A method for determining the characteristics of ferromagnetic resonance overvoltage caused by fault

Abstract

The present invention provides a method for determining fault-induced ferromagnetic resonance overvoltage characteristics, belonging to the technical field of voltage transformers. The method comprises the following steps: collecting electrical data from a voltage transformer with a single fault, establishing a set of ferromagnetic resonance equations and a correction model. An initial model is trained based on the data set. Secondly, the method collects electrical data from voltage transformers with multiple faults, establishes a second training data set, and uses the data set to fine-tune the initial model to obtain a Lora model that can adapt to multiple faults. Finally, the method uses the initial model and the Lora model as a joint model, inputs a single or multiple fault vectors, and outputs a set of equations describing the fault-induced ferromagnetic resonance overvoltage characteristics. The present invention incorporates machine learning technology and can more accurately and comprehensively describe the overvoltage characteristics under different fault conditions, thus resolving the problem of existing methods' insufficient ability to describe overvoltage characteristics under complex fault conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of voltage transformers, and in particular relates to a method for determining ferromagnetic resonance overvoltage characteristics caused by a fault. Background Art

[0002] Electromagnetic voltage transformers, as common voltage detection devices in power systems, play an important role in grid protection, control, and measurement. However, in actual operation, electromagnetic voltage transformers are susceptible to various faults, such as winding short circuits, core faults, and secondary-side grounding. These faults can trigger ferroresonance and cause severe overvoltage faults. Overvoltage faults not only damage the voltage transformer itself but can also endanger the safe and reliable operation of the entire power system. Therefore, accurately analyzing and predicting the ferroresonance overvoltage characteristics under fault excitation is crucial for implementing timely protective measures and mitigating the risks of faults.

[0003] At present, the research on ferromagnetic resonance overvoltage characteristics mainly focuses on two aspects: one is the analysis method based on theoretical models, and the other is the experience summary based on experimental measurements.

[0004] Theoretical analysis methods typically establish mathematical models describing the ferromagnetic resonance process, such as voltage equations, current equations, flux equations, and impedance equations. These equations are then used to characterize the overvoltage characteristics caused by ferromagnetic resonance. This approach has good physical significance, but due to the nonlinearity and complexity of the ferromagnetic resonance process, relying solely on theoretical models cannot fully reflect the actual situation, resulting in certain prediction errors.

[0005] The experimental measurement method involves artificially creating faults and conducting test measurements on actual electromagnetic voltage transformers. The method collects data such as voltage, current, and frequency under fault excitation, and summarizes empirical patterns. This method can accurately obtain fault information, but it cannot be generalized to various fault conditions, and the measured data lacks consistency.

[0006] In other words, existing methods are difficult to achieve the integration of theoretical models and experimental data, and there is a technical problem of insufficient ability to describe overvoltage characteristics under complex fault conditions. Summary of the Invention

[0007] In view of this, the present invention provides a method for determining the overvoltage characteristics of ferromagnetic resonance caused by faults, which can solve the technical problems that the existing methods are difficult to achieve the integration of theoretical models and experimental data, and have insufficient ability to describe the overvoltage characteristics under complex fault conditions.

[0008] The present invention is achieved in that:

[0009] The present invention provides a method for determining a fault-induced ferromagnetic resonance overvoltage characteristic, comprising the following steps:

[0010] S10, collecting electrical data of ferromagnetic resonance excited by multiple different faults of an electromagnetic voltage transformer with a known single fault, including voltage, current, frequency, power factor, temperature, overvoltage, harmonic content, and core saturation, and recording the data as a first data set;

[0011] S20, establishing a ferromagnetic resonance equation group taking into account the electrical data, including a voltage equation, a current equation, a magnetic flux equation, and an impedance equation;

[0012] S30, establishing a combined model of ferromagnetic resonance overvoltage characteristics, including the ferromagnetic resonance equation group and a correction model, wherein the correction model is used to correct the parameters of the ferromagnetic resonance equation group, and the correction model is a neural network with a multi-input and multi-output structure, including a voltage equation parameter correction subnetwork, a current equation parameter correction subnetwork, a flux equation parameter correction subnetwork, an impedance equation parameter correction subnetwork, and a summary correction subnetwork;

[0013] S40. Establishing a first training data set based on the first data set, wherein the training inputs are voltage, current, frequency, power factor, temperature, harmonic content, and core saturation, and the training outputs are overvoltage amplitude, duration, frequency characteristics, and correction values ​​of parameters of each equation; performing fitting training on the ferromagnetic resonance overvoltage characteristic combination model using the first training data set to obtain a fitted and trained ferromagnetic resonance overvoltage characteristic combination model, which is recorded as a first model;

[0014] S50, collecting electrical data of ferromagnetic resonances excited by multiple different faults of an electromagnetic voltage transformer known to have at least one fault, and recording the data as a second data set;

[0015] S60. Using the second data set, establish a second training data set, where the training inputs are voltage, current, frequency, power factor, temperature, harmonic content, core saturation, and fault type, and the training outputs are overvoltage amplitude, duration, frequency characteristics, and correction values ​​of various equation parameters; fine-tune the first model using the second training data set to obtain a Lora model;

[0016] S70 , using the combined model and the Lora model as a joint model, inputting a fault vector of a single fault or a plurality of faults superimposed, and obtaining a ferromagnetic resonance equation group for describing ferromagnetic resonance overvoltage characteristics induced by the fault.

[0017] The fault vector is specifically represented as a vector containing multiple binary bits, each bit representing a possible fault type, and is used to describe a single fault or multiple superimposed faults.

[0018] Among them, the voltage equation parameter correction subnetwork has a training input of voltage data and basic circuit parameters, and a training output of voltage equation parameter correction values, which is used to correct the voltage equation parameters according to actual voltage data. The structure is a three-layer feedforward neural network.

[0019] Furthermore, the current equation parameter correction subnetwork has training inputs of current data and basic circuit parameters and training outputs of current equation parameter correction values, which are used to correct current equation parameters according to actual current data. The structure is a three-layer feedforward neural network.

[0020] Furthermore, the flux equation parameter correction subnetwork has a training input of flux data and core saturation, and a training output of flux equation parameter correction value, which is used to correct the flux equation parameters according to actual flux data. The structure is a three-layer feedforward neural network.

[0021] Furthermore, the impedance equation parameter correction subnetwork has a training input of impedance data and temperature and a training output of impedance equation parameter correction values, which is used to correct the impedance equation parameters according to actual impedance data. The structure is a three-layer feedforward neural network.

[0022] Furthermore, the training input of the summary correction subnetwork is the correction value output by each subnetwork of the correction model that does not contain the summary correction subnetwork, and the training output is a comprehensive correction parameter used to integrate the correction values ​​provided by each subnetwork. The structure is a two-layer feedforward neural network.

[0023] Furthermore, the Lora model includes a fault basis identification subnetwork and a correction model of the ferromagnetic resonance equation group of superimposed fault-excited ferromagnetic resonance.

[0024] Furthermore, the fine-tuning refers to adjusting the parameters of the hidden layer and output layer of each sub-network of the correction model in the first model, so as to adjust the weights and biases of these layers through the gradient descent method to adapt to various types of fault superposition fault situations.

[0025] Furthermore, the fault basis identification subnetwork has electrical data and fault type as training inputs, and fault characteristics as training outputs, which are used to identify and classify different types of faults. Its structure is a four-layer feedforward neural network. The correction model of the ferromagnetic resonance equation group for superimposed fault-excited ferromagnetic resonance has characteristics and fault characteristics of each subnetwork output as training inputs, and correction parameters as training outputs, which are used to correct the ferromagnetic resonance equation group according to the fault situation. Its structure is a five-layer feedforward neural network.

[0026] Furthermore, the step of obtaining the correction value of the equation parameter specifically includes:

[0027] S41. Parameter input: Select multiple sets of different initial parameter values ​​as input. These parameters include but are not limited to basic circuit parameters such as voltage, current, frequency, power factor, and environmental factors such as temperature and core saturation.

[0028] S42, solving the equation group: Substituting the parameter values ​​selected in S41 into the ferromagnetic resonance equation group, and solving the equation group to obtain the output results, including the overvoltage amplitude, duration, frequency characteristics, etc.;

[0029] S43, actual data collection: according to the parameter conditions input in S1, simulate the corresponding fault conditions on the actual electromagnetic voltage transformer and collect multiple sets of electrical data, including the actual measured overvoltage amplitude, duration, frequency characteristics, etc.;

[0030] S44, error calculation: compare the theoretical output results of the equation group in S42 with the actual data collected in S43, and calculate the errors of various indicators;

[0031] S45. Determination of parameter correction values: Based on the error calculated in S44, the parameters of the equation group are iteratively adjusted using an optimization algorithm until the error is reduced to an acceptable range, and the difference between the final determined parameters and the initial parameters is used as the equation parameter correction value.

[0032] The optimization algorithm employed here uses a gradient descent method. This process compares theoretical calculations with actual measured data, continuously adjusting equation parameters to ultimately obtain corrected parameters that accurately describe the fault-induced ferroresonance overvoltage characteristics. This approach, which incorporates both theoretical models and actual data, can effectively improve the model's accuracy and applicability.

[0033] Compared with existing technologies, the method for determining fault-induced ferroresonance overvoltage characteristics provided by this invention offers the following advantages: 1. It combines theoretical and machine learning models, overcoming the inability of a single model to fully describe the complex ferroresonance process. The theoretical model provides the necessary physical foundation for machine learning, while the machine learning model uses measured data to calibrate and refine the theoretical model, enabling the overall model to more accurately predict overvoltage characteristics under fault conditions.

[0034] 2. For single-fault and multi-fault superposition scenarios, an initial model and a LORA fine-tuning model were established, respectively. These models can comprehensively and accurately describe the ferroresonance overvoltage characteristics under different fault conditions. Furthermore, the LORA model does not directly change the weight parameters of the initial model, thereby better preserving the initial model's single-fault information judgment ability and preventing the impact of multi-fault superposition from weakening the single-fault judgment ability. Compared with existing single-fault analysis methods, the proposed method has greater adaptability and robustness.

[0035] 3. In the parameter correction stage, a systematic parameter selection strategy was adopted, including determining the parameter range, Latin hypercube sampling, considering extreme cases and typical working conditions, etc., which made full use of the measured data and improved the accuracy and applicability of the model parameters.

[0036] 4. The entire method is process-oriented and highly automated, and can be easily applied to the operation monitoring and fault diagnosis of electromagnetic voltage transformers, providing strong support for improving the safety and reliability of power systems.

[0037] In general, the method for determining the fault-induced ferromagnetic resonance overvoltage characteristics of the present invention fully utilizes the advantages of theoretical analysis and experimental measurement, integrates machine learning technology, and can more accurately and comprehensively describe the overvoltage characteristics under different fault conditions. It solves the technical problem that existing methods are difficult to achieve the integration of theoretical models and experimental data, and have insufficient ability to describe the overvoltage characteristics under complex fault conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A flow chart of the method provided by the present invention;

[0039] Figure 2 A flowchart of the steps for obtaining the corrected values ​​of the equation parameters;

[0040] Figure 3 It is the time domain waveform of overvoltage;

[0041] Figure 4 It is the time domain waveform of the current;

[0042] Figure 5 It is the time domain waveform diagram of magnetic flux;

[0043] Figure 6 This is the time domain waveform of impedance. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0045] like Figure 1 FIG. 1 is a flow chart of a method for determining a ferromagnetic resonance overvoltage characteristic caused by a fault provided by the present invention. The method comprises the following steps:

[0046] S10, collecting electrical data of ferromagnetic resonance excited by multiple different faults of an electromagnetic voltage transformer with a known single fault, including voltage, current, frequency, power factor, temperature, overvoltage, harmonic content, and core saturation, and recording the data as a first data set;

[0047] S20, establishing a ferromagnetic resonance equation group taking into account electrical data, including a voltage equation, a current equation, a magnetic flux equation, and an impedance equation;

[0048] S30, establishing a combined model of ferromagnetic resonance overvoltage characteristics, including a ferromagnetic resonance equation group and a correction model, wherein the correction model is used to correct the parameters of the ferromagnetic resonance equation group, and the correction model is a neural network with a multi-input and multi-output structure, including a voltage equation parameter correction subnetwork, a current equation parameter correction subnetwork, a flux equation parameter correction subnetwork, an impedance equation parameter correction subnetwork, and a summary correction subnetwork;

[0049] S40. Establishing a first training data set based on the first data set, wherein the training inputs are voltage, current, frequency, power factor, temperature, harmonic content, and core saturation, and the training outputs are overvoltage amplitude, duration, frequency characteristics, and correction values ​​of parameters of each equation; performing fitting training on a ferromagnetic resonance overvoltage characteristic combination model using the first training data set, and obtaining a fitted and trained ferromagnetic resonance overvoltage characteristic combination model, which is recorded as a first model;

[0050] S50, collecting electrical data of ferromagnetic resonances excited by multiple different faults of an electromagnetic voltage transformer known to have at least one fault, and recording the data as a second data set;

[0051] S60. Using the second data set, establish a second training data set, where the training inputs are voltage, current, frequency, power factor, temperature, harmonic content, core saturation, and fault type, and the training outputs are overvoltage amplitude, duration, frequency characteristics, and correction values ​​of various equation parameters; fine-tune the first model using the second training data set to obtain a Lora model;

[0052] S70 , using the combined model and the Lora model as a joint model, inputting a fault vector of a single fault or a plurality of faults superimposed, and obtaining a ferromagnetic resonance equation group for describing ferromagnetic resonance overvoltage characteristics induced by the fault.

[0053] like Figure 2 As shown, the steps for obtaining the equation parameter correction values ​​specifically include:

[0054] S41. Parameter input: Select multiple sets of different initial parameter values ​​as input. These parameters include but are not limited to basic circuit parameters such as voltage, current, frequency, power factor, and environmental factors such as temperature and core saturation.

[0055] S42, solving the equation group: Substituting the parameter values ​​selected in S41 into the ferromagnetic resonance equation group, and solving the equation group to obtain the output results, including the overvoltage amplitude, duration, frequency characteristics, etc.;

[0056] S43, actual data collection: according to the parameter conditions input in S1, simulate the corresponding fault conditions on the actual electromagnetic voltage transformer and collect multiple sets of electrical data, including the actual measured overvoltage amplitude, duration, frequency characteristics, etc.;

[0057] S44, error calculation: compare the theoretical output results of the equation group in S42 with the actual data collected in S43, and calculate the errors of various indicators;

[0058] S45. Determine parameter correction values: Based on the error calculated in S44, use an optimization algorithm (e.g., gradient descent) to iteratively adjust the parameters of the equation system until the error is reduced to an acceptable range. The difference between the finalized parameters and the initial parameters is used as the equation parameter correction value.

[0059] The specific implementation of the above steps is described in detail below:

[0060] Step S10: Collecting electrical data of ferromagnetic resonances caused by various faults of an electromagnetic voltage transformer with a known single fault. The specific implementation of this step includes the following sub-steps:

[0061] Step 10.1 Determine the rated parameters of the electromagnetic voltage transformer to be tested. Including the rated voltage U n , rated frequency f n , rated phase angle φ n wait.

[0062] Step 10.2: Design a device to simulate faults. For example, you can use a trigger circuit, short-circuit switch, etc. to simulate various fault conditions on the primary or secondary side of the voltage transformer, such as short circuit faults, ground faults, and open circuit faults.

[0063] Step 10.3 collects various electrical quantity data of the electromagnetic voltage transformer during the simulated fault, including voltage v, current i, frequency f, power factor cosφ, temperature T, overvoltage peak U p , harmonic content THD, core saturation S, etc. In order to obtain more comprehensive data, a high-speed data acquisition instrument can be used with a sampling frequency of not less than 1kHz.

[0064] Step 10.4 organizes the collected electrical data into a first data set D1 for use in subsequent steps. This data set should contain detailed electrical characteristic data under various single fault conditions.

[0065] Through this step, the detailed electrical parameter data of the electromagnetic voltage transformer under a known single fault condition was obtained, laying the foundation for the subsequent establishment of the ferromagnetic resonance equation group and training of the neural network model.

[0066] Step S20: Establishing a ferromagnetic resonance equation system taking into account the electrical data. The specific implementation of this step includes the following sub-steps:

[0067] Step 20.1: Based on the operating principle of an electromagnetic voltage transformer, establish a set of equations describing the relationship between voltage v, current i, magnetic flux ψ, and impedance Z. These equations should include voltage equations, current equations, magnetic flux equations, and impedance equations, covering the key physical processes of ferromagnetic resonance.

[0068] Step 20.2 introduces the influence of environmental factors such as temperature T, frequency f, and core saturation S into these basic equations to more accurately describe the ferromagnetic resonance characteristics under actual working conditions.

[0069] Step 20.3 For the parameters in the equation, such as inductance L, capacitance C, resistance R, etc., use measurement or fitting methods to obtain their values. For some parameters that are difficult to measure directly, such as the nonlinear coefficient k v 、k i 、k h etc., can be determined by fitting experimental data.

[0070] Step 20.4 organizes the established voltage, current, flux, and impedance equations into a complete set of equations describing the ferromagnetic resonance process. This set of equations will serve as the theoretical basis for the subsequent ferromagnetic resonance overvoltage characteristic prediction model.

[0071] The following is a detailed description of each equation:

[0072] 1. Voltage equation:

[0073]

[0074] Where v is the secondary voltage of the voltage transformer (unit: V); t is the time (unit: s); C is the equivalent capacitance (unit: F), which is obtained by measurement; i is the current (unit: A); R s is the equivalent series resistance (unit: Ω), obtained by measurement; L s is the equivalent series inductance (unit: H), obtained by measurement; k v is the voltage nonlinear coefficient, obtained by fitting the experimental data; V s is the fundamental voltage amplitude (unit V), obtained by Fourier analysis; ω is the angular frequency (unit rad / s), ω = 2πf, f is the system frequency; φ is the fundamental phase angle (unit rad), obtained by Fourier analysis; V n is the nth harmonic voltage amplitude (unit V), obtained by Fourier analysis; φ n is the nth harmonic phase angle (in rad), obtained by Fourier analysis.

[0075] 2. Current equation:

[0076] i=i m +i e +i h ;

[0077]

[0078] Where i m is the magnetizing current (unit A); i e is the eddy current loss current (unit A); i h is the hysteresis loss current (unit A); L m is the main magnetizing inductance (unit H), obtained by measurement; k i is the current nonlinear coefficient, obtained by fitting the experimental data; ψ is the magnetic flux (unit: Wb); C e is the equivalent eddy current capacitance (unit F), obtained by measurement; G e is the equivalent eddy current conductance (unit S), obtained by measurement; I n is the nth harmonic current amplitude (unit: A), obtained by Fourier analysis; θ n is the phase angle of the nth harmonic current (unit: rad), obtained by Fourier analysis; k h is the hysteresis loss coefficient, which is obtained by fitting the experimental data.

[0079] 3. Magnetic flux equation:

[0080] ψ=∫vdt;

[0081]

[0082] Where, B is the magnetic induction intensity (unit T); H is the magnetic field intensity (unit A / m); N is the number of winding turns; A e is the effective cross-sectional area of ​​the core (unit: m 2 ), obtained by measurement; l e is the effective magnetic path length of the core (unit: m), obtained by measurement; μ0 is the vacuum permeability, 4π×10 -7 H / m; μ r is the relative magnetic permeability, dimensionless; B r is the remanence (unit T), obtained through experimental measurement; H c is the coercive force (unit: A / m), obtained through experimental measurement; μ i is the initial magnetic permeability, dimensionless, obtained through experimental measurement; k T is the temperature coefficient, obtained by fitting experimental data; T is the current temperature (unit K); T0 is the reference temperature (unit K), usually room temperature 293.15K; k fis the frequency coefficient, obtained by fitting experimental data; f is the current frequency (unit: Hz); f0 is the reference frequency (unit: Hz), which is usually the rated frequency of 50Hz or 60Hz.

[0083] 4. Impedance equation:

[0084] Z=R+jX;

[0085]

[0086] Where Z is the total impedance (unit: Ω); R is the equivalent resistance (unit: Ω); X is the equivalent reactance (unit: Ω); R0 is the DC resistance (unit: Ω), obtained by measurement; α is the temperature coefficient (unit: 1 / K), obtained by fitting experimental data; k R is the coefficient of influence of frequency on resistance, obtained by fitting experimental data; X0 is the reference reactance (unit Ω), obtained by measurement; L0 is the reference inductance (unit H), obtained by measurement; k X is the influence coefficient of magnetic saturation on reactance, obtained by fitting experimental data; B s is the saturation magnetic induction intensity (unit T), obtained by experimental measurement; S is the core saturation, dimensionless; Z eq is the equivalent impedance (unit: Ω); Z p is the parallel impedance (unit Ω); R p is the parallel resistance (unit Ω), obtained by measurement

[0087] C p is the parallel capacitance (unit: F), obtained by measurement.

[0088] These equations form a complex system of ferroresonance equations, encompassing the relationships between voltage, current, magnetic flux, and impedance. These equations incorporate multiple parameters, taking into account the effects of temperature, frequency, magnetic saturation, and other factors. They also introduce nonlinear terms and higher-order derivatives to more accurately describe the ferroresonance phenomenon. Solving these equations requires the use of numerical methods such as the Runge-Kutta method or the finite element method, and may require iterative calculations to handle the nonlinear terms.

[0089] Through this step, a set of ferromagnetic resonance equations covering the relationship between voltage, current, magnetic flux and impedance was established, providing a theoretical basis for subsequent model construction.

[0090] Step S30: Establishing a ferromagnetic resonance overvoltage characteristic combination model. The specific implementation of this step includes the following sub-steps:

[0091] Step 30.1: Construct a combined model of ferromagnetic resonance overvoltage characteristics. The model consists of two parts: a ferromagnetic resonance equation group and a correction model.

[0092] Step 30.2: The ferromagnetic resonance equation group is the complete equation group established in step S20, which is used to describe the relationship between various physical quantities in the ferromagnetic resonance process.

[0093] Step 30.3 The correction model is a multi-input and multi-output neural network structure, which includes 5 sub-networks: voltage equation parameter correction sub-network, current equation parameter correction sub-network, flux equation parameter correction sub-network, impedance equation parameter correction sub-network and summary correction sub-network.

[0094] Step 30.4: The voltage equation parameter correction subnetwork takes voltage data and basic circuit parameters as input and outputs the corrected values ​​of the voltage equation parameters, which are used to correct the voltage equation. This subnetwork uses a three-layer feedforward neural network structure.

[0095] Step 30.5: The current equation parameter correction subnetwork takes as input the current data and basic circuit parameters, and outputs the corrected values ​​of the current equation parameters, which are used to correct the current equation. This subnetwork also uses a three-layer feedforward neural network structure.

[0096] Step 30.6: The flux equation parameter correction subnetwork takes as input the flux data and core saturation, and outputs the corrected values ​​of the flux equation parameters, which are used to correct the flux equation. This subnetwork also uses a three-layer feedforward neural network structure.

[0097] Step 30.7: The impedance equation parameter correction subnetwork takes impedance data and temperature as input and outputs corrected values ​​of the impedance equation parameters, which are used to correct the impedance equation. This subnetwork also uses a three-layer feedforward neural network structure.

[0098] Step 30.8: The input of the correction sub-network is the correction values ​​output by the other four sub-networks, and the output is a comprehensive correction parameter used to integrate the correction information provided by each sub-network. This sub-network adopts a two-layer feedforward neural network structure.

[0099] Step 30.9: Through this combined model, the theoretical equations established in step S20 can be integrated with the actual measurement data to improve the model's ability to describe the ferromagnetic resonance overvoltage characteristics caused by the fault.

[0100] In general, this step establishes a joint model consisting of a set of ferromagnetic resonance equations and a parameter-corrected neural network, which utilizes the advantages of theoretical models and measured data to improve the accuracy of describing the fault-induced ferromagnetic resonance overvoltage characteristics.

[0101] Step S40: Establish a first training data set based on the first data set, and perform fitting training on the ferromagnetic resonance overvoltage characteristic combination model. The specific implementation of this step includes the following sub-steps:

[0102] Step 40.1 selects training input features from the first data set D1. The training inputs include voltage v, current i, frequency f, power factor cosφ, temperature T, harmonic content THD, core saturation S, etc.

[0103] Step 40.2 Training output includes overvoltage peak value U p , overvoltage duration t p , overvoltage frequency characteristics f p and the corrected values ​​of the parameters of each equation.

[0104] Step 40.3 uses the above training input and output samples to perform fitting training on the combined ferromagnetic resonance overvoltage characteristic model established in step S30. The training algorithm can use gradient descent or other optimization algorithms, with the goal of minimizing the error between the training samples and the model output.

[0105] After the training in step 40.4 is completed, a fitted and trained ferroresonant overvoltage characteristic combination model is obtained, denoted as M1. This model can accurately describe the ferroresonant overvoltage characteristics under a known single fault condition.

[0106] Through this step, an initial ferromagnetic resonance overvoltage characteristic prediction model M1 was obtained based on the training of the first data set D1, laying the foundation for subsequent processing of more complex fault conditions.

[0107] Step S50: Collect electrical data of ferromagnetic resonances caused by multiple different faults of an electromagnetic voltage transformer known to have at least one fault, and record this as a second data set. This step is similar to step S10 and will not be repeated here.

[0108] Step S60: Using the second data set, establish a second training data set and fine-tune the ferromagnetic resonance overvoltage characteristic combination model established in step S30. The specific implementation of this step includes the following sub-steps:

[0109] Step 60.1 selects training input features from the second data set D2. The training inputs include voltage v, current i, frequency f, power factor cosφ, temperature T, harmonic content THD, core saturation S, and fault type F.

[0110] Step 60.2 The training output still includes the overvoltage peak value U p , overvoltage duration t p , overvoltage frequency characteristics f p and the corrected values ​​of the parameters of each equation.

[0111] Step 60.3 uses the LORA (Low-Rank Adaptation) fine-tuning algorithm to adjust the parameters of the initial model M1 trained in step S40. Specifically, LORA fine-tuning uses gradient descent to optimize the parameters of the hidden and output layers of the modified model in M1 to adapt to the situation where multiple types of faults overlap.

[0112] After LORA fine-tuning in step 60.4, a refined model M2 for the composite fault situation is obtained, called the LORA model. This model can better describe the impact of multiple fault superposition on the ferroresonant overvoltage characteristics.

[0113] Through this step, the initial model M1 was LORA-fine-tuned using the second data set D2, and a more robust ferromagnetic resonance overvoltage characteristic prediction model M2 was obtained, which can cope with complex fault conditions.

[0114] Step S70: Using the combined model M1 and the LORA model M2 as a joint model, input a fault vector representing a single fault or multiple faults superimposed on each other to obtain a set of ferromagnetic resonance equations describing the ferromagnetic resonance overvoltage characteristics induced by the fault. The specific implementation of this step includes the following sub-steps:

[0115] Step 70.1 Fault Vector It is a vector containing multiple binary bits, each bit represents a possible fault type, and is used to describe single or multiple superimposed fault conditions.

[0116] Step 70.2: Fault vector As input, the LORA model M2 obtained through training in step S60 can obtain the corrected ferromagnetic resonance equation group parameters.

[0117] Step 70.3 combines the ferromagnetic resonance equations established in step S30 with the output of the LORA model M2 to obtain a complete ferromagnetic resonance equation set that can accurately describe the fault-induced ferromagnetic resonance overvoltage characteristics.

[0118] Step 70.4 LORA model M2 includes two sub-networks: a fault basis identification sub-network and a correction model of the ferromagnetic resonance equations for superimposed fault-induced ferromagnetic resonance.

[0119] Step 70.5: The input of the fault-based identification subnetwork is electrical data and fault type, and the output is fault features, which are used to identify and classify different types of faults. This subnetwork adopts a 4-layer feedforward neural network structure.

[0120] Step 70.6: A correction model for the ferromagnetic resonance equations for superimposed fault-induced ferromagnetic resonance. The inputs are the output characteristics of each subnetwork and the fault characteristics, and the outputs are correction parameters used to correct the ferromagnetic resonance equations based on the fault condition. This subnetwork uses a five-layer feedforward neural network structure.

[0121] Through this step, the ferromagnetic resonance equation group established in step S30 is integrated with the LORA model M2 trained in step S60 to form a joint model that can describe the ferromagnetic resonance overvoltage characteristics under single fault or multiple fault superposition conditions.

[0122] The following is a specific implementation of steps S41-S45:

[0123] Step S41: Parameter input. Multiple sets of different initial parameter values ​​are selected as input. These parameters include but are not limited to basic circuit parameters such as voltage v, current i, frequency f, and power factor cosφ, as well as environmental factors such as temperature T and core saturation S.

[0124] In order to achieve the optimal parameter correction effect, the specific steps for selecting the initial parameters are as follows:

[0125] 1. Determine the parameter range:

[0126] According to the working principle and actual operation of electromagnetic voltage transformer, determine the reasonable range of each parameter, such as voltage 0.8U n 1.2U n , frequency 45Hz~65Hz, power factor 0.8 lagging 1.0~0.8 leading, temperature -40℃~80℃, core saturation 0.6~1.2.

[0127] 2. Using Latin hypercube sampling method:

[0128] The Latin hypercube sampling method is used to generate uniformly distributed sample points within a certain parameter range, ensuring that the samples in the multidimensional parameter space are well representative and uniform.

[0129] 3. Consider extreme cases:

[0130] On the basis of sampling, some extreme parameter combinations are added, such as the maximum voltage and the maximum temperature at the same time, the minimum frequency and the maximum core saturation at the same time, etc., to test the performance of the model under boundary conditions.

[0131] 4. Includes typical working conditions:

[0132] Add some known typical operating condition parameter combinations, which often appear in actual operation or have special significance.

[0133] 5. Consider parameter correlation:

[0134] There may be correlations between some parameters, such as a temperature increase may cause a change in core saturation.

[0135] 6. Dynamic Adjustment:

[0136] After initial training, analyze the model's performance in different parameter ranges. For intervals with poor performance, increase the number of sample points in that interval and perform focused sampling.

[0137] 7. Cross Validation:

[0138] The selected parameter group is divided into training set and validation set, and the cross-validation method is used to evaluate the performance of the model under different parameter combinations to ensure that the selected parameter group has good generalization ability.

[0139] 8. Iterative optimization:

[0140] Based on the initial training results, optimization algorithms (such as Bayesian optimization) are used to guide subsequent parameter selection, and gradually find the parameter combination that best reflects the system characteristics.

[0141] By following these steps, we can systematically select multiple sets of initial parameter values ​​as input, covering a wide range of possible operating conditions and fault scenarios. This helps train a robust model with good generalization capabilities. This approach improves the accuracy of parameter correction and ensures that the model maintains good performance in a variety of practical situations.

[0142] Step S42: Solve the equations. Substitute the parameter values ​​selected in step S41 into the ferromagnetic resonance equations established in step S20, and use a numerical solution method (such as the Runge-Kutta method) to obtain the output results of the equations, including the overvoltage peak value U p , overvoltage duration t p , overvoltage frequency characteristics f p wait.

[0143] Step S43: Actual data collection. According to the parameter conditions input in step S41, the corresponding fault conditions are simulated on the actual electromagnetic voltage transformer, and multiple sets of electrical data are collected, including the actual measured overvoltage peak value U p , overvoltage duration t p , overvoltage frequency characteristics f p wait.

[0144] Step S44: Error calculation. Compare the theoretical output results of the equation group in step S42 with the actual data collected in step S43, and calculate various indicators (overvoltage peak value U p , overvoltage duration t p , overvoltage frequency characteristics f p ) error.

[0145] Step S45: Determine the parameter correction value.

[0146] 1. Based on the error calculated in step S44, use an optimization algorithm (such as gradient descent) to iteratively adjust the parameters of the equation group until the error is reduced to an acceptable range.

[0147] 2. The difference between the final parameters and the initial parameters is used as the correction value of the equation parameters.

[0148] 3. This process continuously adjusts the equation parameters by comparing the theoretical calculation results with the actual measurement data, and finally obtains the corrected parameters that can accurately describe the ferromagnetic resonance overvoltage characteristics of the fault excitation.

[0149] 4. This method takes into account both the theoretical model and the actual data, which can effectively improve the accuracy and applicability of the model.

[0150] In summary, steps S41-S45 compare theoretical calculations with measured data, employing an optimization algorithm to continuously adjust the equation parameters, ultimately yielding a set of corrected parameters that accurately describe the fault-induced ferroresonance overvoltage characteristics. This approach leverages the strengths of both theoretical models and experimental data, improving the model's accuracy and robustness.

[0151] Specifically, the principle of the present invention is to establish a joint prediction framework that combines theoretical models and machine learning models. The specific principles are as follows:

[0152] First, based on the operating principle of an electromagnetic voltage transformer, a complete set of equations describing the relationship between voltage, current, magnetic flux, and impedance was established. These equations include the voltage equation, the current equation, the magnetic flux equation, and the impedance equation. These equations take into account the influence of environmental factors such as temperature, frequency, and core saturation, and can more accurately describe the physical laws of the ferromagnetic resonance process.

[0153] However, relying solely on these theoretical equations makes it difficult to fully reflect the overvoltage characteristics of actual fault conditions, resulting in certain prediction errors. Therefore, this paper introduces a correction model based on machine learning, which consists of five subnetworks: a voltage equation parameter correction subnetwork, a current equation parameter correction subnetwork, a flux equation parameter correction subnetwork, an impedance equation parameter correction subnetwork, and a summary correction subnetwork.

[0154] These subnetworks dynamically modify the parameters of the theoretical equations based on measured voltage, current, magnetic flux, and impedance data, ensuring that the overall model's predictions better match the observed values. Specifically, each subnetwork employs a feedforward neural network structure, taking as input the measured data of the corresponding physical quantity and outputting the parameter corrections for that physical quantity's equations. The aggregate correction subnetwork integrates the corrections from each subnetwork to produce a comprehensive parameter correction.

[0155] By integrating this theoretical model with the machine learning model, the method of the present invention can fully leverage the advantages of both. The theoretical model provides the physical foundation and overall framework, while the machine learning model uses measured data to continuously calibrate and optimize the model parameters, enabling the overall model to better describe the complex fault-induced ferromagnetic resonance process.

[0156] To further enhance the adaptability of the method, the present invention also employs LORA fine-tuning technology. Based on the initial model training, a second dataset containing multiple fault types is used to fine-tune the parameters of the model's correction subnetwork. This allows the model to adapt not only to single fault scenarios but also to complex scenarios involving multiple faults, significantly improving the model's robustness.

[0157] Furthermore, when selecting initial parameter values, the present invention employs a series of strategies, such as determining parameter ranges, Latin hypercube sampling, and considering both extreme and typical operating conditions. This fully leverages measured data and improves the accuracy of parameter correction. Through iterative optimization, a set of correction parameters is ultimately obtained that accurately describes the fault-induced ferroresonance overvoltage characteristics.

[0158] In general, the method of the present invention fully integrates theoretical analysis and machine learning technology, uses measured data to continuously correct and improve the theoretical model, and finally constructs a joint model that can comprehensively and accurately predict the fault-induced ferromagnetic resonance overvoltage characteristics.

[0159] In order to better understand and implement the present invention, a specific embodiment 1 of the present invention is provided below. The steps of this embodiment 1 are specifically described as follows:

[0160] Step S10: Collecting electrical data of ferromagnetic resonances excited by various faults of an electromagnetic voltage transformer with a known single fault.

[0161] In this step, it is necessary to collect detailed electrical data of the voltage transformer under a known single fault condition to provide a basis for subsequent theoretical model establishment and neural network training. Specifically, it includes the following aspects:

[0162] 1. Determine the rated parameters of the voltage transformer to be tested, including the rated voltage U n , rated frequency f n and rated phase angle φn wait.

[0163] 2. Design fault simulation devices, such as trigger circuits, short-circuit switches, etc., to simulate various fault conditions on the primary or secondary side of the voltage transformer, such as short-circuit faults, ground faults, and open circuit faults.

[0164] 3. Collect various electrical quantity data of the voltage transformer during simulated fault, including voltage v, current i, frequency f, power factor cosφ, temperature T, overvoltage peak U p , harmonic content THD and core saturation S, etc. In order to obtain more comprehensive data, a high-speed data acquisition instrument can be used with a sampling frequency of not less than 1kHz.

[0165] 4. Organize the collected electrical data into the first data set D1 for use in subsequent steps. This data set should contain detailed electrical characteristic data under various single fault conditions.

[0166] Step S20: Establishing a ferromagnetic resonance equation group taking into account the electrical data.

[0167] In this step, it is necessary to establish a set of equations describing the relationship between voltage v, current i, magnetic flux ψ, and impedance Z to characterize the key physical processes of the ferromagnetic resonance phenomenon. These equations include:

[0168] Voltage equation:

[0169]

[0170] Where C is the equivalent capacitance, R s is the equivalent series resistance, L s is the equivalent series inductance, k v is the voltage nonlinear coefficient. V s is the fundamental voltage amplitude, ω is the angular frequency, and φ is the fundamental phase angle. n and φ n are the nth harmonic voltage amplitude and phase angle respectively.

[0171] Current equation:

[0172] i=i m +i e +i h

[0173]

[0174] Where, i m is the magnetizing current, i e is the eddy current loss current, i h is the hysteresis loss current. L m Main magnetizing inductance, k iis the current nonlinear coefficient. ψ is the magnetic flux. C e is the equivalent eddy current capacitance, G e is the equivalent eddy current conductance. n and θ n are the amplitude and phase angle of the nth harmonic current, k h is the hysteresis loss coefficient.

[0175] Flux equation:

[0176] ψ=∫vdt

[0177]

[0178]

[0179] Where N is the number of winding turns, A e is the effective cross-sectional area of ​​the core, l e is the effective magnetic path length of the core. μ0 is the vacuum permeability, μ r is the relative magnetic permeability, B r is the remanence, H c is the coercive force, μ i is the initial magnetic permeability. k T is the temperature coefficient, k f is the frequency coefficient.

[0180] Impedance equation:

[0181] Z=R+jX

[0182]

[0183] Where R is the equivalent resistance, X is the equivalent reactance. R0 is the DC resistance, α is the temperature coefficient, k R is the influence coefficient of frequency on resistance. X0 is the reference reactance, L0 is the reference inductance, k X is the influence coefficient of magnetic saturation on reactance, B s is the saturation magnetic induction intensity. S is the core saturation. Z eq is the equivalent impedance, Z p is the parallel impedance, R p is the parallel resistance, C p is a parallel capacitor.

[0184] These equations cover the relationship between voltage, current, magnetic flux and impedance, and take into account the influence of factors such as temperature, frequency, and magnetic saturation. At the same time, nonlinear terms and high-order derivative terms are introduced to more accurately describe the ferromagnetic resonance phenomenon.

[0185] When establishing these equations, it is necessary to use measurement or fitting methods to obtain the values ​​of various parameters, such as capacitance C, resistance R s 、Inductor Ls , main magnetizing inductance L m , initial magnetic permeability μ i , temperature coefficient k T , frequency coefficient k f , the influence coefficient of frequency on resistance k R , the influence coefficient k of magnetic saturation on reactance X For some parameters that are difficult to measure directly, such as the nonlinear coefficient k v 、k i 、k h , can be determined by fitting experimental data.

[0186] By establishing this complete set of ferroresonance equations, a theoretical foundation has been laid for subsequent prediction models of ferroresonance overvoltage characteristics. However, relying solely on these theoretical equations is difficult to fully reflect the overvoltage characteristics under actual fault conditions, and there is a certain amount of prediction error. Therefore, it is necessary to combine these theoretical models with machine learning techniques to improve the accuracy and robustness of predictions.

[0187] Step S30: Establishing a ferromagnetic resonance overvoltage characteristic combination model.

[0188] In this step, a combined model of the ferromagnetic resonance overvoltage characteristics is constructed, consisting of a theoretical set of equations and a modified model. The theoretical set of equations, the complete set established in step S20, describes the relationship between various physical quantities during the ferromagnetic resonance process. The modified model, a multi-input, multi-output structure based on a neural network, dynamically adjusts the parameters of the theoretical set of equations, enabling the overall model to more accurately predict the overvoltage characteristics under fault excitation.

[0189] The revised model includes the following five sub-networks:

[0190] 1. Voltage equation parameter correction subnetwork:

[0191] The input is voltage v data and basic circuit parameters (C, R s , L s 、k v wait)

[0192] The output is the correction value of the voltage equation parameter, which is used to adjust the voltage equation

[0193] This sub-network adopts a 3-layer feedforward neural network structure.

[0194] 2. Current equation parameter correction subnetwork:

[0195] The input is the current i data and basic circuit parameters (L m 、k i 、C e , G e 、kh wait)

[0196] The output is the correction value of the current equation parameter, which is used to adjust the current equation

[0197] It also uses a 3-layer feedforward neural network structure

[0198] 3. Flux equation parameter correction subnetwork:

[0199] The input is the magnetic flux ψ data and the core saturation S

[0200] The output is the correction value of the flux equation parameters, which is used to adjust the flux equation

[0201] The sub-network adopts a 3-layer feedforward neural network structure, and the activation function is Sigmoid

[0202] 4. Impedance equation parameter correction subnetwork:

[0203] The input is impedance Z data and temperature T

[0204] The output is the correction value of the impedance equation parameter, which is used to adjust the impedance equation

[0205] The sub-network also uses a 3-layer feedforward neural network, and the activation function is Tanh

[0206] 5. Summarize and correct the sub-network:

[0207] The input is the correction value of the output of the other 4 sub-networks

[0208] The output is a comprehensive correction parameter, which is used to integrate the correction information provided by each sub-network

[0209] This sub-network contains 2 hidden layers, and the activation function is ReLU

[0210] By integrating this theoretical model with the machine learning model, we hope to leverage the advantages of both: the theoretical model provides the physical basis and overall framework, while the neural network model uses measured data to continuously correct and optimize the model parameters, so that the overall model can better describe the complex fault-induced ferromagnetic resonance process.

[0211] Step S40: establishing a first training data set based on the first data set, and performing fitting training on the ferromagnetic resonance overvoltage characteristic combination model.

[0212] In this step, training input features are selected from the first data set D1, including voltage v, current i, frequency f, power factor cosφ, temperature T, harmonic content THD and core saturation S, etc.

[0213] The training output includes the following aspects:

[0214] 1. Overvoltage peak U p

[0215] 2. Overvoltage duration t p

[0216] 3. Overvoltage frequency characteristic f p

[0217] 4. Correction values ​​of various equation parameters, such as voltage equation parameters (C, R s ,L s ,k v ) correction value, current equation parameter (L m ,k i ,C e ,G e ,k h ) correction value, flux equation parameter (B r ,H c ,μ i ,k T ,k f ) correction value, impedance equation parameters (R0, α, k R ,X0,L0,k X ,B s ) is the corrected value.

[0218] Using a gradient descent method or other optimization algorithm, the combined ferromagnetic resonance overvoltage characteristic model established in step S30 is trained to minimize the error between the training samples and the model output. After training is complete, a well-fitted combined ferromagnetic resonance overvoltage characteristic model M1 is obtained.

[0219] The model M1 can accurately describe the ferroresonance overvoltage characteristics under a known single fault condition. However, in order to further improve the adaptability of the model, it is necessary to fine-tune it using a second dataset containing multiple fault types.

[0220] Step S60: Using the second data set, a second training data set is established to fine-tune the ferromagnetic resonance overvoltage characteristic combination model established in step S30.

[0221] In this step, the training input features are selected from the second data set D2, including voltage v, current i, frequency f, power factor cosφ, temperature T, harmonic content THD, core saturation S and fault type F. The training output still includes the overvoltage peak value U p , overvoltage duration t p , overvoltage frequency characteristics f p and the corrected values ​​of the parameters of each equation.

[0222] To adapt to the situation of multiple faults stacking together, the LORA (Low-Rank Adaptation) fine-tuning algorithm is used to adjust the parameters of the initial model M1 trained in step S40. Specifically, LORA fine-tuning uses gradient descent to optimize the parameters of the hidden and output layers of the modified model in M1 to adapt to the complex fault situation.

[0223] After LORA fine-tuning, a refined model M2 for composite fault conditions is obtained, called the LORA model. This model M2 can better describe the impact of single faults and multiple fault superposition on the ferroresonant overvoltage characteristics.

[0224] LoRa model M2 includes two key sub-networks:

[0225] 1. Fault basis identification subnetwork:

[0226] Inputs are electrical data v, i, f, cosφ, T, THD, S and fault type F

[0227] The output is fault characteristics, which are used to identify and classify different types of faults

[0228] The sub-network adopts a 4-layer feedforward neural network structure, with 32, 16, and 8 hidden layer nodes respectively, and the activation function is ReLU.

[0229] 2. Modified model of ferromagnetic resonance equations for superimposed fault-induced ferromagnetic resonance:

[0230] The input is the fault characteristics output by the fault basis identification sub-network and the parameter correction characteristics output by each sub-network

[0231] The output is the correction parameters of the ferromagnetic resonance equations

[0232] The sub-network adopts a 5-layer feedforward neural network structure, with the number of hidden layer nodes being 64, 32, 16, 8, and 4, and the activation function being Sigmoid.

[0233] Through the collaborative work of these two sub-networks, LoRa model M2 can achieve the following functions:

[0234] 1. First, use the fault basis identification sub-network to identify and classify different types of faults to obtain the fault feature vector.

[0235] 2. Then, these fault characteristics and the outputs of the various parameter correction sub-networks obtained by training in step S40 are input into the correction model of the ferromagnetic resonance equation group of the superimposed fault-induced ferromagnetic resonance.

[0236] 3. The correction model will output the correction values ​​of each parameter of the ferromagnetic resonance equation group established in step S20 according to the fault situation.

[0237] 4. Finally, the theoretical equations are integrated with the output of the LORA model to obtain a complete model that can accurately describe the fault-induced ferromagnetic resonance overvoltage characteristics.

[0238] In this way, the advantages of theoretical models and machine learning models are fully utilized, which not only retains the theoretical basis with clear physical meaning, but also can continuously optimize and improve the model parameters in combination with measured data, greatly improving the prediction accuracy of overvoltage characteristics under complex fault conditions.

[0239] Step S41: Parameter input

[0240] In this step, multiple sets of different initial parameter values ​​need to be selected as input. These parameters include but are not limited to basic circuit parameters such as voltage v, current i, frequency f, power factor cosφ, as well as environmental factors such as temperature T and core saturation S.

[0241] In order to achieve the optimal parameter correction effect, the following strategies are adopted:

[0242] 1. Determine the parameter range:

[0243] According to the working principle and actual operation of the electromagnetic voltage transformer, the reasonable variation range of each parameter is determined, for example:

[0244] Voltage v: 0.8U n ~1.2U n

[0245] Frequency f: 45Hz~65Hz

[0246] Power factor cosφ: 0.8 lagging ~ 1.0 ~ 0.8 leading

[0247] Temperature T: -40℃~80℃

[0248] Core saturation S: 0.6~1.2

[0249] 2. Using Latin hypercube sampling method:

[0250] Latin hypercube sampling is used to generate uniformly distributed sample points within a certain parameter range. This method ensures that the samples in the multidimensional parameter space are well representative and uniform.

[0251] 3. Consider extreme cases:

[0252] On the basis of sampling, some extreme parameter combinations are added, such as the maximum voltage and the maximum temperature at the same time, the minimum frequency and the maximum core saturation at the same time, etc., to test the performance of the model under boundary conditions.

[0253] 4. Includes typical working conditions:

[0254] Add some known typical operating condition parameter combinations, which often appear in actual operation or have special significance.

[0255] 5. Consider parameter correlation:

[0256] There may be correlations between certain parameters. For example, a temperature increase may cause a change in core saturation. When selecting a parameter combination, these correlations should be considered to generate a parameter combination that conforms to the actual situation.

[0257] 6. Dynamic Adjustment:

[0258] After initial training, analyze the model's performance in different parameter ranges. For intervals with poor performance, increase the number of sample points in that interval and perform focused sampling.

[0259] 7. Cross Validation:

[0260] The selected parameter group is divided into training set and validation set, and the cross-validation method is used to evaluate the performance of the model under different parameter combinations to ensure that the selected parameter group has good generalization ability.

[0261] 8. Iterative optimization:

[0262] Based on the initial training results, optimization algorithms (such as Bayesian optimization) are used to guide subsequent parameter selection, and gradually find the parameter combination that best reflects the system characteristics.

[0263] By following these steps, we can systematically select multiple sets of initial parameter values ​​as input, covering a wide range of possible operating conditions and fault scenarios. This helps train a robust model with good generalization capabilities. This approach improves the accuracy of parameter correction and ensures that the model maintains good performance in a variety of practical situations.

[0264] Step S42: Solving the equations

[0265] In this step, the parameter values ​​selected in step S41 are substituted into the ferromagnetic resonance equations established in step S20, and the output results of the equations are obtained by numerical solution methods (such as Runge-Kutta method), including the overvoltage peak value U p , overvoltage duration t p and overvoltage frequency characteristic f p wait.

[0266] Step S43: Actual data collection

[0267] According to the parameter conditions input in step S41, the corresponding fault conditions are simulated on the actual electromagnetic voltage transformer, and multiple sets of electrical data are collected, including the actual measured overvoltage peak value U p, overvoltage duration t p and overvoltage frequency characteristic f p wait.

[0268] Step S44: Error calculation

[0269] In this step, the theoretical output results of the equation group in step S42 are compared with the actual data collected in step S43, and various indicators (overvoltage peak value U p , overvoltage duration t p , overvoltage frequency characteristics f p ) error.

[0270] Step S45: Determine parameter correction value

[0271] 1. Based on the error calculated in step S44, use an optimization algorithm (such as gradient descent) to iteratively adjust the parameters of the equation group until the error is reduced to an acceptable range.

[0272] 2. The difference between the final parameters and the initial parameters is used as the correction value of the equation parameters.

[0273] 3. This process continuously adjusts the equation parameters by comparing the theoretical calculation results with the actual measurement data, and finally obtains the corrected parameters that can accurately describe the ferromagnetic resonance overvoltage characteristics of the fault excitation.

[0274] In summary, in Example 1, steps S41-S45 achieve a method of comparing theoretical calculation results with measured data, continuously adjusting the equation parameters using an optimization algorithm, and ultimately obtaining a set of corrected parameters that accurately describe the fault-induced ferroresonance overvoltage characteristics. This method fully leverages the advantages of both theoretical models and experimental data, improving the accuracy and robustness of the model.

[0275] To further enhance the understanding and implementation of the present invention, Example 2 of a specific application scenario is provided below: A power company recently discovered an anomaly in an electromagnetic voltage transformer at a 220kV substation. The secondary voltage of this voltage transformer frequently experienced severe overvoltage faults, posing a serious threat to the safe and stable operation of the entire power grid. Technicians decided to employ the fault-induced ferromagnetic resonance overvoltage characteristics determination method proposed in this invention to conduct in-depth analysis and diagnosis of this voltage transformer.

[0276] First, the technicians collected electrical data of the voltage transformer under a known single fault condition according to step S10. Specifically, the data includes:

[0277] Voltage transformer rated voltage U n =220kV, rated frequency f n =50Hz.

[0278] Under three single fault conditions, namely short circuit fault, ground fault and open circuit fault, the voltage v, current i, frequency f, power factor cosφ, temperature T, overvoltage peak U p , harmonic content THD and core saturation S, etc., together form the first data set D1. Among them, the value range of each physical quantity is as follows:

[0279] Voltage v: 198kV~242kV

[0280] Current i:80A~120A

[0281] Frequency f: 48Hz~52Hz

[0282] Power factor cosφ: 0.85 lagging ~ 0.95 leading

[0283] Temperature T: 20℃~40℃

[0284] Overvoltage peak U p :1.2U n ~1.8U n

[0285] Harmonic content THD: 2% to 8%

[0286] Core saturation S: 0.7~1.1

[0287] By analyzing the first data set D1, technicians established a set of theoretical equations describing the ferromagnetic resonance process of the voltage transformer, including the voltage equation, current equation, flux equation, and impedance equation, as described in step S20. Taking the voltage equation as an example, its expression is:

[0288]

[0289] Among them, C = 0.01μF is the equivalent capacitance, R s =0.2Ω is the equivalent series resistance, L s =0.5mH is the equivalent series inductance, k v =0.02 is the voltage nonlinear coefficient. Fundamental voltage amplitude V s =195kV, fundamental wave angular frequency ω = 2π × 50rad / s, fundamental wave phase angle φ = 0.1rad. The nth harmonic voltage amplitude V n and phase angle φ n It is obtained through Fourier analysis.

[0290] Similarly, the parameters of other equations are also determined and calibrated based on the first data set D1.

[0291] However, these theoretical equations alone cannot fully describe the overvoltage characteristics under actual fault conditions. Therefore, according to step S30, the technicians establish a combined ferroresonance overvoltage characteristic model consisting of the theoretical equations and the modified model.

[0292] The revised model consists of five sub-networks, all of which adopt a feedforward neural network structure:

[0293] Voltage equation parameter correction subnetwork:

[0294] The input is voltage v data and basic circuit parameters, C, R s , L s 、k v wait.

[0295] The output is the correction value of the voltage equation parameter, which is used to adjust the voltage equation.

[0296] The sub-network contains 3 hidden layers, with the number of hidden layer nodes being 16, 8, and 4 respectively. The activation function is ReLU, and the number of nodes in the final output layer is 4.

[0297] Current equation parameter correction subnetwork:

[0298] The input is the current i data and basic circuit parameters, L m 、k i 、C e , G e 、k h wait.

[0299] The output is the correction value of the current equation parameters, which is used to adjust the current equation.

[0300] This sub-network also contains 3 hidden layers with 16, 8, and 4 nodes respectively, the activation function is ReLU, and the number of output layer nodes is 5.

[0301] Flux equation parameter correction subnetwork:

[0302] The input is the magnetic flux ψ data and the core saturation S.

[0303] The output is the correction value of the flux equation parameters, which is used to adjust the flux equation.

[0304] The number of hidden layer nodes of this sub-network is 12, 6, and 3, the activation function is Sigmoid, and the number of output layer nodes is 3.

[0305] Impedance equation parameter correction subnetwork:

[0306] The input is impedance Z data and temperature T.

[0307] The output is the correction value of the impedance equation parameters, which is used to adjust the impedance equation.

[0308] The number of hidden layer nodes of this sub-network is 10, 5, and 2, the activation function is Tanh, and the number of output layer nodes is 4.

[0309] Summarize the modified sub-network:

[0310] The input is the correction value of the output of the other 4 sub-networks.

[0311] The output is a comprehensive correction parameter, which is used to integrate the correction information provided by each sub-network.

[0312] This sub-network contains 2 hidden layers with 8 and 4 nodes, the activation function is ReLU, and the number of output layer nodes is 1.

[0313] By training the first data set D1, the initial ferromagnetic resonance overvoltage characteristic combination model M1 was obtained.

[0314] To further improve the adaptability of the model, technicians collected a second data set D2 containing multiple fault types according to steps S50 and S60. This data set includes electrical data for short circuit faults, ground faults, open circuit faults, and a combined short circuit fault and ground fault. The value ranges of each physical quantity are as follows:

[0315] Voltage v: 190kV~250kV

[0316] Current i:70A~130A

[0317] Frequency f: 47Hz~53Hz

[0318] Power factor cosφ: 0.8 lagging to 0.98 leading

[0319] Temperature T: 15℃~45℃

[0320] Overvoltage peak U p :1.3U n ~2.0U n

[0321] Harmonic content THD: 3% to 10%

[0322] Core saturation S: 0.6~1.2

[0323] Based on the second dataset D2, technicians fine-tuned the initial model M1 using LoRa and obtained a refined model M2 for complex fault conditions. The LoRa model includes two key sub-networks:

[0324] Fault basis identification subnetwork:

[0325] The inputs are electrical data v, i, f, cosφ, T, THD, S and fault type F.

[0326] The output is fault signature, which is used to identify and classify different types of faults.

[0327] The sub-network adopts a 4-layer feedforward neural network structure, with the number of hidden layer nodes being 32, 16, and 8 respectively, and the activation function being ReLU.

[0328] Corrected model of ferromagnetic resonance equations for superimposed fault-induced ferromagnetic resonance:

[0329] The input is the features output by each sub-network and the fault features.

[0330] The output is the correction parameters to the ferromagnetic resonance equations.

[0331] The sub-network adopts a 5-layer feedforward neural network structure, with the number of hidden layer nodes being 64, 32, 16, 8, and 4, and the activation function being Sigmoid.

[0332] Through LORA fine-tuning, model M2 can better adapt to complex situations of single faults and multiple faults superposition.

[0333] To test the performance of the LORA model, technicians designed the following scenario:

[0334] In a 220kV substation, a short circuit fault occurs on the primary side of the voltage transformer and a ground fault also occurs on the secondary side. The first and second digits represent short circuit faults and ground faults respectively, and the third and fourth digits do not consider open circuit faults and other faults for the time being.

[0335] By inputting this fault vector into the joint model in step S70, the parameters of the modified ferroresonance equations can be obtained. Taking the voltage equation as an example, the modified parameters are as follows:

[0336] C=0.008μF,R s =0.22Ω,L s =0.55mH,k v =0.025

[0337] Fundamental voltage amplitude V s =180kV, fundamental wave phase angle φ = 0.15rad. The voltage amplitudes and phase angles of the 2nd to 5th harmonics also change accordingly.

[0338] Substituting the corrected parameters into the theoretical equations, the time domain waveform of the overvoltage can be obtained by numerical solution. Figure 3As shown in the figure, under the combined condition of a short-circuit fault and a ground fault, the voltage transformer experienced a severe overvoltage fault, with a peak voltage as high as 1.8 times the rated voltage and a duration of approximately 0.1 second. This overvoltage could not only damage the voltage transformer itself but also endanger the safe and stable operation of the entire power grid.

[0339] In order to more comprehensively analyze the ferromagnetic resonance characteristics of this complex fault situation, the technicians further checked the changes in other physical quantities:

[0340] Current waveform Figure 4 As shown, the peak current reaches 2 times the rated current.

[0341] The magnetic flux waveform is as follows Figure 5 As shown in the figure, the peak value of magnetic flux reaches 1.8Wb, which is close to the saturation of the core.

[0342] Impedance changes such as Figure 6 As shown in Figure 2, the impedance amplitude decreases rapidly at the beginning of the fault and then recovers gradually.

[0343] Comprehensive analysis of the above results shows that in the case of a short circuit fault + ground fault, the voltage transformer has a serious ferromagnetic resonance overvoltage fault. The overvoltage peak reaches 1.8U n , lasting about 0.1 seconds, while the current, magnetic flux, and impedance also undergo dramatic changes. This overvoltage fault seriously threatens the safety of the voltage transformer and the entire power grid, and timely protective measures must be taken. This discovery demonstrates the effectiveness of the method of the present invention.

[0344] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed by the present invention, which should be covered by the scope of protection of the present invention.

Claims

1. A method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault, characterized in that: The following steps are involved: S10, collecting electrical data of ferromagnetic resonance excited by multiple different faults of an electromagnetic voltage transformer with a known single fault, including voltage, current, frequency, power factor, temperature, overvoltage, harmonic content, and core saturation, and recording the data as a first data set; S20, establishing a ferromagnetic resonance equation group including the electrical data, including a voltage equation, a current equation, a magnetic flux equation, and an impedance equation; S30, establishing a combined ferromagnetic resonance overvoltage characteristic model including the ferromagnetic resonance equation group and a correction model, wherein the correction model is used to correct the parameters of the ferromagnetic resonance equation group, and the correction model is a neural network with a multi-input and multi-output structure, including a voltage equation parameter correction subnetwork, a current equation parameter correction subnetwork, a flux equation parameter correction subnetwork, an impedance equation parameter correction subnetwork, and a summary correction subnetwork; S40. Establishing a first training data set based on the first data set, wherein the training inputs are voltage, current, frequency, power factor, temperature, harmonic content, and core saturation, and the training outputs are overvoltage amplitude, duration, frequency characteristics, and correction values ​​of parameters of each equation; performing fitting training on the ferromagnetic resonance overvoltage characteristic combination model using the first training data set to obtain a fitted and trained ferromagnetic resonance overvoltage characteristic combination model, which is recorded as a first model; S50, collecting electrical data of ferromagnetic resonances excited by multiple different faults of an electromagnetic voltage transformer known to have at least one fault, and recording the data as a second data set; S60. Using the second data set, establish a second training data set, where the training inputs are voltage, current, frequency, power factor, temperature, harmonic content, core saturation, and fault type, and the training outputs are overvoltage amplitude, duration, frequency characteristics, and correction values ​​of various equation parameters; fine-tune the first model using the second training data set to obtain a Lora model; S70 , using the combined model and the Lora model as a joint model, inputting a fault vector of a single fault or a plurality of faults superimposed, and obtaining a ferromagnetic resonance equation group for describing ferromagnetic resonance overvoltage characteristics induced by the fault.

2. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to claim 1, wherein: The voltage equation parameter correction subnetwork, whose training input is voltage data and basic circuit parameters, includes: 、 、 、 , is the equivalent capacitance, is the equivalent series resistance, is the equivalent series inductance, is the voltage nonlinear coefficient; the training output is the voltage equation parameter correction value, which is used to correct the voltage equation parameters according to the actual voltage data. The structure is a three-layer feedforward neural network.

3. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to claim 2, wherein: The current equation parameter correction subnetwork, whose training input is current data and basic circuit parameters, includes: 、 、 、 、 , Main magnetizing inductance, is the current nonlinear coefficient, is the equivalent eddy current capacitance, is the equivalent eddy current conductance, is the hysteresis loss coefficient, and the training output is the current equation parameter correction value, which is used to correct the current equation parameters according to the actual current data. The structure is a three-layer feedforward neural network.

4. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to claim 3, wherein: The flux equation parameter correction subnetwork has a training input of flux data and core saturation, and a training output of flux equation parameter correction values, which is used to correct flux equation parameters according to actual flux data. The structure is a three-layer feedforward neural network.

5. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to claim 4, wherein: The impedance equation parameter correction subnetwork has impedance data and temperature as training inputs and impedance equation parameter correction outputs, which are used to correct the impedance equation parameters according to actual impedance data. The structure is a three-layer feedforward neural network.

6. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to claim 5, wherein: The training input of the summary correction subnetwork is the correction value output by each subnetwork of the correction model excluding the summary correction subnetwork, and the training output is a comprehensive correction parameter used to integrate the correction values ​​provided by each subnetwork. The structure is a two-layer feedforward neural network.

7. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to claim 6, wherein: The Lora model includes a fault basis identification subnetwork and a correction model of a ferromagnetic resonance equation group for superimposed fault-induced ferromagnetic resonance.

8. The method for determining the fault-induced ferromagnetic resonance overvoltage characteristic according to claim 7, wherein: The fine-tuning refers to adjusting the parameters of the hidden layer and output layer of each sub-network of the correction model in the first model, so as to adjust the weights and biases of these layers by the gradient descent method to adapt to the fault superposition of multiple types of faults.

9. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to claim 7, wherein: The fault basis identification subnetwork has electrical data and fault type as training inputs and fault characteristics as training outputs, which are used to identify and classify different types of faults. Its structure is a four-layer feedforward neural network. The correction model of the ferromagnetic resonance equation group for superimposed fault-excited ferromagnetic resonance has characteristics and fault characteristics of each subnetwork output as training inputs and correction parameters as training outputs, which are used to correct the ferromagnetic resonance equation group according to the fault situation. Its structure is a five-layer feedforward neural network.

10. The method for determining the ferromagnetic resonance overvoltage characteristic caused by a fault according to any one of claims 1 to 9, characterized in that: The step of obtaining the equation parameter correction value specifically includes: S41, parameter input: select multiple sets of different initial parameter values ​​as input, these parameters include at least one of the following: voltage, current, frequency, power factor, temperature, core saturation; S42, solving the equation group: Substituting the parameter values ​​selected in S41 into the ferromagnetic resonance equation group, and solving the equation group to obtain the output results, including the overvoltage amplitude, duration, and frequency characteristics; S43, actual data collection: according to the parameter conditions input in S41, simulate the corresponding fault conditions on the actual electromagnetic voltage transformer and collect multiple sets of electrical data, including the actual measured overvoltage amplitude, duration, and frequency characteristics; S44, error calculation: compare the theoretical output results of the equation group in S42 with the actual data collected in S43, and calculate the errors of various indicators; S45. Determine the parameter correction value: Based on the error calculated in S44, use the optimization algorithm to iteratively adjust the parameters of the equation group until the error is reduced to within a predetermined range, and use the difference between the final determined parameter and the initial parameter as the equation parameter correction value.

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