High-frequency resolution dynamic broadband measurement method

Abstract

The invention discloses a high-frequency-resolution dynamic broadband measurement method, and belongs to the technical field of broadband measurement of a power system. The invention relates to a high-frequency resolution dynamic broadband measurement method, which comprises the following steps of: carrying out discrete sampling on broadband voltage and current electrical quantities of a power system to obtain a discrete sampling value sequence; carrying out all-phase FFT (Fast Fourier Transform) on the discrete sampling value sequence to obtain an all-phase amplitude-frequency spectrum and a phase-frequency spectrum; the spectrum peak of the amplitude frequency spectrum is searched, and broadband component characteristics are identified according to the phase of the phase frequency spectrum corresponding to the three spectrum lines with the maximum amplitudes; the frequency and the amplitude of the static non-dense component are corrected through a three-spectrum ratio method; dense components are distinguished through a matrix pencil method; and calculating the frequency, the amplitude and the phase angle of the dynamic component through a second-order Taylor expansion model. By adopting the high-frequency-resolution dynamic broadband measurement method provided by the invention, the amplitude, frequency and phase angle parameters of broadband voltage and current electrical quantity with time-varying and multi-component superposition parameters can be accurately measured in real time.

Description

Technical Field

[0001] The present invention relates to the technical field of wide - frequency measurement in power systems, and particularly to a high - frequency - resolution dynamic wide - frequency measurement method. Background Technique

[0002] In recent years, with the rapid development of renewable energy and a large number of power electronic devices being connected to the power grid, the power system shows the "dual - high" characteristics of "high proportion of renewable energy" and "high proportion of power electronic devices". Compared with traditional electrical equipment, power electronic devices have significant differences in aspects such as topological structure, control strategy, and dynamic response. When power electronic devices interact with each other and with the power grid, the wide - frequency electrical quantities exhibit complex characteristics of multiple components and time - variation, which poses challenges to existing wide - frequency measurement algorithms.

[0003] Currently, wide - frequency measurement methods can be mainly divided into time - frequency domain methods and spectral estimation methods. Time - frequency domain methods extract different frequency components by transforming time - domain signals into the frequency domain. Time - frequency domain methods often involve complex transformation algorithms such as short - time Fourier transform and wavelet transform. The fast Fourier transform is the most widely used method in practical engineering applications due to its simple algorithm and easy hardware implementation. However, its frequency resolution is directly related to the window length, and its accuracy is affected by spectral leakage and the fence effect. The Hilbert - Huang transform and wavelet analysis method have dynamic measurement capabilities, but the former has problems such as mode mixing, spurious components, and end - point effects; the latter is prone to frequency aliasing, and its real - time performance and stability are not good. The Taylor Fourier transform approximates time - varying amplitude and phase angle through Taylor series and has a certain dynamic measurement ability, but it requires prior knowledge of the frequency of the component to be measured and is currently mostly used in fundamental frequency and harmonic phasor measurements. Spectral estimation methods such as Prony and ESPRIT theoretically have infinitely high frequency resolution. In practice, due to the existence of noise, there is also a limit to the resolution, and the solution process involves large - scale matrix operations. Currently, it is often used for measuring low - frequency oscillations, sub - / super - synchronous oscillations with a small sampling matrix scale.

[0004] It can be seen that the existing time - frequency domain methods and spectral estimation methods for wide - frequency measurement have limitations and are difficult to simultaneously meet high - frequency resolution and dynamic measurement capabilities, and cannot provide effective data support for wide - frequency oscillation analysis and suppression. Summary of the Invention

[0005] The purpose of the present invention is to provide a high - frequency - resolution dynamic wide - frequency measurement method, which can achieve real - time and accurate measurement of wide - frequency voltage and current electrical quantities with time - varying parameters and multiple - component superposition in a high - proportion new - energy distribution network, and provide data support for wide - frequency state estimation, oscillation protection, and suppression.

[0006] To achieve the above - mentioned purpose, the present invention provides a high - frequency - resolution dynamic wide - frequency measurement method, including the following steps: S1. Discretely sample the broadband voltage and current electrical quantities of the power system to obtain a discrete sampling value sequence; S2. Perform a full-phase FFT transformation on the discrete sampling value sequence to obtain the full-phase amplitude spectrum and phase spectrum; S3. Search for the spectral peaks of the amplitude spectrum, and identify the characteristics of the broadband components according to the phases of the phase spectra corresponding to the three spectral lines with the largest amplitudes; S4. If the spectral peak is a static non-dense component, correct the frequency and amplitude of the static non-dense component by the three-spectrum ratio method; S5. If the spectral peak is composed of a dynamic component with time-varying parameters or the superposition of multiple dense components with different frequencies, calculate the frequency, amplitude and phase angle of the component by the matrix pencil method; S6. Calculate the verification coefficient to determine whether it is a dynamic component; S7. Establish a dynamic signal model of the dynamic component, and calculate the frequency, amplitude and phase angle of the dynamic component through the second-order Taylor expansion model.

[0007] Preferably, in S1, the broadband voltage and current electrical quantities of the power system are expressed as: ; wherein, represents the fundamental amplitude, represents the fundamental frequency, represents the fundamental phase angle, W is the number of broadband components included in the signal, represents the th broadband component amplitude, represents the th broadband component frequency, represents the th broadband component phase angle, represents time; The sampling value is: ; wherein, is the sampling point, F s is the sampling frequency. Take 2 -1 sampling points centered on N to form a sampling sequence .

[0008] Preferably, in S2, the full-phase FFT transformation is specifically: Compared with FFT, the full-phase FFT has excellent anti-noise performance and phase characteristics. Multiply the sampling value by the Hanning self-convolution window Multiply and add the data with a sampling point interval of in pairs to obtain the all-phase FFT windowing sequence , ; In the formula, is the time-domain expression of the Hanning window, ; The superscript represents all-phase, and the subscript represents the Hanning window function; Perform an -point FFT transform on the all-phase FFT windowing sequence to obtain the all-phase amplitude spectrum and the phase spectrum , is the spectral index number corresponding to the spectrum.

[0009] Preferably, in S3, the identification of the broadband component characteristics through the phase spectrum is specifically as follows: In this step, find the spectral peak of the amplitude spectrum. If and , it is determined that there is a spectral peak at this place, and record these I ( I ≤ W ) eligible as . The spectral peak may be generated by a single-frequency static broadband component, or may be composed of a dynamically varying component with time-varying parameters or the superposition of multiple dense components with different frequencies. When it is the latter, the error obtained by using the three-spectrum interpolation method is relatively large. Therefore, it is necessary to identify the characteristics of the components.

[0010] The all-phase FFT transform has phase invariance compared with the FFT transform. It can be judged whether the spectral peak is generated by dense components or dynamic components by whether the phases corresponding to the spectral lines around the spectral peak are equal. Considering the influence of noise, set the detection threshold to 0.5°. If , it is considered that there are no dense components or dynamic components, and solve through step S4. Otherwise, solve through steps S5-S7.

[0011] Preferably, in S4, the correction of the frequency and amplitude of the static non-dense components through the three-spectrum ratio method is specifically as follows: Due to the fence effect of the FFT, the spectral peak of the amplitude spectrum is not necessarily equal to the actual spectral peak. Denote the amplitudes of the three spectral lines with the largest amplitudes in the spectral peak as , and , then ; ; ; In the formula, is the frequency-domain expression of the Hanning window, is the frequency index. Let the frequency correction amount be , then ; Denote , substitute it into the above formula, and get ; Thus, an expression is established between the known quantity and the quantity to be solved . Since the frequency-domain expression of the Hanning window is known,can be obtained by polynomial fitting, that is ; The component frequency correction value is: ; Similarly, the amplitude correction value can be obtained as ; The phase angle is the phasecorresponding to the spectral line with the largest amplitude , without correction.

[0012] Preferably, in the step S5, calculating the frequency, amplitude, and phase angle of the component by the matrix pencil method specifically includes: S51. Since the common sampling frequency of the broadband measurement device is 12.8 kHz, a high sampling rate will bring a high matrix calculation dimension, making it difficult to directly use the spectral estimation method with high frequency resolution for real-time calculation. Therefore, first perform frequency shift and downsampling preprocessing on the sampling value : ; ; Among them, is the frequency corresponding to , is the coefficient of the low-pass filter of order , which is obtained by offline design; is the coefficient of the low-pass filter after frequency shift, N is the downsampling sequence of length (2 N r +1), r is the largest integer of N ​r denotes the half-width of the downsampling window, and downsampling F r is the downsampling frequency. Take F r as 200 Hz, and design a low-pass filter using the equiripple method. After processing, other components are filtered out, and the positive-frequency part of the component to be measured is shifted to near the fundamental frequency.

[0013] S52. Use a simplified matrix pencil model to distinguish frequency-dense components; If there are M frequency-dense components in the spectrum peak after the frequency-shifting and downsampling preprocessing, ignore the exponential decay term, and the sampling value expression is ; wherein, is the amplitude of the th frequency-dense component, is the frequency of the th frequency-dense component, is the phase angle of the th frequency-dense component, is the downsampling interval.

[0014] Let , , then ; Construct a Hankel matrix from the downsampling values: ; In the formula, L is the number of columns. Select an appropriate L to improve the noise. Usually take (2 N r +1) / 3~(2 N r +1) / 4. Take from as follows ; Let ; ; ; ; Then ; ; Since and are both full-rank matrices, and The ranks of and are the same. Construct the matrix pencil ; When , the rank of is reduced to . At this time, the matrix is rank-deficient, always holds,

[0015] and ; After resampling, the length of the 1-second sampled data is reduced from 12,800 to less than 200, greatly reducing the dimension of the above matrix operations, enabling real-time and accurate discrimination of dense components through a long time window. After obtaining the eigenvalues, the parameter is obtained from the following formula: ; Thus, the frequencies, amplitudes, and phases of the dense components after frequency shift are obtained as shown in the following formula, which are the frequencies of the components before frequency shift.

[0016] ; ; .

[0017] Preferably, in S5, it is assumed that the frequency-shifted and downsampled sequence only contains dense components, and the model ignores the exponential decay term. When the components undergo a dynamic change process, there are large errors in the parameters obtained by the matrix pencil method. Therefore, a calibration coefficient is introduced to identify the dynamic process In S6, the calibration coefficient is: ; is reconstructed according to the calculation result of S5. Its expression is as follows: ; where is the estimated value of the downsampled value; is the estimated value of the amplitude of the rd dense component, is the estimated value of the frequency of the th dense component, is the estimated value of the th dense component phase angle; when , there is an error caused by the dynamic component.

[0018] Furthermore, in S7, for the dynamic component, a dynamic signal model is established: ; where , , represents the dynamic broadband phasor, represents the frequency complex exponential factor; different from the matrix pencil model, the amplitude and phase included in this model are time-varying quantities. reflects the dynamic change of the amplitude, represents the time-varying behavior of the phase; Perform a second-order Taylor expansion of at : ; Considering that the change rate of the dynamic component is slow, using the second-order expansion term can well approximate the signal within the calculation window. Take - N T to N T of downsampling points, N T is the half-width of the Taylor expansion window. Substitute the Taylor expansion formula into the dynamic signal model to get: ; where is the dynamic phasor column vector, ; is the matrix with the center frequency of ; is the column vector composed of downsampling values, ; .

[0019] Then The least squares estimate of is ; Essentially, it can be regarded as a filter bank with the center frequency of , and its filtering performance can be improved by a weighted diagonal matrix, that is . Denote its last two rows as , , then ; ; Since the frequencies of the components after frequency shifting are close to the fundamental frequency, we can set , calculate the filter bank coefficients offline, and reduce the real-time calculation amount. In the present invention, take , . At this time, The passband of is about 1 Hz, meeting the requirements of dynamic component measurement.

[0020] The amplitude, phase, and frequency of the dynamic component before frequency shifting are obtained from the following equations: ; ; .

[0021] The advantages and positive effects of the high-frequency resolution dynamic broadband measurement method described in the present invention are as follows: Through the phase invariance of the all-phase FFT, the present invention preliminarily analyzes broadband electrical quantities, proposes a simple and practical identification method, and can accurately identify dense components and dynamic components with poor measurement accuracy of the all-phase FFT; According to the identification results, the sampling sequence is preprocessed by frequency shifting and resampling, reducing the mutual interference between components, improving the stability of the improved matrix pencil method, and greatly reducing the computational burden; A second-order Taylor expansion model is established, and using the known frequency range after frequency shifting, the Taylor filter coefficients are calculated offline, simplifying the calculation steps, and finally realizing the real-time measurement of broadband dense components and dynamic components.

[0022] Next, through the drawings and embodiments, the technical solutions of the present invention will be further described in detail. Description of the Drawings

[0023] Figure 1 is a flowchart of an embodiment of a high-frequency resolution dynamic broadband measurement method of the present invention; Figure 2 is a comparison diagram of the interharmonic near fundamental wave analysis error of an embodiment of a high-frequency resolution dynamic broadband measurement method of the present invention, where APTFT is the method of this embodiment; Figure 3 is a comparison diagram of the interharmonic near harmonic analysis error of an embodiment of a high-frequency resolution dynamic broadband measurement method of the present invention, where APTFT is the method of this embodiment; Figure 4 is an experimental platform of an embodiment of a high-frequency resolution dynamic broadband measurement method of the present invention. Detailed Embodiments

[0024] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which this application belongs. In case of inconsistency, the meaning stated in this specification or the meaning derived from the content recorded in this specification shall prevail. Additionally, the terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0025] The following will describe in detail the embodiments of the present invention with reference to the accompanying drawings.

[0026] Embodiment As Figure 1 shown. The high-frequency resolution dynamic broadband measurement method includes the following steps: S1. Discretely sample the broadband voltage and current electrical quantities of the power system to obtain a discrete sampling value sequence.

[0027] The broadband voltage and current electrical quantities of the power system are expressed as: ; where represents the fundamental wave amplitude, represents the fundamental wave frequency, represents the fundamental wave phase angle, W is the number of broadband components included in the signal, represents the th broadband component amplitude, represents the th broadband component frequency, represents the th broadband component phase angle, represents time; The sampling value is: ; where is the sampling point, F s is the sampling frequency. Take 2 -1 sampling points centered on N to form a sampling sequence .

[0028] S2. Perform a full-phase FFT transform on the discrete sampling value sequence to obtain a full-phase amplitude spectrum and a phase spectrum.

[0029] Multiply the sampling value by the Hanning self-convolution window , and add the data with a sampling point interval of in pairs to obtain a full-phase FFT windowing sequence . ; In the formula, is the time-domain expression of the Hanning window, ; The superscript represents all-phase, and the subscript represents the Hanning window function; For the all-phase FFT windowed sequence perform point FFT transformation to obtain the all-phase amplitude spectrum and the phase spectrum , is the index number corresponding to the spectrum.

[0030] S3. Locate the peak of the amplitude spectrum, and identify the characteristics of the broadband components based on the phases of the phase spectra corresponding to the three spectral lines with the largest amplitudes.

[0031] Locate the peak of the amplitude spectrum . If and , it is determined that there is a peak at this location, and record this I ( I ≤ W ) qualified as .

[0032] Perform characteristic identification through the phase spectrum . If , it is considered that there are no dense components or dynamic components, and solve through step S4. Otherwise, solve through steps S5 - S7.

[0033] S4. If the peak is a static non-dense component, correct the frequency and amplitude of the static non-dense component by the three-spectrum ratio method.

[0034] Record the amplitudes of the three spectral lines with the largest amplitudes in the peak as y 1, y 2 and y 3. Let the frequency correction amount be , then ; The frequency correction value of the component is: ; Similarly, the amplitude correction value can be obtained as ; The phase angle is the phase corresponding to the spectral line with the largest amplitude , and no correction is required.

[0035] S5. If the spectral peak is composed of a dynamic component with time-varying parameters or multiple dense components with different frequencies superimposed, calculate the frequency, amplitude, and phase angle of the components by the matrix pencil method.

[0036] For the sampled values Perform preprocessing of frequency shift and downsampling: ; ; Among them, is the corresponding frequency, is the low-pass filter coefficients of order , obtained by offline design; is the low-pass filter coefficient after frequency shift, is the length of the downsampled sequence, is the largest integer of , represents the half-width of the downsampling window, and the downsampling is the downsampling frequency. Take as 200 Hz, and design the low-pass filter by the equiripple method. After processing, other components are filtered out, and the positive-frequency part of the component to be measured is shifted to near the fundamental frequency.

[0037] S52. Use a simplified matrix pencil model to distinguish frequency-dense components; If there are M dense components in the spectral peak after frequency shift and downsampling preprocessing, ignoring the exponentially decaying term, the sampled value expression is ; Among them, is the amplitude of the th dense component, is the frequency of the th dense component, is the phase angle of the k th dense component, is the downsampling interval.

[0038] Let , , then ; Construct a Hankel matrix from the downsampled values: ; In the formula, L is the number of columns. Selecting an appropriate L can improve the noise. Usually take . Take from as follows ; is the generalized eigenvalue of the matrix pencil , and the calculation formula is as follows: ; After obtaining , the parameter is obtained from the following formula: ; Thus, the frequency, amplitude, and phase of the dense components after frequency shift are obtained as shown in the following formula, which are the frequencies of the components before frequency shift.

[0039] ; ; .

[0040] S6. Calculate the check coefficient and determine whether it is a dynamic component.

[0041] The check coefficient is: ; is reconstructed according to the calculation result of S5. Its expression is as follows: ; where is the estimated value of the downsampled value; is the estimated value of the amplitude of the th dense component, is the estimated value of the frequency of the th dense component, is the estimated value of the phase angle of the th dense component; when , there is an error caused by the dynamic component.

[0042] S7. Establish a dynamic signal model for the dynamic component and calculate the frequency, amplitude, and phase angle of the dynamic component through a second-order Taylor expansion model.

[0043] For the dynamic component, establish a dynamic signal model: ; where , , represents the dynamic broadband phasor, represents the frequency complex exponential factor; different from the matrix pencil model, the amplitude and phase included in this model are quantities that change with time. reflects the dynamic change of the amplitude, Represent the time-varying behavior of the phase; Will At Perform a second-order Taylor expansion: ; Considering that the change rate of the dynamic component is slow, using the second-order expansion term can well approximate the signal within the calculation window. Take - N T To N T Of Downsampling points, N T Is the half-width of the Taylor expansion window. Substitute the Taylor expansion into the dynamic signal model to get: ; Among them, Is the column vector of the dynamic phasor, ; Is the matrix with the center frequency of ; Is the column vector composed of the downsampling values, ; .

[0044] Then The least squares estimate of is ; Essentially, it can be regarded as a filter bank with the center frequency of , and its filtering performance can be improved by a weighted diagonal matrix, that is . Denote its last two rows as , , then ; ; Since the frequency of the component after frequency shift is close to the fundamental frequency, let , calculate the filter bank coefficients offline to reduce the real-time calculation amount. In the present invention, take , . At this time, The passband of is about 1 Hz, meeting the requirements of dynamic component measurement.

[0045] The amplitude, phase and frequency of the dynamic component before frequency shift are obtained from the following formula: ; ; .

[0046] To illustrate the technical effects of the method described in this embodiment, the frequency resolution ability, dynamic analysis ability, and broadband measurement ability of the method described in this embodiment are verified. 1. Frequency resolution ability In comparison with IpFFT and K-ESPRIT, the simulation signal is set as ; In the formula, is the sampling interval, is the fundamental frequency, is the interharmonic frequency, , , are the initial phase angles of the fundamental frequency, interharmonic, and harmonic respectively. During the simulation test, Ts = 1 / 12.8 ms is taken, white noise is added, and SNR = 60 dB is taken.

[0047] Keeping the fundamental frequency at 50 Hz, setting the interharmonic frequency to decrease from 58 Hz to 50.5 Hz in steps of 2 Hz. When the interval between the fundamental frequency and the interharmonic is 6 Hz, the frequency, amplitude, and phase errors of the interharmonic calculated by IpFFT are 0.002 Hz, 2.99%, and 1.4° respectively. When the frequency interval is 4 Hz, the two signals can no longer be distinguished, and the simulation results are not given. The simulation results of the method of this embodiment and K-ESPRIT are as Figure 2 shown. In the figure, , , , respectively represent the analysis results of the fundamental wave and interharmonic by the method.

[0048] Keeping the harmonic frequency at 150 Hz, setting the interharmonic frequency to increase from 142 Hz to 149.5 Hz in steps of 2 Hz. The simulation results of the method of this embodiment and ESPRIT are as Figure 3 shown. In the figure, , , , respectively represent the analysis results of the interharmonic and harmonic by the method.

[0049] From Figure 2 and Figure 3 , it can be seen that the method described in this embodiment can accurately distinguish dense signals with a frequency interval of more than 0.5 Hz whether the component amplitude difference is large or small. Compared with K-ESPRIT, the frequency error and phase error are smaller, and the amplitude error increases slightly, not exceeding 0.3%.

[0050] 2. Dynamic analysis ability The simulation signal is set as ; wherein, is the sampling interval, is the fundamental frequency, is the interharmonic frequency, , , are the initial phase angles of the fundamental frequency, interharmonic and harmonic respectively. Among them, the amplitude of the interharmonic changes linearly, and the interharmonics and are equi-amplitude adjacent components with an interval of 0.2 Hz, and the fifth harmonic has phase angle modulation. The fundamental frequency is set to 50.5 Hz, the amplitude change rate is 10%, the modulation frequency is 0.3 Hz, white noise is added, and SNR = 60 dB is taken. The simulation results of this embodiment and IpFFT, K-ESPRIT are shown in Table 1.

[0051] Table 1 Dynamic signal analysis error ;

[0052] For the interharmonic 1 and harmonic of the dynamic components, due to the averaging effect of IpFFT, the analysis error is large. The ESPRIT signal model considers that the amplitude is an exponentially decaying function, and the error is small when the amplitude change is small; for the interharmonic components 2 and 3 with similar frequency intervals, there is only one spectral peak on the IpFFT spectrum, and ESPRIT cannot distinguish them either because the signal subspaces are similar, and they are equivalently calculated as one dynamic component, resulting in a large measurement error. The method described in this embodiment has high measurement accuracy under both dense and dynamic conditions.

[0053] 3. Wideband measurement ability Build a relevant test platform as Figure 4 shown. Use the OMICRON signal generator to generate the signal to be measured, transmit it to the wideband measurement device, and use the proposed algorithm for analysis to obtain information such as the amplitude, frequency, and phase of each component of the wideband signal. Finally, the upper computer reads the data and analyzes the error.

[0054] The test cases are shown in Table 2. Among them, component 3 has amplitude modulation, the modulation frequency is 3 Hz, and the modulation depth is 10%; component 4 has a linear amplitude change, increasing from 1.5 V to 3.0 V at 20% per second.

[0055] Table 2 Test cases ;

[0056] Due to the influence of hardware sampling and environmental noise, the measurement accuracy of each method is finally reduced, as shown in Table 3. For static non-dense components, the measurement errors of the three algorithms are similar. However, for dense components 5 and 6, IpFFT and K-ESPRIT cannot distinguish them; for dynamic components 3 and 4, the method described in this embodiment is significantly better than IpFFT and K-ESPRIT, which verifies its effectiveness. Although the accuracy loss is inevitable in the actual device, its frequency error is still lower than 0.05 Hz and the amplitude error is lower than 0.3%, still meeting the requirements of wide-frequency oscillation monitoring and suppression.

[0057] Table 3 Experimental test results ;

[0058] Therefore, by adopting a high-frequency resolution dynamic wide-frequency measurement method described in the present invention, the wide-frequency electrical quantity with time-varying parameters and multi-component superposition can be accurately and real-time measured, and the actual situation of on-site electrical quantity can be restored to a large extent, having certain engineering application value.

[0059] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A high-frequency resolution dynamic wide-band measurement method, characterized in that, Including the following steps: S1. Discretely sample the broadband voltage and current electrical quantities of the power system to obtain a discrete sampling value sequence; S2. Perform a full-phase FFT transformation on the discrete sampling value sequence to obtain a full-phase amplitude spectrum and a phase spectrum; S3. Search for the spectral peaks of the amplitude spectrum, and identify the characteristics of the broadband components according to the phases of the phase spectra corresponding to the three spectral lines with the largest amplitudes; S4. If the spectral peak is a static non-dense component, correct the frequency and amplitude of the static non-dense component by the three-spectrum ratio method; S5. If the spectral peak is composed of a dynamic component with time-varying parameters or the superposition of multiple dense components with different frequencies, calculate the frequency, amplitude and phase angle of the component by the matrix pencil method; S6. Calculate the calibration coefficient to determine whether it is a dynamic component; S7. Establish a dynamic signal model of the dynamic component, and calculate the frequency, amplitude and phase angle of the dynamic component through a second-order Taylor expansion model.

2. The high-frequency resolution dynamic broadband measurement method according to claim 1, characterized in that: In S1, the broadband voltage and current electrical quantities of the power system are expressed as: ； Among them, represents the fundamental wave amplitude, represents the fundamental wave frequency, represents the fundamental wave phase angle, W is the number of broadband components included in the signal, represents the amplitude of the th broadband component, represents the th broadband component frequency, represents the th broadband component phase angle, represents time; Sampled value is: ； Among them, is the sampling point, F s is the sampling frequency.

3. A high-frequency resolution dynamic broadband measurement method according to claim 2, characterized in that In the above S2, the full-phase FFT transformation is specifically as follows: Multiply the sampled values by a Hanning self-convolution window and add the data with a sampling point interval of in pairs to obtain an all-phase FFT windowed sequence , ； In the formula, is the time-domain expression of the Hanning window, ; Superscript represents all phases, subscript represents the Hanning window function; For the all-phase FFT windowed sequence perform an N-point FFT transformation to obtain the all-phase amplitude spectrum and the phase spectrum , where k is the index number corresponding to the spectrum.

4. A high-frequency resolution dynamic broadband measurement method according to claim 3, characterized in that In S3, through the phase spectrum identifying the characteristics of broadband components specifically includes: Utilize the phase invariance of the full-phase FFT. If the sum of the absolute values of the differences between the phases corresponding to the three spectral lines with the largest amplitudes in a spectral peak is less than or equal to 0.5°, it is considered that there are no dense components or dynamic components in this spectral peak, and it is a static non-dense component, which is solved through step S4; otherwise, it is solved through steps S5 - S7.

5. A high-frequency resolution dynamic broadband measurement method according to claim 4, characterized in that In the above S4, the correction of the frequency and amplitude of the static non-dense component by the three-spectrum ratio method is specifically as follows: The amplitudes of the three spectral lines with the largest amplitudes in the spectral peaks are respectively , and . Denote . Let the correction amount be . ； The corrected value of the component frequency is: ； The corrected value of the component amplitude is: ； In the formula, is the index number of the spectral line with the maximum amplitude.

6. A high-frequency resolution dynamic broadband measurement method according to claim 5, characterized in that In the above S5, the calculation of the frequency, amplitude and phase angle of the component by the matrix pencil method is specifically as follows: S51. Perform preprocessing of frequency shifting and downsampling on the sampling values: ； ； Among them, is the frequency corresponding to the spectral line with the largest amplitude among the spectral peaks with dense components or dynamic components, is the low-pass filter coefficients of order, obtained by offline design; is the low-pass filter coefficients after frequency shift, is the length of the decimated sequence, is the largest integer of, represents the half-width of the decimation window, is the decimation frequency; S52. Use a simplified matrix pencil model to distinguish frequency-dense components; If there are M dense components in the spectrum peak after the frequency shift and downsampling preprocessing, ignoring the exponential decay term, the sampling value expression is ； Among them, is the amplitude of the th intensive component, is the frequency of the th intensive component, is the phase angle of the th intensive component, is the downsampling interval.

7. A high-frequency resolution dynamic broadband measurement method according to claim 6, characterized in that In S6, the verification coefficient is as follows: ； ； Among them, is the estimated value of the decimation value; is the estimated value of the amplitude of the th dense component, is the estimated value of the frequency of the th dense component, is the estimated value of the phase angle of the th dense component; when there is a dynamic component.

8. A high-frequency resolution dynamic broadband measurement method according to claim 7, characterized in that In the above S7, the dynamic signal model is: ； Among them, , ; reflects the dynamic change of amplitude, represents the time-varying behavior of phase; represents the broadband dynamic phasor, represents the frequency complex exponential factor; Will At Perform a second-order Taylor expansion at: ； Take - N T to N T the downsampling points, N T which is the half - width of the Taylor expansion window; Substitute the Taylor expansion into the dynamic signal model, we get: ； Among them, is a dynamic phasor column vector, ; is a matrix with a center frequency of , set = ; is a column vector composed of downsampling values, ; 。

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