Electromagnetic voltage transformer global state sensing system and method

Abstract

The invention relates to the technical field of electromagnetic measurement and state monitoring, and discloses a global state sensing system and method for an electromagnetic voltage transformer. The technical problems that in the prior art, data robustness is insufficient and actual working condition changes of a power grid are difficult to adapt due to the fact that accurate resonance circuit parameters are depended and a single calculation path is adopted are solved. According to the method, ferromagnetic resonance phenomena under various faults are simulated based on electromagnetic transient simulation, phenomenon data are obtained, and influence factors are analyzed to obtain influence rule data. And taking the rule data as input, and adopting a comprehensive solving method combining programming calculation, system structure chart calculation and electromagnetic transient software simulation to obtain a high-reliability state quantity time sequence. Based on the time sequence, a nonlinear model which takes loss into account and does not depend on precise resonant circuit parameters is derived, and explicit mathematical functions of primary current and transient overvoltage of the voltage transformer are obtained.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic measurement and condition monitoring technology, specifically to a global condition sensing system and method for electromagnetic voltage transformers. Background Technology

[0002] In power systems, ferroresonance in electromagnetic voltage transformers is a typical transient phenomenon that threatens equipment safety. Existing technologies mainly rely on accurate electromagnetic transient simulation for analysis. The core of this approach is to construct an equivalent circuit model of a resonant circuit with defined parameters in simulation software, based on known parameters such as line-to-ground capacitance and system inductance. By simulating faults, the electrical response of the voltage transformer can be evaluated.

[0003] This conventional technique has limitations. The reliability of its analysis results highly depends on the accuracy of the linear component parameters in the model, especially the ground capacitance value. However, the actual ground capacitance of the power grid is affected by various operating factors and is a variable that is difficult to obtain accurately in real time. The uncertainty of the parameters leads to deviations between the simulation model and the actual operating conditions. In addition, existing methods generally rely solely on fixed algorithms of specific electromagnetic transient simulation software for calculation. When facing highly nonlinear processes such as core deep saturation, there is a risk of computational convergence, and there is a lack of effective cross-validation mechanisms, resulting in insufficient robustness of the obtained data sequences.

[0004] A novel state-aware method is needed to overcome the dependence on precise resonant circuit parameters and effectively characterize the dynamic behavior of voltage transformers under conditions of parameter uncertainty. Simultaneously, this method needs to improve the quality of generated fundamental state data and enhance data reliability by fusing multiple computational paths, thus providing support for constructing high-precision and practical analytical models. Summary of the Invention

[0005] The purpose of this invention is to provide a global state sensing system and method for electromagnetic voltage transformers to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides a method for global state sensing of an electromagnetic voltage transformer, the method comprising:

[0007] The steps for establishing a nonlinear model include the following:

[0008] A ferromagnetic resonant electromagnetic transient model was built based on electromagnetic transient simulation software.

[0009] Using the aforementioned ferroresonant electromagnetic transient model, the ferroresonant phenomenon under single-phase grounding fault, two-phase grounding fault, phase-to-phase short-circuit fault, and asynchronous switching fault is simulated to obtain phenomenon data reflecting the ferroresonant phenomenon.

[0010] Based on the aforementioned phenomenon data, the influence of four types of factors on the primary current and transient overvoltage of the voltage transformer is investigated: the capacitance to ground corresponding to the overhead line, the capacitance to ground corresponding to the cable length, the excitation characteristic curve of the voltage transformer, and the DC resistance of the voltage transformer. The influence law data is obtained.

[0011] Using the aforementioned data on the influence patterns as input, a comprehensive solution method is used to obtain the time series of each state variable. The comprehensive solution method includes a programming calculation method, a system structure diagram calculation method, and an electromagnetic transient software simulation method.

[0012] Based on the time series of the various state quantities, a nonlinear model that takes into account losses and does not depend on the precise resonant circuit parameters is derived, and mathematical functions of the primary current and transient overvoltage of the voltage transformer are derived based on the nonlinear model.

[0013] Preferably, after obtaining the time series of each state variable using the comprehensive solution method, the following steps are further included:

[0014] Based on the time series of each state variable, draw the phase plane trajectory diagram, Poincaré section diagram, bifurcation diagram and Lyapunov exponent diagram;

[0015] By analyzing the phase plane trajectory diagram, Poincaré section diagram, bifurcation diagram, and Lyapunov exponent diagram, the correlation between resonance parameters and ferromagnetic resonance types is analyzed, and a table of resonance parameter type correspondences is generated.

[0016] Preferably, the electromagnetic voltage transformer global state sensing method further includes a finite element temperature field analysis step; the finite element temperature field analysis step includes the following steps:

[0017] Establish a three-dimensional solid model of the voltage transformer, and define the thermal conductivity, convective heat transfer coefficient and loss density of the material of the three-dimensional solid model;

[0018] Based on the loss data in the nonlinear model, the loss data of the voltage transformer is loaded into the three-dimensional solid model as a heat source;

[0019] The loss data includes core loss data and winding loss data.

[0020] Perform finite element temperature field calculations to obtain the temperature field distribution data of the voltage transformer;

[0021] Based on the temperature field distribution data of the voltage transformer, the highest temperature point of the voltage transformer, i.e., the hottest point, is located.

[0022] Preferably, the finite element temperature field analysis step further includes the following steps:

[0023] By changing the value of the primary current of the voltage transformer in the nonlinear model, loss data under different values ​​of the primary current of the voltage transformer can be obtained.

[0024] Loss data of different voltage transformer primary current values ​​are loaded into the three-dimensional solid model, and finite element temperature field calculation is performed to obtain a series of corresponding voltage transformer temperature field distribution data.

[0025] Based on the temperature field distribution data of the corresponding series of voltage transformers, the mapping relationship between the change of primary current of the voltage transformer and the change of heat loss of the voltage transformer is analyzed, and a table of coupling relationship between current loss and heat generation is established.

[0026] Preferably, the electromagnetic voltage transformer global state sensing method further includes a step of identifying the ferromagnetic resonance type; the step of identifying the ferromagnetic resonance type includes the following steps:

[0027] Obtain the voltage transformer primary current time series and voltage transformer transient overvoltage time series from the time series of each state quantity;

[0028] Phase space reconstruction is performed on the primary current time series and the transient overvoltage time series of the voltage transformer, respectively, to construct the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer;

[0029] Extract nonlinear features from the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer. The nonlinear features include the correlation dimension and the maximum Lyapunov exponent.

[0030] The extracted nonlinear features are compared with the corresponding table of resonance parameter types to identify the types of low-frequency ferromagnetic resonant overvoltage, fundamental frequency ferromagnetic resonant overvoltage, and high-frequency ferromagnetic resonant overvoltage.

[0031] Preferably, the step of performing phase space reconstruction on the primary current time series and the transient overvoltage time series of the voltage transformer, respectively, to construct the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer, includes the following sub-steps:

[0032] For the time series of primary current of voltage transformer, the mutual information method is used to determine the optimal delay time, and the spurious nearest neighbor method is used to determine the optimal embedding dimension.

[0033] Based on the optimal delay time and the optimal embedding dimension, the phase space reconstruction of the voltage transformer primary current time series is performed to obtain the voltage transformer primary current reconstruction sequence.

[0034] For the transient overvoltage time series of voltage transformers, the mutual information method is used to determine the optimal delay time, and the spurious nearest neighbor method is used to determine the optimal embedding dimension.

[0035] Based on the optimal delay time and the optimal embedding dimension, the transient overvoltage time series of the voltage transformer is reconstructed in phase space to obtain the transient overvoltage reconstruction sequence of the voltage transformer.

[0036] Preferably, the step of comparing the extracted nonlinear feature quantities with the resonance parameter type correspondence table to identify the types of low-frequency ferroresonant overvoltage, fundamental-frequency ferroresonant overvoltage, and high-frequency ferroresonant overvoltage specifically includes:

[0037] The extracted correlation dimension and maximum Lyapunov exponent are compared with the range of correlation dimension and range of maximum Lyapunov exponent of low-frequency resonance modes stored in the resonance parameter type correspondence table.

[0038] If all fall within the corresponding range, it is determined to be a low-frequency ferroresonant overvoltage type.

[0039] The extracted correlation dimension and maximum Lyapunov exponent are compared with the range of correlation dimension and range of maximum Lyapunov exponent of fundamental frequency resonant mode stored in the resonant parameter type correspondence table.

[0040] If all fall within the corresponding range, it is determined to be a fundamental frequency ferroresonant overvoltage type;

[0041] The extracted correlation dimension and maximum Lyapunov exponent are compared with the range of correlation dimension and range of maximum Lyapunov exponent of high-frequency resonance modes stored in the resonance parameter type correspondence table.

[0042] If all fall within the corresponding range, it is determined to be a high-frequency ferroresonant overvoltage type.

[0043] Preferably, after the step of identifying the ferromagnetic resonance type, a comprehensive state perception step is further included; the comprehensive state perception step includes the following steps:

[0044] The mathematical functions of the primary current and transient overvoltage of the voltage transformer output by the nonlinear model are integrated, along with the temperature data of the hottest spot of the voltage transformer in the current loss and heat generation coupling relationship table, and the identified ferroresonant overvoltage type.

[0045] Based on the integrated data, a comprehensive status awareness report reflecting the electrical, thermal, and resonant states of the electromagnetic voltage transformer is generated.

[0046] Preferably, the electromagnetic voltage transformer global state sensing method further includes an online monitoring and updating step; the online monitoring and updating step includes the following steps:

[0047] Real-time acquisition of primary current and overvoltage data from operating electromagnetic voltage transformers to form an online monitoring time series;

[0048] The online monitoring time series is input into the step of identifying the ferromagnetic resonance type to perform real-time ferromagnetic resonance overvoltage type identification;

[0049] The data in the current loss and heat generation coupling relationship table is updated using the loss data corresponding to the online monitoring time series.

[0050] The real-time identified ferroresonant overvoltage type, the updated current loss and heating coupling relationship table data, and the online monitored voltage transformer primary current and overvoltage data are integrated into the global status perception report to achieve dynamic updates of the perception report.

[0051] Preferably, the present invention also includes an electromagnetic voltage transformer global state sensing system, the system including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein when the processor executes the computer program, it implements the steps of the electromagnetic voltage transformer global state sensing method described above.

[0052] Compared with the prior art, the beneficial effects of the present invention are:

[0053] The comprehensive solution method integrates three independent technical paths: programming computation, system block diagram calculation, and electromagnetic transient software simulation. These three methods perform parallel computations based on the same set of influencing data to generate time series of state variables describing the phenomena. Programming computation enables autonomous control of the algorithm and computational process; system block diagram calculation utilizes the stable framework of mature commercial solvers; and electromagnetic transient simulation provides industry-standard references to the physical processes. By comparing, calibrating, and organically integrating the data output from different methods, a multi-source data verification and compensation mechanism is established. This method reduces systematic biases caused by reliance on a single algorithm or inherent software settings, especially when dealing with severe nonlinear transient processes, improving the convergence stability and numerical accuracy of the generated data, thereby obtaining higher-quality and more reliable original state sequences.

[0054] Based on the aforementioned highly reliable time series, a nonlinear characterization model incorporating actual loss factors was constructed. The key to this model lies in its construction logic, which does not rely on precise values ​​of parameters such as the capacitance to ground and linear inductance in the resonant circuit. It avoids the step of establishing a parameterized equivalent circuit required in traditional methods, instead directly inducing the dynamic mathematical relationship between the primary current of the voltage transformer and transient overvoltage from the system response data. This makes the model's applicability no longer limited to grid distributed parameters that are difficult to measure accurately in real time, reducing modeling errors caused by unknown or changing parameters. The obtained explicit mathematical function relationship can be directly used for the quantitative assessment of equipment status and the analysis and prediction of transient overvoltage levels within a wider range of operating conditions. Attached Figure Description

[0055] Figure 1 This is a schematic diagram illustrating the working principle of the electromagnetic voltage transformer global state sensing method described in this invention.

[0056] Figure 2 A flowchart for finite element temperature field analysis;

[0057] Figure 3 A flowchart for identifying ferromagnetic resonance types;

[0058] Figure 4 Characteristic distribution of correlation dimension-maximum Lyapunov exponent for different ferromagnetic resonance types;

[0059] Figure 5 Comparison of transient overvoltage waveforms under different ferromagnetic resonance types. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Please see Figure 1This invention provides a method for full-domain state perception of an electromagnetic voltage transformer. The method includes: building a ferroresonant electromagnetic transient model using electromagnetic transient simulation software. The ferroresonant electromagnetic transient model is used to simulate ferroresonant phenomena under single-phase grounding faults, two-phase grounding faults, phase-to-phase short-circuit faults, and asynchronous switching faults, obtaining phenomenon data reflecting the ferroresonant phenomenon. Based on the phenomenon data, the influence of overhead line or cable length-to-ground capacitance, voltage transformer excitation characteristic curve, and voltage transformer DC resistance on the primary current and transient overvoltage of the voltage transformer is investigated, obtaining influence law data. Using the influence law data as input, a comprehensive solution method is used to obtain the time series of each state quantity. The comprehensive solution method includes programming calculation methods, system structure diagram calculation methods, and electromagnetic transient software simulation methods. Based on the time series of each state quantity, a nonlinear model considering losses and independent of precise resonant circuit parameters is derived, and mathematical functions of the primary current and transient overvoltage of the voltage transformer are derived based on the nonlinear model.

[0062] In one embodiment of the present invention, see [reference] Figure 2 Based on the time series of each state variable, phase plane trajectory diagrams, Poincaré section diagrams, bifurcation diagrams, and Lyapunov exponent diagrams are plotted. The correlation between resonance parameters and ferromagnetic resonance types is analyzed using these diagrams, generating a table corresponding to resonance parameter types. The electromagnetic voltage transformer's global state sensing method also includes a finite element temperature field analysis step. This step establishes a three-dimensional solid model of the voltage transformer and defines the thermal conductivity, convective heat transfer coefficient, and loss density of the model materials. Based on the loss data in the nonlinear model, the voltage transformer's loss data is loaded into the three-dimensional solid model as a heat source. Finite element temperature field calculations are performed to obtain the voltage transformer's temperature field distribution data. Based on the voltage transformer's temperature field distribution data, the highest temperature point, i.e., the hottest spot, of the voltage transformer is located. The finite element temperature field analysis step also includes changing the primary current value of the voltage transformer in the nonlinear model to obtain loss data under different primary current values. Loss data for different primary current values ​​of voltage transformers were loaded into a three-dimensional solid model, and finite element temperature field calculations were performed to obtain a series of corresponding temperature field distribution data for the voltage transformers. Based on the temperature field distribution data of the corresponding voltage transformers, the mapping relationship between the change of primary current of the voltage transformer and the change of heat generation from voltage transformer losses was analyzed, and a current loss-heat generation coupling relationship table was established.

[0063] In practical implementation, based on the time series of each state variable obtained from the nonlinear model solution, phase plane trajectory diagrams, Poincaré section diagrams, bifurcation diagrams, and Lyapunov exponent diagrams are plotted. The correlation between resonant parameters and ferromagnetic resonance types is analyzed using these diagrams. Specifically, for different combinations of overhead line or cable lengths and voltage transformer excitation characteristic parameters, bifurcation diagrams are generated through calculation. These diagrams use a system parameter, such as power supply voltage, as the abscissa and the amplitude of the voltage transformer primary current as the ordinate. By observing the changes in the distribution of solutions in the bifurcation diagrams, the system's entry into a chaotic state is identified. Critical parameter points and Lyapunov exponent plots are used to quantify the system's sensitivity to initial conditions. When the maximum Lyapunov exponent obtained by calculating the time series is positive, it indicates that the system is in a chaotic state. By comprehensively comparing the closure of the phase plane trajectory plot under different parameter combinations, the distribution structure of points on the Poincaré section plot, the bifurcation points of the bifurcation plot, and the sign and value of the Lyapunov exponent, the resonance parameters are associated with the ferromagnetic resonance type. Finally, a resonance parameter type correspondence table is generated. This table stores, in the form of a data dictionary, the markings of fundamental frequency resonance, low frequency resonance, or high frequency resonance modes corresponding to a specific range of capacitance to ground and a specific combination of excitation curve parameters.

[0064] In some embodiments, a finite element temperature field analysis step is performed to establish a three-dimensional solid model of the voltage transformer. This model includes the transformer's core, windings, insulation materials, and shell structure, and defines the thermal conductivity, convective heat transfer coefficient, and loss density of the model materials. The thermal conductivity and convective heat transfer coefficient are set based on material properties and boundary conditions. In a specific implementation, loss data of the voltage transformer is loaded into the three-dimensional solid model as a heat source based on loss data from the nonlinear model. This loss data includes core loss data and winding loss data. Core loss data is calculated based on mathematical functions of the voltage transformer's primary current and transient overvoltage derived from the nonlinear model, combined with the loss characteristics of the ferromagnetic material. Winding loss data is calculated using mathematical functions of the voltage transformer's primary current and the winding's DC resistance. Finite element temperature field calculations are performed to solve the heat conduction equation and convective boundary conditions, obtaining the steady-state or transient temperature field distribution data of the voltage transformer under set operating conditions. Based on the temperature field distribution data of the voltage transformer, the highest temperature point of the voltage transformer, i.e. the hottest point, is located by traversing the temperature values ​​of the finite element mesh nodes. This point usually appears on the inner side of the winding or in a local part of the core.

[0065] It is understandable that the finite element temperature field analysis process also includes changing the primary current value of the voltage transformer in the nonlinear model, for example, simulating different operating states from rated current to overcurrent, obtaining loss data under different primary current values ​​of the voltage transformer, loading the loss data under different primary current values ​​of the voltage transformer into the three-dimensional solid model, and performing a series of finite element temperature field calculations to obtain a series of corresponding voltage transformer temperature field distribution data. Based on the series of corresponding voltage transformer temperature field distribution data, the mapping relationship between the change of the primary current of the voltage transformer and the change of the heat generation of the voltage transformer loss is analyzed. The heat generation of the voltage transformer loss can be characterized by integrating the total loss of the model or directly extracting the temperature of the hottest spot. A current loss-heat generation coupling relationship table is established, which records the correspondence between the effective value of the primary current of the voltage transformer, the corresponding total loss value, and the hottest spot temperature value. One expression reflecting the relationship between the primary current of the voltage transformer and the core loss power density is as follows:

[0066]

[0067] in: This represents the power loss density per unit volume of the iron core. Indicates the frequency of the excitation current. This represents the amplitude of the magnetic flux density in the iron core, derived from the mathematical functions of the primary current and transient overvoltage of the voltage transformer. , , A coefficient characterizing the hysteresis loss properties. This is a coefficient characterizing the eddy current loss properties.

[0068] In one embodiment of the present invention, see [reference] Figure 3 This process involves obtaining the primary current time series and transient overvoltage time series of the voltage transformer from the time series of various state quantities to identify the ferroresonant type. Phase space reconstruction is then performed on both the primary current and transient overvoltage time series to construct the primary current reconstruction sequence and the transient overvoltage reconstruction sequence, respectively. Nonlinear features, including correlation dimension and maximum Lyapunov exponent, are extracted from these sequences. The extracted nonlinear features are then compared with a resonance parameter type correspondence table to identify the types of low-frequency ferroresonant overvoltage, fundamental-frequency ferroresonant overvoltage, and high-frequency ferroresonant overvoltage.

[0069] In specific implementation, the ferromagnetic resonance type identification step obtains the voltage transformer primary current time series and voltage transformer transient overvoltage time series from the time series of each state quantity. These time series originate from the simulation output of the nonlinear model establishment step or the real-time data acquired in the online monitoring and updating step. The time series data records the instantaneous values ​​of the voltage transformer primary current and transient overvoltage at fixed sampling intervals. In some embodiments, phase space reconstruction is performed on the voltage transformer primary current time series and voltage transformer transient overvoltage time series respectively, constructing the voltage transformer primary current reconstruction sequence and the voltage transformer transient overvoltage reconstruction sequence. The phase space reconstruction process maps the one-dimensional time series to a high-dimensional phase space to recover the dynamic characteristics of the system. For a discrete time series of length N {x1,x2,...,...} After reconstruction, a trajectory matrix Y is obtained, where each row vector represents a point in the phase space. Nonlinear features are extracted from the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer. These nonlinear features include the correlation dimension and the maximum Lyapunov exponent. The correlation dimension is used to quantify the geometric complexity of the system attractor, and the maximum Lyapunov exponent is used to characterize the divergence rate of the system trajectory, i.e., its sensitivity to initial conditions.

[0070] It is understandable that the calculation of the correlation dimension is based on the correlation integral, which measures the probability that the distance between a pair of points in the phase space is less than a given radius. For the reconstructed phase space trajectory Y, the correlation integral C(ε) is expressed as follows:

[0071]

[0072] in: Indicates the integral related to the relationship. Indicates a given distance radius. This represents the total number of trajectory points in the reconstructed phase space. and Let i and j be the vectors of the i-th and j-th points in the reconstructed phase space, respectively. This is the Herveside step function. The function value is 1 when the value inside the parentheses is greater than or equal to 0, and 0 otherwise. This indicates the calculation of the Euclidean distance between two points. The correlation dimension D is defined as the distance between two points when the radius is... As it approaches 0, the correlation integral and The slope of the linear portion of the double logarithmic relationship curve.

[0073] In some embodiments, the extracted correlation dimension and the nonlinear characteristic of the maximum Lyapunov exponent are compared with a resonance parameter type correspondence table. The resonance parameter type correspondence table stores the typical value range of the correlation dimension and the typical value range of the maximum Lyapunov exponent under different ferromagnetic resonance types. The ferromagnetic resonance overvoltage type is identified by determining which type of numerical range the extracted correlation dimension value and the maximum Lyapunov exponent value fall into. The identified types include low-frequency ferromagnetic resonance overvoltage, fundamental frequency ferromagnetic resonance overvoltage, and high-frequency ferromagnetic resonance overvoltage.

[0074] In one embodiment of the present invention, phase space reconstruction is performed on the primary current time series and the transient overvoltage time series of the voltage transformer, respectively, to construct the primary current reconstruction sequence and the transient overvoltage reconstruction sequence. For the primary current time series, the optimal delay time is determined using the mutual information method, and the optimal embedding dimension is determined using the spurious nearest neighbor method. The primary current time series is then reconstructed using phase space based on the optimal delay time and the optimal embedding dimension to obtain the primary current reconstruction sequence. For the transient overvoltage time series, the optimal delay time is determined using the mutual information method, and the optimal embedding dimension is determined using the spurious nearest neighbor method. The transient overvoltage time series is then reconstructed using phase space based on the optimal delay time and the optimal embedding dimension to obtain the transient overvoltage reconstruction sequence.

[0075] In the specific implementation, phase space reconstruction is performed on the primary current time series and the transient overvoltage time series of the voltage transformer to construct the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer, respectively. This process includes parallel processing for the two independent time series. For the primary current time series, the mutual information method is used to determine the optimal delay time. The mutual information method evaluates the statistical dependence between the original time series and its delayed version by calculating the mutual information. The delay time corresponding to the first local minimum or a decrease to a certain proportion of the initial value of the mutual information is selected as the optimal delay time τ. This process ensures that the coordinate components in the reconstructed phase space have independent characteristics. Subsequently, the false nearest neighbor method is used to determine the optimal embedding dimension. The false nearest neighbor method determines the minimum dimension sufficient to unfold the attractor by examining the change in the proportion of "false" neighbors in the original neighbor relationship when the phase space embedding dimension increases from d to d+1. The dimension corresponding to the false nearest neighbor proportion being lower than a set threshold is determined as the optimal embedding dimension m.

[0076] In some embodiments, the primary current time series of a voltage transformer is reconstructed in phase space based on the optimal delay time τ and the optimal embedding dimension m to obtain the reconstructed primary current sequence of the voltage transformer. Similarly, the mutual information method is used to determine the optimal delay time for the transient overvoltage time series of the voltage transformer, and the spurious nearest neighbor method is used to determine its optimal embedding dimension. Since the transient overvoltage time series and the primary current time series of the voltage transformer have different dynamic characteristics, the optimal delay time and optimal embedding dimension obtained through independent calculations usually have different values. The phase space of the transient overvoltage time series of the voltage transformer is reconstructed based on the optimal delay time and optimal embedding dimension calculated for the transient overvoltage time series to obtain the reconstructed transient overvoltage sequence of the voltage transformer. The reconstruction logic is consistent with that of the primary current time series of the voltage transformer.

[0077] Understandably, in the spurious nearest neighbor method, determining whether a neighbor is a "spurious" neighbor relies on calculating the rate of change of distance. One judgment rule involves comparing the magnitude of the change in distance between two neighbors before and after the increase in embedding dimension, expressed as follows:

[0078]

[0079] in: Let represent the vector at the k-th point in the phase space of embedding dimension d. This represents the vector of its nearest neighbor in d-dimensional space. and These represent the point vectors after the embedding dimension is increased to d+1. Denotes the Euclidean norm. This is a pre-defined distance ratio threshold. When the above inequality holds, the neighbor is considered a false nearest neighbor. The optimal embedding dimension can be determined by systematically increasing the embedding dimension *d* and calculating the proportion of false nearest neighbors. Optionally, the mutual information method involves estimating the joint probability distribution and marginal probability distribution, typically using histogram methods or kernel density estimation to obtain probability distribution information from time series data.

[0080] In one embodiment of the present invention, the extracted correlation dimension and maximum Lyapunov exponent are compared with a resonance parameter type correspondence table to identify low-frequency ferroresonant overvoltage, fundamental frequency ferroresonant overvoltage, and high-frequency ferroresonant overvoltage types. The extracted correlation dimension and maximum Lyapunov exponent are then compared with the low-frequency resonance mode correlation dimension range and the low-frequency resonance mode maximum Lyapunov exponent range stored in the resonance parameter type correspondence table. If both fall within the corresponding range, it is determined to be a low-frequency ferroresonant overvoltage type. The extracted correlation dimension and maximum Lyapunov exponent are then compared with the fundamental frequency resonance mode correlation dimension range and the fundamental frequency resonance mode maximum Lyapunov exponent range stored in the resonance parameter type correspondence table. If both fall within the corresponding range, it is determined to be a fundamental frequency ferroresonant overvoltage type. The extracted correlation dimension and maximum Lyapunov exponent are then compared with the high-frequency resonance mode correlation dimension range and the high-frequency resonance mode maximum Lyapunov exponent range stored in the resonance parameter type correspondence table.

[0081] In specific implementation, the extracted correlation dimension and maximum Lyapunov exponent nonlinear characteristic quantities are compared with a resonance parameter type correspondence table. This table is a pre-generated data mapping structure that stores typical numerical ranges of the correlation dimension and maximum Lyapunov exponent for different ferromagnetic resonant overvoltage types. By comparing the correlation dimension values ​​and maximum Lyapunov exponent values ​​obtained through real-time calculation or offline analysis with the predefined ranges in the resonance parameter type correspondence table, pattern recognition of the ferromagnetic resonant overvoltage type is completed. In some embodiments, the comparison process is executed in the form of logical judgment. The extracted correlation dimension and maximum Lyapunov exponent are compared one by one with the low-frequency resonant mode correlation dimension range and low-frequency resonant mode maximum Lyapunov exponent range stored in the resonance parameter type correspondence table. If the correlation dimension value falls between the lower and upper limits of the low-frequency resonant mode correlation dimension range, and the maximum Lyapunov exponent value falls between the lower and upper limits of the low-frequency resonant mode maximum Lyapunov exponent range, then the state reflected by the current data is determined to be a low-frequency ferromagnetic resonant overvoltage type. It is understandable that the determination of the type of fundamental frequency ferroresonant overvoltage and the type of high frequency ferroresonant overvoltage follows the same logic, that is, the extracted correlation dimension and the maximum Lyapunov exponent are compared with the correlation dimension range and the maximum Lyapunov exponent range defined for the fundamental frequency resonance mode and the high frequency resonance mode respectively in the resonance parameter type correspondence table. Only when the values ​​of the two characteristic quantities fall within the range of the two characteristic quantities corresponding to a certain mode can the type of the mode be determined.

[0082] In some embodiments, the range boundary of the resonance parameter type correspondence table can be set based on the statistical results of historical simulation data and theoretical analysis. One way to express the degree of closeness between the calculated value and the range boundary to assist in the determination is as follows:

[0083]

[0084] in: Indicates the current correlation dimension With the center value of a certain resonant mode The degree of closeness, This represents the actual calculated value of the correlation dimension extracted from the primary current reconstruction sequence or the transient overvoltage reconstruction sequence of the voltage transformer. This represents the center value of the associated dimension range defined for a specific resonance mode in the table corresponding to the resonance parameter type. This represents the radius of the range of the associated dimension of the resonance mode. When the value of a feature quantity is exactly at the boundary of the range, a comprehensive score of multiple features or a combination of other auxiliary features can be used for determination. Optionally, the resonance parameter type correspondence table can be stored and retrieved in the form of a data table. See Table 1, which shows a simplified structure of a resonance parameter type correspondence table.

[0085] Table 1: Correspondence Table of Resonance Parameter Types

[0086]

[0087] Optionally, when performing a collaborative comparison between the extracted correlation dimension and the maximum Lyapunov exponent and the resonance parameter type correspondence table, if one of the features in the correlation dimension and the maximum Lyapunov exponent does not fall into any predefined range, or if the two features fall into the ranges corresponding to different modes, then an "undetermined type" or "mixed feature" flag will be output, and further analysis or an alarm will be triggered.

[0088] See Figure 4In the feature extraction and identification stage of ferromagnetic resonance type identification, this figure presents the distribution patterns of resonance characteristic quantities (correlation dimension D, maximum Lyapunov exponent λ) under different fault scenarios. Specifically, a feature distribution space is constructed with the correlation dimension D as the horizontal axis and the maximum Lyapunov exponent λ as the vertical axis. Based on the resonance parameter type correspondence table, low-frequency, fundamental-frequency, and high-frequency regions are divided: the low-frequency region corresponds to 1.2≤D≤1.8 and 0.05≤λ≤0.15; the fundamental-frequency region corresponds to 2.1≤D≤2.9 and 0.18≤λ≤0.35; and the high-frequency region corresponds to 3.5≤D≤4.5 and 0.40≤λ≤0.70. Different colored nodes in the figure represent the corresponding resonance types: blue nodes (low-frequency ferromagnetic resonance overvoltage) are concentrated in the low-frequency region, yellow nodes (fundamental-frequency ferromagnetic resonance overvoltage) are distributed in the fundamental-frequency region, red nodes (high-frequency ferromagnetic resonance overvoltage) are distributed in the high-frequency region, and gray nodes are "undefined type" samples that do not fall within the predefined range. This distribution intuitively reflects the clustering characteristics of nonlinear characteristic quantities of different ferromagnetic resonance types. The resonance type can be accurately identified through the synergistic comparison of characteristic quantities and regional ranges.

[0089] In one embodiment of the present invention, the integrated state perception step integrates the mathematical functions of the primary current and transient overvoltage of the voltage transformer output by the nonlinear model, the temperature data of the hottest spot of the voltage transformer in the current loss-heating coupling relationship table, and the identified ferroresonant overvoltage type. Based on the integrated data, a comprehensive state perception report reflecting the electrical, thermal, and resonant states of the electromagnetic voltage transformer is generated. The online monitoring and updating step collects the primary current and overvoltage data of the operating electromagnetic voltage transformer in real time to form an online monitoring time series. The online monitoring time series is input to the ferroresonant overvoltage type identification step for real-time ferroresonant overvoltage type identification. The data in the current loss-heating coupling relationship table is updated using the loss data corresponding to the online monitoring time series. The real-time identified ferroresonant overvoltage type, the updated current loss-heating coupling relationship table data, and the online monitored primary current and overvoltage data of the voltage transformer are fused into the comprehensive state perception report to achieve dynamic updating of the perception report.

[0090] In practical implementation, the integrated state perception step integrates the mathematical functions of the primary current and transient overvoltage of the voltage transformer output by the nonlinear model, the hottest spot temperature data of the voltage transformer in the current loss and heat generation coupling relationship table, and the identified ferroresonant overvoltage type. The mathematical function of the primary current of the voltage transformer output by the nonlinear model describes the analytical relationship between current and time under specific operating conditions, the mathematical function of the transient overvoltage of the voltage transformer describes the analytical relationship between overvoltage and time, the current loss and heat generation coupling relationship table provides the corresponding hottest spot temperature values ​​under different effective current values, and the identified ferroresonant overvoltage type is input in the form of type label. Based on the integrated data, a full-domain state perception report reflecting the electrical state, thermal state, and resonant state of the electromagnetic voltage transformer is generated. The full-domain state perception report is presented in the form of a structured document, including the waveform characteristic parameters of the primary current of the voltage transformer, the amplitude and duration of the transient overvoltage of the voltage transformer, the hottest spot temperature value and its location information, the current ferroresonant overvoltage type classification results, and a summary of the correlation analysis between various state quantities.

[0091] In some embodiments, the online monitoring and updating step collects primary current and overvoltage data of the operating electromagnetic voltage transformer in real time to form an online monitoring time series. The acquisition process is achieved through current and voltage sensors installed on the primary side of the voltage transformer. The data is continuously recorded at a fixed sampling frequency and forms equally spaced time series data blocks. The online monitoring time series is input to the ferroresonant type identification step for real-time ferroresonant overvoltage type identification. The ferroresonant type identification step performs phase space reconstruction, nonlinear feature extraction, and comparison with the resonance parameter type correspondence table on the input time series data, and outputs the real-time identified ferroresonant overvoltage type label. The data in the current loss-heating coupling relationship table is updated using the loss data corresponding to the online monitoring time series. The loss data is derived from the loss calculation relationship in the nonlinear model based on the primary current time series of the voltage transformer monitored online. The newly obtained effective current value and the correspondence between the hottest spot temperature are added to the current loss-heating coupling relationship table or used to correct the data in the original relationship table. In practical implementation, the nonlinear model is specifically implemented by using the established mathematical function relationship between the primary current and transient overvoltage of the voltage transformer, combined with the loss characteristic parameters of the ferromagnetic material and the DC resistance value of the voltage transformer winding, to calculate the core loss and winding loss from the online monitored primary current time series of the voltage transformer. The core loss is obtained by substituting the primary current time series into the mathematical function of the primary current of the voltage transformer derived from the nonlinear model to obtain the change law of magnetic flux density in the core, and then quantifying it according to the relationship between the hysteresis loss and eddy current loss characteristics of the ferromagnetic material. The winding loss is obtained by calculating the Joule heating effect from the effective value of the primary current time series. The loss data derived in this way is used as the heat source input to update the corresponding mapping relationship between the effective value of the current and the temperature of the hottest spot in the current loss heating coupling relationship table.

[0092] It is understandable that by ferroresonant overvoltage types identified in real time, updated current loss and heating coupling relationship data, and online monitoring data of the voltage transformer's primary current and overvoltage, the dynamic updating of the sensing report can be achieved. The fusion process includes appending newly generated status information to the report's historical record section and recalculating or evaluating the comprehensive status level of the electromagnetic voltage transformer based on the latest data. One expression for characterizing the report's dynamic update time is as follows:

[0093]

[0094] in: This indicates the planned time for the next update of the global state awareness report. Indicates the time when the report was last generated or updated. This indicates the preset online monitoring and data fusion update cycle. The update cycle can be set to a fixed time interval or triggered by an event, depending on the monitoring requirements. Optionally, the dynamically updated global status awareness report can provide historical status trend graphs, which show the changes in the RMS value of the voltage transformer's primary current, the hottest spot temperature, and the type of ferroresonant overvoltage over time.

[0095] See Figure 5 In the analysis of transient characteristics of ferroresonance, the time-domain waveforms of transient overvoltages corresponding to three ferroresonance types—low frequency, fundamental frequency, and high frequency—are presented. Specifically, the horizontal axis represents time (in seconds), and the vertical axis represents transient overvoltage (per unit, pu). Different colored curves correspond to low-frequency (yellow), fundamental-frequency (red), and high-frequency (purple) ferroresonance modes, respectively: the high-frequency ferroresonance overvoltage waveform exhibits high-frequency oscillation characteristics, with the amplitude rapidly climbing to a peak of approximately 3 p.u. in the initial stage (around 1 second); the fundamental-frequency ferroresonance overvoltage waveform has an oscillation frequency close to the system's fundamental frequency, with the amplitude fluctuating stably between 1 p.u. and 1.5 pu; the low-frequency ferroresonance overvoltage waveform exhibits low-frequency fluctuation characteristics, with the amplitude periodically changing around 0 p.u., and a maximum fluctuation range of approximately ±2 p.u. The differences in waveforms intuitively reflect the amplitude, frequency, and fluctuation characteristics of transient overvoltages under different resonance types, providing an intuitive basis for subsequent resonance type identification based on time-domain characteristics.

[0096] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0097] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for global state sensing of an electromagnetic voltage transformer, characterized in that, The method includes: The steps for establishing a nonlinear model include the following: A ferromagnetic resonant electromagnetic transient model was built based on electromagnetic transient simulation software. Using the aforementioned ferroresonant electromagnetic transient model, the ferroresonant phenomenon under single-phase grounding fault, two-phase grounding fault, phase-to-phase short-circuit fault, and asynchronous switching fault is simulated to obtain phenomenon data reflecting the ferroresonant phenomenon. Based on the aforementioned phenomenon data, the influence of four types of factors on the primary current and transient overvoltage of the voltage transformer is investigated: the capacitance to ground corresponding to the overhead line, the capacitance to ground corresponding to the cable length, the excitation characteristic curve of the voltage transformer, and the DC resistance of the voltage transformer. The influence law data is obtained. Using the aforementioned data on the influence patterns as input, a comprehensive solution method is used to obtain the time series of each state variable. The comprehensive solution method includes a programming calculation method, a system structure diagram calculation method, and an electromagnetic transient software simulation method. Based on the time series of the various state quantities, a nonlinear model that takes into account losses and does not depend on the precise resonant circuit parameters is derived, and mathematical functions of the primary current and transient overvoltage of the voltage transformer are derived based on the nonlinear model.

2. The method for global state sensing of an electromagnetic voltage transformer according to claim 1, characterized in that, After obtaining the time series of each state variable using the comprehensive solution method, the following steps are also included: Based on the time series of each state variable, draw the phase plane trajectory diagram, Poincaré section diagram, bifurcation diagram and Lyapunov exponent diagram; By analyzing the phase plane trajectory diagram, Poincaré section diagram, bifurcation diagram, and Lyapunov exponent diagram, the correlation between resonance parameters and ferromagnetic resonance types is analyzed, and a table of resonance parameter type correspondences is generated.

3. The method for global state sensing of an electromagnetic voltage transformer according to claim 2, characterized in that, The electromagnetic voltage transformer global state sensing method further includes a finite element temperature field analysis step; the finite element temperature field analysis step includes the following steps: Establish a three-dimensional solid model of the voltage transformer, and define the thermal conductivity, convective heat transfer coefficient and loss density of the material of the three-dimensional solid model; Based on the loss data in the nonlinear model, the loss data of the voltage transformer is loaded into the three-dimensional solid model as a heat source; The loss data includes core loss data and winding loss data. Perform finite element temperature field calculations to obtain the temperature field distribution data of the voltage transformer; Based on the temperature field distribution data of the voltage transformer, the highest temperature point of the voltage transformer, i.e., the hottest point, is located.

4. The method for global state sensing of an electromagnetic voltage transformer according to claim 3, characterized in that, The steps for performing finite element temperature field analysis also include the following: By changing the value of the primary current of the voltage transformer in the nonlinear model, loss data under different values ​​of the primary current of the voltage transformer can be obtained. Loss data of different voltage transformer primary current values ​​are loaded into the three-dimensional solid model, and finite element temperature field calculation is performed to obtain a series of corresponding voltage transformer temperature field distribution data. Based on the temperature field distribution data of the corresponding series of voltage transformers, the mapping relationship between the change of primary current of the voltage transformer and the change of heat loss of the voltage transformer is analyzed, and a table of coupling relationship between current loss and heat generation is established.

5. The method for global state sensing of an electromagnetic voltage transformer according to claim 4, characterized in that, The electromagnetic voltage transformer global state sensing method further includes a step of identifying the ferromagnetic resonance type; the step of identifying the ferromagnetic resonance type includes the following steps: Obtain the voltage transformer primary current time series and voltage transformer transient overvoltage time series from the time series of each state quantity; Phase space reconstruction is performed on the primary current time series and the transient overvoltage time series of the voltage transformer, respectively, to construct the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer; Extract nonlinear features from the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer. The nonlinear features include the correlation dimension and the maximum Lyapunov exponent. The extracted nonlinear features are compared with the corresponding table of resonance parameter types to identify the types of low-frequency ferromagnetic resonant overvoltage, fundamental frequency ferromagnetic resonant overvoltage, and high-frequency ferromagnetic resonant overvoltage.

6. The method for global state sensing of an electromagnetic voltage transformer according to claim 5, characterized in that, The step of performing phase space reconstruction on the primary current time series and the transient overvoltage time series of the voltage transformer, respectively, to construct the primary current reconstruction sequence and the transient overvoltage reconstruction sequence of the voltage transformer, includes the following sub-steps: For the time series of primary current of voltage transformer, the mutual information method is used to determine the optimal delay time, and the spurious nearest neighbor method is used to determine the optimal embedding dimension. Based on the optimal delay time and the optimal embedding dimension, the phase space reconstruction of the voltage transformer primary current time series is performed to obtain the voltage transformer primary current reconstruction sequence. For the transient overvoltage time series of voltage transformers, the mutual information method is used to determine the optimal delay time, and the spurious nearest neighbor method is used to determine the optimal embedding dimension. Based on the optimal delay time and the optimal embedding dimension, the transient overvoltage time series of the voltage transformer is reconstructed in phase space to obtain the transient overvoltage reconstruction sequence of the voltage transformer.

7. The method for global state sensing of an electromagnetic voltage transformer according to claim 5, characterized in that, The extracted nonlinear feature quantities are compared with the resonance parameter type correspondence table to identify the types of low-frequency ferromagnetic resonance overvoltage, fundamental frequency ferromagnetic resonance overvoltage, and high-frequency ferromagnetic resonance overvoltage, specifically including: The extracted correlation dimension and maximum Lyapunov exponent are compared with the range of correlation dimension and range of maximum Lyapunov exponent of low-frequency resonance modes stored in the resonance parameter type correspondence table. If all fall within the corresponding range, it is determined to be a low-frequency ferroresonant overvoltage type. The extracted correlation dimension and maximum Lyapunov exponent are compared with the range of correlation dimension and range of maximum Lyapunov exponent of fundamental frequency resonant mode stored in the resonant parameter type correspondence table. If all fall within the corresponding range, it is determined to be a fundamental frequency ferroresonant overvoltage type; The extracted correlation dimension and maximum Lyapunov exponent are compared with the range of correlation dimension and range of maximum Lyapunov exponent of high-frequency resonance modes stored in the resonance parameter type correspondence table. If all fall within the corresponding range, it is determined to be a high-frequency ferroresonant overvoltage type.

8. The method for global state sensing of an electromagnetic voltage transformer according to claim 5, characterized in that, Following the step of identifying the ferromagnetic resonance type, a comprehensive state perception step is also included; the comprehensive state perception step includes the following steps: The mathematical functions of the primary current and transient overvoltage of the voltage transformer output by the nonlinear model are integrated, along with the temperature data of the hottest spot of the voltage transformer in the current loss and heat generation coupling relationship table, and the identified ferroresonant overvoltage type. Based on the integrated data, a comprehensive status awareness report reflecting the electrical, thermal, and resonant states of the electromagnetic voltage transformer is generated.

9. A method for global state sensing of an electromagnetic voltage transformer according to claim 8, characterized in that, The electromagnetic voltage transformer global state sensing method further includes an online monitoring and updating step; the online monitoring and updating step includes the following steps: Real-time acquisition of primary current and overvoltage data from operating electromagnetic voltage transformers to form an online monitoring time series; The online monitoring time series is input into the step of identifying the ferromagnetic resonance type to perform real-time ferromagnetic resonance overvoltage type identification; The data in the current loss and heat generation coupling relationship table is updated using the loss data corresponding to the online monitoring time series. The real-time identified ferroresonant overvoltage type, the updated current loss and heating coupling relationship table data, and the online monitored voltage transformer primary current and overvoltage data are integrated into the global status perception report to achieve dynamic updates of the perception report.

10. A global state sensing system for an electromagnetic voltage transformer, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the electromagnetic voltage transformer global state sensing method according to any one of claims 1 to 9.

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