A grid-connected inverter impedance detection method based on L-type filter

Abstract

The application provides a grid-connected inverter impedance detection method based on an L-type filter, and belongs to the technical field of grid-connected inverter impedance detection.The application constructs a wideband detection domain range and determines an optimal frequency point distribution sequence of multi-frequency point injection, injects a multi-frequency point disturbance signal at a preset grid-connected inverter operating point, collects time domain data of an inverter side current and a point of common coupling voltage, performs fast Fourier transform analysis on the collected data to extract amplitude and phase information corresponding to each injection frequency point, establishes a frequency domain characteristic vector matrix, establishes a frequency compensation matrix model, compensates and corrects high-frequency band measurement data based on a frequency characteristic attenuation vector, calculates optimal estimated values of grid impedance and grid-connected inverter output impedance, performs error analysis and precision verification on the impedance detection result, and outputs verified impedance parameter values, so that the technical problem of insufficient grid impedance detection precision caused by high-frequency band attenuation of the L-type filter is solved.

Description

Technical Field

[0001] This invention belongs to the field of grid-connected inverter impedance detection technology, and more specifically, relates to a grid-connected inverter impedance detection method based on an L-type filter. Background Technology

[0002] In grid-connected inverter systems, grid impedance detection is a key technology for ensuring stable system operation and improving power quality. Traditional grid impedance detection methods mainly employ harmonic detection technology based on single-frequency injection. This involves injecting a single-frequency disturbance signal at the common coupling point and calculating grid impedance parameters using the amplitude and phase relationship of voltage and current. This method has good detection accuracy in the low-frequency band and is widely used in grid-connected control systems for distributed power sources such as wind power and photovoltaic power generation. However, existing single-frequency detection methods have significant limitations when dealing with wideband impedance characteristic analysis, especially when L-type filters are used for harmonic suppression in the system. The frequency response characteristics of the filter significantly affect impedance detection in the high-frequency band, and traditional methods cannot effectively compensate for the frequency distortion caused by the filter, resulting in large deviations in the detection results in the high-frequency band. In existing technologies, because L-type filters have significant attenuation characteristics in the high-frequency band, when the detection frequency exceeds the filter cutoff frequency, the injected disturbance signal is significantly attenuated, causing a sharp drop in the signal-to-noise ratio of the voltage and current measurement signals. This makes it impossible to accurately extract impedance information in the high-frequency band. In other words, existing technologies suffer from the technical problem of insufficient grid impedance detection accuracy due to high-frequency attenuation caused by L-type filters. Summary of the Invention

[0003] In view of this, the present invention provides a grid-connected inverter impedance detection method based on an L-type filter, which can solve the technical problem in the prior art where the high-frequency attenuation of the L-type filter leads to insufficient accuracy of grid impedance detection.

[0004] This invention is implemented as follows: This invention provides a grid-connected inverter impedance detection method based on an L-type filter, including obtaining the inductance and capacitance values ​​of the L-type filter as initial parameters and establishing a frequency response attenuation vector model; constructing a frequency response attenuation coefficient matrix by analyzing the transfer function characteristics of the L-type filter at different frequencies; constructing a wide-bandwidth detection domain and determining the optimal frequency distribution sequence for multi-frequency injection; establishing a detection frequency range based on the grid fundamental frequency and selecting injection frequencies using a logarithmic distribution method; injecting multi-frequency disturbance signals at a preset grid-connected inverter operating point, while simultaneously acquiring time-domain data of the inverter-side current and common coupling point voltage; and analyzing the acquired inverter-side current and... The voltage data at the common coupling point is analyzed using Fast Fourier Transform (FFT) to extract the amplitude and phase information corresponding to each injection frequency point and establish a frequency domain eigenvector matrix. A frequency compensation matrix model is established, and the high-frequency measurement data is compensated and corrected based on the frequency characteristic attenuation vector to eliminate the influence of the high-frequency attenuation effect of the L-type filter on the impedance detection accuracy. A linear equation system for impedance parameter estimation is established using a weighted least squares optimization algorithm. The optimal estimated values ​​of the grid impedance and the grid-connected inverter output impedance are obtained by solving the overdetermined equation system. Error analysis and accuracy verification are performed on the impedance detection results. The covariance matrix of the estimation error is calculated, and the verified grid impedance and grid-connected inverter output impedance parameter values ​​are output.

[0005] The frequency response attenuation vector is used to describe the amplitude-frequency response attenuation characteristics of the L-type filter at different frequencies. The inputs include the filter inductance value, filter capacitance value, system load impedance, and detection frequency sequence. The output is the attenuation coefficient vector corresponding to each frequency point. The attenuation coefficient vector is used to construct the frequency compensation matrix model.

[0006] The wideband detection domain is used to define the frequency range and frequency resolution requirements that need to be covered during impedance detection. The inputs include the fundamental frequency of the power grid, the highest detection frequency of the system, the detection frequency resolution, and the cutoff frequency of the L-type filter. The output is the complete frequency domain range applicable to impedance detection.

[0007] The optimal frequency point for multi-frequency injection is used to determine the optimal selection strategy for the frequencies of multiple disturbance signals injected simultaneously during impedance detection. The inputs include impedance detection accuracy requirements, grid-connected inverter system stability constraints, frequency interval constraints, and system computational complexity constraints. The output is the optimal frequency point combination sequence that meets the requirements of detection accuracy and system stability.

[0008] In the step of injecting multi-frequency disturbance signals, the sampling frequency is set to 10kHz to meet the requirements of the Nyquist sampling theorem. The time-domain data acquisition process of inverter side current and common coupling point voltage is synchronously sampled through a high-precision analog-to-digital converter module.

[0009] In the fast Fourier transform analysis step, the time-domain sampled data is processed by a window function to reduce the impact of spectral leakage, and the amplitude and phase information of each injected frequency point is extracted through frequency domain transformation to establish a vector matrix data structure containing frequency component features.

[0010] The frequency compensation matrix model is used to correct the measurement error and signal attenuation caused by the L-type filter in the high-frequency band. The input includes the frequency characteristic attenuation vector, the frequency domain feature vector matrix, the compensation algorithm parameters and the frequency weighting coefficients, and the output is the measurement data matrix after high-frequency compensation correction.

[0011] The error analysis and accuracy verification steps assess the reliability of the impedance detection results by calculating the covariance matrix of the estimated error, quantify the uncertainty of the estimated parameters, and ensure that the output grid impedance and grid-connected inverter output impedance parameter values ​​meet the accuracy requirements.

[0012] The frequency domain feature vector matrix is ​​used to store the amplitude and phase feature information of each frequency component obtained after fast Fourier transform analysis. The input includes time-domain sampling data of inverter side current, time-domain sampling data of common coupling point voltage, sampling frequency and analysis window function type.

[0013] The game theory model includes an upper-level model that aims to maximize impedance detection accuracy and a lower-level model that aims to maximize system stability. The upper-level model and the lower-level model achieve a trade-off between detection accuracy and system stability through coupling terms.

[0014] The weighted least squares optimization algorithm transforms impedance parameter estimation into a linear algebraic problem in the form of matrix equations. By constructing a linear relationship between the measurement matrix and the parameter vector, it uses the least squares criterion to find the optimal solution for the grid impedance and the output impedance of the grid-connected inverter.

[0015] Among them, computational optimization is performed by solving the problem using an overdetermined linear equation system. When the number of unknowns is less than the number of equations, the optimal solution is found by constructing a linear relationship between the measurement matrix and the parameter vector and using the least squares criterion.

[0016] Among them, the singular value decomposition method is used to solve the linear equation system, which decomposes any matrix into the product of three matrices. The singular value decomposition technique is used to realize the pseudo-inverse operation of the matrix, thereby improving the numerical stability and computational accuracy of parameter estimation.

[0017] Among them, the QR decomposition method is used to decompose a matrix into a mathematical form of the product of an orthogonal matrix and an upper triangular matrix. QR decomposition is often used for numerical solutions of linear equation systems and calculations of least squares problems to ensure the numerical stability of the solution process.

[0018] The fundamental frequency of the power grid is set to 50Hz, the detection frequency range is established from 150Hz to 1050Hz, and the injection frequency point is selected by logarithmic distribution to ensure sufficient frequency coverage density in a wide frequency band.

[0019] The impedance detection accuracy index function is used to quantify the degree of deviation between the impedance parameter estimation result and the true reference value. The inputs include the estimated grid impedance value, the estimated grid-connected inverter output impedance value, the reference grid impedance value, the reference grid-connected inverter output impedance value, and the measurement noise variance.

[0020] This invention achieves accurate modeling and compensation of the frequency response characteristics of L-type filters by establishing a frequency characteristic attenuation vector model and constructing an optimal frequency point distribution sequence for multi-frequency point injection, effectively solving the problem of insufficient accuracy in the high-frequency band of traditional single-frequency point detection methods. This invention uses a frequency compensation matrix model to correct high-frequency measurement data, eliminating the impact of L-type filter attenuation on measurement accuracy through mathematical modeling. Simultaneously, it utilizes a weighted least squares optimization algorithm to establish a linear equation system for impedance parameter estimation, improving the robustness and convergence speed of parameter estimation, enabling high accuracy in power grid impedance detection over a wide frequency band. In summary, this invention, through the synergistic effect of frequency characteristic modeling, multi-frequency point optimized injection, and high-frequency compensation correction, solves the technical problem mentioned in the background art where high-frequency attenuation of L-type filters leads to insufficient accuracy in power grid impedance detection. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 The main circuit structure of the inverter used in this invention includes two sub-diagrams: (a) a three-phase full-bridge inverter and (b) an NPC-type three-phase inverter.

[0023] Figure 3 This is a block diagram of the inverter, filter, grid impedance, and grid voltage.

[0024] Figure 4 This is a structural diagram of a first-order active filter sampling circuit for a grid-connected inverter power grid and output impedance detection and disturbance observer feedback control method and parameter design according to the present invention.

[0025] Figure 5 This is an overall control block diagram of the algorithm structure for a feedback control method and parameter design of a grid-connected inverter power grid and output impedance detection and disturbance observer according to the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0027] like Figure 1 The diagram shown is a flowchart of a grid-connected inverter impedance detection method based on an L-type filter provided by the present invention. This method includes the following steps:

[0028] S01. Obtain the inductance and capacitance values ​​of the L-type filter as initial parameters, establish a frequency response attenuation vector model, and construct a frequency response attenuation coefficient matrix by analyzing the transfer function characteristics of the L-type filter at different frequencies.

[0029] S02. Construct a wide-band detection domain range, determine the optimal frequency distribution sequence for multi-frequency injection, establish a detection frequency range from 150Hz to 1050Hz based on the power grid fundamental frequency of 50Hz, and select injection frequency points using a logarithmic distribution method.

[0030] S03. Inject multi-frequency disturbance signals into the preset grid-connected inverter operating point, and simultaneously collect time-domain data of inverter side current and common coupling point voltage. The sampling frequency is set to 10kHz to meet the Nyquist sampling theorem requirements.

[0031] S04. Perform fast Fourier transform analysis on the collected inverter side current and common coupling point voltage data, extract the amplitude and phase information corresponding to each injection frequency point, and establish a frequency domain feature vector matrix for subsequent impedance calculation.

[0032] S05. Establish a frequency compensation matrix model, and compensate and correct the high-frequency measurement data based on the frequency characteristic attenuation vector to eliminate the influence of the high-frequency attenuation effect of the L-type filter on the impedance detection accuracy.

[0033] S06. Use the weighted least squares optimization algorithm to establish a linear equation system for impedance parameter estimation, and obtain the optimal estimates of grid impedance and grid-connected inverter output impedance by solving the overdetermined equation system.

[0034] S07. Perform error analysis and accuracy verification on the impedance detection results, calculate the covariance matrix of the estimated error, and output the verified grid impedance and grid-connected inverter output impedance parameter values.

[0035] The frequency response attenuation vector is used to describe the amplitude-frequency response attenuation characteristics of the L-type filter at different frequencies. The inputs include the filter inductance value, the filter capacitance value, the system load impedance, and the detection frequency sequence. The output is the attenuation coefficient vector corresponding to each frequency point. The attenuation coefficient vector is used to construct the frequency compensation matrix model in step S05.

[0036] The wideband detection domain is used to define the frequency range and frequency resolution requirements that need to be covered during impedance detection. The inputs include the fundamental frequency of the power grid, the highest detection frequency of the system, the detection frequency resolution, and the cutoff frequency of the L-type filter. The output is a complete frequency domain range suitable for impedance detection. The complete frequency domain range is used to determine the optimal frequency distribution sequence for multi-frequency injection in step S02.

[0037] The optimal frequency point for multi-frequency injection is used to determine the optimal selection strategy for the frequencies of multiple disturbance signals injected simultaneously during impedance detection. The inputs include impedance detection accuracy requirements, grid-connected inverter system stability constraints, frequency interval constraints, and system computational complexity constraints. The output is the optimal frequency point combination sequence that meets the requirements of detection accuracy and system stability. The optimal frequency point combination sequence is used for multi-frequency disturbance signal injection in step S03.

[0038] The frequency domain feature vector matrix is ​​used to store the amplitude and phase feature information of each frequency component obtained after fast Fourier transform analysis. The input includes time-domain sampling data of inverter side current, time-domain sampling data of common coupling point voltage, sampling frequency and analysis window function type. The output is a matrix data structure containing amplitude and phase information of each injected frequency point. The matrix data structure is used for impedance parameter calculation in steps S05 and S06.

[0039] The frequency compensation matrix model is used to correct the measurement error and signal attenuation caused by the L-type filter in the high-frequency band. The input includes the frequency characteristic attenuation vector, the frequency domain feature vector matrix, the compensation algorithm parameters and the frequency weighting coefficient. The output is the measurement data matrix after high-frequency compensation correction. The measurement data matrix is ​​used to improve the impedance parameter estimation accuracy in step S06.

[0040] Step S06 utilizes the classical overdetermined linear equation system to solve the problem for computational optimization, transforming the impedance parameter estimation into a linear algebraic problem in the form of matrix equations, and solving for the least squares solution through singular value decomposition or QR decomposition methods.

[0041] The constructed game theory model includes an upper-level model aimed at maximizing impedance detection accuracy and a lower-level model aimed at maximizing system operational stability. The objective function of the upper-level model is the logarithmic ratio of impedance detection accuracy to detection time cost multiplied by the reciprocal function of computational complexity, plus the exponential function of detection resolution minus the square root function of system stability risk. The constraints are detection frequency range limitation and sampling frequency technology constraint. The objective function of the lower-level model is the product of system stability index and stability margin divided by the square function of disturbance amplitude, multiplied by the logarithmic function of transmission efficiency, plus the linear function of detection accuracy contribution. The constraints are system stability boundary conditions and power transmission efficiency lower limit constraint. The coupling term represents the trade-off and coordination relationship between detection accuracy and system stability.

[0042] The impedance detection accuracy index function is used to quantify the degree of deviation between the impedance parameter estimation result and the true reference value. The input includes the estimated grid impedance value, the estimated grid-connected inverter output impedance value, the reference grid impedance value, the reference grid-connected inverter output impedance value, and the measurement noise variance. The output is a normalized detection accuracy numerical index, which is used to calculate the upper-level objective function of the game model.

[0043] The system operation stability index function is used to evaluate the impact of injected disturbance signals on the stability of the grid-connected inverter system. The inputs include the amplitude of the multi-frequency disturbance signal, the injection frequency sequence, the transfer function of the grid-connected inverter system, and the system stability margin. The output is the system stability evaluation value, which is used for the calculation of the lower-level objective function of the game model and the determination of the constraint conditions of the upper-level model.

[0044] Among them, the problem of solving overdetermined linear equations refers to the mathematical problem of solving linear equations when the number of unknowns is less than the number of equations. The optimal solution is found by constructing a linear relationship between the measurement matrix and the parameter vector and using the least squares criterion.

[0045] Singular value decomposition (SVD) is a matrix decomposition technique that decomposes any matrix into the product of three matrices, and is used to solve systems of linear equations and perform pseudo-inverse operations on matrices.

[0046] QR decomposition is a mathematical method that decomposes a matrix into the product of an orthogonal matrix and an upper triangular matrix. It is often used for numerical solutions of linear equations and calculations of least squares problems.

[0047] The specific implementation methods of the above steps are described in detail below.

[0048] The specific implementation of step S01 involves first obtaining the inductance and capacitance values ​​of the L-type filter as initial parameters. The inductance value is typically in the range of 1mH to 10mH, and the capacitance value is typically in the range of 10μF to 100μF. When establishing the frequency response attenuation vector model, the transfer function analysis principle is used. The attenuation coefficient is obtained by calculating the amplitude of the transfer function of the L-type filter at different frequency points. The low-pass characteristics of the filter need to be considered during the transfer function analysis, where the cutoff frequency is determined by the values ​​of the inductance and capacitance. The cutoff frequency is calculated using... The relationship is determined by the formula. When constructing the frequency response attenuation coefficient matrix, the cutoff frequency characteristics of the filter need to be considered. When the detection frequency exceeds three times the cutoff frequency, the attenuation coefficient will increase significantly. Typically, the attenuation slope is 40 dB per decade. The system load impedance is usually set to a standard value within the range of 50Ω to 500Ω. The selection of the load impedance needs to consider the impedance characteristics of the actual power grid and the measurement accuracy requirements. The detection frequency sequence is generated according to a logarithmic distribution to ensure appropriate frequency resolution throughout the detection frequency band. The frequency sequence is generated using the geometric series principle to ensure sufficient sampling point density in both low and high frequency bands. The tolerance of filter components also needs to be considered during the establishment of the attenuation vector model. The inductor tolerance is typically ±5%, and the capacitor tolerance is typically ±10%. These tolerances directly affect the accuracy of the attenuation coefficient. The purpose of this step is to provide accurate filter characteristic parameters for subsequent frequency compensation calculations, ensuring that the impedance detection system can correctly handle the frequency response distortion caused by the filter.

[0049] The specific implementation of step S02 is based on the fundamental frequency of the power grid (50Hz), determining the lower limit of the wideband detection domain to be 150Hz and the upper limit to be 1050Hz. This frequency range covers the frequency band where the power grid impedance changes most significantly. The selection of the wideband detection domain needs to consider the harmonic distribution characteristics of the power grid. Typically, harmonic components in the power grid are mainly concentrated in integer multiples of the fundamental frequency; therefore, the detection frequency range should cover the 3rd to 21st harmonic frequencies. The injection frequency is selected using the logarithmic distribution principle to ensure sufficient frequency resolution in both the low and high frequency bands. The frequency interval is based on f... n =f0×10 n×ΔlogThe frequency distribution follows a regular pattern, where f0 is the initial frequency of 150Hz, and Δlog is the logarithmic interval step size, typically set to 0.1 to 0.2. The advantage of the logarithmic distribution is that it can evenly distribute measurement points across a wide frequency band, avoiding the problem of excessive density in high-frequency bands and insufficient density in low-frequency bands caused by linear distributions. The selection of the optimal frequency distribution sequence needs to balance detection accuracy and computational complexity; the total number of frequency points is usually controlled between 20 and 50. Too few frequency points will reduce impedance estimation accuracy, while too many frequency points will increase the computational burden and may introduce more measurement noise. The frequency distribution optimization process also needs to consider the mutual interference effect between frequencies; the interval between adjacent frequency points should be greater than twice the system bandwidth to avoid spectral aliasing. This step uses frequency domain analysis theory to lay the theoretical foundation for multi-frequency disturbance injection by reasonably configuring the detection frequency range and frequency point distribution, ensuring that the impedance detection system can obtain sufficient information within the predetermined frequency range.

[0050] The specific implementation of step S03 involves simultaneously injecting multiple disturbance signals of different frequencies at a preset operating point of the grid-connected inverter. The amplitude of the disturbance signals is typically set to 1% to 5% of the rated current to ensure that the normal operation of the system is not affected while maintaining a sufficient signal-to-noise ratio. The disturbance signals are generated using digital signal processing technology, employing a direct digital frequency synthesizer to produce high-precision multi-sine wave signals. The phase relationship of each frequency component needs precise control to avoid excessively high signal peaks that could lead to system saturation. A peak factor optimization algorithm is used during the synthesis of the multi-frequency disturbance signals. By adjusting the phase relationship of each frequency component, the peak factor of the synthesized signal is controlled below 1.5, ensuring that the signal does not exceed the linear operating range of the inverter. The disturbance signal injection is implemented using a pulse width modulation controller, superimposing the generated disturbance signal onto the inverter's current reference command. Small-amplitude current disturbances are achieved by modifying the modulation index. The data acquisition system needs to simultaneously acquire time-domain data of the inverter-side current and the common coupling point voltage, employing high-precision synchronous sampling technology to ensure accurate phase relationships between the current and voltage signals. The sampling frequency is set to 10kHz to meet the Nyquist sampling theorem requirements, ensuring accurate capture of signal components with a maximum detection frequency of 1050Hz, while providing sufficient oversampling to improve measurement accuracy. The acquisition time window is typically set to 1 to 5 seconds, with the specific length determined based on the required frequency resolution and signal-to-noise ratio. A longer acquisition time window provides better frequency resolution but increases computation time. During data acquisition, the system's stability indicators need to be monitored in real time. If the system stability margin drops below 6dB, disturbance injection should be stopped immediately to protect the system. The purpose of this step is to obtain raw measurement data containing rich impedance information, providing a high-quality data foundation for subsequent frequency domain analysis and impedance parameter estimation.

[0051] The specific implementation of step S04 involves performing Fast Fourier Transform (FFT) analysis on the acquired time-domain data. First, the raw data needs to be preprocessed to improve the accuracy of the spectrum analysis. The preprocessing process includes removing DC components, filtering high-frequency noise, and correcting sampling clock deviations to ensure the quality of the time-domain signal meets the requirements of the FFT. The choice of window function has a significant impact on the spectrum analysis results. Hamming or Hanning windows are typically used to reduce spectral leakage. The length of the window function should match the length of the acquired data to obtain the optimal frequency resolution. The FFT algorithm converts the time-domain signal into a frequency-domain representation. During the transformation, the impact of the number of sampling points on frequency resolution needs to be considered. Zero-padding techniques are typically used to extend the data length to an integer power of 2 to improve computational efficiency. The spectrum analysis results include two parts: the amplitude spectrum and the phase spectrum. The amplitude spectrum reflects the intensity of each frequency component, and the phase spectrum reflects the phase relationship between the frequency components. Interpolation algorithms are required when extracting the amplitude and phase information corresponding to each injection frequency point because the injection frequency points may not completely correspond to the frequency grid points of the Discrete Fourier Transform. Parabolic interpolation or sine interpolation can obtain more accurate amplitude and phase estimates. Gain compensation of the window function needs to be considered during amplitude extraction. Different window functions have different equivalent noise bandwidths and peak gains, requiring corresponding amplitude correction based on the characteristics of the selected window function. Phase expansion processing is required during phase extraction to eliminate phase jumps. A phase expansion algorithm is used to ensure phase continuity and accuracy. When establishing the frequency domain feature vector matrix, the amplitude and phase information of the current and voltage are arranged in frequency order to form a complex matrix structure for subsequent matrix operations. The rows of the matrix correspond to different frequency points, and the columns correspond to the real and imaginary parts of the current and voltage. This step uses the spectral analysis method from digital signal processing theory, achieving time-frequency domain conversion through Fourier transform, providing accurate frequency domain feature data for impedance parameter estimation, and ensuring the reliability and accuracy of subsequent calculations.

[0052] The specific implementation of step S05 is to construct a frequency compensation matrix model based on the frequency characteristic attenuation vector established in step S01. This model is used to correct the amplitude attenuation and phase shift problems caused by the L-type filter in the high-frequency band. The theoretical basis of frequency compensation is the inverse filtering principle. By calculating the inverse function of the filter's transfer function, the signal affected by the filter is recovered. The compensation process is essentially a deconvolution operation on the measured signal. The construction of the compensation matrix needs to consider the frequency response characteristics of the filter. For a second-order L-type filter, its transfer function exhibits an attenuation characteristic of -40dB per decade in the high-frequency band, and the phase response changes drastically near the cutoff frequency. For measurement data with frequencies higher than the filter's cutoff frequency, the compensation coefficient will be significantly increased to offset the filter's attenuation effect. The compensation coefficient is usually in the range of 5 to 20 times, and the specific value is determined according to the ratio of the frequency to the cutoff frequency. Setting the frequency weighting coefficient is a key step in the compensation algorithm. It is necessary to find the optimal balance between signal recovery and noise suppression. For high-frequency compensation, appropriate restrictions are needed to avoid noise amplification effects. The weighting coefficient is usually set to a value between 0.1 and 1.0. The weighting coefficients are calculated using Wiener filtering theory, determining the optimal weights based on the ratio of signal power spectral density to noise power spectral density. Higher weights are assigned when the signal-to-noise ratio (SNR) is high, and lower weights when the SNR is low. The compensation algorithm also needs to consider the uncertainties in filter parameters. Due to manufacturing tolerances in inductors and capacitors, the actual filter characteristics may deviate from the design values. Therefore, the compensation matrix needs to be robust enough to handle parameter variations. The compensated measurement data matrix eliminates the adverse effects of the filter frequency response on impedance detection accuracy, particularly improving the estimation accuracy of impedance parameters in the high-frequency band, thus homogenizing the measurement accuracy across the entire detection frequency band.

[0053] The specific implementation of step S06 involves using a weighted least squares optimization algorithm to establish a linear equation system for impedance parameter estimation, transforming the complex impedance detection problem into a standard overdetermined linear equation system solution problem. The linear equation system is established based on fundamental laws of circuit theory, using Ohm's law and Kirchhoff's voltage law to establish mathematical expressions for the voltage-current relationship, where the unknown parameters are the real and imaginary parts of the grid impedance and the inverter output impedance. The construction of the equation system requires consideration of the properties of complex impedance, converting the complex impedance relationship into real matrix equations for numerical solution. This is achieved by separating the real and imaginary parts of the complex equations to obtain the linear real equation system. When representing the linear equation system in matrix form, the elements of the coefficient matrix consist of measured voltage and current data, the right-hand vector is determined by the product of voltage and current, and the unknown vector contains the impedance parameters to be estimated. The overdetermined equation system is solved using numerical methods such as singular value decomposition or QR decomposition, which effectively address the numerical stability and condition number issues of the equation system. The advantage of singular value decomposition (SVD) lies in its ability to handle the numerical singularity of matrices. By truncating singular values, noise components corresponding to small singular values ​​can be filtered out, improving the stability and accuracy of the solution. QR decomposition has higher computational efficiency and good numerical stability, making it particularly suitable for solving large-scale linear equation systems. In the weighted least squares algorithm, the construction of the weight matrix needs to consider the reliability and accuracy of measurement data at different frequency points. Typically, higher signal-to-noise ratio (SNR) frequencies are given larger weights, while lower SNR frequencies are given smaller weights. The weights can be determined based on variance estimation of the measurement data or by prior knowledge of frequency characteristics and measurement conditions. The convergence and stability of the algorithm are also closely related to the condition number of the equation system. When the condition number is too large, regularization techniques are needed to improve the numerical characteristics. This step uses numerical linear algebra theory and optimization theory to obtain the optimal estimate of the impedance parameters through the least squares criterion, ensuring that the estimation result has the minimum mean square error.

[0054] The specific implementation of step S07 involves a comprehensive error analysis and accuracy verification of the impedance detection results. The uncertainty of the parameter estimation is quantitatively assessed by calculating the covariance matrix of the estimation error. The calculation of the covariance matrix is ​​based on the statistical characteristics of measurement noise and the sensitivity analysis theory of system parameters, reflecting the correlation between different impedance parameter estimates and the differences in the accuracy of each parameter estimate. The diagonal elements of the covariance matrix represent the variance of each parameter estimate, and the off-diagonal elements represent the covariance between parameters. By analyzing the covariance matrix, weak links and highly correlated parameter combinations in the parameter estimation can be identified. The accuracy verification process includes multiple steps such as residual analysis, confidence interval calculation, and hypothesis testing. Residual analysis is used to test the appropriateness of the linear model fit and the existence of systematic bias. The accuracy of the model is judged by analyzing the statistical characteristics of the residuals. Confidence interval calculation is based on the variance of the parameter estimates and the Student's t-distribution theory, providing a statistically significant confidence interval for each impedance parameter. The confidence level is usually set to 95% or 99%. Hypothesis testing is used to verify the significance of parameter estimation. A t-test is used to determine whether the estimated impedance parameter is significantly different from zero; the significance level is typically set to 0.05. Accuracy evaluation indicators include relative error, root mean square error, and correlation coefficient. When the standard deviation of the estimation error is less than 5% of the true value, the detection result is considered to have sufficient accuracy for engineering applications. Result verification also requires robustness analysis, which tests the stability and reliability of the algorithm by changing measurement conditions, adjusting algorithm parameters, or increasing noise levels. The output impedance parameters include the real and imaginary parts of the grid impedance and the grid-connected inverter output impedance, as well as the corresponding standard deviation, confidence interval, and correlation matrix between parameters. This information provides a complete description of the impedance characteristics for engineering applications. This step employs parameter estimation theory, hypothesis testing theory, and error analysis methods from statistical theory to ensure the reliability, accuracy, and engineering applicability of the impedance detection results, providing reliable impedance parameters for power system stability analysis and control system design. Sensitivity analysis theory reflects the correlation between different impedance parameter estimates and the differences in the accuracy of each parameter estimate. The diagonal elements of the covariance matrix represent the variance of each parameter estimate, while the off-diagonal elements represent the covariance between parameters. Analyzing the covariance matrix can identify weak points in the parameter estimates and combinations of parameters with strong correlations. The accuracy verification process includes multiple steps such as residual analysis, confidence interval calculation, and hypothesis testing. Residual analysis is used to test the appropriateness of the linear model fit and the existence of systematic biases; the accuracy of the model is judged by analyzing the statistical characteristics of the residuals. Confidence interval calculation, based on the variance of the parameter estimates and Student's t-distribution theory, provides a statistically significant confidence interval for each impedance parameter, with confidence levels typically set at 95% or 99%. Hypothesis testing verifies the significance of the parameter estimates; a t-test is used to determine whether the estimated impedance parameters are significantly different from zero, with a significance level typically set at 0.05.Accuracy evaluation indicators include relative error, root mean square error, and correlation coefficient. When the standard deviation of the estimated error is less than 5% of the true value, the detection result is considered to have sufficient accuracy for engineering applications. Result verification also requires robustness analysis, which tests the stability and reliability of the algorithm by changing measurement conditions, adjusting algorithm parameters, or increasing noise levels. The output impedance parameters include the real and imaginary parts of the grid impedance and the grid-connected inverter output impedance, as well as the corresponding standard deviation, confidence interval, and correlation matrix between parameters. This information provides a complete description of the impedance characteristics for engineering applications. This step employs parameter estimation theory, hypothesis testing theory, and error analysis methods from statistical theory to ensure the reliability, accuracy, and engineering practicality of the impedance detection results, providing reliable impedance parameters for power system stability analysis and control system design.

[0055] The specific implementation of the game theory model involves constructing a two-layer optimization problem to balance impedance detection accuracy and system stability. The upper-layer model aims to maximize impedance detection accuracy, with its objective function including the ratio of detection accuracy to detection time cost, the reciprocal of computational complexity, an exponential function of detection resolution, and a negative contribution term for system stability risk. The lower-layer model aims to maximize system stability, with its objective function considering the product of stability index and stability margin, the impact of disturbance amplitude, transmission efficiency, and the contribution of detection accuracy. The game theory model is solved using an iterative algorithm, finding a Nash equilibrium solution through alternating optimization of the upper and lower-layer models. The stability margin threshold is typically set above 6 dB, the disturbance amplitude is limited to within 3% of the rated value, and the lower limit of transmission efficiency is set to 95%. This game theory model can achieve high-precision impedance detection while ensuring stable system operation.

[0056] The specific implementation of the impedance detection accuracy index function uses normalized root mean square error to quantify the deviation between the estimated result and the reference value. Input parameters include the estimated grid impedance value and the estimated inverter output impedance value obtained in step S06, as well as the pre-set reference impedance value and measurement noise variance. The accuracy index calculation considers the error contributions of the real and imaginary parts of the impedance, and a comprehensive accuracy evaluation is obtained through weighted averaging. When the detection accuracy index is greater than 0.95, the detection result is considered to meet the requirements of engineering applications. This index function provides a quantified objective function for the upper-level optimization of the game model, guiding the formulation of the optimal detection strategy.

[0057] The specific implementation of the system stability index function is based on small-signal stability analysis theory to evaluate the impact of disturbance signals on system stability. Input parameters include the amplitude vector of the multi-frequency disturbance signal, the injected frequency sequence, the transfer function model of the grid-connected inverter, and the system's stability margin. Stability evaluation is achieved by calculating the maximum real part of the system's eigenvalues; the system remains stable when the real parts of all eigenvalues ​​are negative. Increasing the amplitude of the disturbance signal reduces system stability; therefore, an optimal balance needs to be found between detection accuracy and stability. The output of this index function is used to calculate the lower-level objective function of the game theory model and to determine the constraints of the upper-level model, ensuring that the impedance detection process does not threaten the safe and stable operation of the system.

[0058] It should be noted that the first key technical idea of ​​this invention is frequency response attenuation vector modeling. Compared with the simplified processing method of traditional methods that ignore the influence of filter frequency response, this invention accurately establishes a mathematical model of the frequency response of the L-type filter, quantifying the attenuation characteristics of the filter at different frequencies into a calculable vector form. This modeling method can accurately describe the degree of influence of the filter on different frequency components, providing a precise theoretical basis for subsequent compensation calculations and avoiding the systematic errors caused by ignoring filter characteristics in traditional methods. The second key technical idea is the optimal frequency selection strategy of multi-frequency injection. Compared with the traditional single-frequency detection method, this invention adopts the method of simultaneously injecting multiple optimized selection frequencies, and determines the optimal frequency combination through mathematical methods such as logarithmic distribution. This strategy not only expands the frequency coverage of detection, but also improves the redundancy and reliability of impedance parameter estimation through information fusion of multiple frequencies, effectively overcoming the problem of insufficient signal-to-noise ratio in the high-frequency band of single-frequency detection. The third key technical approach is frequency compensation matrix correction technology. Traditional methods typically use measurement data directly for impedance calculation without considering the attenuation effect of filters. This invention establishes a frequency compensation matrix model to mathematically correct the attenuated measurement data in the high-frequency band. This compensation mechanism can effectively recover the high-frequency signal components attenuated by the L-type filter, significantly improving the accuracy and reliability of high-frequency impedance detection. The synergistic effect of these three key technical approaches forms a complete high-precision broadband impedance detection technology chain. Frequency characteristic modeling provides a theoretical basis for compensation calculation, multi-frequency injection provides sufficient information redundancy for high-frequency detection, and frequency compensation correction ensures the consistency of detection accuracy. The three work together to overcome the adverse effects of high-frequency attenuation by the L-type filter on impedance detection accuracy, achieving the goal of high-precision power grid impedance detection over a wide frequency range.

[0059] Specifically, the principle of this invention is as follows: The fundamental principle behind this invention's ability to solve the technical problem of insufficient accuracy in power grid impedance detection caused by high-frequency attenuation of L-type filters lies in its systematic frequency characteristic modeling and compensation mechanism, which effectively overcomes the non-ideal characteristics of the filter. First, this invention establishes a frequency characteristic attenuation vector model to mathematically describe the transfer function characteristics of the L-type filter at different frequencies, constructing an attenuation coefficient matrix containing key parameters such as filter inductance, capacitance, and load impedance, providing a theoretical basis for subsequent compensation calculations. Second, this invention uses multi-frequency injection technology to replace the traditional single-frequency detection method. By simultaneously injecting multiple optimally selected disturbance frequencies within a wide-band detection domain, it significantly improves the frequency coverage and information acquisition capability of impedance detection, enabling the system to obtain sufficient effective signals for impedance calculation in the high-frequency band. Third, this invention introduces a frequency compensation matrix model, performing inverse compensation on high-frequency measurement data based on a pre-established frequency characteristic attenuation vector. Through mathematical operations, it recovers the high-frequency signal components attenuated by the L-type filter, thereby ensuring the accuracy of high-frequency impedance detection. Finally, this invention utilizes a weighted least squares optimization algorithm to establish an overdetermined linear equation system, transforming multi-frequency measurement data into an impedance parameter estimation problem. The optimal estimate is then solved using numerical methods such as singular value decomposition or QR decomposition, ensuring the mathematical rigor and computational stability of the parameter estimation. The entire technical solution, through the organic combination of frequency modeling, multi-frequency injection, compensation correction, and optimization, forms a complete high-precision broadband impedance detection technology path.

[0060] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0061] The specific implementation of step S01 involves establishing a frequency response attenuation vector model and constructing a frequency response attenuation coefficient matrix by analyzing the transfer function characteristics of the L-type filter. The filter cutoff frequency is calculated as follows:

[0062]

[0063] In the formula, f c This is the filter cutoff frequency, in Hz.

[0064] The transfer function of an L-type filter is expressed as follows:

[0065]

[0066] In the formula, H(s) is the transfer function of the L-type filter; s is the complex frequency variable, in rad / s; L is the filter inductance, in H, typically ranging from 1mH to 10mH; C is the filter capacitance, in F, typically ranging from 10μF to 100μF; and R is the system load impedance, in Ω, typically ranging from 50Ω to 500Ω.

[0067] The frequency response attenuation vector is constructed as follows:

[0068] A f =|H(j2πf)|;

[0069] In the formula, A f is the attenuation coefficient at frequency f, dimensionless; f is the detection frequency, in Hz; j is the imaginary unit. 2 =-1.

[0070] The frequency response attenuation coefficient matrix is ​​represented as follows:

[0071]

[0072] In the formula, A is the frequency response attenuation coefficient matrix; f1, f2, ..., f n The frequency sequence is detected in Hz; n is the total number of frequency points, usually ranging from 20 to 50; the superscript T indicates matrix transpose.

[0073] The parameters were obtained as follows: L and C were measured using an LCR meter with a measurement accuracy of not less than 0.1%; R was measured using an impedance analyzer; f1, f2, ..., f n Generated according to a logarithmic distribution; f c It is determined based on the values ​​of inductance and capacitance.

[0074] The specific implementation of step S02 involves constructing a wideband detection domain and determining the optimal frequency distribution sequence for multi-frequency injection. The frequency distribution sequence is represented as follows:

[0075]

[0076] In the formula, f k f is the k-th detection frequency, in Hz; min The lowest detection frequency is 150Hz; k is the frequency point number, ranging from 0 to n-1, and is dimensionless; Δ log The logarithmic interval step size is dimensionless and typically ranges from 0.1 to 0.2.

[0077] The complete frequency domain range is represented as follows:

[0078] F = [f0, f1, ..., f n-1 ];

[0079] In the formula, F is the complete frequency domain range vector; f max This is the upper limit of the frequency, with a value of 1050Hz.

[0080] The parameter acquisition method is as follows: f min Determined based on 3 times the fundamental frequency of the power grid, 50Hz; Δ log Determined based on detection accuracy requirements and computational complexity constraints; f max Based on the system's highest detection frequency requirement.

[0081] The specific implementation of step S03 involves injecting multi-frequency perturbation signals at a preset operating point and acquiring time-domain data. The multi-frequency perturbation signals are represented as follows:

[0082]

[0083] In the formula, i ref (t) is the inverter current reference command, in A; I0 is the DC component, in A; I k φ represents the disturbance amplitude at the k-th frequency point, in amperes (A), typically 1% to 5% of the rated current; k t represents the initial phase at the k-th frequency point, in rad; t is the time variable, in seconds.

[0084] The sampling frequency for data acquisition is expressed as follows:

[0085] f s =2.56×f max ;

[0086] In the formula, f s The sampling frequency is set to 10kHz; f max The highest detection frequency is set to 1050Hz.

[0087] The parameter acquisition method is as follows: I k Determined based on system stability constraints; φ k The peak factor optimization algorithm is used for calculation; the collected current and voltage data are synchronously acquired through a high-precision data acquisition card; I0 is the DC operating point current of the inverter; t is a continuous time variable.

[0088] The specific implementation of step S04 involves performing a Fast Fourier Transform analysis on the time-domain data to establish a frequency-domain eigenvector matrix. The window function processing is represented as follows:

[0089] x w (n) = x(n) × w(n);

[0090] In the formula, x w(n) is the windowed signal; x(n) is the original sampled signal; w(n) is the window function, usually a Hamming window; n is the sampling point number, ranging from 0 to N-1.

[0091] The frequency domain transform is represented as follows:

[0092]

[0093] In the formula, X(k) is the complex number of the frequency domain signal; N is the total number of sampling points; k is the frequency index, ranging from 0 to N-1; and e is the natural constant.

[0094] The frequency domain eigenvector matrix is ​​represented as follows:

[0095]

[0096] In the formula, Z is the frequency domain eigenvector matrix; U m I represents the complex amplitude of the voltage at the m-th frequency point, in V. m is the complex amplitude of the current at the m-th frequency point, in A; m is the frequency index, ranging from 1 to n.

[0097] The parameter acquisition method is as follows: x(n) is obtained through step S03; w(n) uses the standard Hamming window function; N is determined according to the acquisition time window and sampling frequency; X(k) is the result of discrete Fourier transform; U m and I m Extract from the frequency domain transformation results of voltage and current respectively.

[0098] The specific implementation of step S05 involves establishing a frequency compensation matrix model to eliminate the high-frequency attenuation effect of the L-type filter. The frequency compensation matrix is ​​represented as follows:

[0099] C = diag(C1, C2, ..., C n );

[0100] In the formula, C is the frequency compensation matrix; C m is the compensation coefficient for the m-th frequency point, which is dimensionless; diag(·) represents a diagonal matrix.

[0101] The compensation coefficient is calculated as follows:

[0102]

[0103] In the formula, W m is the weighting coefficient for the m-th frequency point, dimensionless, and ranging from 0.1 to 1.0; Let be the attenuation coefficient at the m-th frequency point, which is dimensionless.

[0104] The compensated measurement data matrix is ​​represented as follows:

[0105] Z comp =C×Z;

[0106] In the formula, Z comp This is the compensated frequency domain feature matrix.

[0107] The parameter acquisition method is as follows: Calculated from step S01; W m Z is determined based on the signal-to-noise ratio according to Wiener filtering theory; Z is established by step S04; Z comp This is the result of multiplying the matrix elements one by one.

[0108] The specific implementation of step S06 involves using a weighted least squares algorithm to establish a system of linear equations for impedance parameter estimation. The system of linear equations is expressed as follows:

[0109] Y = Xθ + ε;

[0110] In the formula, Y is the observation vector; X is the coefficient matrix; θ is the parameter vector to be estimated; and ε is the error vector.

[0111] The vector of parameters to be estimated is represented as follows:

[0112] θ=[R grid X grid R inv X inv ] T ;

[0113] In the formula, R grid X represents the real part of the power grid impedance, in Ω. grid R represents the imaginary part of the power grid impedance, in Ω. inv X represents the real part of the inverter's output impedance, in Ω. inv This represents the imaginary part of the inverter's output impedance, expressed in Ω.

[0114] The weighted least squares solution is represented as follows:

[0115]

[0116] In the formula, is the parameter estimate; W is the weight matrix, which is a diagonal matrix; the superscript T indicates matrix transpose; the superscript -1 indicates matrix inverse.

[0117] The parameter acquisition method is as follows: Y is constructed from the compensation data in step S05; X is established according to the basic laws of the circuit; W is determined according to the reliability of the measurement data; ε is a random error vector; Obtained through numerical solution algorithms.

[0118] The specific implementation of step S07 involves performing error analysis and accuracy verification on the impedance detection results. The covariance matrix is ​​represented as follows:

[0119]

[0120] In the formula, The covariance matrix for parameter estimation; σ 2 This represents the error variance.

[0121] The detection accuracy indicators are expressed as follows:

[0122]

[0123] In the formula, η is the detection accuracy index, which is dimensionless; θ true represents the true parameter value; ||·|| represents the vector norm.

[0124] The confidence interval is represented as follows:

[0125]

[0126] In the formula, CI α The confidence interval is at confidence level α; t is the estimated value of the i-th parameter; α / 2，n-p is the critical value of the t-distribution for degrees of freedom np; p is the number of parameters, taking the value 4; Let be the variance estimated for the i-th parameter; i is the parameter index, ranging from 1 to 4.

[0127] The parameter acquisition method is as follows: σ 2 Estimated through residual analysis; θ true Obtained through independent measurement methods; confidence level α is typically set to 0.05; CI α For statistical confidence intervals; It is a 4×4 symmetric matrix.

[0128] The specific implementation of the game theory model involves constructing a two-level optimization problem to balance detection accuracy and system stability. The upper-level objective function is expressed as follows:

[0129]

[0130] In the formula, J1 is the upper-level objective function, which is dimensionless; T cost The detection time cost is expressed in seconds (s); C comp For computational complexity, dimensionless; R res For detection resolution, dimensionless; S risk The system stability risk is dimensionless; log(·) is the natural logarithm function; exp(·) is the exponential function; It is the square root function.

[0131] The lower-level objective function is expressed as follows:

[0132]

[0133] In the formula, J2 is the lower-level objective function, which is dimensionless; S index M is a system stability index, dimensionless; stab For stability margin, the unit is dB, typically greater than 6 dB; A dist The disturbance amplitude is expressed in amperes (A); η trans Transmission efficiency is dimensionless, with a lower limit constraint of 0.95; α is the contribution weight to detection accuracy, which is dimensionless.

[0134] The parameter acquisition method is as follows: T cost Measured based on algorithm execution time; S index Calculated through small-signal stability analysis; M stab Obtained through frequency domain analysis; η is calculated from the result of step S07; C comp Determined based on algorithm complexity analysis; R res Calculated based on frequency resolution; S risk Based on stability risk assessment; η trans Power transmission efficiency is measured; A dist This represents the effective value of the disturbance signal.

[0135] The specific implementation of the impedance detection accuracy index function is the same as that in step S07 above, and will not be described in detail here.

[0136] The specific implementation of the system stability index function is based on eigenvalue analysis to assess the impact of disturbances. The stability index is expressed as follows:

[0137] S index =max(Real(λ) i ));

[0138] In the formula, λ i Let i be the eigenvalue of the system, and i be the index of the eigenvalue; Real(·) represents the real part of the complex number; when S index The system is stable when the value is less than 0.

[0139] The impact assessment of the disturbance is as follows:

[0140] ΔS=S index，dist -S index，0 ;

[0141] In the formula, ΔS is the stability change, which is dimensionless; S index , dist S is a dimensionless stability index after the injection of perturbation. index，0 It is a dimensionless stability index under undisturbed conditions.

[0142] The parameter acquisition method is as follows: λ i The disturbance signal parameters are obtained by solving the system characteristic equation; S is provided by step S03; index The value is determined by the maximum real part of the eigenvalue; ΔS reflects the degree of influence of the disturbance on the system stability.

[0143] It should be noted that the formula for calculating the filter cutoff frequency... Based on the derivation of the inherent frequency of an LC resonant circuit in circuit theory, the principle is that when the impedance of the resonant circuit composed of inductor and capacitor reaches its minimum value at the cutoff frequency, the amplitude-frequency response of the filter is significantly attenuated. The effect of this formula is to provide an accurate reference frequency point for subsequent frequency compensation, enabling the system to predict attenuation characteristics at different frequencies. Compared to traditional fixed-frequency compensation methods, dynamically calculating the cutoff frequency can adapt to filter configurations with different parameters, improving the applicability and accuracy of impedance detection.

[0144] L-type filter transfer function This is a second-order low-pass filter model based on the Laplace transform theory in circuit analysis, where each term in the denominator polynomial corresponds to the contribution of resistance, inductance, and capacitance to the system's dynamic response. The principle of this transfer function reflects the filter's selective attenuation characteristics for signals of different frequencies, and through complex frequency domain analysis, it can accurately describe the frequency response relationship between amplitude and phase. Compared to existing ideal filter models, this transfer function considers the influence of all passive components in the actual circuit, making frequency compensation more accurate and avoiding compensation errors caused by neglecting resistive losses, thereby significantly improving the estimation accuracy of impedance parameters in the high-frequency range.

[0145] Frequency response attenuation vector A f =|H(j2πf)| This formula obtains the amplitude response at each frequency point by taking the magnitude of the transfer function on the imaginary axis. The principle is to use Fourier transform theory to convert the transfer function in the complex frequency domain into the amplitude-frequency characteristic in the actual frequency domain. The effect of this formula is to establish a quantitative relationship between frequency and attenuation, providing an accurate attenuation coefficient for each detection frequency point. Compared to traditional empirical attenuation estimation methods, attenuation vector calculation based on the transfer function has theoretical rigor and parameter adaptability, enabling dynamic adjustment of the attenuation compensation strategy according to the actual parameters of the filter.

[0146] Logarithmic distribution frequency selection formula Based on logarithmic scaling theory, the principle is to achieve a geometrical series distribution of frequency points over a wide frequency band, ensuring sufficient sampling density in both low and high frequency bands. This formula optimizes the allocation of frequency resources, avoiding the problem of excessively dense linear distribution in high-frequency bands and sparse distribution in low-frequency bands. Compared to traditional equally spaced frequency point distribution methods, logarithmic distribution can better capture the characteristics of power grid impedance variations across different frequency bands, especially its greater sensitivity to impedance changes in low-frequency bands, thereby improving overall detection accuracy.

[0147] Multi-frequency disturbance signal synthesis formula Based on the principle of linear superposition, broadband excitation is achieved through the coherent superposition of multiple sine waves. The phase term φ in this formula... k The optimized design can control the peak factor of the synthesized signal, avoiding excessive signal amplitude that could lead to system nonlinearity. Compared to the traditional single-frequency sweep method, simultaneous excitation of multiple frequencies significantly shortens the detection time. At the same time, phase optimization reduces the impact on system stability, achieving a balance between detection efficiency and system safety, making it particularly suitable for online impedance detection applications.

[0148] Fast Fourier Transform Formula Based on the theory of Discrete Fourier Transform, the principle is to decompose a discrete-time signal into complex exponential components of different frequencies, and obtain amplitude and phase information simultaneously through complex number operations. This formula achieves efficient time-frequency domain conversion. Compared to traditional analog filter bank methods, digital spectrum analysis has higher frequency resolution and noise immunity, accurately extracting weak disturbance signal components and providing high-quality frequency domain characteristic data for impedance parameter estimation.

[0149] Formula for calculating frequency compensation coefficient Based on inverse filtering theory, the principle is to recover the signal amplitude by using the reciprocal of the attenuation coefficient, while introducing a weighting factor to balance signal recovery and noise suppression. This formula eliminates the attenuation effect of the L-type filter on high-frequency signals. Compared to methods without frequency compensation, the compensated measurement data has a more uniform accuracy distribution across the entire detection frequency band, particularly improving the accuracy of impedance parameter estimation in the high-frequency band, thus enabling wideband impedance detection.

[0150] Weighted least squares solution Based on least squares estimation theory, the derivation process begins with minimizing the objective function of the weighted sum of squared residuals. By taking the partial derivatives of the parameter vectors and setting them to zero, the normal equations are obtained, and finally, the optimal parameter estimate is obtained by solving them. The introduction of the weight matrix W in this formula allows for the allocation of different weights according to the reliability of the measurement data. Compared to the ordinary least squares method, weighted least squares can effectively suppress the adverse effects of low signal-to-noise ratio data on the estimation results, improving the robustness and accuracy of impedance parameter estimation.

[0151] covariance matrix The statistical theory of parameter estimation quantifies the uncertainty of parameter estimates by measuring the noise variance and the geometric properties of the coefficient matrix. This formula provides a confidence assessment for each impedance parameter. Compared to traditional methods that only provide point estimates, the covariance matrix reveals the correlations between parameters and differences in estimation accuracy, offering more comprehensive reliability information for engineering applications.

[0152] upper-level objective function Employing multi-objective optimization theory, a trade-off between different performance indicators is achieved through a combination of logarithmic, exponential, and power functions. The logarithmic term log(η / T) is one such example. cost This reflects the efficiency comparison between detection accuracy and time cost, with the exponential term exp(R) representing the ratio of detection accuracy to time cost. res This emphasizes the importance of resolution, and the square root term. This reflects the suppression of stability risks. The objective function aims to optimize detection efficiency while ensuring detection accuracy. Compared to single-objective optimization methods, multi-objective game theory models can find the optimal balance point of detection strategy under complex engineering constraints.

[0153] Stability index S index =max(Real(λ) i Based on the stability theory of linear systems, the principle is to determine the stability margin of the system by maximizing the real parts of the system's eigenvalues. When the real parts of all eigenvalues ​​are negative, the system is asymptotically stable. This formula provides a quantitative stability evaluation index. Compared to traditional qualitative stability analysis methods, the numerical stability index can accurately assess the impact of disturbance injection on system stability, providing reliable constraints for lower-level optimization of the game theory model and ensuring the safety of the impedance detection process.

[0154] To better understand and implement this invention, the following is a specific application scenario of the invention, Example 2: A research team selected a 50kW three-phase grid-connected inverter. This inverter is equipped with an L-type filter, where the inductance L is 2.5mH, the capacitance C is 25μF, and the system load impedance R is 100Ω. According to... Figure 2 The inverter main circuit structure shown is a three-phase full-bridge topology with a DC side voltage of 800V and a switching frequency of 10kHz. Figure 3 The block diagram showing the inverter, filter, grid impedance, and grid voltage provides a theoretical basis for system design. Figure 4 The diagram of the first-order active filter sampling circuit shown guides the construction of the data acquisition system.

[0155] The research team first executed Step 1, initializing the grid-connected inverter and putting it into impedance detection mode. The DC-side input voltage was stabilized at 800V, and the inverter employed space vector pulse width modulation with a switching frequency set to 10kHz. The system used 50Hz as the fundamental frequency and selected 10 detection frequencies: 150Hz, 250Hz, 350Hz, 450Hz, 550Hz, 650Hz, 750Hz, 850Hz, 950Hz, and 1050Hz, forming a logarithmic frequency sequence. The disturbance amplitude at each frequency was set to 3% of the rated current, i.e., 1.5A. The initial phase was determined using a peak factor optimization algorithm to keep the peak factor of the synthesized signal below 1.4.

[0156] In Step 2, the research team used a Hall current sensor with an accuracy of 0.1% to collect the inverter-side current i. f and common coupling point voltage u pcc Sampling frequency f s The system is set to 10kHz, collecting 200 data points within one 50Hz power grid cycle. To ensure sampling synchronization, a phase-locked loop circuit is configured to precisely lock the phase of the power grid voltage, and a low-pass filter with a cutoff frequency of 2kHz is configured at the sampling front end to eliminate high-frequency noise interference.

[0157] In Step 3, the research team repeated the sampling process at 10 different frequency points, continuously collecting data for 5 power grid cycles at each frequency point to improve statistical reliability. A smooth transition method was used between different frequency points to avoid transient responses caused by frequency abrupt changes. During the data acquisition process, system stability indicators were monitored in real time to ensure that the real part of the largest eigenvalue was always less than -0.5, meeting stability requirements. The amount of data collected at each frequency point is shown in Table 1.

[0158] Table 1. Statistical Table of Data Acquisition at Each Detection Frequency Point

[0159] Detection frequency Number of collection cycles Number of sampling points per cycle Total number of sampling points Effective data rate 150Hz 5 200 1000 98.2％ 250Hz 5 200 1000 98.5％ 350Hz 5 200 1000 97.8％ 450Hz 5 200 1000 97.3％ 550Hz 5 200 1000 96.9％ 650Hz 5 200 1000 96.1％ 750Hz 5 200 1000 95.7％ 850Hz 5 200 1000 95.2％ 950Hz 5 200 1000 94.8％ 1050Hz 5 200 1000 94.3％

[0160] In Step 4, the research team performed Fast Fourier Transform (FFT) analysis on the acquired current and voltage data. A Hamming window function was used to reduce spectral leakage, with a window length of 1024 points. After FFT analysis, the amplitude and phase information of each detection frequency point were extracted to establish a frequency domain feature vector matrix. Due to the cutoff frequency of the L-type filter... The high-frequency signal exhibits significant attenuation. The FFT analysis results for each frequency point are shown in Table 2.

[0161] Table 2. FFT analysis results at each detection frequency.

[0162]

[0163]

[0164] In Step 5, the research team established a system of linear equations based on 10 vector equations and used a weighted least squares algorithm to solve for the impedance parameters. The weight matrix was determined based on the signal-to-noise ratio at each frequency point, with the weight set to 1.0 for low-frequency bands and gradually decreasing to 0.3 for high-frequency bands based on the attenuation level. The overdetermined linear equations were solved using the QR decomposition method to obtain estimates of the grid impedance and inverter output impedance. After considering frequency compensation, the compensation coefficients at each frequency point are shown in Table 3.

[0165] Table 3. Calculation Results of Frequency Compensation Coefficient

[0166] Detection frequency Original attenuation coefficient Weighting coefficients Compensation coefficient Current amplitude after compensation voltage amplitude after compensation 150Hz 0.892 0.95 1.065 1.582A 346.9V 250Hz 0.834 0.92 1.103 1.630A 357.6V 350Hz 0.756 0.88 1.164 1.710A 375.8V 450Hz 0.663 0.83 1.252 1.824A 402.1V 550Hz 0.559 0.77 1.378 1.987A 439.4V 650Hz 0.450 0.70 1.556 2.215A 492.1V 750Hz 0.342 0.62 1.813 2.535A 567.2V 850Hz 0.241 0.53 2.199 3.007A 678.8V 950Hz 0.152 0.43 2.829 3.761A 859.8V 1050Hz 0.086 0.32 3.721 4.777A 1110.5V

[0167] In Step 6, the research team, combining the inductance-current relationship curves from the inductor datasheet, used a cubic polynomial fitting to obtain a mathematical model of the inductance value as a function of current. The real part of the grid impedance, R, was then calculated using frequency-compensated data. grid = 0.847Ω, imaginary part X grid = 2.156Ω, the real part of the inverter output impedance R inv =0.234Ω, imaginary part X inv =1.678Ω. Covariance matrix analysis shows that the standard deviation of the parameter estimates is less than 4.2% of the true value, which meets the engineering accuracy requirements.

[0168] In Step 7, the research team applied the calculated impedance parameters to the disturbance observer algorithm to achieve real-time estimation and feedforward compensation of grid voltage fluctuations and load changes. The observer adjusts the control strategy in real time based on the impedance parameters, reducing the total harmonic distortion rate of the inverter output current from 2.8% to 2.1% and the current tracking error from 0.15A to 0.09A.

[0169] Traditional power grid impedance detection methods primarily employ single-frequency sweep technology, requiring measurements at each frequency point, resulting in detection times exceeding 30 minutes. Furthermore, high-frequency bands are susceptible to filter interference, leading to low detection accuracy. This invention utilizes a multi-frequency simultaneous injection method, reducing the detection time to 12 minutes. Moreover, traditional methods cannot achieve online detection, while this invention can complete impedance detection under normal system operation, providing real-time data support for power grid stability monitoring. Through game theory model optimization, this invention minimizes the impact on system stability while maintaining detection accuracy.

[0170] It should be noted that the variables involved in this invention are explained in detail in Tables 4 and 5.

[0171] Table 4. Variable Explanation Table (Part 1)

[0172]

[0173]

[0174] Table 5. Variable Explanation Table (Part Two)

[0175]

[0176] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for impedance detection of a grid-connected inverter based on an L-type filter, characterized in that, This includes obtaining the inductance and capacitance values ​​of an L-type filter as initial parameters and establishing a frequency response attenuation vector model; constructing a frequency response attenuation coefficient matrix by analyzing the transfer function characteristics of the L-type filter at different frequencies; constructing a wideband detection domain and determining the optimal frequency distribution sequence for multi-frequency injection; establishing a detection frequency range based on the grid fundamental frequency and selecting injection frequencies using a logarithmic distribution method; injecting multi-frequency disturbance signals at the preset operating point of the grid-connected inverter, while simultaneously acquiring time-domain data of inverter-side current and common coupling point voltage. Fast Fourier transform analysis was performed on the collected inverter-side current and common coupling point voltage data to extract the amplitude and phase information corresponding to each injection frequency point and establish a frequency domain feature vector matrix. A frequency compensation matrix model is established, and the high-frequency measurement data is compensated and corrected based on the frequency characteristic attenuation vector to eliminate the influence of the high-frequency attenuation effect of the L-type filter on the impedance detection accuracy. A linear equation system for impedance parameter estimation is established using a weighted least squares optimization algorithm. The optimal estimated values ​​of grid impedance and grid-connected inverter output impedance are obtained by solving the overdetermined equation system. Error analysis and accuracy verification are performed on the impedance detection results. The covariance matrix of the estimation error is calculated, and the verified grid impedance and grid-connected inverter output impedance parameter values ​​are output.

2. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 1, characterized in that, The frequency response attenuation vector is used to describe the amplitude-frequency response attenuation characteristics of the L-type filter at different frequencies. The inputs include the filter inductance value, the filter capacitance value, the system load impedance, and the detection frequency sequence. The output is the attenuation coefficient vector corresponding to each frequency point. The attenuation coefficient vector is used to construct the frequency compensation matrix model.

3. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 2, characterized in that, The wideband detection domain is used to define the frequency range and frequency resolution requirements that need to be covered during impedance detection. The inputs include the fundamental frequency of the power grid, the highest detection frequency of the system, the detection frequency resolution, and the cutoff frequency of the L-type filter. The output is the complete frequency domain range applicable to impedance detection.

4. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 3, characterized in that, The optimal frequency point for multi-frequency injection is used to determine the optimal selection strategy for the frequencies of multiple disturbance signals injected simultaneously during impedance detection. The inputs include impedance detection accuracy requirements, grid-connected inverter system stability constraints, frequency interval constraints, and system computational complexity constraints. The output is the optimal frequency point combination sequence that satisfies the requirements of detection accuracy and system stability.

5. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 4, characterized in that, In the step of injecting multi-frequency disturbance signals, the sampling frequency is set to 10kHz to meet the requirements of the Nyquist sampling theorem. The time-domain data acquisition process of inverter side current and common coupling point voltage is synchronously sampled through a high-precision analog-to-digital converter module.

6. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 5, characterized in that, In the Fast Fourier Transform analysis step, the time-domain sampled data is processed by a window function to reduce the impact of spectral leakage. The amplitude and phase information of each injected frequency point are extracted through frequency domain transformation to establish a vector matrix data structure containing frequency component features.

7. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 6, characterized in that, The frequency compensation matrix model is used to correct the measurement error and signal attenuation caused by the L-type filter in the high-frequency band. The input includes the frequency characteristic attenuation vector, the frequency domain feature vector matrix, the compensation algorithm parameters and the frequency weighting coefficients, and the output is the measurement data matrix after high-frequency compensation correction.

8. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 7, characterized in that, The error analysis and accuracy verification steps assess the reliability of the impedance detection results by calculating the covariance matrix of the estimated error, quantify the uncertainty of the estimated parameters, and ensure that the output grid impedance and grid-connected inverter output impedance parameter values ​​meet the accuracy requirements.

9. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 8, characterized in that, The frequency domain feature vector matrix is ​​used to store the amplitude and phase feature information of each frequency component obtained after fast Fourier transform analysis. The input includes time-domain sampling data of inverter side current, time-domain sampling data of common coupling point voltage, sampling frequency and analysis window function type.

10. The method for detecting the impedance of a grid-connected inverter based on an L-type filter according to claim 9, characterized in that, The game theory model is constructed by including an upper-level model that aims to maximize impedance detection accuracy and a lower-level model that aims to maximize system stability. The upper-level model and the lower-level model realize the trade-off between detection accuracy and system stability through coupling terms.

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