Reactor magnetic saturation prediction method and device, electronic equipment and storage medium

Abstract

The application provides an electric reactor magnetic saturation prediction method and device, electronic equipment and storage medium, and relates to the technical field of electric engineering electric reactor. The method comprises the following steps: obtaining impedance test data of an electric reactor under different currents, the impedance test data being used to indicate the corresponding relationship between the current and the impedance; preprocessing the impedance test data to obtain preprocessed data; based on the magnetization characteristics of the ferromagnetic material in the electric reactor, modeling the preprocessed data in stages to generate a staged fitting function; and based on the staged fitting function and a preset electromagnetic theory, calculating a magnetic saturation prediction value of the electric reactor under a target current, the magnetic saturation prediction value being used to indicate the magnetic saturation state of the electric reactor. The application is used to improve the prediction accuracy of the magnetic saturation of the electric reactor.

Description

Technical Field

[0001] This application relates to the field of electrical engineering reactor technology, and in particular to a method, device, electronic device and storage medium for predicting the magnetic saturation of a reactor. Background Technology

[0002] In modern power systems, the continuous expansion of power grid scale and increasingly complex operating conditions place higher demands on the safety and reliability of power equipment. Reactors (such as 500kV large-capacity oil-immersed reactors), as key equipment in high-voltage DC and AC transmission systems, undertake important tasks such as limiting short-circuit current and maintaining system voltage stability; their operating status directly affects the safety and reliability of the entire power grid. However, with the increase in grid load and fault current, the magnetic saturation problem of reactor cores is becoming increasingly prominent. Magnetic saturation leads to a decrease in the inductance value of the reactor, limiting its current-limiting capacity, which may cause a series of problems such as system overcurrent and relay protection malfunctions. Therefore, conducting research on reactor magnetic saturation prediction is of great significance for ensuring the safe operation of the power system.

[0003] Currently, the prediction of magnetic saturation characteristics of reactors mainly relies on the traditional direct measurement method of hysteresis loops. This method experimentally obtains the magnetic flux density variation curves (hysteresis loops) of the reactor core material under different magnetic field strengths, and uses these curves to analyze the magnetic saturation characteristics of the material. In practice, specialized precision testing equipment, such as magnetic measuring instruments, high-precision current sources, and magnetic field sensors, is typically used to apply alternating magnetic fields of different amplitudes to the reactor core and measure the corresponding magnetic flux density in real time. Subsequently, using a data acquisition and processing system, the measured magnetic field strength and magnetic flux density data are organized and analyzed to plot the hysteresis loops, thereby determining the magnetic saturation point of the core material and its related characteristic parameters.

[0004] However, existing methods suffer from inaccurate predictions when forecasting the magnetic saturation characteristics of reactors. Summary of the Invention

[0005] The reactor magnetic saturation prediction method, apparatus, electronic device, and storage medium provided in this application are intended to solve the problem of inaccurate prediction in existing methods when predicting the magnetic saturation characteristics of reactors.

[0006] In a first aspect, embodiments of this application provide a method for predicting the magnetic saturation of a reactor, including:

[0007] Obtain impedance test data of the reactor under different currents. The impedance test data is used to indicate the correspondence between current and impedance.

[0008] The impedance test data is preprocessed to obtain preprocessed data;

[0009] Based on the magnetization characteristics of ferromagnetic materials in reactors, the preprocessed data is modeled in stages to generate a staged fitting function.

[0010] Based on the phased fitting function and the preset electromagnetic theory, the predicted value of magnetic saturation of the reactor under the target current is calculated. The predicted value of magnetic saturation is used to indicate the magnetic saturation state of the reactor.

[0011] In one possible implementation, the impedance test data is preprocessed to obtain preprocessed data, including: removing outliers from the impedance test data to obtain effective impedance data; normalizing the effective impedance data to obtain normalized impedance data; and interpolating the normalized impedance data to obtain preprocessed data. The preprocessed data includes multiple equally spaced current points and the impedance value corresponding to each current point.

[0012] In one possible implementation, based on the magnetization characteristics of the ferromagnetic material in the reactor, the preprocessed data is modeled in stages to generate a staged fitting function. This includes: determining staged current thresholds based on the magnetization curve of the ferromagnetic material, where the staged current thresholds include the upper limit current of the unsaturated segment and the lower limit current of the deep saturated segment; dividing the preprocessed data into unsaturated segment data, critically saturated segment data, and deeply saturated segment data based on the staged current thresholds; and performing function fitting on the unsaturated segment data, critically saturated segment data, and deeply saturated segment data respectively to generate a staged fitting function, where the staged fitting function includes an impedance prediction function corresponding to the data of each stage.

[0013] In one possible implementation, function fitting is performed on the unsaturated segment data, the critically saturated segment data, and the deeply saturated segment data respectively to generate a staged fitting function, including: fitting the unsaturated segment data with a quadratic polynomial function to obtain a first impedance prediction function; fitting the critically saturated segment data with an exponential function to obtain a second impedance prediction function; and fitting the deeply saturated segment data with a power function to obtain a third impedance prediction function; wherein the staged fitting function includes the first impedance prediction function, the second impedance prediction function, and the third impedance prediction function.

[0014] In one possible implementation, the predicted magnetic saturation value of the reactor under the target current is calculated based on a staged fitting function and a preset electromagnetic theory. This includes: determining the unsaturated reference impedance value and the deeply saturated reference impedance value according to a staged current threshold, a first impedance prediction function, and a third impedance prediction function; converting the unsaturated reference impedance value and the deeply saturated reference impedance value into an unsaturated reference inductance value and a deeply saturated reference inductance value, respectively, according to the impedance-inductance conversion relationship, which is determined based on a preset electromagnetic theory; determining the target impedance prediction value corresponding to the target current, and converting the target impedance prediction value into a target inductance prediction value according to the impedance-inductance conversion relationship; and determining the predicted magnetic saturation value based on the unsaturated reference inductance value, the deeply saturated reference inductance value, and the target inductance prediction value.

[0015] In one possible implementation, determining the unsaturated reference impedance value and the deep saturated reference impedance value based on the phased current threshold, the first impedance prediction function, and the third impedance prediction function includes: inputting the upper limit current of the unsaturated segment into the first impedance prediction function to obtain the unsaturated reference impedance value; and inputting the lower limit current of the deep saturated segment into the third impedance prediction function to obtain the deep saturated reference impedance value.

[0016] In one possible implementation, the method further includes: acquiring a verification current sequence and the measured magnetic saturation corresponding to the verification current sequence; calculating the predicted magnetic saturation corresponding to each current in the verification current sequence based on a phased fitting function and a preset electromagnetic theory; determining the prediction error based on the measured magnetic saturation and the predicted magnetic saturation; and optimizing and correcting the fitting parameters in the phased fitting function based on the prediction error.

[0017] Secondly, embodiments of this application provide a reactor magnetic saturation prediction device, comprising:

[0018] The acquisition module is used to acquire impedance test data of the reactor under different currents. The impedance test data is used to indicate the correspondence between current and impedance.

[0019] The preprocessing module is used to preprocess the impedance test data to obtain preprocessed data;

[0020] The generation module is used to perform phased modeling of preprocessed data based on the magnetization characteristics of ferromagnetic materials in reactors, and generate phased fitting functions.

[0021] The prediction module is used to calculate the predicted value of the magnetic saturation of the reactor under the target current based on the phased fitting function and the preset electromagnetic theory. The predicted value of magnetic saturation is used to indicate the magnetic saturation state of the reactor.

[0022] Thirdly, embodiments of this application provide an electronic device, including: a memory and a processor;

[0023] The memory stores the instructions that the computer executes;

[0024] The processor executes computer execution instructions stored in memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0025] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed, are used to implement the first aspect and / or various possible implementations of the first aspect.

[0026] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed, implements the first aspect and / or various possible implementations of the first aspect.

[0027] The reactor magnetic saturation prediction method, device, electronic device, and storage medium provided in this application acquire impedance test data of the reactor under different currents. The impedance test data is used to indicate the correspondence between current and impedance. The impedance test data is preprocessed to obtain preprocessed data. Based on the magnetization characteristics of the ferromagnetic material in the reactor, the preprocessed data is modeled in stages to generate a staged fitting function. Based on the staged fitting function and a preset electromagnetic theory, the predicted value of the magnetic saturation of the reactor under the target current is calculated. The predicted value of magnetic saturation is used to indicate the magnetic saturation state of the reactor. By combining the nonlinear magnetization characteristics of the ferromagnetic material with the measurable impedance data in the actual operation of the reactor, and by calculating the predicted value of magnetic saturation through staged modeling and preset electromagnetic theory, the magnetic saturation state of the reactor under the target current can be predicted more accurately. Meanwhile, by acquiring impedance test data and preprocessing it, interference factors in the data are reduced, improving the accuracy and reliability of the data. Furthermore, by establishing corresponding fitting functions for different stages, the relationship between current and impedance can be described more accurately. Compared with existing prediction methods, this staged model can better adapt to the complex characteristic changes of reactors under different currents, further improving the accuracy of prediction. Attached Figure Description

[0028] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0029] Figure 1 Flowchart of the reactor magnetic saturation prediction method provided in this application Figure 1 ;

[0030] Figure 2 Flowchart of the reactor magnetic saturation prediction method provided in this application Figure 2 ;

[0031] Figure 3 The BH curve and optimized curve of the ferromagnetic material of the reactor provided in this application;

[0032] Figure 4 A schematic diagram illustrating the change in resistivity of the reactor under different currents provided in this application;

[0033] Figure 5 The reactor experimental test current-impedance test curve provided in this application is shown below;

[0034] Figure 6 The second experimental test current-impedance curve for the reactor provided in this application;

[0035] Figure 7 A schematic diagram of the reactor magnetic saturation prediction device provided in this application;

[0036] Figure 8 A schematic diagram of the structure of the electronic device provided in this application.

[0037] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0038] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0039] A reactor is a device used in a power system to limit short-circuit current. Its core function is to regulate inductance through the magnetization characteristics of ferromagnetic materials. For example, a 500kV high-capacity oil-immersed reactor. These reactors need to operate under complex conditions for extended periods, not only undertaking routine current limiting tasks under rated load but also withstanding short-circuit current surges several times higher than the rated current during faults. However, the ferromagnetic materials used in reactor cores exhibit significant nonlinear magnetization characteristics: when the current is within the rated range, the material is in an unsaturated state, resulting in stable inductance and reliable current limiting performance; but under extreme short-circuit currents, the magnetic field strength increases sharply, and the ferromagnetic material easily enters the magnetic saturation stage, leading to a sharp drop in permeability and a significant reduction in the reactor's inductance. This inductance decay directly weakens its short-circuit current suppression capability, potentially triggering a chain reaction of risks such as system transient overcurrent and relay protection malfunctions, posing a serious threat to power system safety.

[0040] In existing technologies, the prediction of reactor magnetic saturation characteristics relies on direct measurement of the hysteresis loop (BH curve), requiring high-precision fluxmeters and Helmholtz coils. This complex and costly testing process makes it difficult to meet the needs of rapid verification and batch design in engineering applications. Furthermore, existing methods typically only model the linear region (unsaturated stage) of ferromagnetic materials, failing to adequately fit the nonlinear characteristics of ferromagnetic materials throughout the entire process from unsaturation to deep saturation. This is particularly problematic in the critical saturation range, where errors are significant, leading to inaccurate inductance predictions under extreme short-circuit conditions. This results in inaccurate reactor parameter optimization and operating condition adaptation. For example, when the short-circuit current reaches five times the rated value, the reactor inductance may drop sharply by 30%-50%. Existing methods, lacking sufficient modeling of the impedance-inductance nonlinear relationship in the critical saturation stage, cannot accurately predict the inductance decay trend, thus affecting the formulation of power grid protection strategies. It is evident that existing methods have many limitations in the prediction process, such as insufficient consideration of the nonlinear characteristics of ferromagnetic materials and interference with measurement data. Ultimately, these factors lead to inaccurate predictions when forecasting the magnetic saturation characteristics of reactors, failing to provide reliable guarantees for the safe operation of power systems.

[0041] To address the aforementioned issues, this application provides a method, apparatus, electronic device, and storage medium for predicting the magnetic saturation of a reactor. By collecting impedance data under different currents, a correspondence between current and impedance can be established, providing fundamental data support for subsequent analysis of the reactor's magnetic characteristics. Simultaneously, preprocessing removes the influence of factors such as measurement equipment accuracy and environmental interference on data quality, making the data more accurate and reliable. This provides a high-quality data foundation for subsequent modeling and analysis, ensuring the accuracy and stability of the entire prediction process. Subsequently, staged modeling based on the magnetization characteristics of the ferromagnetic material in the reactor allows for a more detailed depiction of the relationship between current and impedance at different stages. This fully considers the stage-specific differences in the magnetization characteristics of the ferromagnetic material, making the model more closely reflect reality and improving its accuracy and adaptability. Therefore, the predicted magnetic saturation value, calculated based on a precise staged fitting function and preset electromagnetic theory, can more accurately indicate the magnetic saturation state of the reactor under the target current, making the prediction results more scientific and reliable.

[0042] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.

[0043] The execution subject of the reactor magnetic saturation prediction method provided in this application embodiment can be a computing device such as a server or server cluster. The server can be a mobile phone, computer, tablet, or other device. This application embodiment does not impose any particular limitation on the implementation method of the execution subject, as long as the execution subject can obtain impedance test data of the reactor under different currents, the impedance test data is used to indicate the correspondence between current and impedance; the impedance test data is preprocessed to obtain preprocessed data; based on the magnetization characteristics of the ferromagnetic material in the reactor, the preprocessed data is modeled in stages to generate a staged fitting function; based on the staged fitting function and a preset electromagnetic theory, the predicted value of the magnetic saturation of the reactor under the target current is calculated, and the predicted value of the magnetic saturation is used to indicate the magnetic saturation state of the reactor.

[0044] Figure 1 Flowchart of the reactor magnetic saturation prediction method provided in this application Figure 1 The execution entity of this method can be a server storing the reactor magnetic saturation prediction method or other servers. This embodiment does not impose any particular limitations here. Figure 1 As shown, the method may include:

[0045] S101. Obtain impedance test data of the reactor under different currents. The impedance test data is used to indicate the correspondence between current and impedance.

[0046] Here, "different currents" can refer to a series of current values ​​with different numerical values. Impedance test data refers to the impedance values ​​measured by the reactor under different current conditions, including the correspondence between current and impedance. For example, the ZI curve measured through series or parallel power supply methods.

[0047] In one example, 12 sets of impedance test data are obtained as follows: current I=np.array([30,60,70,80,90,100,110,120,130,140,150,160]), and corresponding impedance values ​​Z=np.array([11.85,11.63,11.65,11.50,11.52,11.50,11.45,11.42,11.40,11.37,11.39,11.33]).

[0048] In this step, a preset current source device can be used to apply current of different magnitudes to the reactor. Simultaneously, an impedance measuring instrument (such as an impedance analyzer) is used to measure the corresponding impedance value of the reactor at each current value, and these current-impedance correspondence data are recorded. Furthermore, a programmable current source can be used to apply current to the reactor sequentially according to a preset current value sequence. After each current application stabilizes, a high-precision impedance analyzer is used to measure the impedance to obtain impedance test data in real time. Alternatively, the output current of the current source can be manually adjusted. After each adjustment to a new current value, a period of time is allowed for the reactor to stabilize, and then the impedance is measured using a digital multimeter or other measuring tools and recorded in a table to obtain impedance test data.

[0049] S102. Preprocess the impedance test data to obtain preprocessed data.

[0050] Preprocessing can be the process of processing the raw data to remove noise, outliers and other interfering factors and improve data quality.

[0051] For example, the obtained impedance test data is first checked to identify and remove obviously erroneous data points; then filtering algorithms (such as mean filtering, median filtering, etc.) can be used to smooth the data and reduce the impact of noise.

[0052] As another example, the raw impedance test data is processed by removing outliers, normalizing, and interpolating to generate a dataset, i.e., preprocessed data.

[0053] S103. Based on the magnetization characteristics of ferromagnetic materials in the reactor, the preprocessed data is modeled in stages to generate a staged fitting function.

[0054] The magnetization characteristics of ferromagnetic materials refer to the different degrees of magnetization and magnetic properties exhibited by ferromagnetic materials under different magnetic field strengths. For example, the magnetic induction intensity increases rapidly in the unsaturated stage, slows down in the critical saturation stage, and tends to stabilize in the deep saturation stage. Stage-by-stage modeling refers to establishing mathematical models, or fitting functions, for different stages of the ferromagnetic material's magnetization characteristics (e.g., unsaturated, critically saturated, and deeply saturated). For example, a quadratic polynomial is used in the unsaturated stage, and an exponential function is used in the critically saturated stage. Furthermore, the stage-by-stage fitting function is a mathematical function used to describe the relationship between current and impedance in each stage.

[0055] In this step, the magnetization characteristic curve of the ferromagnetic material can be analyzed to determine the different stages of magnetization characteristics. For each stage, a suitable mathematical model (such as a polynomial function, exponential function, etc.) is selected, and the parameters of the mathematical model are fitted using preprocessed data to obtain the fitting function for each stage.

[0056] In some examples, the stages of magnetization characteristics can be clearly defined by consulting the technical manuals of ferromagnetic materials or conducting additional magnetic property tests. These stages can be categorized as linear or unsaturated, transitional or critically saturated, or saturated or deeply saturated. For the linear or unsaturated stage, a linear polynomial function is used for fitting; for the transitional or critically saturated stage, a quadratic polynomial function is used; and for the saturated or deeply saturated stage, an exponential decay function is selected.

[0057] In some examples, the phase division method can be curvature analysis (such as finding the maximum point of the second derivative of impedance), slope thresholding (such as setting a threshold for the rate of impedance decrease), or cluster analysis (such as automatic grouping by the K-means algorithm).

[0058] As a further example, clustering algorithms in data analysis are used to automatically divide the data into stages based on the distribution characteristics of the preprocessed data. Then, a general function model is selected for each stage, and the function parameters are determined by fitting the data using a preset parameter estimation method (such as least squares, maximum likelihood estimation, robust regression, etc.), generating staged fitting functions. The types of fitting functions can include: 1) Unsaturated stage: linear functions, quadratic polynomials, low-order power functions, etc.; 2) Critically saturated stage: exponential functions, hyperbolic functions, arctangent functions, etc.; 3) Deeply saturated stage: power functions, logarithmic functions, constants plus asymptotic terms, etc.

[0059] S104. Based on the phased fitting function and the preset electromagnetic theory, calculate the predicted value of the magnetic saturation of the reactor under the target current. The predicted value of magnetic saturation is used to indicate the magnetic saturation state of the reactor.

[0060] In this step, the preset electromagnetic theory can refer to a pre-defined and known electromagnetic theory system, which is the basic theory for studying electromagnetic phenomena, such as impedance-inductance relationship, inductance-permeability relationship, definition of magnetic saturation, etc.

[0061] The target current refers to the specific current value that needs to be predicted for the magnetic saturation state of the reactor. In a real power system, this might be the current value at a critical operating point, or a current value where abnormalities may occur.

[0062] The predicted magnetic saturation value is a calculated value used to represent the degree of magnetic saturation of the reactor under the target current. This value can be a quantitative indicator of the degree of decrease in the permeability of the ferromagnetic material, and can be calculated by the ratio of the current inductance to the unsaturated inductance.

[0063] In some embodiments, the specific value of the target current is first determined. This value can be determined according to actual needs; it may be a current value within the normal operating range of the reactor in the power system, or it may be a value exceeding the normal range used to test extreme conditions. Then, based on the magnitude of the target current, it is determined which stage in the phased fitting function it falls into. Because the phased fitting function is constructed according to different stages, each stage has a corresponding function expression. The target current is substituted into the corresponding phased fitting function to calculate the impedance value of the reactor at that target current. Then, according to a preset electromagnetic theory, the impedance value of the reactor at that target current is converted into an inductance value. Based on this inductance value and an inductance reference value, a predicted magnetic saturation value is calculated, where the inductance reference value can be determined based on the stage boundary points of the phased fitting function.

[0064] Optionally, after calculating the predicted value of magnetic saturation of the reactor under the target current, the method may further include: generating an oversaturation warning signal for the reactor in response to the predicted value of magnetic saturation exceeding a preset saturation threshold, to indicate whether the reactor has entered an oversaturated state; and adjusting and controlling the operating parameters of the reactor based on the oversaturation warning signal, such as adjusting the operating current of the reactor or triggering a protection action.

[0065] The preset saturation threshold can be a value pre-set based on the reactor's design parameters, operating requirements, and practical experience. When the predicted magnetic saturation value exceeds this threshold, the reactor is considered to have entered an oversaturated state. The reactor oversaturation warning signal is a signal used to indicate that the reactor may be oversaturated; it can be an electrical signal, an optical signal, or a specific identifier in the software.

[0066] Operating parameters can include various parameters related to reactor operation, such as current, voltage, and power. Adjusting the reactor's operating current can be achieved by changing the magnitude of the current applied to the reactor, thus removing it from an oversaturated state. Triggering protection actions can be a series of protective measures taken when the reactor's oversaturation is severe, such as cutting off the power supply and activating backup equipment, to prevent damage to the reactor or further impact on the power system.

[0067] In one example, the calculated predicted magnetic saturation value is compared with a preset saturation threshold. If the predicted value exceeds the threshold, an early warning signal generation mechanism is triggered, generating a corresponding oversaturation early warning signal. Then, based on the severity of the early warning signal and a preset control strategy, the operating current is adjusted or a protection action is triggered. Adjusting the operating current can be achieved by regulating the output of the current source or changing the resistance in the circuit. If a protection action is triggered, the corresponding operation is performed according to a preset protection procedure to prevent damage to the reactor due to oversaturation, ensuring the stable operation of the power system and improving the safety and reliability of the reactor operation.

[0068] The reactor magnetic saturation prediction method provided in this application reduces interference factors and improves data accuracy and reliability by acquiring and preprocessing impedance test data. Accurate data is the foundation for subsequent analysis and prediction, avoiding prediction errors caused by data issues and laying a solid foundation for the entire magnetic saturation prediction process. The staged modeling approach fully considers the nonlinear characteristics of the magnetization properties of ferromagnetic materials, establishing corresponding fitting functions for different stages. This allows for a more precise description of the relationship between current and impedance. Compared to traditional single models, this staged model better adapts to the complex characteristic changes of reactors under different currents, improving model accuracy and fitting precision. Furthermore, based on the accurate staged fitting function and electromagnetic theory calculation of the predicted magnetic saturation value, the magnetic saturation state of the reactor under the target current can be predicted more accurately, improving the adaptability and practicality of the prediction. This is of great significance for the operation and maintenance of power systems, enabling early detection of potential magnetic saturation problems in reactors, timely adjustment and optimization measures, avoiding system failures and safety hazards caused by magnetic saturation, and ensuring the safe and stable operation of the power system.

[0069] However, in the actual process of acquiring impedance test data, due to various factors such as the accuracy of measuring equipment, environmental interference, and human error, the acquired impedance test data may contain problems such as outliers, inconsistent data ranges, and uneven data point intervals. If these problems are not addressed, they will directly affect the accuracy of subsequent phased modeling and the reliability of magnetic saturation prediction values. Therefore, in order to process impedance test data more accurately and improve the prediction accuracy and stability of the entire method, a detailed description of preprocessing is provided based on the above embodiments. Specifically, the method for preprocessing impedance test data to obtain preprocessed data may include: outlier removal from the impedance test data to obtain effective impedance data; normalization of the effective impedance data to obtain normalized impedance data; and interpolation completion of the normalized impedance data to obtain preprocessed data. The preprocessed data includes multiple equally spaced current points and the corresponding impedance values ​​for each current point.

[0070] Outliers are data points that deviate significantly from normal data, possibly due to measurement errors, equipment malfunctions, or external interference. Outlier removal refers to the process of identifying and removing outlier data points. Effective impedance data, on the other hand, consists of data points that have been filtered and retained, reflecting the true physical characteristics of the data. Outlier removal improves data reliability and prevents individual erroneous measurements from affecting the overall modeling accuracy.

[0071] In some examples, certain detection methods can be used to identify outliers in impedance test data and then remove them from the dataset, retaining the remaining valid data as valid impedance data. For instance, statistical methods, such as the 3σ criterion, can be used to determine |Zz|. mean Data with a 3σ threshold is considered outlier. Physical constraints can also be used, such as monotonicity constraints (e.g., impedance should monotonically decrease with increasing current) and range constraints (e.g., impedance values ​​should be within the theoretical range). Machine learning methods can also be employed, such as isolation forests (e.g., automatically identifying outliers), local anomaly factors (e.g., considering local data density), and cluster analysis (e.g., points far from all cluster centers are considered outliers).

[0072] In some embodiments, outlier removal (3σ criterion) can specifically be as follows: 1) Calculate the mean (z_mean) and standard deviation (z_std) of the impedance data Z: z_mean, z_std = np.mean(Z), np.std(Z); 2) Create a Boolean mask: only retain data points where |Z - z_mean| < 3σ, i.e. 3) Apply mask filtering to the current and impedance arrays: I,Z=I[mask],Z[mask].

[0073] Normalization refers to the process of mapping data of different dimensions and ranges to a unified standard interval. The purpose is to eliminate the differences in dimensions and orders of magnitude between different data, improve numerical stability, and facilitate the comparison of data from different reactors.

[0074] In some examples, for effective impedance data, each data point can be calculated and transformed according to a selected normalization method to adjust its value to the target range, resulting in normalized impedance data. For example, linear function normalization can be used to normalize the effective impedance data to the [0,1] interval. Alternatively, the Z-score normalization method can be used to calculate the mean and standard deviation of the data, and then the data can be transformed into standardized data with a mean of 0 and a standard deviation of 1.

[0075] In some embodiments, data normalization (scaling to [0,1]) can specifically be: 1) Current normalization: I_norm=(II.min()) / (I.max()-I.min()); 2) Impedance normalization: Z_norm=(ZZ.min()) / (Z.max()-Z.min()).

[0076] Interpolation is a method of estimating the value of unknown data points using known data points. Interpolation completion, on the other hand, uses interpolation to add new data points at appropriate locations when missing or unevenly distributed points exist in the data, making the data more complete and uniform. Equally spaced current points refer to a sequence of current values ​​uniformly distributed within a current range. Uniformly distributed data points provide sufficient density of input data for piecewise fitting.

[0077] In some examples, the locations requiring interpolation are identified, and based on known normalized impedance data points, a suitable interpolation algorithm is selected to calculate the impedance values ​​at these locations. This yields preprocessed data containing multiple equally spaced current points and their corresponding impedance values. The interpolation algorithm can employ linear interpolation, cubic spline interpolation, polynomial interpolation, etc.

[0078] In some embodiments, interpolation completion (generating uniform current points) can specifically be as follows: 1) Generate 100 equally spaced points between the minimum current value (such as 30A in the 12 sets of data in the above embodiment) and the maximum current value (such as 160A): I_new=np.linspace(I.min(),I.max(),100); 2) Calculate the impedance value corresponding to these new current points using linear interpolation np.interp(): Z_new=np.interp(I_new,I,Z).

[0079] By performing operations such as outlier removal, normalization, and interpolation completion, problems such as anomalies, inconsistent dimensions, and uneven intervals in the original data can be solved, improving data quality and providing a more accurate and stable data foundation for subsequent phased modeling and magnetic saturation prediction, thereby further improving the accuracy and reliability of the entire reactor magnetic saturation prediction method.

[0080] Based on the above embodiments, a method for generating a staged fitting function by modeling the preprocessed data in stages based on the magnetization characteristics of the ferromagnetic material in the reactor may include: determining staged current thresholds according to the magnetization curve of the ferromagnetic material, wherein the staged current thresholds include the upper limit current of the unsaturated segment and the lower limit current of the deep saturated segment; dividing the preprocessed data into unsaturated segment data, critically saturated segment data, and deeply saturated segment data based on the staged current thresholds; and performing function fitting on the unsaturated segment data, critically saturated segment data, and deeply saturated segment data respectively to generate a staged fitting function, wherein the staged fitting function includes an impedance prediction function corresponding to each stage of data.

[0081] In this embodiment, the magnetization curve can be a curve describing the relationship between the magnetic induction intensity B (or magnetic polarization intensity) of a ferromagnetic material and the magnetic field intensity H (i.e., the BH curve). It reflects the magnetization characteristics of the ferromagnetic material under the action of an applied magnetic field. The magnetization curves of different materials have different shapes and are affected by factors such as temperature and material composition. The magnetic induction intensity of the ferromagnetic material under different magnetic field intensities can be measured experimentally, and the measurement data can be plotted as a curve, which is the magnetization curve.

[0082] The staged current threshold refers to the critical current value that divides different saturation stages. Among them, the upper limit current of the unsaturated stage is the boundary current value between the unsaturated stage and the critical saturation stage of the ferromagnetic material (such as I1); the lower limit current of the deep saturation stage is the boundary current value between the critical saturation stage and the deep saturation stage of the ferromagnetic material (such as I2).

[0083] In some examples, the magnetization curves of ferromagnetic materials are analyzed to observe the trend of magnetic flux density as a function of magnetic field strength (related to current). When the magnetic flux density increases approximately linearly with the increase of magnetic field strength, the corresponding current range is the unsaturated segment, and the current corresponding to its upper limit is the upper limit current of the unsaturated segment; when the magnetic flux density hardly changes with the increase of magnetic field strength, the corresponding current is the lower limit current of the deep saturation segment.

[0084] In some embodiments, the upper limit current I1 of the unsaturated segment can be determined by: the current corresponding to a 10% decrease in permeability μ from its maximum value; or the end point of the linear segment of the BH curve (fitting the linear segment and calculating the residual abrupt change point). For example, by measuring the BH curve, it was found that when H > 500 A / m, μ decreases by more than 10%, corresponding to a current I1 = 70 A.

[0085] The lower limit current I2 in the deep saturation range can be determined as follows: the current corresponding to the permeability dropping to 1.1μ0 (close to the vacuum permeability); the starting point where the slope of the BH curve stabilizes at its minimum value. For example, when H > 1200 A / m, μ stabilizes at 1.05μ0, corresponding to a current I2 = 120 A.

[0086] Alternatively, I1 and I2 can be determined based on the characteristics of the ZI curve. For example, the impedance change rate can be calculated based on the ZI curve characteristics, and the point where the impedance begins to decrease rapidly can be identified as I1, while the point where the impedance change tends to level off can be identified as I2. Furthermore, optimization algorithms can be used to find the optimal dividing point to determine the staged current threshold, ensuring the scientific validity of the stage division.

[0087] Furthermore, based on the determined staged current thresholds, the current values ​​in the preprocessed data are compared with the thresholds, and the data are classified into unsaturated segment data, critically saturated segment data, and deeply saturated segment data respectively, to ensure that each stage has sufficient and reasonable data for fitting and reasonable boundary processing.

[0088] In one example, iterate through each current point in the preprocessed data, and if the current value is less than or equal to the upper limit current of the unsaturated segment (i.e., I0), it checks if the current value is greater than or equal to the upper limit current of the unsaturated segment (i.e., I0). new If the current value is greater than the upper limit current of the unsaturated segment and less than the lower limit current of the deep saturated segment (i.e., I1 < I), then the data point is classified as unsaturated segment data; if ... new <I2), classified as critical saturation range data; if the current value is greater than or equal to the lower limit current of deep saturation range (i.e., I2), it is classified as critical saturation range data; new ≥I2), classified as deep saturation segment data.

[0089] Function fitting refers to determining the parameters of a function by selecting an appropriate function form and using known data points, so that the function can accurately describe the trend of data change. In this embodiment, function fitting is performed on data from different stages to generate impedance prediction functions corresponding to each stage. For example, an appropriate fitting function form can be selected, such as a polynomial function or an exponential function. Using fitting algorithms such as the least squares method, the data from different stages are substituted into the function to calculate the parameters, resulting in the function expression that best fits the data, i.e., the impedance prediction function.

[0090] Furthermore, it can be understood that the impedance prediction function can be a functional expression of the input current value and the output predicted impedance value. The staged fitting function is an overall model composed of impedance prediction functions in three stages.

[0091] In some examples, for unsaturated segment data, assuming it conforms to a quadratic polynomial function: Z = a1x² + b1x + c1, the coefficients a1, b1, and c1 are calculated using the least squares method based on the data points to obtain the impedance prediction function for the unsaturated segment. A similar method can be used for critically saturated and deeply saturated segment data, selecting an appropriate function form for fitting based on the data characteristics.

[0092] By accurately determining the staged current threshold, rationally dividing the data stages, and performing effective function fitting, the generated impedance prediction function can more accurately reflect the impedance change law of ferromagnetic materials in different saturation stages, thereby improving the accuracy and reliability of reactor magnetic saturation prediction.

[0093] Based on the above embodiments, the method for generating phased fitting functions by performing function fitting on unsaturated segment data, critically saturated segment data, and deeply saturated segment data respectively may include: fitting the unsaturated segment data with a quadratic polynomial function to obtain a first impedance prediction function; fitting the critically saturated segment data with an exponential function to obtain a second impedance prediction function; and fitting the deeply saturated segment data with a power function to obtain a third impedance prediction function; wherein the phased fitting function includes the first impedance prediction function, the second impedance prediction function, and the third impedance prediction function.

[0094] In this process, current-impedance data points are collected in the unsaturated region, with the current denoted as x and the impedance as Z. These data points are then substituted into the quadratic polynomial Z = a1x² + b1x + c1, and fitting algorithms such as the least squares method are used to calculate the values ​​of a1, b1, and c1, thus obtaining the first impedance prediction function. Next, current-impedance data points are collected in the critical saturation region, and these data points are substituted into the exponential function Z = a²e² / a²x + c1 ... -b2x +c2, determine the values ​​of a2, b2, and c2 using a suitable optimization algorithm (such as gradient descent) to obtain the second impedance prediction function. Collect current-impedance data points in the deep saturation segment and substitute these data points into the power function Z=a3x -b3 +c3, using a fitting method to find the values ​​of a3, b3, and c3, thus obtaining the third impedance prediction function.

[0095] In some embodiments, the fitting method for the unsaturated stage may include:

[0096] 1) Data segmentation: Current I new Data points ≤ I1 (e.g., I_stage1=I_new[I_new<=I1]), and their corresponding impedance values ​​(e.g., Z_stage1=Z_new[I_new<=I1]);

[0097] 2) Model definition: ;

[0098] 3) Parameter fitting: p1 = optimize.curve_fit(poly2, I_stage1, Z_stage1) to obtain the fitting parameters (i.e., a1, b1, c1 = p1).

[0099] Among them, the quadratic polynomial is suitable for describing mild non - linear changes and is applicable to the scenario where the magnetic core is not saturated and the impedance decreases slowly when the current is small. Further, a1 is the curvature coefficient, reflecting the degree of non - linearity; b1 is the first - order term coefficient, reflecting the linear change trend; c1 is the constant term, which is the basic impedance value.

[0100] The fitting method for the critical saturation stage can include:

[0101] 1) Data segmentation:

[0102] Data points where I1 < I new < I2 (such as I_stage2 = I_new[(I_new > I1) & (I_new < I2)]), and the corresponding impedance values (such as Z_stage2 = Z_new[(I_new > I1) & (I_new < I2)]);

[0103] 2) Model definition: ;

[0104] 3) Parameter fitting:

[0105] p2 = optimize.curve_fit(exp_func, I_stage2, Z_stage2, p0 = [Z_stage2[0], 0.001, Z_stage2[-1]]) to obtain the fitting parameters (i.e., a2, b2, c2 = p2).

[0106] Among them, the exponential decay function is suitable for describing the rapidly changing transition process and is applicable to the scenario where the impedance drops sharply when the current approaches the saturation point. Further, a2 is the exponential term amplitude; b2 is the decay coefficient, reflecting the change rate; c2 is the asymptotic value, which is the stable impedance that it tends to.

[0107] The fitting method for the deep saturation stage can include:

[0108] 1) Data segmentation: I new ≥I2 data points (such as I_stage3 = I_new[I_new >= I2]), and the corresponding impedance values (such as Z_stage3 = Z_new[I_new >= I2]);

[0109] 2) Model definition: ;

[0110] 3) Parameter fitting:

[0111] p3=optimize.curve_fit(power_func,I_stage3,Z_stage3,p0=[Z_stage3[0],0.5,Z_stage3[-1]]), to obtain the fitting parameters (i.e. a3,b3,c3=p3).

[0112] The power function is suitable for describing a gradual stabilization process and is applicable to scenarios where the current is sufficiently large, the magnetic core is deeply saturated, and the impedance decays slowly. Furthermore, a3 is the power term coefficient; b3 is the power exponent, reflecting the decay rate; and c3 is the limiting impedance value.

[0113] By employing a quadratic polynomial to accurately capture the slight nonlinearity of the unsaturated segment, an exponential function to effectively describe the rapid decay characteristics of the critical saturation segment, and a power function to accurately characterize the asymptotic stabilization trend of the deep saturation segment, these three functions are not only mathematically complementary but also physically correspond one-to-one with the three stages of the magnetization characteristics of ferromagnetic materials, ensuring the model's high-precision fitting capability and clear physical interpretability. Simultaneously, this approach makes the fitting functions for each stage more closely resemble the actual changes in the data, providing a more reliable and accurate mathematical model foundation for magnetic saturation prediction, thereby improving the accuracy of reactor magnetic saturation prediction.

[0114] Based on the above embodiments, and based on a phased fitting function and a preset electromagnetic theory, the method for calculating the predicted magnetic saturation value of a reactor under a target current may include: determining an unsaturated reference impedance value and a deeply saturated reference impedance value according to a phased current threshold, a first impedance prediction function, and a third impedance prediction function; converting the unsaturated reference impedance value and the deeply saturated reference impedance value into an unsaturated reference inductance value and a deeply saturated reference inductance value, respectively, according to the impedance-inductance conversion relationship, wherein the impedance-inductance conversion relationship is determined based on a preset electromagnetic theory; determining the predicted target impedance value corresponding to the target current, and converting the predicted target impedance value into a predicted target inductance value according to the impedance-inductance conversion relationship; and determining the predicted magnetic saturation value based on the unsaturated reference inductance value, the deeply saturated reference inductance value, and the predicted target inductance value.

[0115] In this embodiment, the saturation reference impedance value can refer to the impedance value calculated at the boundary point I1 between the unsaturated segment and the critical saturation segment, denoted as Z_unsat; the deep saturation reference impedance value can refer to the impedance value calculated at the boundary point between the critical saturation segment and the deep saturation segment. The impedance value calculated at that point is denoted as Z_sat.

[0116] The impedance-inductance conversion relationship refers to the relationship between the impedance Z, inductance L, and frequency f of an inductive element in an AC circuit: Z = 2πfL, then the inductance L = Z / (2πf). In practical applications, based on the specific circuit conditions and electromagnetic theory, the impedance value can be obtained by measurement or calculation, and the inductance value can then be derived based on this conversion relationship. Correspondingly, the unsaturated reference inductance value after conversion is L_unsat, and the deeply saturated reference inductance value is L_sat.

[0117] In this embodiment, the target current I is determined, and the predicted target impedance value Z_fit is calculated piecewise. For example, when I ≤ I1, Z_fit = poly2(I,a1,b1,c1); when I1 < I < I2, Z_fit = exp_func(I,a2,b2,c2); when I ≥ I2, Z_fit = power_func(I,a3,b3,c3). Therefore, the predicted target inductance value can be: The predicted value of magnetic saturation can be: S=(L_unsat-L) / (L_unsat-L_sat).

[0118] For example, suppose If I=80A is in the critical saturation range, then calculate Z_fit=exp_func(80,a2,b2,c2); convert the inductance L=Z_fit / (2π×50); calculate the saturation S=(L_unsat-L) / (L_unsat-L_sat), and get S=0.45, which means 45% saturation.

[0119] This approach solves the problem of transforming a staged, fitted impedance function into a magnetic saturation index with clear physical meaning by determining the reference impedance value based on a staged current threshold, performing impedance-to-inductance conversion based on electromagnetic theory, calculating the predicted target inductance value, and using a normalized formula to calculate the magnetic saturation. This method not only ensures the accuracy of the calculation results but also provides a unified saturation measurement standard, enabling quantitative comparison and evaluation of the magnetic saturation state of different reactors under different operating conditions.

[0120] Based on the above embodiments, the method for determining the unsaturated reference impedance value and the deep saturated reference impedance value according to the staged current threshold, the first impedance prediction function and the third impedance prediction function may include: inputting the upper limit current of the unsaturated segment into the first impedance prediction function to obtain the unsaturated reference impedance value; and inputting the lower limit current of the deep saturated segment into the third impedance prediction function to obtain the deep saturated reference impedance value.

[0121] Furthermore, by utilizing the phased current threshold, the upper limit current of the unsaturated segment is substituted into the first impedance prediction function, and the result is the unsaturated reference impedance value. For example, .

[0122] Substituting the lower limit current of the deep saturation segment into the third impedance prediction function yields the deep saturation reference impedance value, which reflects the impedance characteristics under deep saturation conditions. For example, .

[0123] By clarifying the specific calculation method for the reference impedance value, the consistency, repeatability, and physical correctness of the reference value calculation are ensured, providing a more accurate data basis for subsequent calculations of magnetic saturation.

[0124] Based on the above embodiments, the method may further include: obtaining a verification current sequence and the measured magnetic saturation corresponding to the verification current sequence; calculating the predicted magnetic saturation corresponding to each current in the verification current sequence based on a phased fitting function and a preset electromagnetic theory; determining the prediction error based on the measured magnetic saturation and the predicted magnetic saturation; and optimizing and correcting the fitting parameters in the phased fitting function based on the prediction error.

[0125] The verification current sequence can be a set of current values ​​with a specific order and range, either pre-set or actually measured. These current values ​​are used to verify and optimize existing magnetic saturation prediction methods. Their selection should cover the current range in which the reactor may operate, and can include different stages such as unsaturated, critically saturated, and deeply saturated, to ensure the comprehensiveness and accuracy of the verification. For example, the verification current sequence could be test_I_list=np.array([40,70,90,120]).

[0126] The measured magnetic saturation can be obtained by testing the reactor under different currents using actual experimental methods, resulting in a numerical value representing the degree of magnetic saturation of the reactor. Measurement methods may include using specialized magnetic measuring instruments and operating according to relevant physical principles and standards. For example, the measured magnetic saturation could be expressed as `true_S=np.array([0.1,0.4,0.7,0.9])`.

[0127] The predicted magnetic saturation is the magnetic saturation value predicted using the method described in the above embodiments. For example, the predicted magnetic saturation is pred_S=[get_saturation(i)foriintest_I_list].

[0128] Prediction error refers to the difference between the measured magnetic saturation and the predicted magnetic saturation calculated based on a staged fitting function and a pre-defined electromagnetic theory. It can be measured using methods such as absolute error (the absolute value of the difference between the predicted and measured values) or relative error (the ratio of the absolute error to the measured value). For example, prediction error is the average relative error. And output print(f"Average relative error: {err:.2f}%").

[0129] In some embodiments, a verification current sequence can be extracted from an experimental data repository or a specially designed test scheme, while simultaneously acquiring measured magnetic saturation data obtained experimentally under the same current conditions. These data should accurately record the current values ​​and their corresponding magnetic saturation measurement results. For each current value in the verification current sequence, the predicted magnetic saturation corresponding to each current is calculated sequentially based on a staged fitting function and a preset electromagnetic theory, according to the method described in the above embodiments. That is, the saturation stage corresponding to each current is first determined, the corresponding impedance prediction function is selected for calculation, and then the predicted magnetic saturation is obtained through a series of transformations and calculations. Then, the measured magnetic saturation under each current is compared with the calculated predicted magnetic saturation, and the prediction error corresponding to each current point is calculated according to the selected error calculation method (such as absolute error or relative error). Finally, based on the calculated prediction error, a suitable optimization algorithm (such as least squares method, gradient descent method, etc.) is used to adjust the fitting parameters (such as a1, b1, c1, a2, b2, c2, a3, b3, c3) in the staged fitting function, so that the prediction error is minimized overall, thereby improving the accuracy and reliability of the staged fitting function.

[0130] By introducing a verification current sequence and measured magnetic saturation, calculating the prediction error, and optimizing and correcting the parameters of the staged fitting function, the accuracy and reliability of the staged fitting function can be effectively improved, making the magnetic saturation prediction results closer to the actual situation, thereby improving the quality and practicality of the entire reactor magnetic saturation prediction method.

[0131] In addition, based on the above embodiments, the method may further include data visualization. In one example, the visualization outputs a segmented impedance-current fitting curve (plt.figure(figsize=(10,6))): 1) Plot the original data points, showing the original measurement data as red scatter points to intuitively display the data distribution and the comparison of fitting effects: plt.scatter(I, Z, label='Original test data', color='red'); 2) Plot the fitting curve for the unsaturated section. Among them, for the range I≤I1, the green curve is the fitting result of the quadratic polynomial. The list comprehension calculates the fitting impedance value for each current point: plt.plot(I_new[I_new<=I1], [poly2(i, a1, b1, c1) for i in I_new if i<=I1], label='Unsaturated section fitting', color='green'); 3) Plot the fitting curve for the critical saturation section. Among them, for the range I1<I<I2, the blue curve is the fitting result of the exponential function: plt.plot(I_new[(I_new>I1)&(I_new<I2)], [exp_func(i, a2, b2, c2) for i in I_new if (i>I1)&(i<I2)], label='Critical section fitting', color='blue'); 4) Plot the fitting curve for the deep saturation section. Among them, for the range I≥I2, the orange curve is the fitting result of the power function: plt.plot(I_new[I_new>=I2], [power_func(i, a3, b3, c3) for i in I_new if i>=I2], label='Deep section fitting', color='orange'); 5) Chart decoration: Specify the axis labels (plt.xlabel('Current I (A)'); plt.ylabel('Impedance Z (Ω)')), legend (plt.legend(); plt.title('Segmented impedance-current fitting curve')), grid lines (plt.grid(True)), and display the graph (plt.show()).

[0132] In another example, visualize the output current-magnetic saturation curve: 1) Generate a current range, such as 200 uniformly distributed current values ​​from minimum to maximum current, to generate a smooth curve: I_range=np.linspace(I.min(),I.max(),200); 2) Calculate the magnetic saturation sequence, such as calculating the magnetic saturation for 200 current points to obtain 200 corresponding saturation values ​​S_range: S_range=[get_saturation(i)foriinI_range]; 3) Plot the saturation curve, where the purple curve... To show the current-magnetic saturation relationship and display the continuous trend of saturation change: plt.figure(figsize=(10,6)); plt.plot(I_range,S_range,label='Magnetic Saturation S',color='purple'); 4) Chart decoration: specify axis labels (plt.xlabel('Current I (A)'); plt.ylabel('Magnetic Saturation S')), legend (plt.legend(); plt.title('Current-Magnetic Saturation Curve')), grid lines, and display the graph.

[0133] Based on the above embodiments, it is evident that the reactor magnetic saturation prediction method provided in this application can be applied to the scenario of predicting the magnetic saturation characteristics of 500kV large-capacity oil-immersed reactors, specifically covering aspects such as power system planning, reactor design optimization, operational status monitoring, and fault emergency response. In power systems, reactors need to withstand complex operating conditions (such as short-circuit current surges) for extended periods, and the magnetic saturation risk of their ferromagnetic materials directly affects inductance and current-limiting performance. This solution uses current-impedance test data (such as series / parallel power supply tests) as input, combined with the optimized physical laws of the ferromagnetic material's BH curve, to construct a phased nonlinear model. This model can evaluate the magnetic saturation of the reactor under different currents in real time, providing data support for grid dispatching, equipment selection, and fault early warning. For example, when a short-circuit fault occurs, the system can quickly determine whether the reactor has entered a magnetic saturation state through this solution, thereby adjusting protection strategies or switching to backup equipment to avoid cascading faults caused by current-limiting failure.

[0134] Figure 2 Flowchart of the reactor magnetic saturation prediction method provided in this application Figure 2 In this embodiment Figure 1 Based on the examples, a detailed explanation of the reactor magnetic saturation prediction method is provided to accurately predict the impact of ferromagnetic material saturation on reactor performance and avoid adverse consequences such as current-limiting failure and system fluctuations caused by magnetic saturation under extreme operating conditions. Figure 2 As shown, the method may include:

[0135] S201. Test the magnetic characteristic curves of ferromagnetic materials and optimize the curves. At the same time, obtain the impedance test data of the reactor under different currents, complete the data preprocessing, and lay the foundation for prediction modeling.

[0136] Among these, the core magnetic properties of ferromagnetic materials include magnetization curves, hysteresis loops, permeability, and magnetic saturation. These properties directly affect the inductance of reactors; a sharp drop in inductance at saturation weakens their current-limiting capability. In this step, outliers can be removed using the 3σ criterion, and data preprocessing, including normalization and interpolation, can be completed.

[0137] In some examples, Figure 3 The BH curve and optimized curve of the ferromagnetic material of the reactor provided in this application are as follows: Figure 3 As shown, the curves representing the relationship between the magnetic flux density B and the magnetic field strength H of the reactor yoke (i.e., the BH curve) are plotted. The horizontal axis represents the magnetic field strength H (unit: A / m), and the vertical axis represents the magnetic flux density B (unit: T). The black curve represents the original BH curve of the reactor yoke, while the gray curve represents the optimized BH curve. The curve trends show that the optimized yoke exhibits rapid growth in magnetic flux density in the low magnetic field strength range (H < 50 A / m), stabilizing after reaching a certain range. The original yoke curve, however, shows continuous growth with increasing magnetic field strength across the entire range (with a slower growth rate in the saturation stage). This optimized BH curve improves the magnetic saturation characteristics of ferromagnetic materials, providing a fundamental basis for predicting magnetic saturation risk and optimizing current-limiting performance of reactors under extreme short-circuit conditions.

[0138] As a further example, this curve can be determined in the following way:

[0139] In some examples, Figure 4 This is a schematic diagram illustrating the change in resistivity of the reactor under different currents provided in this application, as shown below. Figure 4 As shown, this schematic diagram can be used as impedance test data for reactors under different currents. The horizontal axis represents the current (0A~250A), and the vertical axis represents the corresponding impedance value (approximately 3.22Ω~2.92Ω). The curve intuitively reflects the law that the impedance continues to decrease as the current increases. This data is the physical basis of the entire prediction method.

[0140] S202. Based on the optimized ferromagnetic characteristic curves and current-impedance data, the ferromagnetic material is divided into three stages: unsaturated, critically saturated, and deeply saturated. The current-impedance fitting function for each stage is constructed accordingly. By combining electromagnetic theory, the impedance is converted into inductance, and a nonlinear mapping model is established to achieve accurate correlation of magnetic saturation characteristics.

[0141] Among them, the nonlinear mapping model uses reactor current-impedance test data to construct ZI fitting functions for each stage by dividing the ferromagnetic material into three stages: unsaturated, critically saturated, and deeply saturated. Then, based on electromagnetic theory, the impedance is converted into inductance and finally correlated with the magnetic saturation, so as to achieve direct prediction from current input to magnetic saturation characteristics.

[0142] Furthermore, the impedance change rate can be used to divide the material into three stages: unsaturated, critically saturated, and deeply saturated. For the physical characteristics of each stage, the impedance-current relationship can be fitted using quadratic polynomials, exponential functions, and power functions, respectively. Then, by leveraging the electromagnetic correlation between impedance → inductance (L=Z / (2πf)) → magnetic saturation (the ratio of current inductance to unsaturated inductance), the magnetic saturation of ferromagnetic materials under any current can be accurately predicted.

[0143] In some examples, Figure 5 The reactor experimental test current-impedance test curve provided in this application is as follows: Figure 5 As shown, this curve is the series current-impedance curve of the reactor winding during reactor experimental testing. The impedance generally decreases with increasing current: from 30 to 70A, the impedance drops rapidly from 11.83Ω, then rebounds slightly, and enters a continuous decreasing phase after 70A. Although there are slight fluctuations, the overall trend is a gradual decrease, reflecting the process of the yoke gradually developing from unsaturated to saturated. Figure 6 The second experimental test current-impedance curve for the reactor provided in this application is as follows: Figure 6 As shown, this curve represents the parallel power supply current-impedance curve of the reactor windings during reactor testing. From 0 to 40A, the yoke is in an unsaturated state, and the impedance initially rises slightly to 3.03Ω before decreasing. From 40 to 120A, the saturation stage occurs, with the impedance continuously decreasing from 3.03Ω accompanied by slight fluctuations, indicating gradual saturation of the yoke and a gradual decrease in impedance. After 120A, the system enters a deep saturation stage, with the impedance stabilizing in the 2.88~2.90Ω range, while the inductance remains almost unchanged.

[0144] S203. Use experimental data to verify the accuracy of the model and correct errors to ensure the accuracy of the prediction of the magnetic saturation degree of ferromagnetic materials and the saturation inductance of reactors.

[0145] Furthermore, by reserving experimental data to verify accuracy, and by conforming to the overall magnetization physical laws of ferromagnetic materials, quantitative and efficient technical support is provided for the prediction of magnetic saturation risk and design optimization of 500kV reactors.

[0146] It should be noted that the embodiments of this application comprehensively consider various factors that may affect the prediction accuracy and applicability. The specific factors are as follows:

[0147] (1) The intrinsic relationship between impedance and ferromagnetic properties:

[0148] The impedance and inductance of a reactor are directly related, and the inductance is determined by the permeability of the ferromagnetic material. The permeability, in turn, depends on the nonlinear relationship between the magnetic flux density and the magnetic field strength of the material. This relationship is the core basis for the prediction process, which uses impedance data to infer magnetic saturation characteristics. The accurate capture of this correlation directly affects the physical consistency of the prediction model.

[0149] (2) Nonlinear fit at different saturation stages:

[0150] As ferromagnetic materials transition from unsaturation to deep saturation, the BH curve exhibits phased characteristics, and the corresponding ZI curve also displays differentiated nonlinearities. The prediction method in this embodiment, with its identification of characteristics at each stage and targeted fitting, is crucial for ensuring prediction accuracy across the entire current range.

[0151] The saturation condition of ferromagnetic materials refers to the operating state where, as the applied magnetic field strength gradually increases, the internal magnetic domains of a ferromagnetic material tend to achieve complete alignment, and the magnetic induction intensity reaches its limit, no longer showing a significant increase with the magnetic field strength. At this point, the material's magnetization capacity reaches its upper limit, the permeability decreases sharply, and hysteresis losses increase. This condition is an important consideration in the design of electromagnetic equipment and is one of the core operating conditions for achieving reactance regulation in devices such as adjustable reactors.

[0152] (3) Matching of experimental data with model accuracy:

[0153] The completeness, accuracy, and uniformity of impedance test data directly affect the model training effect. Simultaneously, the model needs to be validated using hysteresis loop calibration data to ensure that the deviation between the predicted magnetic saturation and the actual ferromagnetic properties is within the acceptable engineering range.

[0154] Compared to other magnetic saturation prediction methods, the prediction method in this embodiment comprehensively considers the intrinsic relationship between impedance and ferromagnetic properties. By analyzing the nonlinear mapping law between BH and ZI, a staged fitting function is constructed. Combined with data preprocessing and multi-source verification, accurate reverse inference from impedance data to magnetic saturation characteristics is achieved. By incorporating the above factors into a unified modeling framework, a new method for predicting the magnetic saturation characteristics of reactors based on impedance test data is formed.

[0155] Furthermore, this method considers the impedance-current nonlinearity characteristics of ferromagnetic materials at each saturation stage, with different fitting functions corresponding to different stages, and fits the piecewise function expression of current-impedance for each stage; considering the electromagnetic correlation between impedance, inductance, and magnetic saturation, the piecewise impedance function is coupled with the mapping relationship between permeability and magnetic saturation; the above piecewise fitting function and electromagnetic correlation model are substituted into the prediction process for iterative calculation.

[0156] The reactor magnetic saturation prediction method provided in this application constructs a nonlinear mapping model of current-impedance-magnetic saturation characteristics based on impedance test data of the reactor under different currents. Through algorithm optimization, it achieves accurate prediction of the magnetic saturation degree of ferromagnetic materials and the saturation inductance of the reactor. It conducts research on the accuracy verification and error correction of prediction under magnetic saturation conditions, and provides an efficient and reliable technical means for the optimized design, operating condition adaptation and power system safety protection of 500kV large-capacity oil-immersed reactors.

[0157] Furthermore, this prediction method deeply integrates the magnetic characteristic curves of ferromagnetic materials. For 500kV high-capacity oil-immersed reactors, it optimizes the ferromagnetic characteristic curves through testing, combining piecewise fitting and electromagnetic theory to overcome the limitations of traditional measurements and achieve direct prediction from current input to magnetic saturation characteristics. This method closely aligns with engineering practice, fully utilizing the nonlinear characteristics of the magnetic characteristic curves. It is computationally efficient and predictively accurate, providing strong support for the optimized design of reactors under extreme short-circuit conditions, the selection of ferromagnetic materials, and power system safety protection. It effectively solves the inductance attenuation problem caused by ferromagnetic material saturation, ensuring the operational stability of high-voltage power grids during short-circuit faults.

[0158] Figure 7 A schematic diagram of the reactor magnetic saturation prediction device provided in this application is shown below. Figure 7 As shown, the reactor magnetic saturation prediction device 70 provided in this embodiment includes:

[0159] The acquisition module 701 is used to acquire impedance test data of the reactor under different currents. The impedance test data is used to indicate the correspondence between current and impedance.

[0160] Preprocessing module 702 is used to preprocess the impedance test data to obtain preprocessed data;

[0161] The generation module 703 is used to perform phased modeling of preprocessed data based on the magnetization characteristics of ferromagnetic materials in the reactor, and generate phased fitting functions.

[0162] The prediction module 704 is used to calculate the predicted value of the magnetic saturation of the reactor under the target current based on the phased fitting function and the preset electromagnetic theory. The predicted value of magnetic saturation is used to indicate the magnetic saturation state of the reactor.

[0163] In one possible implementation, the preprocessing module 702 can also be used to: perform outlier removal processing on the impedance test data to obtain effective impedance data; perform normalization processing on the effective impedance data to obtain normalized impedance data; and perform interpolation completion processing on the normalized impedance data to obtain preprocessed data, wherein the preprocessed data includes multiple equally spaced current points and the impedance value corresponding to each current point.

[0164] In one possible implementation, the generation module 703 can also be used to: determine the staged current thresholds based on the magnetization curve of the ferromagnetic material, the staged current thresholds including the upper limit current of the unsaturated segment and the lower limit current of the deep saturated segment; divide the preprocessed data into unsaturated segment data, critically saturated segment data and deep saturated segment data based on the staged current thresholds; and perform function fitting on the unsaturated segment data, critically saturated segment data and deep saturated segment data respectively to generate a staged fitting function, the staged fitting function including the impedance prediction function corresponding to each stage of data.

[0165] In one possible implementation, the generation module 703 can also be used to: fit the unsaturated segment data with a quadratic polynomial function to obtain a first impedance prediction function; fit the critically saturated segment data with an exponential function to obtain a second impedance prediction function; and fit the deeply saturated segment data with a power function to obtain a third impedance prediction function; wherein the staged fitting function includes the first impedance prediction function, the second impedance prediction function, and the third impedance prediction function.

[0166] In one possible implementation, the prediction module 704 can also be used to: determine the unsaturated reference impedance value and the deeply saturated reference impedance value based on the phased current threshold, the first impedance prediction function, and the third impedance prediction function; convert the unsaturated reference impedance value and the deeply saturated reference impedance value into the unsaturated reference inductance value and the deeply saturated reference inductance value respectively according to the impedance-inductance conversion relationship, wherein the impedance-inductance conversion relationship is determined based on a preset electromagnetic theory; determine the target impedance prediction value corresponding to the target current, and convert the target impedance prediction value into the target inductance prediction value according to the impedance-inductance conversion relationship; and determine the magnetic saturation prediction value based on the unsaturated reference inductance value, the deeply saturated reference inductance value, and the target inductance prediction value.

[0167] In one possible implementation, the prediction module 704 can also be used to: input the upper limit current of the unsaturated segment into the first impedance prediction function to obtain the unsaturated reference impedance value; and input the lower limit current of the deep saturated segment into the third impedance prediction function to obtain the deep saturated reference impedance value.

[0168] In one possible implementation, the prediction module 704 can also be used to: obtain the verification current sequence and the measured magnetic saturation corresponding to the verification current sequence; calculate the predicted magnetic saturation corresponding to each current in the verification current sequence based on the phased fitting function and the preset electromagnetic theory; determine the prediction error based on the measured magnetic saturation and the predicted magnetic saturation; and optimize and correct the fitting parameters in the phased fitting function based on the prediction error.

[0169] The reactor magnetic saturation prediction device provided in this embodiment can execute the method provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0170] Figure 8 A schematic diagram of the structure of the electronic device provided in this application. Figure 8 As shown, the electronic device 80 provided in this embodiment includes at least one processor 801 and a memory 802. Optionally, the device 80 further includes a communication component 803. The processor 801, memory 802, and communication component 803 are connected via a bus 804.

[0171] In a specific implementation, at least one processor 801 executes computer execution instructions stored in memory 802, causing at least one processor 801 to perform the above-described method.

[0172] The specific implementation process of processor 801 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0173] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0174] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0175] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0176] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0177] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0178] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0179] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0180] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0181] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0182] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0183] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0184] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0185] It should be understood that the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover but not exclude inclusion. For example, a product or device that includes a series of components is not necessarily limited to those components that are explicitly listed, but may include other components that are not explicitly listed or that are inherent to such product or device.

[0186] As used in this application, the term "module" means any known or subsequently developed hardware, software, firmware, artificial intelligence, fuzzy logic, or combination of hardware and / or software code capable of performing the functions associated with that element.

[0187] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for predicting magnetic saturation of a reactor, characterized in that, include: Obtain impedance test data of the reactor under different currents, and the impedance test data is used to indicate the correspondence between current and impedance; The impedance test data is preprocessed to obtain preprocessed data; Based on the magnetization characteristics of the ferromagnetic material in the reactor, the preprocessed data is modeled in stages to generate a staged fitting function. Based on the staged fitting function and the preset electromagnetic theory, the predicted value of the magnetic saturation of the reactor under the target current is calculated. The predicted value of the magnetic saturation is used to indicate the magnetic saturation state of the reactor.

2. The method according to claim 1, characterized in that, The preprocessing of the impedance test data to obtain preprocessed data includes: Outlier removal is performed on the impedance test data to obtain valid impedance data; The effective impedance data is normalized to obtain normalized impedance data; The normalized impedance data is interpolated to obtain the preprocessed data, which includes multiple equally spaced current points and the impedance value corresponding to each current point.

3. The method according to claim 1, characterized in that, The step of modeling the preprocessed data in stages based on the magnetization characteristics of the ferromagnetic material in the reactor to generate a staged fitting function includes: Based on the magnetization curve of the ferromagnetic material, the staged current threshold is determined, which includes the upper limit current of the unsaturated segment and the lower limit current of the deep saturated segment. Based on the staged current threshold, the preprocessed data is divided into unsaturated segment data, critically saturated segment data, and deeply saturated segment data. The unsaturated segment data, the critically saturated segment data, and the deeply saturated segment data are respectively fitted with functions to generate the staged fitting function, which includes the impedance prediction function corresponding to each stage of data.

4. The method according to claim 3, characterized in that, The step of performing function fitting on the unsaturated segment data, the critically saturated segment data, and the deeply saturated segment data respectively to generate the staged fitting function includes: The unsaturated segment data is fitted with a quadratic polynomial function to obtain the first impedance prediction function; The critical saturation range data are fitted using an exponential function to obtain the second impedance prediction function; The data in the deep saturation segment are fitted using a power function to obtain the third impedance prediction function; The phased fitting function includes the first impedance prediction function, the second impedance prediction function, and the third impedance prediction function.

5. The method according to claim 4, characterized in that, The step of calculating the predicted magnetic saturation value of the reactor under the target current based on the phased fitting function and the preset electromagnetic theory includes: Based on the phased current threshold, the first impedance prediction function, and the third impedance prediction function, determine the unsaturated reference impedance value and the deeply saturated reference impedance value; Based on the impedance-inductance conversion relationship, the unsaturated reference impedance value and the deeply saturated reference impedance value are respectively converted into an unsaturated reference inductance value and a deeply saturated reference inductance value. The impedance-inductance conversion relationship is determined based on a preset electromagnetic theory. Determine the target impedance prediction value corresponding to the target current, and convert the target impedance prediction value into the target inductance prediction value according to the impedance-inductance conversion relationship; The predicted magnetic saturation value is determined based on the unsaturated reference inductance value, the deeply saturated reference inductance value, and the predicted target inductance value.

6. The method according to claim 5, characterized in that, The step of determining the unsaturated reference impedance value and the deeply saturated reference impedance value based on the phased current threshold, the first impedance prediction function, and the third impedance prediction function includes: The upper limit current of the unsaturated segment is input into the first impedance prediction function to obtain the unsaturated reference impedance value; The lower limit current of the deep saturation segment is input into the third impedance prediction function to obtain the deep saturation reference impedance value.

7. The method according to any one of claims 1-6, characterized in that, The method further includes: Obtain the verification current sequence and the measured magnetic saturation corresponding to the verification current sequence; Based on the staged fitting function and the preset electromagnetic theory, the predicted magnetic saturation degree corresponding to each current in the verification current sequence is calculated. The prediction error is determined based on the measured magnetic saturation and the predicted magnetic saturation. Based on the prediction error, the fitting parameters in the staged fitting function are optimized and corrected.

8. A reactor magnetic saturation prediction device, characterized in that, include: The acquisition module is used to acquire impedance test data of the reactor under different currents, and the impedance test data is used to indicate the correspondence between current and impedance; The preprocessing module is used to preprocess the impedance test data to obtain preprocessed data; The generation module is used to perform phased modeling on the preprocessed data based on the magnetization characteristics of the ferromagnetic material in the reactor, and generate a phased fitting function. The prediction module is used to calculate the predicted value of the magnetic saturation of the reactor under the target current based on the phased fitting function and the preset electromagnetic theory. The predicted value of magnetic saturation is used to indicate the magnetic saturation state of the reactor.

9. An electronic device, characterized in that, include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed, are used to implement the method as described in any one of claims 1-7.

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