Modeling and online identification method and system for dynamic error of transformer under hybrid excitation

Abstract

A method and system for modeling and online identification of dynamic errors in instrument transformers under hybrid excitation includes: establishing a field-circuit-excitation coupled dynamic error model and calculating the parameter sensitivity vector at candidate test frequencies; adaptively selecting several test frequencies from all candidate test frequencies based on the parameter sensitivity vector, and adaptively setting the disturbance amplitude of each test frequency to generate a micro-amplitude broadband active detection signal with a set code; injecting the micro-amplitude broadband active detection signal into the secondary circuit of the instrument transformer, acquiring the voltage and current on the secondary side of the instrument transformer, and calculating the measured complex response at each test frequency; based on the measured complex response and the field-circuit-excitation coupled dynamic error model, constructing a complex response residual objective function with model constraints, identifying the instrument transformer parameters through the objective function, and calculating the dynamic error results of the instrument transformer. This invention provides reliable support for metering compensation, protection early warning, and condition-based maintenance.

Description

Technical Field

[0001] This invention belongs to the field of power measurement and sensing technology, and more specifically, relates to a method and system for modeling and online identification of dynamic errors of current transformers under hybrid excitation. Background Technology

[0002] With the widespread adoption of new energy grid connection, high-voltage direct current transmission, and power electronic loads, the current waveform of the power system exhibits a significant non-sinusoidal characteristic: in addition to the fundamental wave, it contains multiple harmonics, and DC and aperiodic components may appear under fault, switching, or control conditions. These factors alter the operating point of the instrument transformer core and introduce additional magnetic flux and losses, causing significant dynamic changes in the transformer's transmission characteristics, resulting in increased metering deviations and the risk of protection maloperation / failure to operate.

[0003] Traditional instrument transformer error analysis is mostly based on the assumption of a sinusoidal steady state at power frequency. It usually uses a simplified equivalent circuit to establish an error model and uses offline verification results as the basis for operational accuracy. However, under mixed excitation conditions, the DC bias magnetization of the iron core, harmonic frequency conversion loss and secondary circuit parameter changes have strong coupling and time-varying characteristics, which makes it difficult for traditional models and offline verification to reflect operational errors, and thus cannot provide reliable data support for metering, protection and operation and maintenance.

[0004] Therefore, there is an urgent need for a technical solution that can construct a dynamic error model of the current transformer at the mechanistic level under mixed excitation conditions, and identify key parameters and output errors in real time during operation, so as to support adaptive metering compensation, protection early warning and predictive maintenance. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for modeling and online identification of dynamic errors in current transformers under hybrid excitation.

[0006] The present invention adopts the following technical solution.

[0007] The first aspect of this invention proposes a method for modeling and online identification of dynamic errors in current transformers under hybrid excitation, comprising: S1. For the mixed excitation condition where the primary side current contains both DC bias component and multiple harmonic components, a field-circuit-excitation coupled dynamic error model is established, which includes DC bias magnetization characteristics, harmonic frequency-varying loss characteristics and secondary circuit parameters. The parameter sensitivity vector at the candidate test frequency point is calculated based on the coupled dynamic error model. S2. Based on the parameter sensitivity vector, adaptively select several test frequencies from all candidate test frequencies and adaptively set the disturbance amplitude of each test frequency. Generate a micro-amplitude broadband active detection signal with a set code according to all test frequencies and the corresponding disturbance amplitude. S3. Inject the micro-amplitude wideband active detection signal into the secondary circuit of the current transformer, and simultaneously collect the voltage and current on the secondary side of the current transformer. S4. Calculate the measured complex response at each test frequency point based on the voltage and current on the secondary side of the transformer. S5. Based on the measured complex response and field-circuit-excitation coupled dynamic error model at each test frequency, construct a complex response residual objective function with model constraints, and identify the transformer parameters through the objective function; S6. Based on the identified transformer parameters and the complex transmission error relationship under hybrid excitation, calculate the dynamic error result of the transformer, which includes ratio error and angle error.

[0008] Preferably, the parameter sensitivity matrix at the candidate test frequency point is calculated based on the coupled dynamic error model, specifically as follows: The parameters of the current transformer include DC bias related parameters, magnetization characteristic parameters, frequency conversion loss parameters, and secondary circuit equivalent parameters; all parameters are combined into a parameter vector; The theoretical complex response function is obtained based on the field-path-excitation coupling dynamic error model. This function calculates the theoretical complex response under different parameter vectors and different frequency points. The complex response is the ratio of the complex amplitude of the transformer output to the complex amplitude of the input. Substituting each candidate test frequency point into the theoretical complex response function, the relationship function between different parameter vectors and the complex response at the corresponding candidate test frequency point is obtained. For each candidate test frequency point, the partial derivative of the corresponding relationship function with respect to each parameter is calculated. The partial derivatives with respect to all parameters form the sensitivity vector of the corresponding candidate test frequency point.

[0009] Preferably, several test frequencies are adaptively selected from all candidate test frequencies, specifically as follows: Randomly select a number of test frequency points as a test frequency point set, and form a sensitivity matrix by combining the sensitivity vectors of all test frequency points; Multiply the conjugate transpose of the sensitivity matrix by the inverse of the sampling noise covariance matrix, then multiply by the sensitivity matrix again. Add the product of the set regularization coefficient and the identity matrix to the multiplication result, calculate the determinant of the resulting matrix, and input the calculation result into the set logarithmic function. Calculate the penalty term based on the correlation of the test frequency points, subtract the penalty term from the output of the logarithmic function, and obtain the target function for frequency point selection. The set of test frequencies that maximizes the objective function for frequency selection is used as the final set of selected test frequencies.

[0010] Preferably, the penalty term is calculated based on the correlation of the test frequency points, specifically as follows: Calculate the reciprocal of the absolute value of the frequency difference between any two test frequency points, sum all the reciprocals, and multiply by the set penalty coefficient to obtain the penalty term.

[0011] Preferably, the disturbance amplitude at each test frequency point is adaptively set, specifically as follows: The disturbance amplitude at each test frequency point is randomly varied within the set amplitude range. Construct a diagonal matrix, where the diagonal elements of the k-th row are the elements of the first row. k The noise variance corresponding to the test frequency point and the first test frequency point k The ratio of the squares of the disturbance amplitudes at each test frequency point; Multiply the conjugate transpose of the sensitivity matrix of the final selected test frequency point set by the inverse of the diagonal matrix, then multiply by the corresponding sensitivity matrix. Add the product of the set regularization coefficient and the identity matrix to the product of the result of the multiplication, and calculate the trace of the inverse matrix of the matrix obtained after the addition as the objective function for perturbation amplitude screening. The set of test frequencies that minimizes the objective function for selecting the disturbance amplitude is obtained as the final set of test frequencies.

[0012] Preferably, a micro-amplitude broadband active detection signal with a set code is generated based on all test frequency points and corresponding disturbance amplitudes, specifically as follows: A phase coding sequence is formed by setting several phases. The kth test frequency point is used as the frequency of the sine function, the kth phase in the phase coding sequence is used as the phase of the sine function, and the amplitude of the kth test frequency point is used as the amplitude of the sine function, so as to obtain the sine function corresponding to the kth test frequency point. The sinusoidal functions of all test frequencies are superimposed. If the instantaneous value of the superimposed signal is higher than the set normal amplitude threshold at at least one moment, the instantaneous value at the corresponding moment is changed to the set normal amplitude threshold, and the modified superimposed signal is used as the micro-amplitude broadband active detection signal. Otherwise, the superimposed signal is used as the micro-amplitude broadband active detection signal.

[0013] Preferably, the complex response residual objective function with model constraints is constructed as follows: The characteristics of multi-frequency complex response include measured complex response and various losses, including core loss, insulation loss and stray loss; For each test frequency, calculate the square of the L2 norm of the difference between the measured complex response and the theoretical complex response, and sum the squares of the adaptive norms of all test frequencies to obtain the complex response residual. Calculate the square of the L2 norm of the difference between the parameter vector obtained in the current iteration and the parameter vector obtained in the previous iteration, and multiply the square by the set first constraint coefficient to obtain the first constraint term; Calculate the differential constraint term of frequency-dependent loss along the frequency direction, and multiply the square of the L2 norm of the differential constraint term by the set second constraint coefficient to obtain the second constraint term; The frequency-dependent loss differential constraint term along the frequency direction is as follows: Construct a function between each loss and the frequency point and parameter vector; For each loss, calculate the difference between the loss of each test frequency point and the loss of the previous test frequency point in the current iteration, divided by the difference between the corresponding test frequency point and the previous test frequency point, to obtain the differential term of the corresponding test frequency point; calculate the average value of the differential terms of all test frequency points except the first test frequency point to obtain the differential constraint term of the corresponding loss; calculate the square of the L2 norm of the vector composed of the differential constraint terms of all losses as the second constraint term. The complex response residual, the first constraint term, and the second constraint term are added together to obtain the objective function of the complex response residual.

[0014] Preferably, the adaptive norm is specifically: For the k-th test frequency, the index of the adaptive norm is the inverse of the noise matrix of the k-th test frequency; the noise matrix of the k-th test frequency is a diagonal matrix, and each element of the diagonal matrix is ​​the inverse of the noise matrix of the k-th test frequency. k The noise variance corresponding to the test frequency point and the first test frequency point k The ratio of the squares of the disturbance amplitudes at each test frequency point.

[0015] Preferably, based on the identified transformer parameters and the complex transfer error relationship under hybrid excitation, the dynamic error result of the transformer is calculated, specifically as follows: Substituting the identified transformer parameters into the field-circuit-excitation coupled dynamic error model, we obtain the estimated secondary-side harmonic current of a set order. Divide the estimated secondary harmonic current of the set order by the corresponding primary harmonic current component, multiply by the rated transformer ratio, and subtract 1 from the result to obtain the complex error factor. The comprehensive complex error is obtained by superimposing the product of all the complex error factors of the set number of times and the set weights; The real part of the comprehensive complex error is the ratio difference; The argument of the sum of the complex error and 1 is the angle difference.

[0016] The second aspect of this invention proposes a modeling and online identification system for dynamic errors of current transformers under hybrid excitation based on the method described in the first aspect of this invention. This system includes a field-path-excitation coupling modeling and sensitivity analysis module, an adaptive coding active detection signal generation and injection module, a data acquisition module, a multi-frequency complex response extraction module, a complex response residual identification module, and a dynamic error calculation module. Specifically: Field-Circuit-Excitation Coupling Modeling and Sensitivity Analysis Module: This module is used to establish a field-circuit-excitation coupling dynamic error model that includes DC bias magnetization characteristics, harmonic frequency-varying loss characteristics, and secondary circuit parameters for mixed excitation conditions where the primary current contains both DC bias components and multiple harmonic components. Based on the coupling dynamic error model, the module calculates the parameter sensitivity vector at candidate test frequencies. Adaptive coding active detection signal generation and injection module: Based on the parameter sensitivity vector, it adaptively selects several test frequencies from all candidate test frequencies and adaptively sets the disturbance amplitude of each test frequency. It then generates a micro-amplitude broadband active detection signal with set coding according to all test frequencies and the corresponding disturbance amplitude. Data acquisition module: used to inject the micro-amplitude broadband active detection signal into the secondary circuit of the current transformer, and simultaneously acquire the voltage and current on the secondary side of the current transformer; Multi-frequency complex response extraction module: used to calculate the measured complex response at each test frequency point based on the voltage and current on the secondary side of the transformer; Complex response residual identification module: Based on the measured complex response and field-circuit-excitation coupled dynamic error model at each test frequency, a complex response residual objective function with model constraints is constructed, and the transformer parameters are identified through the objective function; Dynamic error calculation module: Based on the identified transformer parameters and the complex transmission error relationship under hybrid excitation, the dynamic error result of the transformer is calculated, which includes ratio error and angle error.

[0017] A third aspect of the invention provides an apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor performing steps of modeling and online identification of dynamic errors of mutual inductors under hybrid excitation as described in the first aspect of the invention.

[0018] A fourth aspect of the present invention is a computer-readable storage medium storing a computer program that, when executed by a processor, uses the steps of the method for modeling and online identification of dynamic errors of mutual inductors under hybrid excitation as described in the first aspect of the present invention.

[0019] The beneficial effects of this invention are as follows: Compared with the prior art, this invention can explain the generation process of dynamic error of current transformers from the mechanism level under mixed excitation conditions, and improve the observability and identifiability of the parameters to be identified by guiding the selection of active detection frequency points and the allocation of disturbance amplitude through the model sensitivity matrix; it suppresses the uncertainty caused by direct identification of ordinary voltage and current characteristics through the objective function of multi-frequency complex response residuals; and it calculates the ratio difference and angle difference through mixed excitation complex error factors, avoiding the reliance on general algorithms such as least squares or Kalman filtering, thereby providing reliable support for metering compensation, protection early warning and condition-based maintenance. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a framework diagram of the system of the present invention; Figure 3 This is a schematic diagram of the extraction of micro-amplitude broadband active detection signals and multi-frequency complex responses. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0022] like Figure 1 As shown, Embodiment 1 of the present invention proposes a method for modeling and online identification of dynamic errors of current transformers under hybrid excitation, including: S1. For the mixed excitation condition where the primary side current contains both DC bias component and multiple harmonic components, a field-circuit-excitation coupled dynamic error model is established, which includes DC bias magnetization characteristics, harmonic frequency-varying loss characteristics and secondary circuit parameters. The parameter sensitivity vector at the candidate test frequency point is calculated based on the coupled dynamic error model. Specifically, the formula for the mixed excitation condition where the primary current simultaneously contains both DC bias components and multiple harmonic components is expressed as:

[0023] in, This refers to the primary side current; This is the DC current value; This is the DC bias coefficient; For the first h Subharmonic content coefficient; This represents the amplitude of the fundamental current. For the first h Subharmonic phase; The fundamental frequency; For harmonic order; For a specific moment; H This is the set highest harmonic order. It should be noted that... α dc ( t ), The non-periodic components introduced from DC power transmission converters, grid connection of new energy sources such as photovoltaics / wind power, various power electronic loads, and fault transients or switching processes cause the core operating point to shift and couple with harmonic components, affecting dynamic errors.

[0024] The DC bias magnetization characteristics are described by the DC bias magnetic field. H dc Introducing the magnetization relationship of the iron core:

[0025] in, B ( t ) represents the magnetic flux density. H ( t () represents the alternating magnetic field strength. f (·) represents the magnetization function of the iron core under DC bias. Furthermore, the coupled dynamic error model includes equivalent permeability or equivalent excitation inductance parameters to characterize the shift in the iron core's operating point caused by DC bias, which vary with... H dc Things have changed.

[0026] The secondary circuit parameters At least including the secondary side equivalent resistance R s 、 Equivalent Inductance L s Equivalent capacitance C s and load impedance Z load One or more of them, and participate in the unified modeling of the coupled dynamic error model.

[0027] The coupled dynamic error model characterizes the harmonics in the hybrid excitation according to their frequency components, and focuses on the h-th harmonic frequency. f h = hf 1. Establish a parameterized mapping relationship between the harmonic excitation component and the additional magnetic flux component under the combined effects of the DC bias magnetic field, harmonic frequency, and equivalent impedance of the secondary circuit. Its form is as follows:

[0028] in, For the first h The magnetic flux component corresponding to the subharmonic; For the first h Subharmonics in a DC bias magnetic field H dc Harmonic frequencies hf 1 and equivalent impedance of secondary circuit Z s Magnetic flux amplitude mapping coefficient under combined action;I h For the first h The amplitude of the second harmonic current; f 1 represents the fundamental frequency; For the first h Phase of the subharmonic current; This represents the flux phase correction caused by DC bias, frequency conversion loss, and secondary circuit parameter coupling. The parameterized mapping relationship is used to reflect the influence of additional magnetic flux generated by harmonics of different frequencies in the iron core on the dynamic error of the transformer.

[0029] S2, such as Figure 3 As shown, based on the parameter sensitivity vector, several test frequencies are adaptively selected from all candidate test frequencies and the disturbance amplitude of each test frequency is adaptively set. A micro-amplitude broadband active detection signal with a set code is generated according to all test frequencies and the corresponding disturbance amplitude. In this preferred embodiment, the parameter sensitivity matrix at the candidate test frequency point is calculated based on the coupled dynamic error model, specifically as follows: The parameters of the current transformer include DC bias related parameters, magnetization characteristic parameters, frequency conversion loss parameters, and secondary circuit equivalent parameters; all parameters are combined into a parameter vector; The theoretical complex response function, obtained from the field-circuit-excitation coupling dynamic error model, is a function for calculating the theoretical complex response under different parameter vectors and different frequency points. The complex response is the ratio of the complex amplitude of the transformer output to the complex amplitude of the input. In this embodiment, the input signal is selected as voltage, and the output signal can be the voltage or current of the secondary side. Substituting each candidate test frequency point into the theoretical complex response function, the relationship function between different parameter vectors and the complex response at the corresponding candidate test frequency point is obtained. For each candidate test frequency point, the partial derivative of the corresponding relationship function with respect to each parameter is calculated. The partial derivatives with respect to all parameters form the sensitivity vector of the corresponding candidate test frequency point, as shown in the formula:

[0030] in, For the k-th candidate test frequency point The sensitivity vector; This is the theoretical complex response function; For parameter vectors; , … These are the 1st, 2nd, ..., mth parameters.

[0031] In this preferred embodiment, several test frequency points are adaptively selected from all candidate test frequency points, specifically as follows: Randomly select a number of test frequency points as a test frequency point set, and form a sensitivity matrix by combining the sensitivity vectors of all test frequency points; Multiply the conjugate transpose of the sensitivity matrix by the inverse of the sampling noise covariance matrix, then multiply by the sensitivity matrix again. Add the product of the set regularization coefficient and the identity matrix to the multiplication result, calculate the determinant of the resulting matrix, and input the calculation result into the set logarithmic function. Calculate the penalty term based on the correlation of the test frequency points, subtract the penalty term from the output of the logarithmic function, and obtain the target function for frequency point selection. The set of test frequencies that maximizes the objective function for frequency selection is used as the final set of selected test frequencies. The formula is as follows:

[0032] in, This is the final set of test frequency points selected. For the set of candidate test frequency points; This is the set of test frequency points for the current iteration; The set of test frequency points for the current iteration The sensitivity matrix, each element is The sensitivity vector of each test frequency point; Indicates conjugate transpose; Represents a determinant; The sampling noise covariance matrix; The set regularization coefficient; It is the identity matrix; As a penalty item, This is the penalty coefficient; In this preferred embodiment, the penalty term is calculated based on the correlation of the test frequency points, specifically as follows: Calculate the reciprocal of the absolute value of the frequency difference between any two test frequency points, sum all the reciprocals, and multiply by the set penalty coefficient to obtain the penalty term.

[0033] In this preferred embodiment, the disturbance amplitude at each test frequency point is adaptively set, specifically as follows: The disturbance amplitude at each test frequency point is randomly varied within the set amplitude range. Construct a diagonal matrix, where the diagonal elements of the k-th row are the elements of the first row. k The noise variance corresponding to the test frequency point and the first test frequency point k The ratio of the squares of the disturbance amplitudes at each test frequency point; Multiply the conjugate transpose of the sensitivity matrix of the final selected test frequency point set by the inverse of the diagonal matrix, then multiply by the corresponding sensitivity matrix. Add the product of the set regularization coefficient and the identity matrix to the product of the result of the multiplication, and calculate the trace of the inverse matrix of the matrix obtained after the addition as the objective function for perturbation amplitude screening. The set of test frequencies that minimizes the objective function for perturbation amplitude selection is used as the final set of selected test frequencies. The formula is as follows:

[0034] The constraints are:

[0035] in, This refers to the perturbation amplitude of the k-th test frequency point in the final selected set of test frequency points; The set of disturbance amplitudes at all test frequencies; This is the set of perturbation amplitudes at the test frequency points in the current iteration; Represents the trace of a matrix; This is the sensitivity matrix for the final selected set of test frequency points; This represents the upper limit of the total disturbance amplitude; For the first k Each test frequency point does not affect the single-frequency amplitude ratio of normal measurements; U N This is the rated measurement quantity for the secondary side.

[0036] In this preferred embodiment, a micro-amplitude broadband active detection signal with a set code is generated based on all test frequency points and corresponding disturbance amplitudes, specifically as follows: A phase coding sequence is formed by setting several phases. The kth test frequency point is used as the frequency of the sine function, the kth phase in the phase coding sequence is used as the phase of the sine function, and the amplitude of the kth test frequency point is used as the amplitude of the sine function, so as to obtain the sine function corresponding to the kth test frequency point. The formula for superimposing the sinusoidal functions of all test frequencies is:

[0037] in, The signal is the result of superimposing sine functions; This is the kth test frequency point; This represents the k-th phase in the phase encoding sequence.

[0038] If the instantaneous value of the superimposed signal is higher than the set normal amplitude threshold at at least one moment, the instantaneous value at the corresponding moment is changed to the set normal amplitude threshold, and the modified superimposed signal is used as the micro-amplitude broadband active detection signal; otherwise, the superimposed signal is used as the micro-amplitude broadband active detection signal; ensuring that the detection signal remains below the preset threshold that affects normal measurement within any processing window.

[0039] S3. Inject the micro-amplitude wideband active detection signal into the secondary circuit of the current transformer, and simultaneously collect the voltage and current on the secondary side of the current transformer. S4. Calculate the measured complex response at each test frequency point based on the voltage and current on the secondary side of the transformer. whenu p ( t When using multi-frequency coding, the module performs synchronous demodulation at each test frequency to extract the corresponding amplitude and phase responses; when using other coding methods, response features corresponding to the active detection signal can be obtained through correlation analysis or frequency domain separation, thereby constructing an identification input-output feature set. U k , I k , G k}.in, U k Indicates the first k Voltage response at each test frequency point I k Indicates the first k The current response at each test frequency point is based on the input voltage at the corresponding frequency point on the primary side and the voltage response at the corresponding frequency point on the secondary side. U k or current response I k calculate G k , G k This represents the frequency transfer characteristic quantity composed of the voltage response characteristics and current response characteristics, i.e., the first... k The measured complex response characteristics obtained from the voltage or current response at each test frequency point .

[0040] S5. Based on the measured complex response and field-circuit-excitation coupled dynamic error model at each test frequency, construct a complex response residual objective function with model constraints, and identify the transformer parameters through the objective function; In this preferred embodiment, the complex response residual objective function with model constraints is constructed as follows: The characteristics of multi-frequency complex response include measured complex response and various losses, including core loss, insulation loss and stray loss; For each test frequency, calculate the square of the L2 norm of the difference between the measured complex response and the theoretical complex response, and sum the squares of the adaptive norms of all test frequencies to obtain the complex response residual. Calculate the square of the L2 norm of the difference between the parameter vector obtained in the current iteration and the parameter vector obtained in the previous iteration, and multiply the square by the set first constraint coefficient to obtain the first constraint term; Calculate the differential constraint term of frequency-dependent loss along the frequency direction, and multiply the square of the L2 norm of the differential constraint term by the set second constraint coefficient to obtain the second constraint term; The frequency-dependent loss differential constraint term along the frequency direction is as follows: Construct a function between each loss and the frequency point and parameter vector; For each loss, calculate the difference between the loss of each test frequency point and the loss of the previous test frequency point in the current iteration, divided by the difference between the corresponding test frequency point and the previous test frequency point, to obtain the differential term of the corresponding test frequency point; calculate the average value of the differential terms of all test frequency points except the first test frequency point to obtain the differential constraint term of the corresponding loss; calculate the square of the L2 norm of the vector composed of the differential constraint terms of all losses as the second constraint term. The objective function of the complex response residual is obtained by adding the complex response residual, the first constraint term, and the second constraint term. The formula is:

[0041] in, For the first k The measured complex response characteristics obtained from the voltage or current response at each test frequency point. The field-path-excitation coupled dynamic error model at the frequency point f k Theoretical complex response at the point, R k Let k be the noise matrix for test frequencies, and each element of the diagonal matrix be the first element. k The noise variance corresponding to the test frequency point and the first test frequency point k The ratio of the squares of the disturbance amplitudes at each test frequency point; This is the parameter vector generated during the current iteration. The parameter vector from the previous time step. D f R loss ( f , θ ) represents the differential constraint term for frequency-dependent loss parameters along the frequency direction. f Indicates frequency; , These are the first constraint coefficient and the second constraint coefficient, respectively.

[0042] S6. Based on the identified transformer parameters and the complex transmission error relationship under hybrid excitation, calculate the dynamic error result of the transformer, which includes ratio error and angle error.

[0043] In this preferred embodiment, the dynamic error result of the current transformer is calculated based on the identified transformer parameters and the complex transfer error relationship under hybrid excitation, specifically as follows: Substituting the identified transformer parameters into the field-circuit-excitation coupled dynamic error model, we obtain the estimated secondary-side harmonic current of a set order. Divide the estimated secondary harmonic current of the set order by the corresponding primary harmonic current component, then multiply by the rated transformer ratio, and subtract 1 from the result to obtain the complex error factor. ;

[0044] in, The first is calculated from the online updated core dynamic parameters and the field-path-excitation coupled dynamic error model. h Second harmonic second-side current estimate For the first side h Second harmonic current components K n The rated transformation ratio of the current transformer; The comprehensive complex error is obtained by superimposing the products of all the set complex error factors and set weights. ;

[0045] in, ω h ( t ) is the set number h Dynamic weighting of subharmonic components in hybrid excitation; The real part of the comprehensive complex error is the ratio difference. ; The argument of the sum of the complex error and 1 is the angle difference. ;

[0046] like Figure 2 As shown, Embodiment 2 of the present invention proposes a modeling and online identification system for dynamic errors of mutual inductors under hybrid excitation based on the method described in Embodiment 1 of the present invention. The system includes a field-path-excitation coupling modeling and sensitivity analysis module, an adaptive coding active detection signal generation and injection module, a data acquisition module, a multi-frequency complex response extraction module, a complex response residual identification module, and a dynamic error calculation module. Specifically: Field-Circuit-Excitation Coupling Modeling and Sensitivity Analysis Module: This module is used to establish a field-circuit-excitation coupling dynamic error model that includes DC bias magnetization characteristics, harmonic frequency-varying loss characteristics, and secondary circuit parameters for mixed excitation conditions where the primary current contains both DC bias components and multiple harmonic components. Based on the coupling dynamic error model, the module calculates the parameter sensitivity vector at candidate test frequencies. Adaptive coding active detection signal generation and injection module: Based on the parameter sensitivity vector, it adaptively selects several test frequencies from all candidate test frequencies and adaptively sets the disturbance amplitude of each test frequency. It then generates a micro-amplitude broadband active detection signal with set coding according to all test frequencies and the corresponding disturbance amplitude. Data acquisition module: used to inject the micro-amplitude broadband active detection signal into the secondary circuit of the current transformer, and simultaneously acquire the voltage and current on the secondary side of the current transformer; Multi-frequency complex response extraction module: used to calculate the measured complex response at each test frequency point based on the voltage and current on the secondary side of the transformer; Complex response residual identification module: Based on the measured complex response and field-circuit-excitation coupled dynamic error model at each test frequency, a complex response residual objective function with model constraints is constructed, and the transformer parameters are identified through the objective function; Dynamic error calculation module: Based on the identified transformer parameters and the complex transmission error relationship under hybrid excitation, the dynamic error result of the transformer is calculated, which includes ratio error and angle error.

[0047] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0048] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0049] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0050] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0051] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A modeling and online identification method for dynamic errors of a mutual inductor under mixed excitation, characterized in that, include: S1. For the mixed excitation condition where the primary side current contains both DC bias component and multiple harmonic components, a field-circuit-excitation coupled dynamic error model is established, which includes DC bias magnetization characteristics, harmonic frequency-varying loss characteristics and secondary circuit parameters. The parameter sensitivity vector at the candidate test frequency point is calculated based on the coupled dynamic error model. S2. Based on the parameter sensitivity vector, adaptively select several test frequencies from all candidate test frequencies and adaptively set the disturbance amplitude of each test frequency. Generate a micro-amplitude broadband active detection signal with a set code according to all test frequencies and the corresponding disturbance amplitude. S3. Inject the micro-amplitude wideband active detection signal into the secondary circuit of the current transformer, and simultaneously collect the voltage and current on the secondary side of the current transformer. S4. Calculate the measured complex response at each test frequency point based on the voltage and current on the secondary side of the transformer. S5. Based on the measured complex response and field-circuit-excitation coupled dynamic error model at each test frequency, construct a complex response residual objective function with model constraints, and identify the transformer parameters through the objective function; S6. Based on the identified transformer parameters and the complex transmission error relationship under hybrid excitation, calculate the dynamic error result of the transformer, which includes ratio error and angle error.

2. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation as described in claim 1, characterized in that: The parameter sensitivity matrix at the candidate test frequency points is calculated based on the coupled dynamic error model, specifically as follows: The parameters of the current transformer include DC bias related parameters, magnetization characteristic parameters, frequency conversion loss parameters, and secondary circuit equivalent parameters; all parameters are combined into a parameter vector; The theoretical complex response function is obtained based on the field-path-excitation coupling dynamic error model. This function calculates the theoretical complex response under different parameter vectors and different frequency points. The complex response is the ratio of the complex amplitude of the transformer output to the complex amplitude of the input. Substituting each candidate test frequency point into the theoretical complex response function, the relationship function between different parameter vectors and the complex response at the corresponding candidate test frequency point is obtained. For each candidate test frequency point, the partial derivative of the corresponding relationship function with respect to each parameter is calculated. The partial derivatives with respect to all parameters form the sensitivity vector of the corresponding candidate test frequency point.

3. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation as described in claim 1, characterized in that: Several test frequencies are adaptively selected from all candidate test frequencies, specifically: Randomly select a number of test frequency points as a test frequency point set, and form a sensitivity matrix by combining the sensitivity vectors of all test frequency points; Multiply the conjugate transpose of the sensitivity matrix by the inverse of the sampling noise covariance matrix, then multiply by the sensitivity matrix. Add the product of the set regularization coefficient and the identity matrix to the multiplication result, calculate the determinant of the matrix obtained by the sum, and input the calculation result into the set logarithmic function. The penalty term is calculated based on the correlation of the test frequency points. The penalty term is then subtracted from the output of the logarithmic function to obtain the objective function for frequency point selection. The set of test frequencies that maximizes the objective function for frequency selection is used as the final set of selected test frequencies.

4. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation as described in claim 3, characterized in that: The penalty term is calculated based on the correlation of the test frequency points, specifically as follows: Calculate the reciprocal of the absolute value of the frequency difference between any two test frequency points, sum all the reciprocals, and multiply by the set penalty coefficient to obtain the penalty term.

5. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation as described in claim 4, characterized in that: The disturbance amplitude at each test frequency point is adaptively set as follows: The disturbance amplitude at each test frequency point is randomly varied within the set amplitude range. Construct a diagonal matrix, the diagonal element of the kth row of the diagonal matrix is the ratio of the noise variance corresponding to the kth test frequency point to the square of the disturbance amplitude of the kth test frequency point k k the square of the disturbance amplitude of the kth test frequency point​ Multiply the conjugate transpose of the sensitivity matrix of the final selected test frequency point set by the inverse of the diagonal matrix, then multiply by the corresponding sensitivity matrix. Add the product of the set regularization coefficient and the identity matrix to the product of the result of the multiplication, and calculate the trace of the inverse matrix of the matrix obtained after the addition as the objective function for perturbation amplitude screening. The set of test frequencies that minimizes the objective function for selecting the disturbance amplitude is obtained as the final set of test frequencies.

6. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation as described in claim 1, characterized in that: A micro-amplitude broadband active detection signal with a set code is generated based on all test frequencies and corresponding disturbance amplitudes, specifically: A phase coding sequence is formed by setting several phases. The kth test frequency point is used as the frequency of the sine function, the kth phase in the phase coding sequence is used as the phase of the sine function, and the amplitude of the kth test frequency point is used as the amplitude of the sine function, so as to obtain the sine function corresponding to the kth test frequency point. The sinusoidal functions of all test frequencies are superimposed. If the instantaneous value of the superimposed signal is higher than the set normal amplitude threshold at at least one moment, the instantaneous value at the corresponding moment is changed to the set normal amplitude threshold, and the modified superimposed signal is used as the micro-amplitude broadband active detection signal. Otherwise, the superimposed signal is used as the micro-amplitude broadband active detection signal.

7. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation as described in claim 1, characterized in that: Construct the complex response residual objective function with model constraints, specifically as follows: The characteristics of multi-frequency complex response include measured complex response and various losses, including core loss, insulation loss and stray loss; For each test frequency, calculate the square of the L2 norm of the difference between the measured complex response and the theoretical complex response, and sum the squares of the adaptive norms of all test frequencies to obtain the complex response residual. Calculate the square of the L2 norm of the difference between the parameter vector obtained in the current iteration and the parameter vector obtained in the previous iteration, and multiply the square by the set first constraint coefficient to obtain the first constraint term; Calculate the differential constraint term of frequency-dependent loss along the frequency direction, and multiply the square of the L2 norm of the differential constraint term by the set second constraint coefficient to obtain the second constraint term; The frequency-dependent loss differential constraint term along the frequency direction is as follows: Construct a function between each loss and the frequency point and parameter vector; For each loss, calculate the difference between the loss of each test frequency point and the loss of the previous test frequency point in the current iteration, divided by the difference between the corresponding test frequency point and the previous test frequency point, to obtain the differential term of the corresponding test frequency point; calculate the average value of the differential terms of all test frequency points except the first test frequency point to obtain the differential constraint term of the corresponding loss; calculate the square of the L2 norm of the vector composed of the differential constraint terms of all losses as the second constraint term. The complex response residual, the first constraint term, and the second constraint term are added together to obtain the objective function of the complex response residual.

8. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation as described in claim 7, characterized in that: The adaptive norm is specifically: For the kth test frequency point, the subscript of the adaptive norm is the inverse matrix of the noise matrix of the kth test frequency point; the noise matrix of the kth test frequency point is a diagonal matrix, and each element of the diagonal matrix is the ratio of the noise variance corresponding to the kth test frequency point to the square of the disturbance amplitude of the kth test frequency point. k k test frequency point.​ 9. The method for modeling and online identification of dynamic errors of current transformers under hybrid excitation according to claim 1, characterized in that: Based on the identified transformer parameters and the complex transfer error relationship under hybrid excitation, the dynamic error result of the transformer is calculated as follows: Substituting the identified transformer parameters into the field-circuit-excitation coupled dynamic error model, we obtain the estimated secondary-side harmonic current of a set order. Divide the estimated secondary harmonic current of the set order by the corresponding primary harmonic current component, multiply by the rated transformer ratio, and subtract 1 from the result to obtain the complex error factor. The comprehensive complex error is obtained by superimposing the product of all the complex error factors of the set number of times and the set weights; The real part of the comprehensive complex error is the ratio difference; The argument of the sum of the complex error and 1 is the angle difference.

10. A system for modeling and online identification of dynamic errors of current transformers under hybrid excitation based on the method of any one of claims 1-9, comprising a field-circuit-excitation coupling modeling and sensitivity analysis module, an adaptive coding active detection signal generation and injection module, a data acquisition module, a multi-frequency complex response extraction module, a complex response residual identification module, and a dynamic error calculation module, characterized in that: Field-Circuit-Excitation Coupling Modeling and Sensitivity Analysis Module: This module is used to establish a field-circuit-excitation coupling dynamic error model that includes DC bias magnetization characteristics, harmonic frequency-varying loss characteristics, and secondary circuit parameters for mixed excitation conditions where the primary current contains both DC bias components and multiple harmonic components. Based on the coupling dynamic error model, the module calculates the parameter sensitivity vector at candidate test frequencies. Adaptive coding active detection signal generation and injection module: Based on the parameter sensitivity vector, it adaptively selects several test frequencies from all candidate test frequencies and adaptively sets the disturbance amplitude of each test frequency. It then generates a micro-amplitude broadband active detection signal with set coding according to all test frequencies and the corresponding disturbance amplitude. Data acquisition module: used to inject the micro-amplitude broadband active detection signal into the secondary circuit of the current transformer, and simultaneously acquire the voltage and current on the secondary side of the current transformer; Multi-frequency complex response extraction module: used to calculate the measured complex response at each test frequency point based on the voltage and current on the secondary side of the transformer; Complex response residual identification module: Based on the measured complex response and field-circuit-excitation coupled dynamic error model at each test frequency, a complex response residual objective function with model constraints is constructed, and the transformer parameters are identified through the objective function; Dynamic error calculation module: Based on the identified transformer parameters and the complex transmission error relationship under hybrid excitation, the dynamic error result of the transformer is calculated, which includes ratio error and angle error.

11. An apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: The processor performs the steps of modeling and online identification of dynamic errors of mutual inductors under hybrid excitation as described in any one of claims 1 to 9.

12. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program that, when executed by a processor, uses the steps of the method for modeling and online identification of dynamic errors of mutual inductors under hybrid excitation as described in any one of claims 1 to 9.

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