Transmission line bus resonance band effect path aggregation impedance analysis method

Abstract

The invention relates to the technical field of power transmission, and discloses a transmission line bus resonance band effect path aggregation impedance analysis method, which comprises the following steps of S1, establishing a frequency impedance model for each path in a transmission line bus; s2, constructing a coupling impedance tensor to express the coupling effect between the paths; s3, according to the coupling impedance tensor, the spectral radius of the transmission line bus is calculated; s4, identifying the resonance band frequency band of the transmission line bus based on the change of the spectral radius of the transmission line bus; s5, generating equivalent impedance of path aggregation; and S6, outputting a frequency response spectrogram. According to the method, the spectral radius is calculated by establishing the frequency impedance model and combining the coupling impedance tensor and the complex impedance matrix, accurate recognition of the frequency band of the branching resonance band in the transmission line bus is achieved, complex impedance changes of multiple lines in the resonance frequency band can be captured, and then the accuracy and response speed of decentralized control over the bus are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power transmission, in particular to a transmission line bus resonance band effect path aggregation impedance analysis method. BACKGROUND

[0002] In the power transmission system, the performance of the transmission line bus is crucial to the stability of the system. However, the resonance band phenomenon of the transmission line often leads to a sharp change in impedance, which can cause excessive gain or increased reflection in signal transmission, thereby affecting the stability and performance of the entire system. In the prior art, although some methods attempt to deal with the resonance band problem through traditional impedance matching or frequency adjustment, these methods often cannot provide accurate solutions due to the inability to accurately identify and quantify the coupling effect in the resonance band frequency range, resulting in a significant performance bottleneck.

[0003] Traditional resonance band analysis methods mostly use static impedance modeling or linear frequency scanning to identify the response characteristics of the bus system. However, since these methods are based on discrete calculations at pre-set frequency points, they cannot accurately capture the system-level resonance phenomenon caused by the interaction of each path, resulting in a large error in identifying the resonance frequency range, which further affects the dispersion control of the transmission bus and system stability. SUMMARY

[0004] To overcome the shortcomings of the prior art, the present application provides a transmission line bus resonance band effect path aggregation impedance analysis method, which solves the problem of the prior art that cannot accurately capture the system-level resonance phenomenon caused by the interaction of each path, resulting in a large error in identifying the resonance frequency range, which further affects the dispersion control of the transmission bus and system stability.

[0005] To achieve the above purpose, the present application is implemented by the following technical scheme: a transmission line bus resonance band effect path aggregation impedance analysis method, comprising the following steps:

[0006] Step S1, a frequency impedance model is established for each path in the transmission line bus to represent the impedance of each path;

[0007] Step S2, based on the impedance of each path, a coupling impedance tensor is constructed to represent the coupling effect between each path;

[0008] Step S3, according to the coupling impedance tensor, the spectral radius of the transmission line bus is calculated;

[0009] Step S4, based on the change of the spectral radius of the transmission line bus, the resonance band frequency range of the transmission line bus is identified;

[0010] Step S5, based on the identified resonance band frequency range, an equivalent impedance of path aggregation is generated;

[0011] Step S6, outputting a frequency response spectrum of the equivalent impedance of the path aggregation.

[0012] Preferably, in the step S1, the impedance of each path includes a resistance part and a reactance part, the resistance part is the DC impedance of the path, and the reactance part is the inductive and capacitive impedance of the path; the frequency impedance model further includes a temperature and humidity coupling model, which is established based on the temperature and humidity of each path in the transmission line bus as input, and is used to add a temperature and humidity coefficient correction term in the frequency impedance model.

[0013] Preferably, in the step S2, the diagonal elements of the coupling impedance tensor are the impedances of each path itself, and the non-diagonal elements are the mutual impedances between each path.

[0014] Preferably, in the step S3, the calculation of the spectral radius of the transmission line bus is based on the coupling impedance tensor as input, and is performed by an eigenvalue decomposition algorithm, the eigenvalue decomposition algorithm includes:

[0015] The coupling impedance tensor is constructed into a complex impedance matrix:

[0016]

[0017] In the formula, z(ω) is a complex impedance matrix; is an n×n matrix in a complex number set; n is the number of paths;

[0018] All eigenvalues λ i (ω) of the complex impedance matrix z(ω) are calculated, and the spectral radius ρ(ω) is obtained, and the calculation formula of the spectral radius ρ(ω) is:

[0019]

[0020] In the formula, λ i (ω) is all eigenvalues of the complex impedance matrix z(ω), and ω is an angular frequency.

[0021] Preferably, the spectral radius of the transmission line bus is the maximum eigenvalue of the coupling impedance tensor, which is used to quantify the coupling gain of the transmission line bus at different frequencies.

[0022] Preferably, in the step S4, in the resonant band frequency range of the transmission line bus, when the change of the spectral radius of the transmission line bus exceeds a preset critical value in a certain frequency range, it is a resonant band.

[0023] Preferably, the judgment standard that the change of the spectral radius of the transmission line bus exceeds the preset critical value is:

[0024] Let the spectral radius be a frequency function ρ(ω), and the critical value be a constant ρ th Then the frequency interval satisfying the following formula is the resonance band:

[0025] ω∈{ω∣ρ(ω)>ρ th};

[0026] In the formula, ω is the angular frequency; {ω∣ρ(ω)>ρ th} is a set, representing a frequency band interval composed of all angular frequency points satisfying the spectral radius exceeding the threshold value, which is the system resonance band.

[0027] Preferably, in the step S5, the equivalent impedance of the path aggregation is obtained by performing principal eigenvector projection on the coupling impedance tensor, and is used to represent the comprehensive impedance response of the identified resonance band frequency range.

[0028] Preferably, the calculation method of performing principal eigenvector projection on the coupling impedance tensor comprises:

[0029] The normalized eigenvector v max corresponding to the maximum modulus value of the complex impedance matrix is obtained agg The calculation formula of the equivalent impedance Z

[0030]

[0031] In the formula, ω is the angular frequency; Z(ω) is the complex impedance matrix at the frequency ω, and the dimension is n×n, where n is the number of paths; v max is the normalized complex eigenvector of the maximum eigenvalue in Z(ω), and the dimension is n×1; is the conjugate transpose of v max , and the dimension is 1×n; Z agg (ω) is the equivalent impedance of path aggregation, representing the principal direction equivalent impedance of the bus coupling response in the resonance band frequency range.

[0032] Preferably, in the step S6, the frequency response spectrum includes the curves of the spectral radius and the equivalent impedance of path aggregation with the frequency, and demarcates the resonance band interval, displays the potential impedance abnormal frequency range, and is used for impedance response and potential risk assessment.

[0033] The application provides a transmission line bus resonance band effect path aggregation impedance analysis method. The application has the following beneficial effects:

[0034] 1、The present application realizes accurate identification of the resonant band of the branch line in the busbar of the transmission line bus by establishing a frequency impedance model for each path in the busbar of the transmission line, combining the coupling impedance tensor and the complex impedance matrix to calculate the spectral radius, and then capturing the complex impedance change of multiple lines in the busbar in the resonant band, realizing more accurate frequency response analysis, thereby significantly improving the accuracy and response speed of subsequent dispersion control of the busbar.

[0035] 2、The present application generates an equivalent impedance of path aggregation, combines it with the change of the spectral radius, and outputs a frequency response spectrum, which can help identify potential abnormal impedance frequency bands, so that abnormal gain and signal distortion in the frequency response can be found and analyzed in time, improving the accuracy and practicality of risk assessment.

[0036] 3、The present application generates an equivalent impedance of path aggregation by projecting the feature vector, which can quantify the coupling response in the resonant band, compared with the traditional method, the prior art is more focused on single-path impedance analysis, while the present application considers the coupling effect between multiple paths, providing a more comprehensive and stable system optimization scheme. This makes the performance of the busbar of the transmission line more stable in complex environments, which helps to improve the stability of distributed control of the busbar in the power transmission system. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The present application is a method flowchart. DETAILED DESCRIPTION

[0038] The technical solutions in the embodiments of the present application will be described in detail below with reference to the drawings in the specification of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0039] In order to better understand the present application, the above content will be described in detail below in combination with specific embodiments.

[0040] Please refer to the accompanying drawings Figure 1 The present application provides a transmission line bus resonant band effect path aggregation impedance analysis method, comprising the following steps:

[0041] Step S1, a frequency impedance model is established for each path in the busbar of the transmission line, which is used to represent the impedance of each path;

[0042] In this embodiment, a frequency impedance model is established for each path in the transmission line bus, and then the electrical impedance of each path is characterized in order to analyze the response of each path in detail in subsequent steps. Specifically, the frequency impedance model takes into account the resistance and reactance parts of the path, which directly affect the signal transmission characteristics.

[0043] Specifically, the impedance of each path includes two main parts:

[0044] Resistance part: This part represents the DC impedance of the path, which is usually caused by the material properties of the transmission line (such as conductor resistance). In the low frequency range, the effect of the resistance part is more significant.

[0045] Reactance part: This part consists of the inductive and capacitive effects of the path, which represent the response of the path to alternating current signals. At higher frequencies, the effect of the reactance part usually becomes more pronounced, especially for inductive and capacitive elements. The reactance part includes impedance representations of inductance and capacitance, expressed as:

[0046] Inductive impedance Z L The formula is expressed as:

[0047] Z L = jωL;

[0048] Capacitive impedance Z C The formula is expressed as:

[0049]

[0050] where j is the imaginary unit, ω is the angular frequency, L and C are the inductance and capacitance values of the path, respectively.

[0051] And after establishing the temperature and humidity coupling model, the influence parameters of temperature and humidity on each path in the bus can be obtained; used to correct the impedance characteristics and coupling behavior of the transmission line bus under different climate conditions. At the same time, the dynamic influence of the transmission environment on the system electrical parameters (such as conductivity, dielectric constant, line loss, etc.) is considered, so that the resonance frequency band identification and frequency response analysis are more close to the actual operating state, and the environmental adaptability and prediction accuracy of the model are improved. The expression formulas of the temperature term and the humidity term are:

[0052] Temperature term:

[0053] R(t) = R0(1 + α(t - t0));

[0054] where R(t) is the resistance value at the current temperature t; R0 is the reference resistance value at the reference temperature t0; α is the temperature coefficient;

[0055] Humidity term:

[0056] C(T) = C0(1 + β(T - T0));

[0057] In the formula, C(T) is the resistance value at the current humidity T; C0is the reference resistance value at the reference humidity T0; β is the temperature coefficient,

[0058] Combining the above resistance part, reactance part, temperature part, humidity part, the total impedance Z of the path can be represented as:

[0059]

[0060] In the formula, Z is the total complex impedance of the busbar path, R(T) is the resistance term containing temperature influence, L is the inductance value of the path, C(T) is the capacitance term containing humidity influence, and ω is the angular frequency. Through the model, the impedance characteristics of each path at different frequencies can be accurately characterized.

[0061] Generally, the frequency response of each path is affected by the combination of resistance, inductance, and capacitance. Therefore, the model should select appropriate resistance, inductance, and capacitance values according to the physical characteristics of the transmission line. In some possible embodiments, the impedance of the path may exhibit a more complex frequency dependence, which requires further electrical analysis methods such as impedance matching and resonance frequency band analysis.

[0062] As an option, the impedance model of the path in different frequency ranges can also be modified or optimized in this embodiment to better adapt to the changes of the transmission line busbar during actual use. For example, some paths may exhibit significant reactance characteristics in a certain frequency band, while the resistance part is more prominent in other frequency bands, and when establishing the frequency impedance model, the temperature and humidity of each path in the transmission busbar are used as input, and a temperature and humidity coupling model is further established to add temperature and humidity coefficient correction terms to the frequency impedance model to avoid the phenomenon of resonance band drift caused by high temperature and high humidity, thereby causing detection errors.

[0063] Specifically, the frequency impedance model in this embodiment not only covers the conventional DC resistance and AC reactance, but also may need to adjust the impedance value according to different transmission line layouts, materials, and structures, as well as temperature and humidity. In addition, the reactance part (including inductance and capacitance) may need to consider different model accuracy and correction coefficients at a certain frequency to more accurately describe the characteristics of the transmission line at high or low frequencies.

[0064] In one possible implementation, the impedance value of each path is further accurately calculated by measuring the geometric parameters of the transmission line busbar and combining electromagnetic field simulation technology. This can be realized by numerical simulation tools such as finite element analysis, and the simulation results will provide the impedance characteristics of each path and provide data support for subsequent steps of analysis.

[0065] Therefore, from the above, it can be clearly understood from the above description that how to establish the frequency impedance model in step S1. The model not only considers the resistance part, but also includes the effects of inductance and capacitance, and is described in detail by mathematical formula. The characteristics of the impedance of each path varying with frequency are fully considered and described to ensure that the resonant band effect of the transmission line bus can be accurately identified and analyzed in the subsequent steps.

[0066] Step S2, based on the impedance of each path, a coupling impedance tensor is constructed to represent the coupling effect between each path.

[0067] In this embodiment, based on the frequency impedance model of each path established in step S1, a coupling impedance tensor is further constructed to represent the coupling effect between each path. The coupling impedance tensor is used to describe the interaction between multiple transmission paths, and can consider the electromagnetic coupling effect between different paths. By constructing the coupling impedance tensor, the mutual impedance relationship between each path can be effectively represented, and data support is provided for subsequent frequency response analysis.

[0068] When constructing the coupling impedance tensor, its structure and composition need to be determined first.

[0069] Specifically, the coupling impedance tensor is a matrix, and its elements reflect the interaction between different paths, especially the coupling effect of impedance.

[0070] The diagonal elements of the matrix correspond to the impedance of each path itself, and the non-diagonal elements represent the mutual impedance between paths. In this way, the electrical characteristics of each path can be coupled with the electrical characteristics of other paths, thereby providing a complete description of the multi-path transmission effect.

[0071] Specifically, assuming that there are n paths, the dimension of the coupling impedance tensor Z is n x n, where the diagonal elements represent the impedance of each path itself, and the non-diagonal elements represent the mutual impedance between different paths. The formula is as follows:

[0072]

[0073] In the formula, Z i is the impedance of the i-th path, and Z ij (i≠j) is the mutual impedance between path i and path j.

[0074] Further, in this embodiment, the calculation of mutual impedance can be performed by considering the electromagnetic field interaction between paths. The mutual impedance between different paths usually depends on the distance between paths, relative position, and electromagnetic wave propagation characteristics. Therefore, when constructing the coupling impedance tensor, the influence of these factors needs to be considered.

[0075] Generally, the mutual impedance Z ij can be represented by the following equation:

[0076] Z ij = f(r ij , ω);

[0077] where r ij is the distance between path i and path j, ω is the angular frequency, and the function f(.) is used to describe the electromagnetic response characteristics of the coupling between paths.

[0078] By constructing the coupling impedance tensor, the coupling effects between different paths can be further analyzed and understood. In some embodiments, the tensor is used for spectral radius analysis, resonance band identification, and other operations, in order to identify potential resonance frequency bands in the frequency response of the transmission line bus.

[0079] In one possible implementation, the coupling impedance tensor not only plays an effective description in the time domain, but is also widely used in frequency domain analysis. For example, when analyzing the frequency response spectrum of the system, the coupling impedance tensor can be used to generate accurate impedance data for each path and its coupling effects, thereby providing in-depth evaluation of the performance of the system.

[0080] Extensions in technical implementation

[0081] In some embodiments, more complex electromagnetic field models can be introduced to accurately model the coupling effects between paths. At the same time, numerical calculation methods such as finite element method (FEM) or boundary element method (BEM) can be used to solve the coupling impedance under complex structures. In addition, the coupling impedance tensor can also be combined with other parameters such as temperature, material properties, geometric parameters, etc., for dynamic adjustment to adapt to changes under different working conditions.

[0082] Finally, by constructing the coupling impedance tensor, the present application effectively solves the problem of coupling effects between multiple paths, providing a powerful mathematical tool for subsequent impedance analysis. In the diagonal elements and non-diagonal elements of the coupling impedance tensor, the self-impedance of the path and the mutual impedance between the paths are described in detail, respectively, thereby ensuring the comprehensiveness and feasibility of the technical solution. In addition, the calculation of mutual impedance and its application in frequency response further enhances the practicality of the technical solution.

[0083] Step S3, a complex impedance matrix is established according to the coupling impedance tensor, and then the spectral radius of the transmission line bus is calculated through the complex impedance matrix;

[0084] In this embodiment, based on the coupling impedance tensor established in step S2, a complex impedance matrix is further constructed for the calculation of the spectral radius. The complex impedance matrix is an important tool for describing the characteristics of the system under frequency response, especially in analyzing the multi-path coupling effect, the complex impedance matrix can accurately quantify the electrical coupling behavior between different paths.

[0085] Specifically, the complex impedance matrix is realized by converting the coupling impedance tensor into a matrix in the complex domain. In this process, the diagonal elements of the coupling impedance tensor still represent the impedance of each path itself, while the off-diagonal elements correspond to the mutual impedance between different paths. These impedance values constitute the basic data of the complex impedance matrix.

[0086] Therefore, based on the formula of the coupling impedance tensor Z in the above steps, the formula of the complex impedance matrix can be obtained as follows:

[0087]

[0088] Therefore, it can be simplified as:

[0089]

[0090] In the formula, z(ω) is the complex impedance matrix; is an n x n matrix in the complex number set; n is the number of paths;

[0091] When the complex impedance matrix z(ω) is constructed, the next step is to calculate the eigenvalues of the complex impedance matrix by the eigenvalue decomposition algorithm, and then obtain the spectral radius. The spectral radius is a key parameter for measuring the stability and coupling gain of the system, which corresponds to the maximum eigenvalue of the complex impedance matrix. Through the spectral radius, the coupling gain of the transmission line bus at different frequencies can be quantified.

[0092] Specifically, the calculation steps of the spectral radius are as follows:

[0093] 1. Eigenvalue decomposition: through the eigenvalue decomposition algorithm, all eigenvalues of the complex impedance matrix are solved. Let the complex impedance matrix be z(ω), and its eigenvalues be λ i (i = 1, 2, …, N), then the eigenvalue decomposition of the matrix can be expressed as:

[0094] z(ω)u i = λ i u i ;

[0095] In the formula, λ i is the i-th eigenvalue, and u i is the corresponding eigenvector.

[0096] 2. Definition of spectral radius: the spectral radius p(ω) is defined as the maximum value of all eigenvalues of the complex impedance matrix, and the calculation formula is:

[0097]

[0098] where λ i (ω) are all eigenvalues of the complex impedance matrix z(ω) and ω is the angular frequency.

[0099] At this time, the spectral radius of the transmission line bus obtained can be used to measure an important indicator of the coupling gain of the system. By calculating the change of the spectral radius at different frequencies, the coupling effect of the transmission line bus in a certain frequency band can be quantified. For example, in some frequency bands, the increase of the spectral radius may mean that the coupling gain of the transmission line bus increases, which may cause signal distortion or interference. Therefore, through the calculation and analysis of the spectral radius, the resonance band and the potential impedance abnormal frequency band of the system can be effectively identified.

[0100] In some embodiments, the calculation result of the spectral radius can also be used to dynamically adjust the system parameters to optimize the coupling characteristics of the transmission line bus. For example, by tracking the trend of the change of the spectral radius in the frequency response, the impedance matching or the appropriate frequency range can be adjusted in real time to improve the stability and performance of the system.

[0101] Extension of the calculation process

[0102] In one possible implementation, more system parameters such as temperature, relative position between paths and material characteristics can be combined to further optimize the construction of the complex impedance matrix and the calculation of the spectral radius. The introduction of these factors can more accurately reflect the electrical behavior of the transmission line bus in actual use, especially in high frequency or complex environment, the coupling effect of the system may be affected by multiple factors.

[0103] Further, the spectral radius of the transmission line bus is successfully calculated by the construction of the complex impedance matrix and the eigenvalue decomposition algorithm in this step. The spectral radius not only can quantify the coupling gain of the system at different frequencies, but also can effectively identify the potential resonance band frequency, thereby providing an important basis for subsequent frequency response analysis. Through reasonable technical implementation, the present application provides an effective solution for describing and analyzing the electrical coupling characteristics of the multi-path transmission system.

[0104] Step S4, identifying the resonance band frequency of the transmission line bus based on the change of the spectral radius of the transmission line bus;

[0105] In this embodiment, based on the spectral radius of the transmission line bus calculated in the foregoing step S3, the resonance band frequency of the transmission line bus can be effectively identified by analyzing the change of the spectral radius in the frequency domain. The change of the spectral radius is a key indicator for measuring the coupling gain and stability of the system, and the resonance band frequency is a frequency band in which the transmission line bus exhibits significant electrical coupling characteristics in a certain frequency range.

[0106] In some embodiments, the identification criterion for the resonant band is based on comparing the variation of the spectral radius with a pre-set threshold value. When the spectral radius of the transmission line bus experiences a sudden change or exceeds the pre-set threshold value in a certain frequency range, it can be determined that the frequency range is the resonant band. Specifically, assuming the spectral radius as a function of frequency is ρ(ω), and setting the threshold value as a constant ρ th , then the frequency interval that satisfies the following condition is the resonant band of the system:

[0107] ω∈{ω∣ρ(ω)>ρ th};

[0108] In the formula, ω is the angular frequency; {ω∣ρ(ω)>ρ th} is a set, representing the frequency range composed of all angular frequency points that satisfy the spectral radius exceeding the threshold value, which is the resonant band of the system.

[0109] In a specific embodiment, the calculation method of the resonant band frequency range

[0110] In this embodiment, first, the frequency response function ρ(ω) is obtained through the calculation of the spectral radius, and then based on the pre-set threshold value ρ th , the spectral radius is detected point by point. If the change of the spectral radius exceeds the threshold value in a certain frequency range, it can be determined that the interval is the resonant band. The specific calculation method can be carried out through the following steps:

[0111] Frequency scanning: select an angular frequency range ω start to ω end , calculate each frequency point ω in the range.

[0112] Spectral radius and threshold value comparison: for each frequency point, calculate the spectral radius ρ(ω) and compare it with the set threshold value ρ th .

[0113] Resonant band identification: when the spectral radius of a plurality of consecutive frequency points exceeds the threshold value, it is determined that the frequency range is the resonant band. The start and end frequencies of the frequency range, i.e. the boundaries of the resonant band, can be further determined.

[0114] For example, in some embodiments, if the spectral radius ρ(ω) in a certain frequency range is greater than the set threshold value ρ th and the duration of the frequency range is long, it can be further confirmed that the frequency range is the resonant band of the system.

[0115] Further expansion of resonant band identification

[0116] In another possible implementation, identifying the resonance band of the transmission line bus can also take into account more physical factors, such as the geometry of the transmission line, the ambient temperature, the electromagnetic properties of the material, etc. Changes in these factors can affect the change in spectral radius, so when identifying the resonance band, the correction of these factors in the frequency calculation can be considered.

[0117] Application of identifying the resonance band

[0118] Identifying the resonance band of the transmission line bus is of great significance to practical applications. In some embodiments, by accurately identifying the resonance band, excessive gain of the transmission line in the resonance frequency band can be effectively avoided, thereby reducing signal distortion and interference in the system. Especially in high-frequency transmission systems, resonance bands often lead to unstable transmission behavior, so accurate identification and adjustment of these frequency bands are crucial to optimizing system performance.

[0119] Therefore, the present embodiment identifies the resonance band frequency range of the transmission line bus based on the change in spectral radius, and further judges the start and end frequency range of the resonance band by comparing the spectral radius with the preset critical value. This method not only helps to identify the resonance characteristics of the system in frequency response analysis, but also provides an important basis for the optimization of the transmission line bus;

[0120] In another embodiment, in step 4 of the embodiment, the critical value ρ th is a fixed constant used to judge the change in spectral radius to identify the resonance band frequency range. However, in actual operating environments, system load and external interference factors have strong dynamics, and a fixed threshold value is prone to misjudgment or omission, especially in scenarios with significant load fluctuations, where accuracy is significantly reduced. Therefore, the present application further optimizes the scheme by expanding the original fixed critical value to a dynamic threshold mechanism.

[0121] After optimization, the following dynamic threshold formula is used for judgment:

[0122] ρ th (t) = μ(ρ) + k·σ(ρ);

[0123] where ρ th (t) is the critical value at the current time t; μ(ρ) is the historical spectral radius mean; k is an adaptive coefficient (dynamically adjusted according to system stability requirements); σ(ρ) is the standard deviation.

[0124] Therefore, by introducing this dynamic threshold mechanism, it can more effectively adapt to changes in actual working conditions, significantly reduce the resonance band identification error caused by abnormal fluctuations in spectral radius due to system load fluctuations or interference, improve the discrimination robustness and reliability of the model in a dynamic environment, and reduce the resonance band misjudgment rate in load fluctuation scenarios;

[0125] Finally, in another possible implementation:

[0126] The present invention introduces deep learning technology to assist in predicting the trend of spectrum radius changes, so as to further improve the foresight and intelligence level of resonance band identification. Specifically, a prediction model based on long short-term memory network (LSTM) is constructed, and the historical frequency band spectrum radius data sequence ρ is used to predict the change trend of the spectrum radius. (w1) , ρ (w2) ,...,ρ (wn) As input, it outputs the probability distribution of possible resonance bands in the future frequency range.

[0127] The model's network architecture consists of two stacked LSTM layers, each containing 128 neurons. A dropout layer (with a dropout rate of 0.2) is used to prevent overfitting, and a fully connected output layer is connected at the end to generate predictions. The training data is derived from 1,000 sets of measured spectral radius samples of transmission buses under different operating conditions, ensuring the model's good generalization and adaptability to various load conditions.

[0128] Through this deep learning prediction mechanism, the system can predict the risks of potential frequency bands before resonance occurs, thereby intervening in advance, effectively improving the real-time and reliability of resonance band identification, and is particularly suitable for transmission line monitoring and control scenarios in complex dynamic environments.

[0129] Step S5: generating an equivalent impedance of path aggregation based on the identified resonant band frequency band;

[0130] In this embodiment, step S5 further generates an equivalent impedance of the path aggregation based on the resonant band frequency band identified in step 4. The equivalent impedance is obtained by projecting the principal eigenvector of the coupling impedance tensor and is used to represent the comprehensive impedance response of the transmission line bus within the identified resonant band frequency band.

[0131] The equivalent impedance of the path aggregation reflects the coupling characteristics of the system within the resonant band. By performing eigenvalue decomposition on the complex impedance matrix, we can extract the eigenvectors associated with the system's principal coupling directions. Using these principal eigenvectors, we can project the coupling impedance tensor to obtain an equivalent complex impedance that represents the coupling response of the transmission line busbar within the resonant band.

[0132] Specifically, in some embodiments, the calculation of the complex impedance matrix Z(ω) is based on the coupled impedance tensor, so the impedance response in the main direction can be extracted by the normalized eigenvector corresponding to the maximum eigenvalue of the matrix. The equivalent impedance of the path aggregation can be obtained by obtaining the normalized eigenvector v corresponding to the maximum modulus value based on the complex impedance matrix. max , then the equivalent impedance Z of the path aggregation agg (ω) is calculated as:

[0133]

[0134] where ω is the angular frequency; Z(ω) is the complex impedance matrix at frequency ω, with dimension n x n, where n is the number of paths; v max is the normalized complex eigenvector of the largest eigenvalue in Z(ω), with dimension n x 1; is the conjugate transpose of v max , with dimension 1 x n; Z agg (ω) is the equivalent impedance of the path aggregation, representing the dominant direction equivalent impedance of the coupling response of the bus in the resonant band frequency range.

[0135] Moreover, the equivalent impedance of the path aggregation describes the comprehensive impedance characteristics of the coupling response of each path in the bus of the transmission line within a specific resonant band frequency range. Through this equivalent impedance, the coupling effect of the system in this frequency range can be effectively quantified, especially in the resonant frequency range, where the system may exhibit significant gain or loss. Therefore, accurately calculating the equivalent impedance helps to evaluate the performance of the transmission line and avoid excessive gain or interference in certain frequency ranges.

[0136] In some embodiments, the generated equivalent impedance of the path aggregation Z agg (ω) can be used to further optimize the system design, especially in signal transmission, where the resonant frequency range may cause excessive signal gain or distortion. By analyzing the equivalent impedance, designers can adjust system parameters to reduce these undesirable effects. In addition, this equivalent impedance can also be used as a key indicator for system stability analysis to determine whether the coupling gain in different frequency ranges is within a safe range.

[0137] Meanwhile, in another possible implementation, the equivalent impedance of the path aggregation calculation not only considers the principal eigenvector of the complex impedance matrix, but also takes into account the influence of the geometric structure between paths, material properties, and environmental factors on the impedance, thereby further accurately modeling the coupling characteristics of the system. Especially in complex transmission systems, considering these factors will help improve the accuracy of the calculation results and optimize system performance.

[0138] In this way, by projecting the principal eigenvector of the coupling impedance tensor, the equivalent impedance of the path aggregation can be successfully generated. This equivalent impedance not only effectively quantifies the coupling response in the resonant band frequency range, but also provides an important basis for the optimization of the bus of the transmission line. By further combining actual environmental factors and system parameters, this technical solution can be widely applied in the design and optimization of multi-path transmission systems, improving the stability and performance of the system.

[0139] Step S6: Output the frequency response spectrum based on the equivalent impedance of the path aggregation.

[0140] In this embodiment, step S6 shows the curve of the spectral radius and the equivalent impedance of the path aggregation varying with frequency based on the previously generated equivalent impedance of the path aggregation through the frequency response spectrum diagram, and further calibrates the resonance band interval. The frequency response spectrum diagram can display the results, and the coupling characteristics of the system at different frequencies can be displayed, especially to help identify potential impedance abnormal frequency bands, so as to perform risk assessment and optimization design.

[0141] Specifically, the frequency response spectrum diagram not only shows the change of the spectral radius with frequency, but also shows the change of the equivalent impedance of the path aggregation. The different change trends of the two curves in the spectrum diagram reflect the different response characteristics of the system at different frequency bands. The spectral radius curve can display the coupling gain of the system at different frequencies, and the equivalent impedance curve can reflect the comprehensive coupling impedance between the paths in the resonance band frequency band.

[0142] In some embodiments, the frequency response spectrum diagram can be drawn in a numerical calculation or experimental data point manner according to the previously calculated function relationship between the spectral radius and the equivalent impedance of the path aggregation. These data points obtained by frequency scanning will show different trends in the graph. For example, in a certain frequency band, the spectral radius may rise sharply, indicating that the coupling gain in this frequency band increases significantly. The equivalent impedance may change dramatically in this frequency band, which may indicate that the frequency band is in the resonance state of the system.

[0143] In the frequency response spectrum diagram, calibrating the resonance band interval is a key part of this step. The identification of the resonance band is based on the change of the spectral radius. Generally, when the spectral radius changes significantly in a certain frequency band and exceeds a predetermined threshold, the frequency band will be calibrated as a resonance band. At this time, the impedance response in this interval may exhibit instability, resulting in a decrease in signal transmission quality or excessive gain of the system. By clearly calibrating these frequency bands in the spectrum diagram, designers can quickly identify and focus on these potential risk frequency bands.

[0144] Specifically, in the frequency response spectrum diagram, the resonance band interval can be defined by the significant rise of the spectral radius, the sharp change of the impedance, etc. These frequency bands not only show large fluctuations in the graph, but also usually have signal gain or distortion of the system instability. After calibrating these intervals, users can evaluate the risk level of the system in these frequency bands through further analysis means and take corresponding measures for optimization.

[0145] Another important function of the frequency response spectrum is to show potential impedance abnormality frequency bands. Potential impedance abnormalities usually occur at the resonant frequency bands of the system or in the regions where extreme changes appear in the frequency scan. These frequency bands can cause unstable behavior in the signal transmission process, such as increased reflection, signal distortion, or nonlinear effects. Therefore, in the frequency response spectrum, not only the changes in the spectral radius and the equivalent impedance are displayed, but also these potential abnormal frequency bands are highlighted in the graph to facilitate the subsequent optimization work of the designers.

[0146] In some embodiments, the identification of potential impedance abnormality frequency bands not only depends on the change in the spectral radius, but also combines the phase change of the impedance, the amplitude change of the frequency response curve, and other factors. By comprehensively analyzing these factors, the spectrum can more accurately identify the frequency bands that may cause adverse effects in the system and mark and warn these frequency bands as the basis for further analysis and adjustment.

[0147] The ultimate goal of the frequency response spectrum is to evaluate the impedance response and potential risks. By displaying the curves of the spectral radius and the equivalent impedance of the path aggregation changing with frequency, system designers can intuitively see the coupling gain and impedance change in different frequency bands, and better identify the risk points in the system. After identifying potential resonant bands or impedance abnormality frequency bands, designers can take appropriate measures, such as optimizing impedance matching, adjusting transmission line configuration, or using different material properties, to reduce their impact.

[0148] Specifically, the frequency response spectrum can help designers determine whether the resonant frequency bands of the system are in a dangerous frequency range and whether the frequency response needs to be adjusted to avoid excessive gain or instability in the system. For example, in the frequency band where the spectral radius significantly increases, designers can consider adjusting the frequency response of the system to ensure that the system does not cause electrical distortion or performance degradation when operating in these frequency bands.

[0149] As an extended option, this embodiment can also combine different environmental factors, such as temperature changes, electromagnetic interference, etc., to further adjust the calculation method of the frequency response spectrum. Changes in these environmental factors can affect the impedance response of the system, causing changes in the frequency response spectrum. By considering these external factors, the frequency response spectrum can more accurately reflect the performance of the system under actual working conditions.

[0150] Therefore, this embodiment successfully displays the curves of the spectrum radius and the equivalent impedance of the path aggregation as a function of frequency by outputting a frequency response spectrum based on the equivalent impedance of the path aggregation, effectively calibrating the resonant band frequency band. This graph not only helps designers identify potential impedance anomaly frequency bands but also provides intuitive data support for system risk assessment and optimization. This method allows designers to fully understand the coupling characteristics of the system at different frequency bands, allowing them to take appropriate measures to optimize system performance and ensure stable operation.

[0151] In addition, in modern power systems, the busbar is a key node connecting numerous distributed power sources, energy storage units and variable loads, and its stability directly affects the performance of the entire distributed network. The precise frequency response spectrum generated by the present invention plays a vital guiding role in realizing distributed control or decentralized control of the busbar system. The spectrum converts the complex system-level resonance problem caused by multi-path coupling into a clear and quantifiable control target. The various control units in the distributed control system (such as the inverter of the distributed power source) can collaboratively adjust their control parameters (such as the harmonic components or impedance characteristics of the output current) based on the resonance band information identified by the spectrum, actively damp specific dangerous frequency bands, or change the overall response of the system to avoid resonance. This enables the control strategy to change from passive, local adjustment to active, system-level collaborative optimization, thereby effectively suppressing resonance and ensuring the stable and efficient operation of the entire distributed control system.

[0152] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A transmission line bus resonant strip effect path aggregated impedance analysis method, characterized by, The method comprises the following steps: Step S1, establishing a frequency impedance model for each path in the transmission line bus, for representing the impedance of each path; Step S2, constructing a coupling impedance tensor based on the impedance of each path, for representing the coupling effect between each path; Step S3, establishing a complex impedance matrix according to the coupling impedance tensor, and then calculating the spectral radius of the transmission line bus through the complex impedance matrix; Step S4, identifying the resonant band of the transmission line bus based on the change of the spectral radius of the transmission line bus; Step S5, generating an equivalent impedance of path aggregation based on the identified resonant band; Step S6, outputting a frequency response spectrum based on the equivalent impedance of path aggregation.

2. The method of claim 1, wherein, In the step S1, the impedance of each path includes a resistance part and a reactance part, the resistance part is the DC impedance of the path, and the reactance part is the inductance and capacitance impedance of the path; The frequency impedance model further comprises a temperature and humidity coupling model, which is established based on the temperature and humidity of each path in the transmission line bus as input, for adding temperature and humidity coefficient correction terms in the frequency impedance model.

3. The method of claim 1, wherein, In the step S2, the diagonal elements of the coupling impedance tensor are the impedances of each path itself, and the non-diagonal elements are the mutual impedances between each path.

4. The method of claim 1, wherein, In the step S3, the calculation of the spectral radius of the transmission line bus is based on the coupling impedance tensor as input to establish the complex impedance matrix, and then the complex impedance matrix is solved through the eigenvalue decomposition algorithm, which comprises: The coupling impedance tensor is constructed into a complex impedance matrix: where z(ω) is a complex impedance matrix; is an n x n matrix in the set of complex numbers; n is the number of paths; calculating all eigenvalues λ of the complex impedance matrix z(ω) i (ω), i.e. the spectral radius p(ω) is obtained, which is calculated as where λ i (ω) are all eigenvalues of the complex impedance matrix z(ω), and ω is the angular frequency.

5. The method of claim 4, wherein, The spectral radius of the transmission line bus is the maximum eigenvalue of the coupling impedance tensor, for quantifying the coupling gain of the transmission line bus at different frequencies.

6. The method of claim 5, wherein, In the step S4, when the change of the spectral radius of the transmission line bus exceeds a preset critical value in a certain frequency band, it is identified as a resonant band.

7. The method of claim 6, wherein the method further comprises: The judgment standard for the change of the spectral radius of the transmission line bus exceeding the preset critical value is: Let the spectral radius be a frequency function p(ω), and the critical value be a constant p th The frequency interval satisfying the following formula is the resonance band: ω e {ω | p(ω) > p th}; where ω is the angular frequency; {ω | p(ω) > p th} is the set of all angular frequency points that satisfy the condition that the spectral radius exceeds the threshold value, and is the system resonance band.

8. The method of claim 1, wherein, In the step S5, in the generation of the equivalent impedance of path aggregation, the equivalent impedance is obtained by projecting the principal eigenvector of the coupling impedance tensor, for representing the comprehensive impedance response of the identified resonant band.

9. The method of claim 8, wherein the method further comprises: The calculation method of projecting the principal eigenvector of the coupling impedance tensor comprises: The normalized eigenvector v corresponding to the maximum modulus value of the complex impedance matrix is obtained max The equivalent impedance Z of the path aggregation is agg The calculation formula of the complex impedance matrix Z(ω) is: where ω is the angular frequency; Z(ω) is the complex impedance matrix at frequency ω, dimension n x n, where n is the number of paths; v max is the normalized complex eigenvector of the largest eigenvalue in Z(ω), dimension n x 1; is the conjugate transpose of v max , dimension 1 x n; Z agg (ω) is the equivalent impedance of the path aggregation, representing the principal direction equivalent impedance of the bus coupling response in the resonant band.

10. The method of claim 1, wherein, In the step S6, the frequency response spectrum comprises the change curve of the spectral radius and the equivalent impedance of path aggregation with frequency, and demarcates the resonant band interval, displays the potential impedance abnormal frequency band, and is used for impedance response and potential risk assessment.

Images