Adaptive filter mutual inductor error dynamic compensation method and system

Abstract

The present application relates to a kind of self-adapting filter mutual inductor error dynamic compensation method and system, it is related to mutual inductor technical field, including the following steps, to the current, voltage sampling of mutual inductor secondary side and temperature measurement, construct working condition parameter matrix;In combination with pre-calibrated iron core hysteresis curve, mapping obtains prior excitation sequence;Through residual feedback and gain update generation posteriori excitation sequence;Accordingly, the error of secondary electric quantity is converted, obtains dynamic compensation sequence, and inverse superposition obtains correction secondary sequence;Finally, according to the ratio conversion, restore primary electric quantity sequence, the problem that the prior art cannot track the dynamic change of iron core hysteresis nonlinearity and operating condition in real time is solved, leading to excitation error is difficult to accurately separate from secondary side signal, and then influence primary side electric quantity restoration precision problem.

Description

Technical Field

[0001] This invention relates to the field of instrument transformer technology, and in particular to a dynamic error compensation method and system for instrument transformers using adaptive filtering. Background Technology

[0002] Traditional electromagnetic current transformers are affected by nonlinear characteristics such as core hysteresis, residual magnetism and saturation during operation. Their excitation error changes dynamically with load and operating conditions. Existing error compensation methods are mostly based on offline modeling or steady-state assumptions, which makes it difficult to track the transient process of core magnetization in real time. This results in the inability to accurately separate the excitation error component from the secondary side signal, which seriously affects the accuracy and reliability of primary side electrical quantity restoration. Summary of the Invention

[0003] The main objective of this invention is to provide an adaptive filtering method for dynamic compensation of transformer errors, which solves the problem that existing technologies cannot track the dynamic changes in core hysteresis nonlinearity and operating conditions in real time, making it difficult to accurately separate excitation errors from secondary side signals, thus affecting the accuracy of primary side electrical quantity restoration.

[0004] To achieve the above objectives, the present invention provides an adaptive filtering method for dynamic compensation of transformer errors, comprising the following steps:

[0005] The current and voltage of the secondary side of the current transformer are sampled to obtain the secondary electrical quantity sequence, and the temperature of the current transformer body is measured. Based on the temperature measurement results and the secondary electrical quantity sequence, the operating condition parameter matrix is ​​constructed.

[0006] By mapping the core magnetization state of the secondary electric charge sequence to the core using the pre-calibrated hysteresis characteristic curve of the transformer core and the operating condition parameter matrix, a priori excitation sequence based on the secondary side is obtained.

[0007] Based on the secondary charge sequence, residual feedback and gain update are performed on the prior excitation sequence to obtain the posterior excitation sequence.

[0008] Based on the posterior excitation sequence, the error of the secondary charge sequence is calculated to obtain a dynamic compensation sequence;

[0009] The corrected secondary sequence is obtained by inversely superimposing the secondary energy sequence based on the dynamic compensation sequence.

[0010] The corrected secondary sequence is converted according to the transformer ratio to obtain the restored primary sequence.

[0011] Furthermore, based on the pre-calibrated hysteresis characteristic curve of the transformer core, and combined with the operating condition parameter matrix, the secondary charge sequence is mapped to the core magnetization state to obtain a priori excitation sequence based on the secondary side, including:

[0012] The phase space of the secondary charge sequence is decoupled to separate the induced potential component, and the induced potential component is accumulated in the time domain and constrained in the space based on the Faraday induction mechanism to obtain the transient flux sequence.

[0013] The operating condition parameter matrix is ​​subjected to feature dimensionality reduction to extract load state parameters. Based on the load state parameters and the hysteresis characteristic curve of the transformer core, the transient flux linkage sequence is analyzed for magnetic domain deflection and reconstructed for hysteresis state to obtain the magnetic field strength sequence.

[0014] Based on the Ampere loop topology, the magnetic field strength sequence is analyzed by spatial magnetic circuit analysis to generate an equivalent magnetomotive force. The equivalent magnetomotive force is then matched by winding coupling and mapped by current dimension to obtain the a priori excitation sequence.

[0015] Furthermore, the step of performing spatial magnetic circuit analysis on the magnetic field intensity sequence based on the Ampere loop topology to generate an equivalent magnetomotive force includes:

[0016] Based on the pre-acquired geometric structure data of the transformer core, combined with the Ampere loop topology, the calibration magnetic field intensity distribution data is spatially meshed and the node coordinates are mapped to obtain the spatial magnetic field distribution matrix. The gradient calculation and boundary flux integration of the spatial magnetic field distribution matrix are then performed to obtain the local leakage flux sequence.

[0017] Based on the local leakage flux sequence, the spatial magnetic field distribution matrix is ​​subjected to non-uniform coefficient extraction and magnetic circuit segmentation to obtain a set of segmented magnetic circuit lengths. Then, the magnetic impedance weights are assigned to the set of segmented magnetic circuit lengths to obtain the magnetic circuit weight vector in advance.

[0018] The equivalent magnetomotive force is obtained by weighted summation and path integration of the magnetic field strength sequence based on the magnetic circuit weight vector.

[0019] Furthermore, the non-uniform coefficient extraction and magnetic circuit segmentation of the spatial magnetic field distribution matrix based on the local leakage flux sequence yields a set of segmented magnetic circuit lengths, including:

[0020] Based on the local leakage flux sequence, flux divergence and distortion mapping are performed on the spatial magnetic field distribution matrix to obtain a magnetic field distortion distribution map. The spatial gradient derivative and extremum normalization are then performed on the magnetic field distortion distribution map to obtain a non-uniform coefficient vector.

[0021] Based on the non-uniform coefficient vector, the local curvature extremum detection of the sliding window and the zero-crossing determination of the second derivative in the neighborhood are performed, and the truncation sensitivity factor is dynamically adjusted according to the mean square error of the coefficients in the current window to obtain the magnetic circuit truncation node set.

[0022] Based on the set of magnetic circuit truncation nodes, the spatial magnetic field distribution matrix is ​​subjected to geometric path integration and infinitesimal segmentation to obtain a set of segmented magnetic circuit lengths.

[0023] Furthermore, the step of performing residual feedback and gain update on the prior excitation sequence based on the secondary charge sequence to obtain the posterior excitation sequence includes:

[0024] The prior excitation sequence is subjected to measurement space mapping to generate a predicted observation sequence. Based on phase space metric constraints, the predicted observation sequence is compared with the secondary charge sequence to extract the state information sequence.

[0025] Multi-scale time-frequency analysis is performed on the state information sequence to extract the perturbation feature tensor;

[0026] The perturbation feature tensor is evaluated for confidence and weighted based on the state covariance evolution mechanism to generate a dynamic gain matrix;

[0027] Based on the dynamic gain matrix, a multidimensional orthogonal mapping is performed on the state information sequence to generate state correction parameters;

[0028] Based on the state correction parameters, the prior excitation sequence is reconstructed in phase and time domain and updated to obtain the posterior excitation sequence.

[0029] Furthermore, the step of performing phase-track reconstruction and time-domain update on the prior excitation sequence based on the state correction parameters to obtain the posterior excitation sequence includes:

[0030] Based on the hysteresis characteristic curve of the transformer core, and combined with the prior excitation sequence, the hysteresis loop derivative and slope extraction are performed to obtain the differential permeability set.

[0031] Based on the differential permeability set, the state correction parameters are tangent-mapped and saturation-adaptive limiting is performed to obtain the limited correction component.

[0032] Based on the prior excitation sequence, waveform extreme values ​​are retrieved to obtain a set of historical turning points.

[0033] Based on the set of historical turning points, the restricted correction components are spliced ​​in phase space and fitted with curves to obtain the transition phase trajectory curve.

[0034] The transition phase trajectory curve is projected onto the time axis and sampled at equal intervals to obtain discrete state nodes. The discrete state nodes are then rearranged in time and replaced with numerical values ​​to obtain the posterior excitation sequence.

[0035] Furthermore, the step of performing error reduction on the secondary charge sequence based on the posterior excitation sequence to obtain a dynamic compensation sequence includes:

[0036] The fundamental phase of the secondary charge sequence is extracted and the amplitude is calculated to obtain the fundamental phasor sequence, and the posterior excitation sequence is determined as the excitation current component.

[0037] Based on the excitation current component, the fundamental phasor sequence is phase-aligned and error-allocated to obtain an error phasor sequence. The error phasor sequence is then time-domain discretely reconstructed to obtain a dynamic compensation sequence.

[0038] Furthermore, the step of inversely superimposing the secondary energy sequence based on the dynamic compensation sequence to obtain the corrected secondary sequence includes:

[0039] The secondary power sequence and the dynamic compensation sequence are aligned by clock cycle and matched by data window. The instantaneous error amplitude of the corresponding sampling node is extracted, and the instantaneous error amplitude is inverted algebraically to obtain the inverse compensation sequence.

[0040] The reverse compensation sequence and the secondary electrical quantity sequence are added point by point to obtain the basic correction sequence. The basic correction sequence is then subjected to local extremum detection and step change point smoothing to obtain the corrected secondary sequence.

[0041] Furthermore, the step of performing ratio conversion on the corrected secondary sequence according to the transformer ratio to obtain the restored primary sequence includes:

[0042] Based on the transformer ratio, the correction quadratic sequence is scaled and linearly solved to obtain the primary waveform on the primary side. Then, the primary waveform on the primary side is analyzed by a sliding window and the extreme value envelope is extracted to obtain the transient boundary envelope.

[0043] Based on the transient boundary envelope, the primary waveform on the first side is subjected to envelope smoothing filtering and high-frequency noise suppression to obtain a noise-reduced pure waveform. The noise-reduced pure waveform is then zero-point anchored to obtain the restored primary sequence.

[0044] The present invention also provides an adaptive filtering dynamic compensation system for transformer errors, comprising:

[0045] The sampling and measurement module is used to sample the current and voltage on the secondary side of the current transformer to obtain the secondary electrical quantity sequence, and to measure the temperature of the current transformer body. Based on the temperature measurement results and the secondary electrical quantity sequence, the operating condition parameter matrix is ​​constructed.

[0046] The mapping module is used to map the core magnetization state of the secondary electric charge sequence by combining the pre-calibrated hysteresis characteristic curve of the transformer core with the operating condition parameter matrix, so as to obtain the a priori excitation sequence based on the secondary side.

[0047] The update module is used to perform residual feedback and gain update on the prior excitation sequence based on the secondary charge sequence to obtain the posterior excitation sequence.

[0048] An error conversion module is used to perform error conversion on the secondary charge sequence based on the posterior excitation sequence to obtain a dynamic compensation sequence.

[0049] The superposition module is used to inversely superimpose the secondary energy sequence based on the dynamic compensation sequence to obtain a corrected secondary sequence;

[0050] The transformer ratio conversion module is used to convert the correction secondary sequence according to the transformer ratio to obtain the restored primary sequence.

[0051] This invention provides an adaptive filtering method for dynamic error compensation of a current transformer, comprising the following steps: sampling current and voltage on the secondary side of the current transformer to obtain a secondary electrical quantity sequence, and measuring the temperature of the current transformer body; constructing an operating condition parameter matrix based on the temperature measurement results and the secondary electrical quantity sequence; mapping the core magnetization state of the secondary electrical quantity sequence using a pre-calibrated hysteresis characteristic curve of the current transformer core, combined with the operating condition parameter matrix, to obtain a priori excitation sequence based on the secondary side; performing residual feedback and gain update on the priori excitation sequence based on the secondary electrical quantity sequence to obtain a posterior excitation sequence; and performing residual feedback and gain update on the priori excitation sequence based on the posterior excitation sequence. Error calculation is performed on the secondary electrical quantity sequence to obtain a dynamic compensation sequence. The secondary electrical quantity sequence is then inversely superimposed based on the dynamic compensation sequence to obtain a corrected secondary sequence. The corrected secondary sequence is then ratio-calculated according to the transformer's turns ratio to obtain the restored primary sequence. This solves the problem that existing technologies cannot track the dynamic changes in core hysteresis nonlinearity and operating conditions in real time, leading to difficulties in accurately separating excitation errors from the secondary side signal, thus affecting the accuracy of primary side electrical quantity restoration. This method achieves online identification and dynamic compensation of excitation errors, significantly improving the accuracy of primary side electrical quantity restoration and system stability under complex operating conditions. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a schematic diagram of the steps of an adaptive filtering method for dynamic compensation of transformer error in one embodiment of the present invention;

[0054] Figure 2This is a structural block diagram of an adaptive filtering current transformer error dynamic compensation system according to an embodiment of the present invention;

[0055] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0056] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0057] The following describes in detail, with reference to the accompanying drawings, a dynamic compensation method for current transformer errors based on adaptive filtering according to an embodiment of the present invention. First, the dynamic compensation method for current transformer errors based on adaptive filtering according to an embodiment of the present invention will be described in detail with reference to the accompanying drawings.

[0058] like Figure 1 As shown, Figure 1 This invention provides an adaptive filtering method for dynamic compensation of transformer errors, comprising the following steps:

[0059] S1. Sample the current and voltage on the secondary side of the current transformer to obtain the secondary electrical quantity sequence, and measure the temperature of the current transformer body. Based on the temperature measurement results and the secondary electrical quantity sequence, construct the operating condition parameter matrix.

[0060] Specifically, in implementation, the secondary current and voltage channels of the current transformer are connected to a synchronous acquisition unit, sampled at equal intervals according to a unified clock, and then processed through anti-aliasing filtering, analog-to-digital conversion, and timestamp alignment to form a secondary electrical quantity sequence. Temperature sensors are placed at the shell measuring points near the iron core to continuously record the body temperature; when the temperature sampling time is inconsistent with the electrical quantity sampling time, interpolation alignment is performed based on adjacent temperature measurements. Subsequently, a sliding window is divided according to integer cycles, and the effective values ​​of current, voltage, phase difference, frequency, and average temperature within the window are extracted. These are arranged with the window as rows and the parameters as columns to construct an operating condition parameter matrix. In this embodiment, the above scheme achieves synchronous characterization of electrical quantity and temperature, providing a time-consistent operating condition input for subsequent magnetization state mapping.

[0061] S2, by using the pre-calibrated hysteresis characteristic curve of the transformer core and combining it with the operating condition parameter matrix, the magnetic core magnetization state of the secondary electric charge sequence is mapped to obtain the a priori excitation sequence based on the secondary side.

[0062] S21, the phase space decoupling of the secondary charge sequence is performed to separate the induced potential component, and the time domain accumulation and spatial boundary constraint of the induced potential component are performed based on the Faraday induction mechanism to obtain the transient flux sequence.

[0063] S22, perform feature dimensionality reduction on the operating condition parameter matrix, extract load state parameters, and perform domain deflection analysis and hysteresis state reconstruction on the transient flux linkage sequence based on the load state parameters and the hysteresis characteristic curve of the transformer core to obtain the magnetic field strength sequence.

[0064] Specifically, the secondary electrical quantity sequence is first read based on a unified timestamp. DC bias elimination and band-limited filtering are then applied to the secondary voltage and current, while retaining low-frequency transient components caused by faults and load surges. Using the fundamental phase of the secondary voltage as a rotating reference, in-phase and quadrature components are generated through orthogonal filtering, projecting the secondary voltage and current onto the same phase space. Based on pre-calibrated secondary winding resistance and leakage inductance parameters, the winding resistance voltage drop is determined from the in-phase change of the secondary current, and the leakage current voltage drop is determined from the rate of change of the secondary current. Then, according to the calibration polarity of the transformer's secondary winding, voltage balance reconstruction is performed with the port voltage to separate the induced electromotive force component.

[0065] To avoid noise from the current differential amplification sampling, the current change rate is determined by the local fitting slope within adjacent sampling windows. When the current amplitude is below the effective lower limit of sampling, the leakage flux drop is stopped from being updated, and the previous effective value is maintained and smoothly decayed. Subsequently, according to the Faraday induction mechanism, the induced electromotive force component is accumulated in the time domain in the opposite direction of the winding polarity, with the accumulation step size being the time interval between adjacent sampling times. When the system starts, the flux linkage corresponding to the pre-calibrated residual magnetism is used as the initial flux linkage, and during continuous operation, the flux linkage value at the end of the previous processing window is used. Combining the number of turns of the secondary winding, the effective cross-sectional area of ​​the iron core, and the maximum magnetic flux density covered by the hysteresis characteristic curve, the physical upper and lower boundaries of the transient flux linkage are determined. When the accumulated result continuously deviates and approaches the boundary only due to a small DC bias, the bias amount is slowly adjusted back. When a sudden load change causes a real flux linkage transition, its direction and amplitude are preserved, thus obtaining a continuous transient flux linkage sequence. Subsequently, the effective values ​​of current, effective values ​​of voltage, phase difference, frequency and temperature in the operating condition parameter matrix are normalized in terms of dimensions. The characteristic projection relationship formed by the calibration operating condition is used to merge the voltage and current features with high correlation, while retaining the independent physical coordinates corresponding to temperature and frequency. Load state parameters that can characterize load amplitude, equivalent load impedance, power factor and thermal state are extracted.

[0066] Based on the number of turns in the secondary winding and the effective cross-sectional area of ​​the core, the transient flux linkage is converted into magnetic flux density at each sampling time. The current operating range is determined according to load state parameters, and continuous interpolation is performed between the core hysteresis characteristic curves corresponding to adjacent temperature and frequency calibration conditions. The direction of increase or decrease in magnetic flux density relative to the previous sampling time is analyzed; when it increases, it enters the rising magnetization branch, and when it decreases, it enters the falling magnetization branch. When a reversal of the change direction is detected, the turning point of the magnetic domain deflection is recorded, and the local secondary loop is reconstructed according to the regression path of the hysteresis loop to avoid misjudging the residual magnetism state as the main hysteresis loop state. Finally, on the selected hysteresis branch, interval interpolation is performed using the current magnetic flux density as the positioning basis to obtain the corresponding magnetic field strength. Continuity verification is performed by combining the branch state of the previous time, forming a magnetic field strength sequence in chronological order. In this embodiment, the above scheme can suppress integral drift and retain transient hysteresis memory, providing a reliable magnetization state basis for subsequent excitation error estimation.

[0067] S23, based on the Ampere loop topology, perform spatial magnetic circuit analysis on the magnetic field strength sequence to generate an equivalent magnetomotive force, and perform winding coupling matching and current dimension mapping on the equivalent magnetomotive force to obtain the a priori excitation sequence.

[0068] S231, based on the pre-acquired geometric structure data of the transformer core, combined with the Ampere loop topology, the calibration magnetic field intensity distribution data is spatially meshed and the node coordinates are mapped to obtain the spatial magnetic field distribution matrix. The gradient calculation and boundary flux integration are performed on the spatial magnetic field distribution matrix to obtain the local leakage flux sequence.

[0069] Specifically, the hysteresis characteristic curve of a current transformer core refers to a closed curve formed by the change of magnetic flux density with magnetic field strength. During calibration, the current transformer is isolated from the operating line and the primary side is kept open. The secondary winding is connected to a low-distortion programmable excitation source, and the secondary terminal voltage, excitation current, core temperature, and tangential magnetic field strength at preset measurement points are collected simultaneously. Before calibration begins, alternating positive and negative demagnetizing currents with gradually decreasing amplitudes are applied to the secondary winding until the continuously measured residual magnetism response is lower than the resolution limit of the calibration equipment, so as to unify the initial magnetization state of each calibration.

[0070] The calibration conditions are set with multiple temperature nodes according to the specified operating temperature range of the transformer, and the temperature is kept constant at each temperature node until the core temperature enters the preset stable range. The excitation frequency must at least cover the lower limit, rated value, and upper limit of the allowable operating frequency. Subsequently, the excitation amplitude is gradually increased from a low level, so that the core successively experiences the near-linear magnetization region, hysteresis transition region, inflection point region, and allowable saturation initiation region. Each level of excitation maintains a complete cycle, and data is recorded only after the trajectories of adjacent cycles basically overlap. After reaching the calibration upper limit, the excitation amplitude is gradually reduced and the excitation is reversed to obtain complete rising and falling magnetization branches. At the same time, the excitation direction is changed at several locations with different magnetic flux densities, and the corresponding historical turning points and local secondary hysteresis loops are recorded to cover residual magnetism and the regression path after load abrupt changes.

[0071] During data processing, the winding resistance voltage drop and leakage inductance voltage drop are subtracted from the secondary terminal voltage to obtain the actual induced electromotive force. This is then accumulated in the time domain to obtain the flux linkage, which is converted to magnetic flux density based on the effective number of turns in the secondary winding and the effective cross-sectional area of ​​the core. The excitation current is converted to magnetic field strength based on the effective number of turns in the secondary winding and the average magnetic path length of the core. The polarities of both are unified according to the relationship between the winding terminals of the same name, and magnetic flux density, magnetic field strength, magnetization direction, historical turning points, temperature, and frequency are correlated in chronological order. An interpolation method that maintains the monotonicity of the branches is used to form a family of calibration hysteresis characteristic curves. Calibration is repeated at least once under the same operating conditions. If the loop closure deviation or the difference in repeated results exceeds the preset calibration tolerance, the system is demagnetized again and retested.

[0072] The calibration of the hysteresis characteristic curve itself does not involve unknown loads to avoid the secondary load impedance incorporating the core material characteristics. After the curve is formed, light loads, typical loads, and rated loads within the allowable range of the current transformer are connected for verification, covering the corresponding resistive and inductive power factor conditions. Load state parameters are only used to determine the actual operating range and trajectory on the hysteresis curve and do not change the physical definition of the curve. During the calibration process, the measured values ​​of each tangential magnetic field probe are saved with the same timestamp as the magnetic flux density, temperature, and excitation phase, thus forming the magnetic field strength distribution data required for subsequent spatial grid mapping. In this embodiment, the above scheme can obtain a hysteresis characteristic curve that takes into account temperature, frequency, saturation degree, and hysteresis memory effect, providing a traceable calibration basis for magnetic field state reconstruction.

[0073] S232, based on the local leakage flux sequence, the spatial magnetic field distribution matrix is ​​subjected to non-uniform coefficient extraction and magnetic circuit segmentation to obtain a segmented magnetic circuit length set, and the segmented magnetic circuit length set is assigned magnetic impedance weights to obtain a magnetic circuit weight vector in advance.

[0074] S2321, Based on the local leakage flux sequence, the flux divergence and distortion mapping of the spatial magnetic field distribution matrix are performed to obtain the magnetic field distortion distribution map, and the spatial gradient derivative and extreme value normalization of the magnetic field distortion distribution map are performed to obtain the non-uniform coefficient vector.

[0075] S2322, based on the non-uniform coefficient vector, perform local curvature extremum detection of the sliding window and zero-crossing determination of the second derivative in the neighborhood, and dynamically adjust the truncation sensitivity factor according to the mean square error of the coefficients in the current window to obtain the magnetic circuit truncation node set;

[0076] S2323, Based on the set of magnetic circuit truncation nodes, perform geometric path integration and infinitesimal segmentation on the spatial magnetic field distribution matrix to obtain a set of segmented magnetic circuit lengths.

[0077] The magnetic impedance weights are assigned to the segmented magnetic circuit length set to obtain the magnetic circuit weight vector in advance.

[0078] Specifically, the local leakage flux sequence is first aligned frame-by-frame with the spatial magnetic field distribution matrix according to a unified timestamp. Then, based on the core hysteresis branch, local effective permeability, and air permeability corresponding to each grid node, the nodal magnetic field strength is converted into a directional magnetic flux density. For each grid cell, the normal magnetic flux density of each boundary surface is extracted, and the inflow and outflow flux are calculated in conjunction with the boundary surface area. The local flux divergence is then characterized by the degree of change of the signed difference between the two relative to the cell volume. The local leakage flux sequence only constrains the total leakage flux at the core-air interface; the relative distribution between nodes is still determined by the spatial magnetic field distribution matrix, preventing the repeated superposition of the same leakage flux result. After calculation, the flux directions of adjacent grid cells on both sides of the interface are checked in pairs. If the flux imbalance in the entire computational domain exceeds a preset numerical convergence limit, the corresponding region's grid is densified and recalculated to ensure magnetic flux continuity. The flux divergence represents the local numerical imbalance formed by the transfer of the main magnetic flux from the computational domain to the air domain and is not considered a physical representation of the magnetic charge.

[0079] Subsequently, a calibration state with matching total flux linkage, temperature, and frequency, and without significant local leakage flux concentration, was selected as the reference state. The flux divergence of each grid cell was compared with the flux divergence at the same coordinate position under the reference state, and the positive and negative directions, absolute amplitudes, and corresponding node coordinates of the differences were associated and written into the core geometric grid to form a magnetic field distortion distribution map. Positive differences indicate increased local outflow flux, while negative differences indicate a relative decrease in flux in adjacent main magnetic circuits. Along the tangent of the Ampere loop and the normal of the core surface, the spatial gradient of the magnetic field distortion distribution map was differentiated using the actual spatial distance between adjacent nodes to avoid artificially inflated gradients due to varying grid density. Then, using the maximum and minimum absolute values ​​of the gradient within the same calibration time as normalization boundaries, the gradient amplitude of each node was mapped to a dimensionless interval of zero to one. When the difference between the maximum and minimum values ​​is lower than the calibration noise limit, the node coefficients at that time were set to zero. The normalized results of all valid calibration times are weighted and summarized according to the proportion of the corresponding local leakage flux absolute value in the total leakage flux absolute value, resulting in a non-uniform coefficient vector consistent with the node order of the Ampere loop. The more drastic the local magnetic field change, the closer its coefficient is to one.

[0080] Next, the sliding window moves along the cumulative arc length direction of the Ampere loop, with each window covering at least the central node and two adjacent nodes on each side. A cubic curve fit is performed on the non-uniform coefficients within the window, using the actual arc length of the node as the independent variable. The local curvature is determined by the first-order trend and second-order curvature trend of the fitted curve. The position where the absolute value of curvature reaches an extreme relative to adjacent windows is first detected, and then the second derivative in the neighborhood of that position is checked to see if it changes from positive to negative or vice versa. Only when the curvature extreme value and the zero-crossing position of the second derivative fall within the same neighborhood are the grid nodes closest to the zero-crossing position listed as truncation candidate nodes. The root mean square error of the coefficients within the current window is obtained by averaging the squares of the deviations of each coefficient from the window mean and then taking the square root. The truncation sensitivity factor is defined as the multiple of the actual decision threshold relative to the calibration reference threshold. This multiple is increased when the root mean square error increases to suppress false truncation caused by local fluctuations; the multiple is decreased when the root mean square error decreases to retain small but persistent magnetic field mutations. The multiple is always limited to the upper and lower limits determined in advance by calibration noise. A magnetic circuit truncation node is confirmed only when the curvature amplitude, the zero-crossing characteristic of the second derivative, and the difference in coefficients on both sides of the window simultaneously meet the dynamic threshold. For multiple candidate nodes falling within a single grid scale, the node with the largest difference in coefficients on both sides is retained and added to the topological reference node of the Ampere loop, forming a set of magnetic circuit truncation nodes arranged according to the loop direction. Here, magnetic circuit truncation represents segmentation of the computational path and does not change the physical structure of the transformer core.

[0081] Finally, the magnetic circuit truncated nodes are projected onto the center path of the Ampere loop, sorted according to their cumulative arc length, and the center path between adjacent truncated nodes is taken as a segmented magnetic circuit. Each time the path crosses a mesh boundary, material interface, or cross-sectional change point, a magnetic circuit micro-element is defined. The local arc length is determined based on the coordinates of the nodes at both ends of the micro-element, and then continuously accumulated along the path to obtain a set of segmented magnetic circuit lengths in meters. For closed Ampere loops, the path length from the last truncated node back to the topological reference node is also calculated to ensure that the magnetic circuit has no missing segments and no repetitions. Based on the segmented magnetic circuit length, effective cross-sectional area, and effective permeability corresponding to the calibrated hysteresis branches, the equivalent magnetic impedance of each segment to alternating magnetic flux is determined. The magnetic impedance increases with increasing magnetic circuit length and air gap ratio, and decreases with increasing effective cross-sectional area or effective permeability. The proportion of each segment's magnetic impedance to the total magnetic impedance of the closed magnetic circuit is used as the corresponding weight. After normalization, a magnetic circuit weight vector is formed in which each component is not less than zero and the sum is one. This vector is pre-stored according to temperature, frequency, and load calibration status for subsequent matching and retrieval. In this embodiment, the above scheme can accurately identify the boundary of abrupt magnetic field changes and obtain segmented magnetic circuit weights with clear physical constraints.

[0082] S233, based on the magnetic circuit weight vector, the magnetic field strength sequence is weighted and summed and path integrated to obtain the equivalent magnetomotive force.

[0083] Specifically, based on the current temperature, frequency, and load status, the corresponding magnetic circuit weight vector is invoked and aligned with the magnetic field strength sequence according to the segmented magnetic circuit number. Using the Ampere loop direction as the positive integration direction, the magnetic field strength at each sampling moment is projected onto the corresponding path tangent. Interpolation is performed at the center of each magnetic circuit element, and then continuously accumulated along the element length to obtain the magnetomotive force (MTF) of each segmented magnetic circuit. Subsequently, each segmented MMF is multiplied by the corresponding dimensionless magnetic circuit weight, and a signed sum is performed according to the direction to obtain the equivalent MMF characterized in ampere-turns. In this embodiment, the above scheme can account for the influence of non-uniform magnetic circuits on the MMF distribution, improving the accuracy of magnetization state characterization.

[0084] The equivalent magnetomotive force (MMF) is subjected to winding coupling matching and current dimension mapping to obtain a priori excitation sequence. Specifically, the equivalent MMF is subjected to winding coupling matching and current dimension mapping to obtain a priori excitation sequence. Using the secondary winding as the current conversion reference, the effective coupling turns of the secondary winding are determined based on the number of turns, winding direction, and pre-calibrated magnetic coupling coefficient of the primary and secondary windings. The positive and negative directions of the equivalent MMF are unified according to the relationship between the winding terminals of the same name. Then, the equivalent MMF at each sampling time is divided by the corresponding effective coupling turns to complete the dimensional conversion from ampere-turns to ampere. The conversion results are timestamped and arranged sequentially to form the a priori excitation sequence. In this embodiment, the above scheme realizes the accurate conversion of the core magnetization state to the secondary side excitation current.

[0085] S3, based on the secondary charge sequence, perform residual feedback and gain update on the prior excitation sequence to obtain the posterior excitation sequence.

[0086] S31, the prior excitation sequence is subjected to measurement space mapping to generate a predicted observation sequence, and the predicted observation sequence is compared with the secondary charge sequence based on phase space metric constraints to extract the state information sequence;

[0087] S32, perform multi-scale time-frequency analysis on the state information sequence to extract the perturbation feature tensor;

[0088] S33, Based on the state covariance evolution mechanism, the confidence level of the perturbation feature tensor is evaluated and weights are assigned to generate a dynamic gain matrix;

[0089] S34, perform multidimensional orthogonal mapping on the state information sequence based on the dynamic gain matrix to generate state correction parameters.

[0090] Specifically, based on the secondary winding turns, sampling channel gain, winding resistance, and leakage inductance calibration results, an observation mapping relationship is established from the excitation state to the excitation-sensitive components in the secondary current and voltage. The prior excitation sequence is input into this mapping relationship at each sampling time, generating a predicted observation sequence with the same timestamp and channel order as the secondary charge sequence. Subsequently, delayed coordinate embedding is performed on both the predicted observation sequence and the secondary charge sequence, constructing a phase space trajectory using the current sample value and its preceding sample values. This trajectory is then normalized according to the calibration noise scale of each current and voltage channel to avoid direct comparison between amperes and volts. The calibration noise covariance is used to constrain the metric distance between the two trajectories at the same time. The observed value of the secondary charge trajectory in the excitation-sensitive direction is subtracted from the corresponding predicted value to obtain the state information sequence. Samples exceeding the allowable distance in the phase space are not directly deleted but marked as low-confidence samples for subsequent gain adjustment.

[0091] The state information sequence is decomposed using discrete wavelet packet decomposition with a causal sliding window. The decomposition scale is determined based on the sampling frequency and the rated frequency of the transformer, so that the low-frequency scale represents the gradual changes in temperature and load, the intermediate scale covers the magnetization deviation near the fundamental frequency, and the high-frequency scale retains load abrupt changes, saturation spikes, and sampling disturbances. The wavelet coefficient energy, local modulus extrema, phase continuity, and duration are extracted for each observation channel at different time windows and frequency scales, and dimensionlessized based on the calibration noise energy of the corresponding channel. The components are then arranged according to the observation channel, time window, frequency scale, and feature type to form a disturbance feature tensor.

[0092] Then, taking the posterior state covariance from the previous sampling moment, the current prior state covariance is deduced through the excitation state transition relationship. If the disturbance characteristics appear continuously in adjacent time windows and multiple low and mid-frequency scales, it is determined that the model has not fully tracked the actual magnetization changes, and the process uncertainty is increased accordingly. If the disturbance is mainly concentrated in a single high-frequency scale and lacks temporal continuity, it is determined that the measurement is affected by impulse noise, and the measurement uncertainty of that observation channel is increased accordingly. The confidence level increases with the improvement of cross-scale consistency and temporal persistence, and decreases with the increase of isolated high-frequency energy and phase space deviation. Based on this, the weight allocation of each observation channel is completed. Symmetry verification and non-negative eigenvalue constraints are performed on the updated covariance matrix, and then the dynamic gain matrix between the predicted state and the measurement information is solved by combining the observation mapping relationship. The gain increases when the state prediction uncertainty increases or the measurement confidence increases, and the gain decreases when the measurement noise increases.

[0093] Finally, based on the characteristic directions of the innovation covariance, mutually orthogonal observation bases are established. The state innovation sequence is projected into non-repeating in-phase, orthogonal, and slowly varying perturbation components, which are then mapped to the excitation state space through a dynamic gain matrix. The mapping results in each direction are recombined according to the original observation bases to form state correction parameters converted to the ampere dimension. When the correction amplitude exceeds the confidence range defined by the current state covariance, constraints are applied according to the boundary of this range to prevent overcorrection caused by isolated anomalies. In this embodiment, the above scheme can distinguish between real magnetization perturbations and measurement noise, and generate state correction parameters that adaptively adjust with changes in operating conditions.

[0094] Specifically, S33 is expressed by the following formula: based on the state covariance evolution mechanism, the confidence of the perturbation feature tensor is evaluated and weights are assigned to generate a dynamic gain matrix.

[0095] ;

[0096] in, Let be the prior state covariance matrix. For measurement mapping matrix, Let Frobenius norm be the perturbation feature tensor. The preset confidence decay coefficient, Basic measurement noise covariance matrix, perturbation characteristic tensor Dynamic gain matrix ;

[0097] S34, perform multidimensional orthogonal mapping on the state information sequence based on the dynamic gain matrix to generate state correction parameters;

[0098] ;

[0099] Among them, the dynamic gain matrix State information sequence State correction parameters ;

[0100] S35, based on the state correction parameters, the prior excitation sequence is reconstructed in phase and time domain and updated to obtain the posterior excitation sequence.

[0101] ;

[0102] Among them, the posterior excitation sequence Prior excitation sequence .

[0103] S35, based on the state correction parameters, the prior excitation sequence is reconstructed in phase and time domain and updated to obtain the posterior excitation sequence.

[0104] S351, Based on the hysteresis characteristic curve of the transformer core, and combined with the prior excitation sequence, the hysteresis loop derivative and slope extraction are performed to obtain the differential permeability set.

[0105] S352, based on the differential permeability set, the state correction parameter is tangent-mapped and saturation adaptively limited to obtain the limited correction component;

[0106] S353, Based on the prior excitation sequence, perform waveform extreme value retrieval to obtain a set of historical turning points;

[0107] S354, Based on the set of historical turning points, phase space splicing and curve fitting are performed on the restricted correction components to obtain the transition phase trajectory curve;

[0108] S355, the transition phase trajectory curve is projected onto the time axis and sampled at equal intervals to obtain discrete state nodes, and the discrete state nodes are rearranged in time and replaced with numerical values ​​to obtain the posterior excitation sequence.

[0109] Specifically, in implementation, the prior excitation sequence is first converted to the magnetic field strength coordinates of the core hysteresis characteristic curve at each sampling time based on the effective number of coupled turns of the secondary winding, the segmented magnetic circuit length, and the magnetic circuit weight. The direction of increase or decrease of adjacent sampled values ​​determines whether the current operating point is on the rising or falling magnetization branch. If the sampling time is at a position where the magnetization direction reverses, the unilateral trend is extracted along the reversed hysteresis branch. For the discretely calibrated hysteresis characteristic curve, piecewise interpolation that maintains the monotonicity of the curve is used to recover the continuous curve between adjacent calibration points, and the slope of the local magnetic flux density change is extracted according to the actual magnetic field strength interval. The obtained slope represents the differential permeability of the magnetic flux density as a function of the magnetic field strength, with dimensions in Henry per meter. The differential permeabilities are arranged according to the sampling time, hysteresis branch, and segmented magnetic circuit number to obtain a differential permeability set. A unilateral slope is used for the ends of the curve, and operating points outside the calibration range are fixed at the nearest effective boundary to avoid unfounded extrapolation.

[0110] The state correction parameters are then mapped to each segment of the magnetic circuit according to the corresponding sampling time. The current correction is converted into a magnetomotive force change based on the effective number of coupling turns, and then converted into a magnetic field strength change based on the segment length. Local tangent mapping is performed using the differential permeability of the current operating point to determine the possible change in magnetic flux density caused by this change in magnetic field strength. The residual magnetic flux density interval from the current operating point to the corresponding hysteresis branch boundary on the hysteresis characteristic curve is used as the correction margin, and the saturation is determined based on the proximity of the current magnetic flux density to the calibration saturation boundary. The closer the operating point is to the saturation boundary, the smaller the correction amplitude allowed to continue changing towards saturation; after reaching the saturation boundary, only the correction direction that returns the operating point to the unsaturated region is retained. For operating points far from the saturation region, the correction amplitude is still constrained by the effective interval of the current local tangent to prevent a single correction from crossing the hysteresis branch. The limited magnetic flux density change is converted back to the Ampere dimension along the original mapping path to form a constrained correction component.

[0111] The prior excitation sequence is then smoothed to preserve phase, reducing sampling noise without shifting the true peak time. The waveform trend is then retrieved along the time axis. When the direction of change in adjacent segments changes from increasing to decreasing, or from decreasing to increasing, and the prominence of the extreme value relative to neighborhood fluctuations exceeds a threshold determined based on calibration noise, the corresponding sampling point is identified as a historical turning point. Each historical turning point is associated with a timestamp, excitation current value, turning direction, and the hysteresis branch at that time. If a new extreme value surpasses an existing outer extreme value in the same direction, the inner turning point surrounded by the new loop is deleted, retaining only valid records that reflect the memory of the hysteresis loop return point, thus obtaining the set of historical turning points.

[0112] Based on this, phase space coordinates are constructed using excitation current and its rate of change, and dimensionless coordinates are obtained using rated excitation current and calibrated maximum rate of change, respectively. The prior excitation state is used as the original trajectory point, and the sum of the prior excitation current and the constrained correction component is used as the target trajectory point. Historical turning points are used as phase trajectory splicing anchor points. If the original trajectory point and the target trajectory point are located in the same magnetization direction segment, a piecewise cubic curve maintaining monotonicity is used for connection. If there is a historical turning point between them, the trajectory is split at the turning point, and the current rate of change at the turning point is constrained to zero. The rising and falling segments before and after the turning point are fitted separately. Adjacent fitted segments maintain continuous current value and continuous tangential change at the splicing position, while restricting the fitted curve from exceeding the current hysteresis branch envelope, thus obtaining the transition phase trajectory curve.

[0113] Finally, based on the original timestamps of adjacent historical turning points, the transition phase track curve is projected onto a strictly increasing time axis, and sampling is performed at equal intervals using the sampling interval of the secondary charge sequence to obtain discrete state nodes containing timestamps, corrected excitation current values, and magnetization direction identifiers. The discrete state nodes are reordered according to their timestamps, retaining nodes with higher confidence for repeated timestamps, and replacing the original values ​​in the prior excitation sequence with the corrected excitation current values ​​of the corresponding nodes; sampling positions not covered by the transition phase track retain their original prior values, ultimately forming the posterior excitation sequence. In this embodiment, the above scheme can smoothly introduce state correction while adhering to hysteresis memory and saturation boundaries, avoiding non-physical abrupt changes in the posterior excitation waveform.

[0114] S4. Based on the posterior excitation sequence, the error of the secondary charge sequence is calculated to obtain a dynamic compensation sequence.

[0115] S41, perform fundamental phase extraction and amplitude calculation on the secondary charge sequence to obtain the fundamental phasor sequence, and determine the posterior excitation sequence as the excitation current component;

[0116] S42, based on the excitation current component, the fundamental phasor sequence is phase-aligned and error-allocated to obtain an error phasor sequence, and the error phasor sequence is then time-domain discretely reconstructed to obtain a dynamic compensation sequence.

[0117] Specifically, in implementation, the fundamental phase of the secondary voltage is used as a synchronization reference. The fundamental frequency at each sampling moment is obtained through phase-locked tracking, and the sliding analysis window is adjusted accordingly to cover the complete fundamental period. The DC bias of the secondary voltage and secondary current are eliminated, and then correlated and demodulated with a quadrature reference signal of the same frequency to extract the in-phase and quadrature components. These two components determine the fundamental amplitude expressed in RMS value and the continuously expanded fundamental phase. The center time, fundamental amplitude, and fundamental phase of each analysis window are sequentially correlated to form a fundamental phasor sequence that retains the dimensions of volts and amperes, respectively, avoiding direct mixing of voltage and current phasors in calculations.

[0118] Subsequently, the posterior excitation sequence is orthogonally demodulated using the same analysis window to obtain the fundamental amplitude and phase corresponding to the excitation current component. Since the posterior excitation sequence has already been converted to the secondary side, the positive and negative directions are unified based only on the winding end-to-end relationship during processing, and the fixed phase delay obtained from the sampling channel calibration is compensated; the turns conversion is not repeated. Using the direction of the secondary current fundamental phasor as the phase angle alignment reference, the excitation current component is decomposed into in-phase and orthogonal directions, where the in-phase component represents the fundamental amplitude deviation, and the orthogonal component represents the phase deviation. According to the compensation direction that can restore the secondary current to the primary side converted current, the two error components are recombined to obtain the error phasor sequence corresponding to the fundamental phasor sequence at each time step. When the secondary current fundamental amplitude is lower than the effective measurement lower limit, the unstable phase deviation is not output separately, but the error phasor corresponding to the excitation current is retained.

[0119] Finally, the phase of the error phasor sequence is continuously expanded, and the amplitude and phase are smoothly interpolated between the centers of adjacent windows. Based on the sampling times of the original quadratic charge sequence, the interpolated error phasors are restored to discrete waveforms in the ampere dimension through orthogonal synthesis at the same frequency. The overlapping regions of adjacent windows are superimposed using a window function with weights set to one, eliminating amplitude jumps caused by window switching, thus obtaining a dynamic compensation sequence. In this embodiment, the above scheme can accurately allocate the posterior excitation current into amplitude and phase errors, forming a continuous time-domain compensation quantity.

[0120] S5, the secondary energy sequence is inversely superimposed based on the dynamic compensation sequence to obtain a corrected secondary sequence.

[0121] S51, perform clock cycle alignment and data window matching on the secondary power sequence and the dynamic compensation sequence, extract the instantaneous error amplitude of the corresponding sampling node, and invert the algebraic sign of the instantaneous error amplitude to obtain the reverse compensation sequence.

[0122] S52, the reverse compensation sequence and the secondary electrical quantity sequence are added point by point to obtain the basic correction sequence, and the basic correction sequence is subjected to local extremum detection and step change point smoothing to obtain the corrected secondary sequence.

[0123] Specifically, in implementation, the secondary current channel with ampere dimensions is first extracted from the secondary charge sequence, and its sampling clock is used as a unified time reference. The processing delay formed during the fundamental phasor extraction, phase interpolation, and discrete reconstruction of the dynamic compensation sequence is read, and this delay is compensated to the timestamp of the dynamic compensation sequence. Then, resampling is performed according to the sampling period of the secondary current channel. For sampling moments that cannot be directly overlapped, interpolation is performed using effective compensation nodes before and after to maintain waveform monotonicity; a data window is established only within the effective time interval covered by both sequences to prevent false compensation caused by boundary extrapolation. Subsequently, sampling nodes are matched one by one according to the timestamp, and the corresponding instantaneous error amplitude is read from the dynamic compensation sequence. The instantaneous error amplitude retains the positive and negative polarities of the error waveform, rather than taking the absolute value of the error. The algebraic sign of the secondary current channel is inverted according to the unified polarity direction, forming a reverse compensation sequence with the same sampling rate, timestamp, and ampere dimension as the secondary current channel.

[0124] The inverse compensation sequence is added point-by-point to the secondary current channel to obtain the basic correction sequence. A local detection window is set along the time direction, and local peaks and valleys are identified based on the first-order change direction of adjacent sampled values. The normal fluctuation amplitude within the window is used to determine whether the peaks and valleys exceed the change envelope formed by adjacent valid data. At the same time, the amplitude difference between adjacent nodes is calculated, and the change positions that significantly exceed the local noise level are marked as step candidate points. If the step has a synchronous abrupt change in both direction and time in the original secondary current channel, it is determined to be a real load change and is retained; if the step only appears in the basic correction sequence and coincides with the compensation window boundary or interpolation node, it is determined to be a non-physical abrupt change introduced by the compensation process. For such abrupt changes, consecutive valid nodes before and after it are selected, and a monotonic curve that maintains the endpoint amplitude and change direction is used for local replacement to make the transition region continuous, while not changing the original correction result outside the window. After processing, the corrected secondary current channel is re-associated with the time-aligned secondary voltage channel to form a corrected secondary sequence; the secondary voltage channel is only used for phase reference and is not numerically added to the inverse compensation sequence with ampere dimensions. In this embodiment, the above scheme can eliminate excitation error and suppress pseudo-step at the compensation boundary, while retaining the true charge change.

[0125] S6. The correction secondary sequence is converted according to the transformation ratio of the mutual inductor to obtain the restored primary sequence.

[0126] S61, based on the transformer ratio, the correction quadratic sequence is scaled and linearly solved to obtain the primary waveform on the primary side, and the primary waveform on the primary side is analyzed by sliding window and extracted by extreme value envelope to obtain the transient boundary envelope.

[0127] S62, based on the transient boundary envelope, the primary waveform on the first side is subjected to envelope smoothing filtering and high-frequency noise suppression to obtain a noise-reduced pure waveform, and the noise-reduced pure waveform is zero-point reference anchored to obtain the restored primary sequence.

[0128] Specifically, in practice, the corrected secondary current path is extracted from the correction secondary sequence, and the transformer nameplate ratio and the actual ratio obtained from the factory calibration are read. The ratio is determined according to the ratio of the primary rated current to the secondary rated current, and is a dimensionless parameter. The waveform polarity is unified according to the winding terminal relationship, and the secondary current values ​​at each sampling node are scaled and amplified according to the actual ratio, while keeping the original sampling timestamp and sampling interval unchanged, resulting in the primary waveform on the primary side in amperes. This process only performs linear conversion from the secondary side to the primary side, without repeatedly introducing excitation error correction. If the correction secondary sequence also retains the secondary voltage path, it is mapped independently according to the corresponding voltage ratio and is not mixed with the current value in the calculation.

[0129] Subsequently, a sliding time window is set based on the real-time fundamental frequency, ensuring that each time window covers at least one complete fundamental cycle. The locations where the direction of change of adjacent sampled values ​​reverses are retrieved along the primary waveform on the primary side, and spurious extrema caused by single-point jitter are eliminated by combining local noise levels and the prominence of extreme values. Each effective local peak value is interpolated in chronological order to maintain monotonicity, forming the upper boundary envelope; each effective local valley value is connected in the same way to form the lower boundary envelope. These two boundaries together constitute the transient boundary envelope, used to characterize the true amplitude range that the primary waveform on the primary side is allowed to maintain during load changes, core transient recovery, and steady-state operation.

[0130] Robust local smoothing is applied to the transient boundary envelope to suppress boundary spikes caused by isolated extrema, while maintaining the positions of persistent peaks and troughs. The filter bandwidth is adaptively adjusted based on the rate of change of the smoothed envelope: the passband is narrowed when the envelope changes slowly to enhance high-frequency noise attenuation; the passband is appropriately widened when the envelope expands or contracts rapidly to avoid weakening the true transient edges. Envelope smoothing only constrains the slowly varying amplitude boundaries of the waveform, while high-frequency noise suppression acts on the rapid residual between the primary waveform on the primary side and the central trend of the envelope; both processes handle different frequency components. High-frequency components in the rapid residual below the calibrated noise threshold are attenuated, while transient components that cross adjacent time windows and have amplitudes significantly higher than the noise threshold are retained, resulting in a denoised and clean waveform.

[0131] Finally, the slowly changing DC baseline is estimated at the midpoint between the smoothed upper and lower boundary envelopes, and this baseline is subtracted from the denoised clean waveform. Adjacent sampling nodes with opposite signs are retrieved, and the true zero-crossing time is determined through local interpolation. The first stable positive zero-crossing point is used as the time and polarity reference. When no valid zero-crossing point exists within the current time window, the previous valid reference is used without forcibly changing the transient waveform. After baseline and time reference correction, the nodes are arranged according to the original sampling order to obtain the reconstructed primary sequence. In this embodiment, the above scheme can suppress high-frequency noise and zero-point drift while maintaining the true transient boundary, improving the accuracy of primary waveform reconstruction.

[0132] The above describes the adaptive filtering method for dynamic compensation of transformer errors in embodiments of the present invention. The following describes the adaptive filtering system for dynamic compensation of transformer errors in embodiments of the present invention. Please refer to [link to relevant documentation]. Figure 2 One embodiment of the adaptive filtering current transformer error dynamic compensation system of the present invention includes:

[0133] The sampling and measurement module 21 is used to sample the current and voltage on the secondary side of the current transformer to obtain the secondary electrical quantity sequence, and to measure the temperature of the current transformer body. Based on the temperature measurement results and the secondary electrical quantity sequence, the operating condition parameter matrix is ​​constructed.

[0134] The mapping module 22 is used to map the core magnetization state of the secondary electric charge sequence by combining the pre-calibrated hysteresis characteristic curve of the transformer core with the operating condition parameter matrix, so as to obtain the a priori excitation sequence based on the secondary side.

[0135] Update module 23 is used to perform residual feedback and gain update on the prior excitation sequence based on the secondary charge sequence to obtain the posterior excitation sequence;

[0136] Error conversion module 24 is used to perform error conversion on the secondary charge sequence based on the posterior excitation sequence to obtain a dynamic compensation sequence;

[0137] The superposition module 25 is used to perform reverse superposition of the secondary energy sequence based on the dynamic compensation sequence to obtain a corrected secondary sequence;

[0138] The transformer ratio conversion module 26 is used to convert the correction secondary sequence according to the transformer ratio to obtain the restored primary sequence.

[0139] In this embodiment, the specific implementation of each unit in the above system embodiment is described in the above method embodiment, and will not be repeated here.

Claims

1. A dynamic compensation method for current transformer errors using adaptive filtering, characterized in that, Includes the following steps: S1. Sample the current and voltage on the secondary side of the current transformer to obtain the secondary electrical quantity sequence, and measure the temperature of the current transformer body. Based on the temperature measurement results and the secondary electrical quantity sequence, construct the operating condition parameter matrix. S2, by using the pre-calibrated hysteresis characteristic curve of the transformer core and combining it with the operating condition parameter matrix, the magnetic core magnetization state of the secondary electric charge sequence is mapped to obtain the a priori excitation sequence based on the secondary side. S3, based on the secondary charge sequence, perform residual feedback and gain update on the prior excitation sequence to obtain the posterior excitation sequence; S4, Based on the posterior excitation sequence, the secondary charge sequence is subjected to error reduction to obtain a dynamic compensation sequence; S5, based on the dynamic compensation sequence, the secondary energy sequence is inversely superimposed to obtain the corrected secondary sequence; S6. The correction secondary sequence is converted according to the transformation ratio of the mutual inductor to obtain the restored primary sequence.

2. The adaptive filtering method for dynamic compensation of transformer errors according to claim 1, characterized in that, The process involves mapping the core magnetization state of the secondary charge sequence using a pre-calibrated current transformer core hysteresis characteristic curve and the operating condition parameter matrix, resulting in a priori excitation sequence based on the secondary side. This sequence includes: S21, the phase space decoupling of the secondary charge sequence is performed to separate the induced potential component, and the time domain accumulation and spatial boundary constraint of the induced potential component are performed based on the Faraday induction mechanism to obtain the transient flux sequence. S22, perform feature dimensionality reduction on the operating condition parameter matrix, extract load state parameters, and perform domain deflection analysis and hysteresis state reconstruction on the transient flux linkage sequence based on the load state parameters and the hysteresis characteristic curve of the transformer core to obtain the magnetic field strength sequence. S23, based on the Ampere loop topology, perform spatial magnetic circuit analysis on the magnetic field strength sequence to generate an equivalent magnetomotive force, and perform winding coupling matching and current dimension mapping on the equivalent magnetomotive force to obtain the a priori excitation sequence.

3. The adaptive filtering method for dynamic compensation of transformer errors according to claim 2, characterized in that, The spatial magnetic circuit analysis of the magnetic field intensity sequence based on Ampere's loop topology to generate an equivalent magnetomotive force includes: S231, based on the pre-acquired geometric structure data of the transformer core, combined with the Ampere loop topology, the calibration magnetic field intensity distribution data is spatially meshed and the node coordinates are mapped to obtain the spatial magnetic field distribution matrix, and the gradient calculation and boundary flux integration of the spatial magnetic field distribution matrix are performed to obtain the local leakage flux sequence. S232, Based on the local leakage flux sequence, the spatial magnetic field distribution matrix is ​​subjected to non-uniform coefficient extraction and magnetic circuit segmentation to obtain a set of segmented magnetic circuit lengths, and magnetic impedance weights are assigned to the set of segmented magnetic circuit lengths to obtain a magnetic circuit weight vector in advance. S233, based on the magnetic circuit weight vector, the magnetic field strength sequence is weighted and summed and path integrated to obtain the equivalent magnetomotive force.

4. The adaptive filtering method for dynamic compensation of transformer errors according to claim 3, characterized in that, The non-uniform coefficient extraction and magnetic circuit segmentation of the spatial magnetic field distribution matrix based on the local leakage flux sequence yields a set of segmented magnetic circuit lengths, including: S2321, Based on the local leakage flux sequence, the flux divergence and distortion mapping of the spatial magnetic field distribution matrix are performed to obtain the magnetic field distortion distribution map, and the spatial gradient derivative and extreme value normalization of the magnetic field distortion distribution map are performed to obtain the non-uniform coefficient vector. S2322, based on the non-uniform coefficient vector, perform local curvature extremum detection of the sliding window and zero-crossing determination of the second derivative in the neighborhood, and dynamically adjust the truncation sensitivity factor according to the mean square error of the coefficients in the current window to obtain the magnetic circuit truncation node set; S2323, Based on the set of magnetic circuit truncation nodes, perform geometric path integration and infinitesimal segmentation on the spatial magnetic field distribution matrix to obtain a set of segmented magnetic circuit lengths.

5. The adaptive filtering method for dynamic compensation of transformer errors according to claim 1, characterized in that, The step of performing residual feedback and gain update on the prior excitation sequence based on the secondary charge sequence to obtain the posterior excitation sequence includes: S31, the prior excitation sequence is subjected to measurement space mapping to generate a predicted observation sequence, and the predicted observation sequence is compared with the secondary charge sequence based on phase space metric constraints to extract the state information sequence; S32, perform multi-scale time-frequency analysis on the state information sequence to extract the perturbation feature tensor; S33, Based on the state covariance evolution mechanism, the confidence level of the perturbation feature tensor is evaluated and weights are assigned to generate a dynamic gain matrix; S34, perform multidimensional orthogonal mapping on the state information sequence based on the dynamic gain matrix to generate state correction parameters; S35, based on the state correction parameters, the prior excitation sequence is reconstructed in phase and time domain and updated to obtain the posterior excitation sequence.

6. The adaptive filtering method for dynamic compensation of transformer errors according to claim 5, characterized in that, The step of performing phase-track reconstruction and time-domain update on the prior excitation sequence based on the state correction parameters to obtain the posterior excitation sequence includes: S351, Based on the hysteresis characteristic curve of the transformer core, and combined with the prior excitation sequence, the hysteresis loop derivative and slope extraction are performed to obtain the differential permeability set. S352, based on the differential permeability set, the state correction parameter is tangent-mapped and saturation adaptively limited to obtain the limited correction component; S353, Based on the prior excitation sequence, perform waveform extreme value retrieval to obtain a set of historical turning points; S354, Based on the set of historical turning points, phase space splicing and curve fitting are performed on the restricted correction components to obtain the transition phase trajectory curve; S355, the transition phase trajectory curve is projected onto the time axis and sampled at equal intervals to obtain discrete state nodes, and the discrete state nodes are rearranged in time and replaced with numerical values ​​to obtain the posterior excitation sequence.

7. The adaptive filtering method for dynamic compensation of transformer errors according to claim 1, characterized in that, The step of performing error reduction on the secondary charge sequence based on the posterior excitation sequence to obtain a dynamic compensation sequence includes: S41, perform fundamental phase extraction and amplitude calculation on the secondary charge sequence to obtain the fundamental phasor sequence, and determine the posterior excitation sequence as the excitation current component; S42, based on the excitation current component, the fundamental phasor sequence is phase-aligned and error-allocated to obtain an error phasor sequence, and the error phasor sequence is then time-domain discretely reconstructed to obtain a dynamic compensation sequence.

8. The adaptive filtering method for dynamic compensation of transformer errors according to claim 1, characterized in that, The step of inversely superimposing the secondary energy sequence based on the dynamic compensation sequence to obtain the corrected secondary sequence includes: S51, perform clock cycle alignment and data window matching on the secondary power sequence and the dynamic compensation sequence, extract the instantaneous error amplitude of the corresponding sampling node, and invert the algebraic sign of the instantaneous error amplitude to obtain the reverse compensation sequence. S52, the reverse compensation sequence and the secondary electrical quantity sequence are added point by point to obtain the basic correction sequence, and the basic correction sequence is subjected to local extremum detection and step change point smoothing to obtain the corrected secondary sequence.

9. The adaptive filtering method for dynamic compensation of transformer errors according to claim 1, characterized in that, The step of performing ratio conversion on the corrected secondary sequence according to the transformer ratio to obtain the restored primary sequence includes: S61, based on the transformer ratio, the correction quadratic sequence is scaled and linearly solved to obtain the primary waveform on the primary side, and the primary waveform on the primary side is analyzed by sliding window and extracted by extreme value envelope to obtain the transient boundary envelope. S62, based on the transient boundary envelope, the primary waveform on the first side is subjected to envelope smoothing filtering and high-frequency noise suppression to obtain a noise-reduced pure waveform, and the noise-reduced pure waveform is zero-point reference anchored to obtain the restored primary sequence.

10. A dynamic error compensation system for an adaptive filter current transformer, characterized in that, include: The sampling and measurement module is used to sample the current and voltage on the secondary side of the current transformer to obtain the secondary electrical quantity sequence, and to measure the temperature of the current transformer body. Based on the temperature measurement results and the secondary electrical quantity sequence, the operating condition parameter matrix is ​​constructed. The mapping module is used to map the core magnetization state of the secondary electric charge sequence by combining the pre-calibrated hysteresis characteristic curve of the transformer core with the operating condition parameter matrix, so as to obtain the a priori excitation sequence based on the secondary side. The update module is used to perform residual feedback and gain update on the prior excitation sequence based on the secondary charge sequence to obtain the posterior excitation sequence. An error conversion module is used to perform error conversion on the secondary charge sequence based on the posterior excitation sequence to obtain a dynamic compensation sequence. The superposition module is used to inversely superimpose the secondary energy sequence based on the dynamic compensation sequence to obtain a corrected secondary sequence; The transformer ratio conversion module is used to convert the correction secondary sequence according to the transformer ratio to obtain the restored primary sequence.

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