Mutual inductor error self-compensation method based on dynamic flux linkage reconstruction

Abstract

The invention discloses a mutual inductor error self-compensation method based on dynamic flux linkage reconstruction, and relates to the technical field of mutual inductor error self-compensation. According to the method, a weighted double-domain integral noise suppression flux linkage reconstruction algorithm is used for processing, the fast response of time domain integral and the anti-noise capability of frequency domain integral are fused, and then a dynamic error extension state observer is constructed by taking a flux linkage estimation value as input; and estimating system errors caused by nonlinearity, hysteresis and environmental disturbance of the iron core and dynamic characteristics of the system errors based on extended Kalman filtering recursion. And finally, generating a time-varying compensation amount according to the estimated error and the derivative thereof. According to the method, the contradiction between precision and response speed in traditional flux linkage reconstruction is overcome, the problem that a static error model cannot adapt to dynamic working conditions is solved, high-precision real-time self-compensation of nonlinear time-varying errors of the mutual inductor is realized, and the measurement accuracy and dynamic performance of electric energy metering and protection equipment under complex operation conditions are improved.

Description

Technical Field

[0001] This invention relates to the field of instrument transformer error self-compensation technology, and in particular to an instrument transformer error self-compensation method based on dynamic flux linkage reconstruction. Background Technology

[0002] Current transformers and voltage transformers, as key sensing elements in power equipment such as electricity meters, play a crucial role in safely and reliably converting high-voltage, high-current signals from the primary side into low-level signals that can be processed by secondary equipment. Their output signals are directly used in electricity metering, fault detection, relay protection, and process control, forming the basis for ensuring the stable operation of the power system and the accuracy of automated control.

[0003] In actual operating environments, the measurement accuracy of instrument transformers is constrained by a variety of non-ideal factors. On the one hand, the nonlinear permeability, hysteresis loop, and remanence of the transformer core material cause its magnetization characteristics to deviate from the ideal linear model, especially under dynamic load or overcurrent conditions, which can easily lead to local saturation and instantaneous errors. On the other hand, the distributed resistance, parasitic capacitance, and coupling interference during signal transmission of the secondary winding further introduce additional phase shifts and amplitude distortions. The combined effect of these factors causes the secondary output signal of the instrument transformer to produce nonlinear and dynamically changing errors relative to the actual primary signal. Moreover, these errors are cumulative and difficult to observe directly, seriously affecting the accuracy of measurement results and the long-term stability of the system.

[0004] To address the aforementioned issues, existing technologies primarily employ two methods to compensate for transformer errors. One method is feedforward compensation based on static calibration, which corrects errors using a pre-established relationship between voltage or current and the error. However, this method cannot adapt to dynamic changes in operating conditions and lags in responding to time-varying nonlinear errors. The other method reconstructs the internal flux linkage of the transformer through time-domain integration, thereby inferring the primary current. However, direct integration is susceptible to noise interference, leading to severe baseline drift and accumulated errors in the integration results. This is particularly problematic in complex electromagnetic environments or situations with rapidly changing loads, where the reconstructed flux linkage is significantly distorted, resulting in decreased reconstruction accuracy. Furthermore, while some frequency-domain inversion methods can suppress some noise, they often sacrifice system response speed, leading to insufficient transient signal tracking capabilities and difficulty meeting measurement requirements under high dynamic conditions. Therefore, existing solutions generally suffer from inaccurate mapping of the secondary-side signal of the transformer and low overall correction accuracy. Summary of the Invention

[0005] This invention proposes a self-compensation method for transformer errors based on dynamic flux linkage reconstruction. Its purpose is to solve the problems of inaccurate mapping of secondary side signals of transformers and limited overall correction accuracy in existing technologies, to achieve high-precision real-time compensation for nonlinear and dynamically changing errors, and to take into account the system response speed and anti-interference capability.

[0006] The technical solution of this invention is as follows:

[0007] A method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration includes the following steps:

[0008] Step S1: During the operation of the current transformer, the secondary voltage signal and the secondary current signal are collected. The weighted dual-domain integral noise-suppressed flux linkage reconstruction algorithm is used to process the secondary voltage signal and the secondary current signal to obtain the flux linkage estimate of the current transformer.

[0009] Step S2: Using the flux linkage estimate obtained in step S1 as the state input, construct a dynamic error extended state observer, estimate the system error through a nonlinear error prediction model based on time continuous state estimation, further generate the error compensation amount, and perform error self-compensation on the secondary current signal.

[0010] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, step S1 includes the following sub-steps:

[0011] Step S1-1: Calculate the estimated value of the first magnetic flux linkage through the time-domain integration path;

[0012] Step S1-2: Calculate the estimated value of the second magnetic flux through the frequency domain integration path;

[0013] Step S1-3: Using a weighted dynamic fusion mechanism, the first flux linkage estimate and the second flux linkage estimate are fused to obtain the final flux linkage estimate.

[0014] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, in step S1-1, the calculation of the first flux linkage estimate through the time-domain integration path specifically involves integrating from the initial time to the current time, and integrating the value of the secondary voltage signal minus the product of the secondary loop resistance and the secondary current signal.

[0015] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, in step S1-2, the calculation of the second flux linkage estimate through the frequency domain integration path is specifically as follows: the secondary voltage signal is transformed in the frequency domain, processed by the frequency domain integration operator combined with low-pass filtering, and then inverse transformed to obtain the second flux linkage estimate in the time domain.

[0016] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, in step S1-3, the weighted dynamic fusion mechanism specifically involves: dynamically adjusting the fusion weight factor of the time domain path and the frequency domain path according to the deviation between the first flux linkage estimate and the second flux linkage estimate at the current time, and using the weighted sum as the final flux linkage estimate.

[0017] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, step S2, specifically includes constructing a dynamic error extension state observer:

[0018] Step S2-1: Define a state vector that includes the flux linkage estimate, secondary current signal, flux linkage rate of change, system-level error state, and periodic disturbance term;

[0019] Step S2-2: Based on the extended Kalman filter mechanism, the state vector is recursively estimated and updated until the convergence condition is met, and the final state estimate including the system error estimate is obtained.

[0020] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, in step S2-2, the extended Kalman filter mechanism introduces an adaptive covariance disturbance factor in each iteration. This factor dynamically adjusts the calculation of the Kalman gain according to the rate of change of the system error state.

[0021] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, in step S2, the error compensation amount is generated by multiplying the system error and its derivative in the final state estimate by the time gain coefficient and the derivative gain coefficient respectively, and then summing them to obtain the error compensation amount.

[0022] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, both the time gain coefficient and the derivative gain coefficient change with time. The time gain coefficient approaches 1 as the running time increases, while the derivative gain coefficient is larger in the early stage of operation and then gradually decreases.

[0023] As a further improvement to the current transformer error self-compensation method based on dynamic flux linkage reconstruction, step S2 specifically involves performing error self-compensation on the secondary current signal by adding the generated error compensation amount to the acquired secondary current signal to obtain the compensated secondary current signal.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] 1. This invention introduces a weighted dual-domain integral noise-suppressed flux linkage reconstruction algorithm, simultaneously constructing two integration paths in the time and frequency domains: the time-domain path directly integrates to preserve the system's dynamic response speed, while the frequency-domain path uses an integral operator combined with low-pass filtering to suppress high-frequency noise and DC offset. A weighted dynamic fusion mechanism is employed to dynamically adjust the fusion weights based on the real-time deviation between the estimation results of the two paths. This prioritizes the noise resistance of the frequency domain results during stable signal periods and the rapid tracking capability of the time domain results during transient processes. This method solves the problem of balancing response speed and estimation accuracy under a single integration path, obtaining accurate and stable flux linkage estimates. It balances response speed and estimation stability, fundamentally improving the accuracy and robustness of flux linkage estimation, and laying a reliable signal foundation for subsequent high-precision error compensation.

[0026] 2. This invention constructs a dynamic error extended state observer, realizing the systematic observation and prediction of complex time-varying errors. This observer incorporates the flux linkage estimate, secondary current and its rate of change, system-level error state, and even periodic disturbance terms into an extended state vector, establishing a continuous state-space model capable of describing the nonlinear dynamic behavior of the transformer. Through recursive estimation and updating based on the extended Kalman filter mechanism, and by introducing an adaptive covariance disturbance factor dynamically adjusted according to the error rate of change, this observer can accurately estimate the total system error and its dynamic characteristics caused by core nonlinearity, hysteresis, remanence, and environmental disturbances in real time. This method transforms the error compensation model from a static, feedforward mode to a dynamic, adaptive mode, overcoming the limitation of insufficient adaptability of traditional static calibration compensation models to changes in operating conditions. This effectively solves the problem of compensation lag and inaccuracy caused by the inability to track dynamic changes in operating conditions in existing technologies, enabling the compensation system to actively track and quantify the dynamic errors generated during operation.

[0027] 3. This invention constructs a time-varying error compensation quantity and feeds it back to the secondary current signal to form a closed-loop correction. The compensation quantity is generated by multiplying the error estimate and its derivative by a time-varying gain coefficient and then summing the results. The time gain coefficient approaches 1 as the system stabilizes, while the derivative gain coefficient is relatively large initially and then gradually decreases. This design allows the system to quickly apply compensation during periods of rapid error change, such as startup or sudden load changes, suppressing transient deviations. After entering steady state, the system smoothly transitions, relying mainly on the error itself for correction, avoiding overcompensation or the introduction of oscillation risks. The entire closed-loop architecture of "magnetic flux reconfiguration-state observation-error feedback" achieves high-precision real-time self-compensation for the nonlinear and dynamically changing errors of the transformer, significantly improving the overall measurement accuracy and dynamic performance of power metering or protection equipment under complex electromagnetic environments and varying load conditions. Attached Figure Description

[0028] Figure 1This is a flowchart illustrating the self-compensation method for transformer errors based on dynamic flux linkage reconfiguration. Detailed Implementation

[0029] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0031] The following is in conjunction with the appendix Figure 1 This invention describes the specific implementation process of a mutual inductor error self-compensation method based on dynamic flux linkage reconfiguration provided in an embodiment of the present invention. The method includes the following steps:

[0032] Step S1: During the operation of the current transformer, the secondary voltage signal and the secondary current signal are collected. The weighted dual-domain integral noise-suppressed flux linkage reconstruction algorithm is used to process the secondary voltage signal and the secondary current signal to obtain the flux linkage estimate of the current transformer.

[0033] Specifically, during the operation of the instrument transformer, the secondary voltage signal of the target instrument transformer is acquired through a high-precision isolated voltage sensor and a current transformer. and secondary current signal By reconstructing the instantaneous flux linkage value inside the current transformer using these two methods, the actual magnetomotive force changes occurring in the current transformer system can be restored.

[0034] To avoid the serious noise accumulation and baseline drift problems associated with directly integrating voltage signals using traditional time-domain integration methods, as well as the difficulty in suppressing high-frequency interference in conventional frequency-domain inversion methods, this invention introduces a weighted dual-domain integration noise suppression flux linkage reconstruction algorithm to overcome the noise accumulation, integration drift, and signal distortion problems caused by a single time-domain integration mechanism.

[0035] The weighted dual-domain integral noise suppression flux reconstruction algorithm calculates the voltage integral in parallel from both the time and frequency domains, and introduces a set of adaptive weighting factors to adjust the fusion degree of the two domain information. Specifically, it includes the following sub-steps:

[0036] Step S1-1: Calculate the estimated value of the first magnetic flux linkage through the time-domain integration path. .

[0037] The time-domain integral model starts from the initial time. (Usually set to 0) Integrate to the current time. Its expression is:

[0038]

[0039] In the above formula, The flux linkage estimate is the result of preliminary time-domain reconstruction, representing the value of the secondary side of the current transformer at... arrive The total change in magnetic flux over a period of time describes the process of magnetic field energy accumulation; It is the start time; The secondary circuit resistance includes the sum of the secondary winding resistance of the transformer, cable resistance, and wiring resistance. Its function is to compensate for the systematic error caused by the voltage drop across the resistor. It can be measured using a four-wire system. It is the integration variable, the time variable in the integration process, used for iteration. Time range; , Representing time respectively The target current transformer has secondary voltage and secondary current signals. In this formula, the voltage term provides the induced electromotive force, while the resistor voltage multiplied by the current term needs to be discarded to restore the essential change in magnetic flux.

[0040] Step S1-2: Calculate the estimated value of the second flux linkage through the frequency domain integration path. .

[0041] To further enhance anti-interference capability, a frequency domain integration mechanism is introduced. Its structure is based on the frequency domain integration expression after inverse Fourier transform, and its form is:

[0042]

[0043] In the above formula, It is the instantaneous value of flux linkage obtained by frequency domain path estimation, representing the time domain expression of the secondary side flux of the current transformer, and is the flux linkage signal recovered by frequency domain method; This is the inverse Fourier transform operator; It is the secondary voltage signal of the target transformer. In the frequency domain, the complex spectrum is obtained by performing a Fast Fourier Transform (FFT) on the secondary voltage signal. This is the regularization constant for the integrator kernel, used to stabilize the integration effect of low-frequency components in the frequency domain and prevent the integrator kernel from being activated when the frequency is low. The problem of dividing by zero; It is the complex frequency domain expression of the ideal integral operator. In the Fourier transform, the time-domain integral corresponds to the frequency domain division. , It is the imaginary unit of complex numbers; This is a Gaussian window low-pass filter, whose function is to suppress high-frequency components and prevent noise from being amplified during integration. It is the frequency attenuation factor, which controls the descent rate of the window function. It is based on the dual Fourier transform result of the time-domain window function broadening parameter, with a reference value range of [value missing]. The overall operation is built upon the frequency domain integral operator. The time domain is then restored using an inverse Fourier transform.

[0044] Steps S1-3: Using a weighted dynamic fusion mechanism, the first flux linkage estimate and the second flux linkage estimate are fused to obtain the final flux linkage estimate. .

[0045] The two flux linkage estimates mentioned above each have their own advantages. It has good response speed but poor noise immunity, while The result is smooth but lagging. Therefore, a weighted dynamic fusion mechanism is introduced to construct the final flux linkage estimate for the current time step. :

[0046]

[0047] In the above formula, For the current moment Final flux linkage estimate; and These are the dynamic fusion weight factors for the time-domain path and the frequency-domain path, respectively, satisfying... .

[0048] The initial value of the weighting factor can be set to The weights are dynamically adjusted based on the deviation between the two estimates. First, the absolute value of the deviation at the current moment is calculated. This deviation is then input into a moving average filter to generate a deviation index. Its update formula is:

[0049]

[0050] In the above formula, For the current moment Deviation index; The deviation index is the indicator from the previous moment. It is a smoothing coefficient, and its value range is usually within... Between these values, the degree of influence of historical information is controlled.

[0051] Fusion weights of frequency domain paths Follow Increase and strengthen, its update formula is set as:

[0052]

[0053] In the above formula, To adjust the sensitivity factor, for example, a value of 1500 can be used to control the sensitivity of the deviation index to weight adjustments. Simultaneously, the weights of the time-domain path are updated as follows: This mechanism enables the frequency domain path proportion to be increased when high-frequency interference is enhanced, while reverting to the time domain dominant path under low-frequency steady-state conditions, thereby dynamically optimizing the flux linkage reconstruction quality and achieving a balance between fast response and robustness.

[0054] At this point, the flux linkage estimation is complete. The acquisition of.

[0055] Step S2: Using the flux linkage estimate obtained in step S1 as the state input, construct a dynamic error extended state observer, estimate the system error through a nonlinear error prediction model based on time continuous state estimation, further generate the error compensation amount, and perform error self-compensation on the secondary current signal.

[0056] In obtaining the flux linkage estimate Then, using this as the core input, a dynamic error extension state observer is constructed. This observer is implemented by constructing a nonlinear error prediction model based on time-continuous state estimation. It observes and estimates the nonlinear structural error term, which cannot be directly measured, through state variable extension, and dynamically adjusts the confidence level between the prediction model and the observed quantities based on the error change rate during the observation process. The specific implementation process is as follows:

[0057] Step S2-1: Define the state vector and initialize it.

[0058] Define the current time. state vector for:

[0059]

[0060] In the above formula, It is the current moment. The state vector; Indicates the transpose operation; It is the flux linkage estimate obtained in step S1; It is the secondary current signal of the target current transformer collected at the current moment; At any moment The rate of change of the estimated flux linkage on the magnet is determined based on the flux linkage derivative of Faraday's law of electromagnetic induction, and this calculation method is existing technology. It is a system-level error state, which serves as an extended implicit state variable. It is used to model errors that cannot be explicitly modeled due to nonlinearity of the transformer core, residual hysteresis, temperature drift, and fluctuations in saturation permeability. Its initial value can be set to 0. This is a periodic disturbance term used to model disturbances such as power frequency harmonics or PWM pulsations. It can be represented by a sine function, for example... ,in , , It can be preset according to typical interference characteristics.

[0061] Step S2-2: Based on the extended Kalman filter mechanism, the state vector is recursively estimated and updated.

[0062] Obtain the current moment flux linkage estimate And construct the initial state vector Subsequently, in order to accurately estimate the systematic errors that cannot be directly measured... This step employs an extended Kalman filter as the iterative update mechanism. This mechanism updates at time... Internally, the process involves iterative recursion to progressively optimize the state estimate. The structure of the state estimate is related to the state vector. Same. Let's assume... index for internal iteration ( ), representing the first This is the second update. During initialization, let... The initial value of the state estimate The prediction error covariance matrix, process noise covariance matrix, and observation noise covariance matrix are initialized.

[0063] For the In the next iteration, the following recursive estimation steps are performed:

[0064] First, state prediction is performed. Based on the... State estimate of the next iteration and proceed with the first Input at the next iteration , and To conduct the first In the next iteration, the secondary voltage and current of the target transformer are obtained through a nonlinear state transition function. Calculate the first State estimate of the next iteration :

[0065]

[0066] In the above formula, It is a nonlinear state transition function, which is constructed based on the electromagnetic dynamics model of the target transformer. It describes the evolution of state variables (magnetic flux, current, error, etc.) over time. It is constructed based on existing mature electromagnetic measurement modeling and state space modeling methods. The construction process is well known to those skilled in the fields of control engineering and electromagnetic measurement, and will not be elaborated here. For the first Kalman gain matrix at the next iteration; yes The actual observation value of the nth iteration, i.e., the nth The secondary current of the target transformer during the next iteration ; To predict the observed values, a nonlinear observation function is determined by inverse derivation based on the fundamental induction law of mutual inductors. get.

[0067] Furthermore, the Kalman gain matrix The calculation method introduces an adaptive covariance perturbation factor. To enhance dynamic adaptability, the calculation formula is as follows:

[0068]

[0069] In the above formula, For the first The prediction error covariance matrix at the nth iteration represents the prediction error covariance matrix at the nth iteration. The uncertainty brought about by the prediction in the next iteration, that is, the degree of distrust in the current predicted state, is obtained by propagating the error covariance matrix of the previous state and combining it with the process noise covariance. For observation function The Jacobian matrix, calculated from the derivative of the observation function with respect to the state variables, is used to describe a linear approximation of how the state variables are mapped to the observation space. To observe the noise covariance matrix, which represents the variance characteristics of the measurement errors of the secondary voltage and secondary current of the target transformer, it can be obtained statistically based on the sensor accuracy index or historical sampling data. It is used to characterize the system's confidence in the sensor measurement in filtering. This is an adaptive covariance perturbation factor; It is an identity matrix.

[0070] Furthermore, the prediction error covariance matrix The calculation method is as follows:

[0071]

[0072] In the above formula, State transition function The Jacobian matrix is ​​used to reflect the system's prediction dependence structure on state variables; It is the error covariance of the previous iteration, representing the "uncertainty" of the state estimation; Given the process noise covariance matrix, the Jacobian matrix of the process noise is obtained through the state transition function. With noise variance matrix It is constructed that, i.e. .

[0073] Then, update the error covariance for this iteration:

[0074] .

[0075] Furthermore, the adaptive covariance perturbation factor The calculation method is as follows:

[0076]

[0077] In the above formula, The preset disturbance adjustment gain is used to control the sensitivity of the error slope to Kalman gain adjustment, and is determined based on expert experience. and They are from the first Second and third The system-level error state is obtained from the state estimate of the next iteration. The role of this factor is to automatically adjust the gain calculation when the system error changes drastically, thereby improving the robustness of the observer in dynamic processes.

[0078] After completing one iteration, let Increase by 1, and repeat the above recursive estimation steps until the preset convergence condition is met:

[0079]

[0080] In the above formula, The error tolerance threshold is preset based on expert experience and is a small positive number, for example... .

[0081] When the iteration converges, the current time step is terminated. The internal recursive process, and the state estimate obtained from the last iteration. As of the present moment The final state estimate is denoted as The system-level error state term is denoted as That is, the current moment Systematic errors.

[0082] Step S2-3: Based on the estimated system error, generate dynamic error compensation amount.

[0083] Based on the final state estimate Systematic errors in and its derivative calculation error compensation amount :

[0084]

[0085] In the above formula, It is the error compensation amount, representing the current time. The error correction current for the secondary current signal will be used to superimpose or cancel the secondary output to approximate the true primary current. It is the time gain coefficient, which controls the contribution of the current error body to the correction. It is the derivative gain coefficient, which controls the strength of the influence of the current error rate of change on the correction; It is the derivative of the systematic error, describing the rate of change of the systematic error. It is used to predict error trends and to respond and compensate in a timely manner when the error changes abruptly. It is calculated by first-order difference.

[0086] Furthermore, the time gain coefficient and derivative gain coefficient The calculation formula is:

[0087]

[0088]

[0089] In the above formula, This is a response speed adjustment factor, a manually set parameter with a value range of [value missing]. This design can quickly respond to error changes in the initial stage of compensation, and automatically reduce the compensation intensity after the system is running stably, avoiding overcorrection or causing oscillations.

[0090] Step S2-4: Perform error self-compensation on the secondary current signal.

[0091] Based on error compensation amount For the secondary current signal of the current transformer Real-time correction is performed to obtain the compensated secondary current signal. :

[0092]

[0093] In the above formula, It is the current moment. The secondary current signal after self-compensation.

[0094] In summary, this invention, through the high-precision, anti-interference flux linkage reconstruction in step S1 and the dynamic error estimation and closed-loop compensation based on extended state observation in step S2, forms a closed-loop control system of "flux linkage estimation → state observation → error feedback → signal correction". This effectively solves the technical problems of inaccurate mapping of the secondary output signal of the current transformer and low correction accuracy. In particular, it exhibits excellent adaptive compensation capability under dynamic and nonlinear error scenarios.

[0095] It should be noted that, as will be apparent to those skilled in the art, the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics thereof. The scope of the present invention is defined by the claims rather than the foregoing description.

Claims

1. A method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration, characterized in that, Includes the following steps: Step S1: During the operation of the current transformer, the secondary voltage signal and the secondary current signal are collected. The weighted dual-domain integral noise-suppressed flux linkage reconstruction algorithm is used to process the secondary voltage signal and the secondary current signal to obtain the flux linkage estimate of the current transformer. Step S2: Using the flux linkage estimate obtained in step S1 as the state input, construct a dynamic error extended state observer, estimate the system error through a nonlinear error prediction model based on time continuous state estimation, further generate the error compensation amount, and perform error self-compensation on the secondary current signal.

2. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 1, characterized in that, In step S1, the weighted dual-domain integral noise-suppressing flux linkage reconstruction algorithm includes the following sub-steps: Step S1-1: Calculate the estimated value of the first magnetic flux linkage through the time-domain integration path; Step S1-2: Calculate the estimated value of the second magnetic flux through the frequency domain integration path; Step S1-3: Using a weighted dynamic fusion mechanism, the first flux linkage estimate and the second flux linkage estimate are fused to obtain the final flux linkage estimate.

3. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 2, characterized in that, In step S1-1, the calculation of the first flux estimate through the time-domain integration path specifically involves integrating from the start time to the current time, and integrating the value of the secondary voltage signal minus the product of the secondary loop resistance and the secondary current signal.

4. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 2, characterized in that, In step S1-2, the calculation of the second flux linkage estimate through the frequency domain integration path specifically involves: performing a frequency domain transformation on the secondary voltage signal, using a frequency domain integration operator combined with low-pass filtering, and then performing an inverse transformation to obtain the second flux linkage estimate in the time domain.

5. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 2, characterized in that, In steps S1-3, the weighted dynamic fusion mechanism specifically involves: dynamically adjusting the fusion weight factors of the time-domain path and the frequency-domain path based on the deviation between the first flux linkage estimate and the second flux linkage estimate at the current time, and using the weighted sum as the final flux linkage estimate.

6. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 1, characterized in that, In step S2, constructing the dynamic error spread state observer specifically includes: Step S2-1: Define a state vector that includes the flux linkage estimate, secondary current signal, flux linkage rate of change, system-level error state, and periodic disturbance term; Step S2-2: Based on the extended Kalman filter mechanism, the state vector is recursively estimated and updated until the convergence condition is met, and the final state estimate including the system error estimate is obtained.

7. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 6, characterized in that, In step S2-2, the extended Kalman filter mechanism introduces an adaptive covariance perturbation factor in each iteration. This factor dynamically adjusts the calculation of the Kalman gain according to the rate of change of the system error state.

8. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 6, characterized in that, In step S2, generating the error compensation amount specifically involves multiplying the system error and its derivative in the final state estimate by the time gain coefficient and the derivative gain coefficient respectively, and then summing them to obtain the error compensation amount.

9. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 8, characterized in that, Both the time gain coefficient and the derivative gain coefficient change with time. The time gain coefficient approaches 1 as the running time increases, while the derivative gain coefficient is larger in the early stage of operation and then gradually decreases.

10. The method for self-compensation of transformer errors based on dynamic flux linkage reconfiguration as described in claim 1, characterized in that, In step S2, the error self-compensation of the secondary current signal is specifically performed by adding the generated error compensation amount to the acquired secondary current signal to obtain the compensated secondary current signal.

Images