and linearly reduce the population size to balance global exploration and local exploitation, as follows:

[0015] in, , These are the initial population size and the minimum population size, respectively. The maximum number of iterations, This is a rounding operation; S35. Determine whether the iteration termination condition for the current round is met. If not, return to step S32 to continue iteration; otherwise, stop the current round of iteration. S36. Repeat steps S32-S35 several times to collect the globally optimal solution that converges in several rounds and construct a candidate solution set for the stray capacitance parameter.

[0016] Furthermore, the step of performing probability density statistical analysis on the candidate solution set and selecting the parameter with the highest clustering degree as the optimal stray capacitance parameter specifically includes the following steps: S41. Standardize the two-dimensional parameters to eliminate dimensional differences, as shown in the following formula:

[0017] in, The parameters to be identified in the two-dimensional parameter space. For the first One valid sample point; It is the inverse square root of the bandwidth matrix; S42. Calculate the kernel function value at the point of the parameter to be evaluated using the two-dimensional standard Gaussian kernel function;

[0018] in, It is an exponential function; S43. Normalize and superimpose the kernel functions of all valid samples to obtain the joint probability density at the point to be evaluated.

[0019] in, This represents the total number of sample points within the candidate solution set. S44. Traverse within the physically constrained region of stray capacitance parameters. A continuous and smooth joint probability density surface is constructed, and its global peak point is searched to obtain the physical value corresponding to the global peak point, as shown in the following equation:

[0020] in, This is the physical value of stray capacitance. This represents the physical constraint range for stray capacitance parameters.

[0021] Furthermore, the reverse calculation to obtain the corrected first-side harmonic voltage specifically includes the following steps: S51. The identified stray capacitance parameters Substitute into the CVT wideband equivalent model and calculate the transfer function under each harmonic. ; S52. Constructing the inverse transfer function Establish a mapping relationship between the secondary side measured values ​​and the primary side harmonic voltage values; S53. Perform FFT analysis on the voltage data measured in real time on the secondary side of the CVT to extract the amplitude and phase of each harmonic. S54. Substitute the amplitude and phase of each harmonic on the second side into the inverse transfer function. The corrected first-side harmonic voltage is obtained by reverse calculation, as shown in the following formula:

[0022] in, This is the corrected first harmonic voltage. The measured second-side harmonic voltage.

[0023] This invention also provides a system for correcting wideband harmonic errors in CVTs. The system executes the above-described method during operation and includes the following modules: The feature extraction module is used to perform multi-dimensional feature enhancement on the amplitude transfer ratio and phase difference of the low harmonics on the secondary side of the capacitive voltage transformer, which are obtained by acquisition and calculation, to generate feature vectors. The objective function construction module is used to construct the CVT wideband equivalent model and uses feature vectors to construct the objective function for identifying stray capacitance parameters. The parameter optimization module is used to perform several rounds of parameter optimization using the LSHADE algorithm under the physical value range constraints of the stray capacitance of the compensation reactor and the stray capacitance to ground on the primary side of the intermediate transformer, with the goal of minimizing the objective function, to obtain a candidate solution set for the stray capacitance parameters. The parameter confirmation module is used to perform probability density statistical analysis on the candidate solution set and substitute the parameter with the highest clustering degree as the optimal stray capacitance parameter into the broadband equivalent model. The output module is used to reverse-engineer the corrected first-side harmonic voltage.

[0024] The advantages of this invention are: (1) This invention utilizes the characteristic that stray capacitors have large capacitive reactance under low-frequency operating conditions, and their interference with voltage transfer characteristics is negligible, so the measurement results are almost unaffected. By mapping the weak disturbances generated by stray capacitors in the low-frequency band to a high-sensitivity feature space, the identification sensitivity is significantly improved, and only a small amount of local frequency sweep data of low-frequency harmonics is needed to achieve high-precision stray capacitor parameter estimation, which significantly reduces the hardware cost and implementation difficulty of on-site testing.

[0025] (2) The present invention adopts the LSHADE-KDE joint optimization architecture. The bottom layer uses the adaptive optimization mechanism of the LSHADE algorithm to effectively overcome the high non-convexity and multiple extrema problems caused by the complex equivalent model of CVT. The top layer models the probability density through two-dimensional kernel density estimation (2D-KDE) to accurately lock the global optimal solution. This effectively solves the problems of multiple solutions and random errors that traditional heuristic algorithms are prone to getting trapped in local optima and have large fluctuations in the results of multiple rounds of optimization.

[0026] (3) Based on the identification of the optimal stray capacitance parameters, the present invention can accurately back-calculate the wideband harmonic voltage by substituting them into the CVT wideband inverse model. The back-calculation accuracy fully meets the accuracy requirements of wideband harmonic monitoring of the power grid and has good engineering applicability. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the method for correcting CVT broadband harmonic errors according to an embodiment of the present invention. Figure 2 This is a schematic diagram comparing the harmonic amplitude correction results of embodiments of the present invention; Figure 3 This is a schematic diagram comparing the harmonic phase correction results of an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. 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.

[0029] Example 1 This embodiment provides a method for correcting broadband harmonic errors in CVTs. It aims to map weak disturbances caused by stray capacitance in the low-frequency band to a high-sensitivity feature space using only limited frequency sweep data from the low-frequency band of a capacitive voltage transformer. Simultaneously, it employs a joint architecture combining global optimization and probabilistic statistics, effectively overcoming the problems of traditional algorithms easily getting trapped in local optima and experiencing large fluctuations in results after multiple rounds of optimization. Ultimately, it achieves high-precision estimation of stray capacitance parameters, thereby correcting broadband harmonic measurement errors. The specific implementation process is as follows: Figure 1 As shown, it includes the following steps: S1. The amplitude transfer ratio and phase difference under the low harmonics of the secondary side of the capacitive voltage transformer, obtained through acquisition and calculation, are subjected to multi-dimensional feature enhancement to generate feature vectors; the specific implementation process includes: S11. Use a voltage acquisition device to synchronously acquire the voltage signals of the primary and secondary sides of the CVT; a conventional power frequency measurement device can be used for the voltage acquisition device.

[0030] S12. Perform a Fast Fourier Transform on the acquired voltage signal to extract the amplitude and phase of the 2nd, 3rd, and 4th harmonics, respectively. It should be noted that all the input data required for parameter identification can be obtained by acquiring the power frequency voltage signal from the secondary side of the CVT and extracting the low-order harmonic components. This embodiment only requires local frequency sweep data at the 2nd to 4th frequency points, which greatly improves the efficiency of on-site implementation compared to traditional methods that require acquiring data from multiple frequency bands.

[0031] S13. Calculate the voltage transfer ratio of the CVT relative to the fundamental wave and the phase difference relative to the fundamental wave under each harmonic.

[0032] S2. Construct a wideband equivalent model of the CVT and use feature vectors to construct an objective function for identifying stray capacitance parameters; the specific implementation process includes: S21. Calculate the first-order slope and second-order curvature of the amplitude transfer ratio and phase difference as a function of frequency for each harmonic. S22. Concatenate the amplitude transfer ratio, phase difference, first-order slope of amplitude transfer ratio, second-order curvature of amplitude transfer ratio, first-order slope of phase difference, and second-order curvature of phase difference in sequence to generate a feature vector, as shown in the following formula:

[0033] in, and These are the amplitude transfer ratio and phase difference of the low-order harmonic amplitude and phase relative to the fundamental wave on the secondary side of the CVT, respectively. and This refers to the attenuation or shift trend of amplitude transfer ratio and phase difference as a function of frequency; and The degree of nonlinear distortion of the trend.

[0034] Through the above-mentioned high-sensitivity feature extraction process, the weak disturbances generated by stray capacitance in the low-frequency band are amplified, significantly improving the signal-to-noise ratio of parameter identification and effectively solving the problem that weak features in the low-frequency band are easily submerged by noise.

[0035] S3. Under the physical constraints of the stray capacitance of the compensating reactor and the stray capacitance to ground on the primary side of the intermediate transformer, with the goal of minimizing the identification objective function, the LSHADE algorithm is executed for several rounds of parameter optimization to obtain a candidate solution set for the stray capacitance parameters; the identification objective function is specifically: Construct the identification objective function in the form of a weighted sum of squares, as follows:

[0036] in, For the actual feature vector, The parameters to be identified are the stray capacitance parameters in the two-dimensional parameter space. To compensate for the stray capacitance of the reactor, This refers to the stray capacitance to ground on the primary side of the intermediate transformer. The theoretical feature vector is generated by substituting the stray capacitance parameters to be identified into the CVT wideband equivalent model; For feature dimensions; Adaptive penalty weights for each dimension of features. The smaller the value, the closer the candidate stray capacitance combination is to the actual value.

[0037] The specific implementation process of step S3 also includes: S31. Initialize the parameter memory and iteration counter to generate an initial population within the stray capacitance physical constraint range, as shown in the following equation:

[0038] in, For indexing individuals in the population, Index for variable dimensions, This represents a random number that follows a uniform distribution within the interval [0,1]. and For physical boundaries; S32. Using the identification objective function Calculate the fitness value of each individual in the initial population; then dynamically sample the scaling factor and crossover probability, using the current individual... A difference vector is constructed between the mutant individuals and the top 20% of the population in terms of fitness, thereby generating the mutant individuals. As shown in the following formula:

[0039] in, Individuals randomly selected from the top 20% of the current population in terms of fitness; For the first Individual adaptive scaling factor; and These represent two distinct random individuals randomly selected from the current population or an external historical archive, respectively. S33. Perform a binomial crossover experiment to generate individuals from the current individual and the variant individuals. ; test individuals The included parameters are then substituted back into the CVT wideband equivalent model and the identification objective function to calculate its theoretical eigenvector and obtain the fitness value of the experimental individuals. The next generation is selected by greedily choosing individuals with small feature matching errors, as shown in the following formula:

[0040] in, This represents the current fitness value of the individual. S34. Update the parameter memory and linearly reduce the population size to balance global exploration and local exploitation, as follows:

[0041] in, , These are the initial population size and the minimum population size, respectively. The maximum number of iterations, This is a rounding operation; S35. Determine whether the iteration termination condition for the current round is met. If not, return to step S32 to continue iteration; otherwise, stop the current round of iteration. S36. Repeat steps S32-S35 several times to collect the globally optimal solution that converges in several rounds and construct a candidate solution set for the stray capacitance parameter.

[0042] S4. Perform probability density statistical analysis on the candidate solution set, and substitute the parameter with the highest clustering degree as the optimal stray capacitance parameter into the broadband equivalent model; the specific implementation process includes: S41. Standardize the two-dimensional parameters to eliminate dimensional differences, as shown in the following formula:

[0043] in, The parameters to be identified in the two-dimensional parameter space. For the first One valid sample point; It is the inverse square root of the bandwidth matrix; S42. Calculate the kernel function value at the point of the parameter to be evaluated using the two-dimensional standard Gaussian kernel function;

[0044] in, It is an exponential function; S43. Normalize and superimpose the kernel functions of all valid samples to obtain the joint probability density at the point to be evaluated.

[0045] in, This represents the total number of sample points within the candidate solution set. S44. Traverse within the physically constrained region of stray capacitance parameters. A continuous and smooth joint probability density surface is constructed, and its global peak point is searched to obtain the physical value corresponding to the global peak point, as shown in the following equation:

[0046] in, This is the physical value of stray capacitance. This represents the physical constraint range for stray capacitance parameters. In practice, the stability of the identification results can be further quantitatively evaluated by using peak offset and parameter back-fitting error.

[0047] S5. The corrected first-side harmonic voltage is obtained by reverse calculation. The specific implementation process includes: S51. The identified stray capacitance parameters Substitute into the CVT wideband equivalent model and calculate the transfer function under each harmonic. ; S52. Constructing the inverse transfer function Establish a mapping relationship between the secondary side measured values ​​and the primary side harmonic voltage values; S53. Perform FFT analysis on the voltage data measured in real time on the secondary side of the CVT to extract the amplitude and phase of each harmonic. S54. Substitute the amplitude and phase of each harmonic on the second side into the inverse transfer function. The corrected first-side harmonic voltage is obtained by reverse calculation, as shown in the following formula:

[0048] in, This is the corrected first harmonic voltage. The measured second-side harmonic voltage.

[0049] This embodiment also provides comparative experimental results on the measurement of harmonic amplitude and harmonic phase of capacitive voltage transformers, comparing whether or not the proposed correction method is used. Figure 2 As shown, the uncorrected second-side harmonic content deviates significantly from the true reference across the entire frequency range from 1 to 60. After amplitude back-calculation correction using the CVT broadband transfer function, the corrected second-side curve closely matches the true 10% sweep baseline, significantly suppressing amplitude errors and accurately restoring the actual harmonic content level of the first side. Figure 3 As shown, the uncorrected phase on the secondary side exhibits significant frequency shift characteristics and obvious phase lag. After phase correction using the transfer function, the corrected phase on the secondary side basically coincides with the true 0° sweep baseline, effectively correcting the phase distortion of the CVT within a wide frequency range of 1 to 60.

[0050] Furthermore, as can be seen from the above, this embodiment does not require any hardware modification to the CVT equipment. Parameter identification and error correction can be completed solely through software algorithms. No substation power outage is required, and on-site implementation can be carried out while the equipment is running. It has good engineering practicality and promotional value.

[0051] Example 2 It should be further explained that, based on the same inventive concept, the embodiment provides a CVT broadband harmonic error correction system. When the system is running, it executes the method described in Embodiment 1, including the following modules: The feature extraction module is used to perform multi-dimensional feature enhancement on the amplitude transfer ratio and phase difference of the low harmonics on the secondary side of the capacitive voltage transformer, which are obtained by acquisition and calculation, to generate feature vectors. The objective function construction module is used to construct the CVT wideband equivalent model and uses feature vectors to construct the objective function for identifying stray capacitance parameters. The parameter optimization module is used to perform several rounds of parameter optimization using the LSHADE algorithm under the physical value range constraints of the stray capacitance of the compensation reactor and the stray capacitance to ground on the primary side of the intermediate transformer, with the goal of minimizing the objective function, to obtain a candidate solution set for the stray capacitance parameters. The parameter confirmation module is used to perform probability density statistical analysis on the candidate solution set and substitute the parameter with the highest clustering degree as the optimal stray capacitance parameter into the broadband equivalent model. The output module is used to reverse-engineer the corrected first-side harmonic voltage.

[0052] In the feature extraction module, the amplitude transfer ratio and phase difference under the low harmonics of the secondary side of the capacitive voltage transformer, obtained by acquisition and calculation, are specifically executed as follows: A voltage acquisition device is used to simultaneously acquire the voltage signals of the primary and secondary sides of the CVT; The acquired voltage signal was subjected to Fast Fourier Transform to extract the amplitude and phase of the 2nd, 3rd and 4th harmonics, respectively. Calculate the voltage transfer ratio of the CVT relative to the fundamental frequency and the phase difference relative to the fundamental frequency for each harmonic.

[0053] In the feature extraction module, the multi-dimensional feature enhancement and feature vector generation are performed as follows: Calculate the amplitude transfer ratio and the first-order slope and second-order curvature of the phase difference as a function of frequency for each harmonic; The amplitude transfer ratio, phase difference, first-order slope of amplitude transfer ratio, second-order curvature of amplitude transfer ratio, first-order slope of phase difference, and second-order curvature of phase difference are concatenated in sequence to generate a feature vector, as shown in the following formula:

[0054] in, and These are the amplitude transfer ratio and phase difference of the low-order harmonic amplitude and phase relative to the fundamental wave on the secondary side of the CVT, respectively. and This refers to the attenuation or shift trend of amplitude transfer ratio and phase difference as a function of frequency; and The degree of nonlinear distortion of the trend.

[0055] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for correcting wideband harmonic errors in CVT, characterized in that, The amplitude transfer ratio and phase difference under low harmonics on the secondary side of the capacitive voltage transformer, obtained by acquisition and calculation, are enhanced in multiple dimensions to generate feature vectors. A wideband equivalent model of CVT is constructed, and the feature vectors are used to construct the objective function for identifying stray capacitance parameters. Under the physical value range constraints of the stray capacitance of the compensation reactor and the stray capacitance to ground on the primary side of the intermediate transformer, the LSHADE algorithm is executed for several rounds of parameter optimization with the goal of minimizing the objective function, to obtain the candidate solution set of stray capacitance parameters. Probability density statistical analysis is performed on the candidate solution set, and the parameter with the highest clustering degree is substituted into the broadband equivalent model as the optimal stray capacitance parameter to deduce the corrected first harmonic voltage.

2. The method for correcting CVT wideband harmonic errors according to claim 1, characterized in that, The amplitude transfer ratio and phase difference under low harmonics on the secondary side of the capacitive voltage transformer, obtained by acquisition and calculation, specifically include the following steps: S11. A voltage acquisition device is used to synchronously acquire the voltage signals of the primary and secondary sides of the CVT; S12. Perform a fast Fourier transform on the acquired voltage signal to extract the amplitude and phase of the 2nd, 3rd and 4th harmonics respectively. S13. Calculate the voltage transfer ratio of the CVT relative to the fundamental wave and the phase difference relative to the fundamental wave under each harmonic.

3. The method for correcting wideband harmonic errors in a CVT according to claim 1, characterized in that, The aforementioned multi-dimensional feature enhancement Generating feature vectors specifically includes the following steps: S21. Calculate the first-order slope and second-order curvature of the amplitude transfer ratio and phase difference as a function of frequency for each harmonic. S22. Concatenate the amplitude transfer ratio, phase difference, first-order slope of amplitude transfer ratio, second-order curvature of amplitude transfer ratio, first-order slope of phase difference, and second-order curvature of phase difference in sequence to generate a feature vector, as shown in the following formula: in, and These are the amplitude transfer ratio and phase difference of the low-order harmonic amplitude and phase relative to the fundamental wave on the secondary side of the CVT, respectively. and This refers to the attenuation or shift trend of amplitude transfer ratio and phase difference as a function of frequency; and The degree of nonlinear distortion of the trend.

4. The method for correcting CVT wideband harmonic errors according to claim 1, characterized in that, The identification target function is specifically as follows: Construct the identification objective function in the form of a weighted sum of squares, as follows: in, For the actual feature vector, The parameters to be identified are the stray capacitance parameters in the two-dimensional parameter space. To compensate for the stray capacitance of the reactor, This refers to the stray capacitance to ground on the primary side of the intermediate transformer. The theoretical feature vector is generated by substituting the stray capacitance parameters to be identified into the CVT wideband equivalent model; For feature dimensions; Adaptive penalty weights for each dimension of features.

5. The method for correcting wideband harmonic errors in a CVT according to claim 4, characterized in that, Under the physical constraints of the stray capacitance of the compensating reactor and the stray capacitance to ground on the primary side of the intermediate transformer, the LSHADE algorithm is executed for several rounds of parameter optimization with the goal of minimizing the objective function, to obtain a candidate solution set for the stray capacitance parameters. Specifically, this includes the following steps: S31. Initialize the parameter memory and iteration counter to generate an initial population within the stray capacitance physical constraint range, as shown in the following equation: in, For indexing individuals in the population, Index for variable dimensions, This represents a random number that follows a uniform distribution within the interval [0,1]. and For physical boundaries; S32. Using the identification objective function Calculate the fitness value of each individual in the initial population; then dynamically sample the scaling factor and crossover probability, using the current individual... A difference vector is constructed between the mutant individuals and the top 20% of the population in terms of fitness, thereby generating the mutant individuals. As shown in the following formula: in, Individuals randomly selected from the top 20% of the current population in terms of fitness; For the first Individual adaptive scaling factor; and These represent two distinct random individuals randomly selected from the current population or an external historical archive, respectively. S33. Perform a binomial crossover experiment to generate individuals from the current individual and the variant individuals. ; test individuals The included parameters are then substituted back into the CVT wideband equivalent model and the identification objective function to calculate its theoretical eigenvector and obtain the fitness value of the experimental individuals. The next generation is selected by greedily choosing individuals with small feature matching errors, as shown in the following formula: in, This represents the current fitness value of the individual. S34. Update the parameter memory and linearly reduce the population size to balance global exploration and local exploitation, as follows: in, , These are the initial population size and the minimum population size, respectively. The maximum number of iterations, This is a rounding operation; S35. Determine whether the iteration termination condition for the current round is met. If not, return to step S32 to continue iteration; otherwise, stop the current round of iteration. S36. Repeat steps S32-S35 several times to collect the globally optimal solution that converges in several rounds and construct a candidate solution set for the stray capacitance parameter.

6. The method for correcting wideband harmonic errors in a CVT according to claim 1, characterized in that, The step of performing probability density statistical analysis on the candidate solution set and selecting the parameter with the highest clustering degree as the optimal stray capacitance parameter specifically includes the following steps: S41. Standardize the two-dimensional parameters to eliminate dimensional differences, as shown in the following formula: in, The parameters to be identified in the two-dimensional parameter space. For the first One valid sample point; It is the inverse square root of the bandwidth matrix; S42. Calculate the kernel function value at the point of the parameter to be evaluated using the two-dimensional standard Gaussian kernel function; in, It is an exponential function; S43. Normalize and superimpose the kernel functions of all valid samples to obtain the joint probability density at the point to be evaluated. in, This represents the total number of sample points within the candidate solution set. S44. Traverse within the physically constrained region of stray capacitance parameters. A continuous and smooth joint probability density surface is constructed, and its global peak point is searched to obtain the physical value corresponding to the global peak point, as shown in the following equation: in, This is the physical value of stray capacitance. This represents the physical constraint range for stray capacitance parameters.

7. The method for correcting wideband harmonic errors in a CVT according to claim 1, characterized in that, The reverse calculation to obtain the corrected first-side harmonic voltage specifically includes the following steps: S51. The identified stray capacitance parameters Substitute into the CVT wideband equivalent model and calculate the transfer function under each harmonic. ; S52. Constructing the inverse transfer function Establish a mapping relationship between the secondary side measured values ​​and the primary side harmonic voltage values; S53. Perform FFT analysis on the voltage data measured in real time on the secondary side of the CVT to extract the amplitude and phase of each harmonic. S54. Substitute the amplitude and phase of each harmonic on the second side into the inverse transfer function. The corrected first-side harmonic voltage is obtained by reverse calculation, as shown in the following formula: in, This is the corrected first harmonic voltage. The measured second-side harmonic voltage.

8. A CVT wideband harmonic error correction system, characterized in that, Includes the following modules: The feature extraction module is used to perform multi-dimensional feature enhancement on the amplitude transfer ratio and phase difference of the low harmonics on the secondary side of the capacitive voltage transformer, which are obtained by acquisition and calculation, to generate feature vectors. The objective function construction module is used to construct the CVT wideband equivalent model and uses feature vectors to construct the objective function for identifying stray capacitance parameters. The parameter optimization module is used to perform several rounds of parameter optimization using the LSHADE algorithm under the physical value range constraints of the stray capacitance of the compensation reactor and the stray capacitance to ground on the primary side of the intermediate transformer, with the goal of minimizing the objective function, to obtain a candidate solution set for the stray capacitance parameters. The parameter confirmation module is used to perform probability density statistical analysis on the candidate solution set and substitute the parameter with the highest clustering degree as the optimal stray capacitance parameter into the broadband equivalent model. The output module is used to reverse-engineer the corrected first-side harmonic voltage.

9. A CVT wideband harmonic error correction system according to claim 8, characterized in that, In the feature extraction module, the amplitude transfer ratio and phase difference under the low harmonics of the secondary side of the capacitive voltage transformer, obtained by acquisition and calculation, are specifically executed as follows: A voltage acquisition device is used to simultaneously acquire the voltage signals of the primary and secondary sides of the CVT; The acquired voltage signal was subjected to Fast Fourier Transform to extract the amplitude and phase of the 2nd, 3rd and 4th harmonics, respectively. Calculate the voltage transfer ratio of the CVT relative to the fundamental frequency and the phase difference relative to the fundamental frequency for each harmonic.

10. A CVT wideband harmonic error correction system according to claim 8, characterized in that, In the feature extraction module, the multi-dimensional feature enhancement and feature vector generation are performed as follows: Calculate the amplitude transfer ratio and the first-order slope and second-order curvature of the phase difference as a function of frequency for each harmonic; The amplitude transfer ratio, phase difference, first-order slope of amplitude transfer ratio, second-order curvature of amplitude transfer ratio, first-order slope of phase difference, and second-order curvature of phase difference are concatenated in sequence to generate a feature vector, as shown in the following formula: in, and These are the amplitude transfer ratio and phase difference of the low-order harmonic amplitude and phase relative to the fundamental wave on the secondary side of the CVT, respectively. and This refers to the attenuation or shift trend of amplitude transfer ratio and phase difference as a function of frequency; and The degree of nonlinear distortion of the trend.

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