A high frequency resolution dynamic broadband measurement method

Abstract

The present invention discloses a high-frequency resolution dynamic broadband measurement method, which belongs to the technical field of broadband measurement of power systems. The high-frequency resolution dynamic broadband measurement method includes the following steps: discrete sampling of broadband voltage and current electrical quantities of the power system to obtain a discrete sampling value sequence; full-phase FFT transformation of the discrete sampling value sequence to obtain a full-phase amplitude spectrum and phase spectrum; finding the spectrum peak of the amplitude spectrum, and identifying the broadband component characteristics according to the phase of the phase spectrum corresponding to the three spectrum lines with the largest amplitude; the static non-dense components are corrected for frequency and amplitude by the three-spectrum ratio method; the dense components are distinguished by the matrix bundle method; the frequency, amplitude and phase angle of the dynamic components are calculated by the second-order Taylor expansion model. The high-frequency resolution dynamic broadband measurement method described in the present invention can accurately measure the amplitude, frequency and phase angle parameters of broadband voltage and current electrical quantities with time-varying parameters and multi-component superposition in real time.

Description

Technical Field

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

[0002] In recent years, the rapid development of renewable energy and the integration of a large number of power electronic devices into the power grid have resulted in the power system exhibiting a "dual high" characteristic: a high proportion of renewable energy and a high proportion of power electronic devices. Compared to traditional electrical equipment, power electronic devices exhibit significant differences in topology, control strategies, and dynamic response. When power electronic devices interact with each other and with the power grid, broadband electrical quantities exhibit complex, multi-component, and time-varying characteristics, posing a challenge to existing broadband measurement algorithms.

[0003] Currently, broadband measurement methods can be primarily categorized as time-frequency domain methods and spectral estimation methods. Time-frequency domain methods extract different frequency components by transforming the time-domain signal into the frequency domain. These methods often involve complex transform algorithms such as the short-time Fourier transform and wavelet transform. The fast Fourier transform (FFT) is the most widely used method in practical engineering applications due to its simplicity and ease of hardware implementation. However, its frequency resolution is directly related to the window length, and its accuracy is affected by spectral leakage and picket fence effects. The Hilbert-Huang transform and wavelet analysis have dynamic measurement capabilities, but the former suffers from modal aliasing, spurious components, and endpoint effects; the latter is prone to frequency aliasing and suffers from poor real-time and stability. The Taylor Fourier transform (TFT) uses Taylor series to approximate time-varying amplitudes and phase angles, offering some dynamic measurement capabilities. However, it requires prior knowledge of the frequency of the component to be measured and is currently primarily used for fundamental frequency and harmonic phasor measurements. Spectral estimation methods such as Prony and ESPRIT theoretically have infinite frequency resolution. However, in practice, due to the presence of noise, there is also a resolution limit, and the solution process involves large-scale matrix operations. Currently, they are often used to measure low-frequency oscillations and sub / supersynchronous oscillations with small sampling matrices.

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

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

[0006] To achieve the above object, the present invention provides a high frequency resolution dynamic broadband measurement method, comprising the following steps:

[0007] S1. Discretely sample the broadband voltage and current electrical quantities of the power system to obtain a discrete sequence of sampled values;

[0008] S2. Perform full-phase FFT transformation on the discrete sampling value sequence to obtain full-phase amplitude spectrum and phase spectrum;

[0009] S3. Find the peak of the amplitude spectrum and identify the broadband component characteristics based on the phase of the phase spectrum corresponding to the three spectral lines with the largest amplitudes;

[0010] S4. If the spectrum peak is a static non-dense component, correct the frequency and amplitude of the static non-dense component by using the three-spectrum ratio method;

[0011] S5. If the spectrum peak is composed of a dynamic component with time-varying parameters or a superposition of multiple dense components of different frequencies, the frequency, amplitude and phase angle of the component are calculated by the matrix bundle method;

[0012] S6. Calculate the calibration coefficient to determine whether it is a dynamic component;

[0013] 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.

[0014] Preferably, in said S1, the power system broadband voltage, current electrical quantity Expressed as:

[0015] ;

[0016] in, represents the fundamental amplitude, represents the fundamental frequency, represents the fundamental phase angle, W is the number of broadband components contained in the signal, Indicates the The amplitude of the broadband component, Indicates the The frequency of the broadband component, Indicates the The phase angle of the broadband component, Indicates time;

[0017] Sample value for:

[0018] ;

[0019] in, is the sampling point, F s is the sampling frequency. Centered 2 N-1 sampling point constitutes a sampling sequence .

[0020] Preferably, in S2, the full-phase FFT transformation is specifically:

[0021] Compared with FFT, full-phase FFT has excellent noise immunity and phase characteristics. With Hanning self-convolution window Multiply and space the sampling points as The data are added two by two to obtain the full-phase FFT window sequence ,

[0022] ;

[0023] Where, is the time domain expression of the Hanning window, ;

[0024] superscript Indicates full phase, subscript represents the Hanning window function;

[0025] Full-phase FFT windowing sequence do Point FFT transformation to obtain the full phase amplitude spectrum Sum and phase spectrum , is the index number corresponding to the spectrum.

[0026] Preferably, in said S3, by phase spectrum The identification of broadband component characteristics is specifically as follows:

[0027] In this step, the peak of the amplitude spectrum is found. and , then it is judged that there is a spectrum peak at this location, and this I indivual( I ≤ W ) for A spectral peak may be caused by a single-frequency, static, broadband component, a dynamic component with time-varying parameters, or the superposition of multiple closely spaced components of different frequencies. In the latter case, the error obtained using the trispectral interpolation method is large. Therefore, it is necessary to identify the characteristics of the component.

[0028] Compared with FFT transformation, full-phase FFT transformation has phase invariance. It can be judged whether the spectrum peak is generated by dense components or dynamic components by whether the corresponding phases of the spectrum lines around the spectrum peak are equal. Considering the influence of noise, the detection threshold is set to 0.5°. , then it is considered that there is no dense component or dynamic component, and the solution is obtained through step S4. Otherwise, the solution is obtained through steps S5-S7.

[0029] Preferably, in S4, the frequency and amplitude of the static non-dense component are corrected by the three-spectrum ratio method as follows:

[0030] Due to the fence effect of FFT, the amplitude spectrum The peak of the spectrum is not necessarily equal to the actual peak. The amplitudes of the three spectral lines with the largest amplitude in the peak are 、 and ,

[0031] but

[0032] ;

[0033] ;

[0034] ;

[0035] Where, is the frequency domain expression of the Hanning window, Frequency The index of . Assume the frequency correction amount is ,but

[0036] ;

[0037] remember , substituting into the above formula, we get

[0038] ;

[0039] Thus, the known quantity and the quantity to be demanded The expression between Since the frequency domain expression of the Hanning window is known, it can be obtained by polynomial fitting. ,Right now

[0040] ;

[0041] The component frequency correction value is:

[0042] ;

[0043] Similarly, the amplitude correction value can be obtained as

[0044] ;

[0045] The phase angle is the spectral line with the maximum amplitude The corresponding phase , no correction is needed.

[0046] Preferably, in said S5, the frequency, amplitude and phase angle of the component are calculated by the matrix bundle method as follows:

[0047] S51. Since the sampling frequency of broadband measurement devices is usually 12.8 kHz, high sampling rate will lead to higher matrix calculation dimensions, making it difficult to directly use high frequency resolution spectrum estimation methods for real-time calculation. Therefore, the sampling value Perform frequency shift downsampling preprocessing:

[0048] ;

[0049] ;

[0050] in, for The corresponding frequency, for The low-pass filter coefficients of order are obtained by offline design; is the low-pass filter coefficient after frequency shift, is the length (2 N r +1) downsampling sequence, N r for The largest integer, N r Indicates the half width of the downsampling window, downsampling F r is the downsampling frequency. F r The frequency of the low-pass filter is 200Hz, and the equiripple method is used to design the low-pass filter. After processing, other components are filtered out and the positive frequency part of the component to be measured is moved to the vicinity of the fundamental frequency.

[0051] S52, using a simplified matrix bundle model to distinguish frequency-dense components;

[0052] If the spectrum peak exists after frequency shift downsampling preprocessing M dense components, ignoring the exponential decay term, the sampling value expression is

[0053] ;

[0054] in, For the The amplitude of the dense component, For the The frequency of the dense components, For the The phase angle of the dense component, is the downsampling interval.

[0055] make , ,but

[0056] ;

[0057] Construct the Hankel matrix from the downsampled values:

[0058] ;

[0059] Where, L For the number of columns, select the appropriate L Can improve noise, usually take (2 N r +1) / 3~(2 N r +1) / 4. From Winning as follows

[0060] ;

[0061] make

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] but

[0067] ;

[0068] ;

[0069] because and are all full-rank matrices, and The rank of the diagonal matrix and The rank of is the same. Construct a matrix bundle

[0070] ;

[0071] when hour, The rank of . In this case, the matrix is ​​not full rank, Heng is established, Therefore, the problem of solving the frequency of dense components is transformed into the problem of solving the generalized eigenvalue of the matrix bundle, thus solving the problem that the FFT frequency resolution is limited by the time window length.

[0072] The calculation formula of generalized eigenvalue is as follows:

[0073] ;

[0074] After resampling, the length of 1 second sample data is reduced from 12800 to less than 200, which greatly reduces the dimension of the above matrix operation, making it possible to accurately distinguish dense components in real time through a long time window. It is derived from the following formula:

[0075] ;

[0076] Thus, the frequency, amplitude and phase of the dense component after frequency shift are obtained as shown in the following formula: That is the frequency of each component before frequency shift.

[0077] ;

[0078] ;

[0079] .

[0080] Preferably, in S5, it is assumed that the frequency shift downsampling sequence contains only dense components and the model ignores the exponential decay term. When the components undergo a dynamic change process, the parameters obtained by the matrix bundle method have large errors. Therefore, the calibration coefficient is introduced To identify dynamic processes

[0081] In S6, the calibration coefficient for:

[0082] ;

[0083] It is reconstructed based on the calculation results of S5. Its expression is as follows:

[0084] ;

[0085] in, is the estimated value of the downsampled value; For the An estimate of the magnitude of the dense component, For the The estimated values ​​of the frequencies of dense components, For the The estimated value of the phase angle of the dense component; when When , there is an error caused by the dynamic component.

[0086] Furthermore, in S7, for the dynamic component, a dynamic signal model is established:

[0087] ;

[0088] in, , , represents a dynamic broadband phasor, Represents the frequency complex exponential factor; unlike the matrix bundle model, the amplitude and phase contained in this model are time-varying quantities. Reflects the dynamic changes of amplitude, Represents the time-varying behavior of the phase;

[0089] Will exist Perform a second-order Taylor expansion at:

[0090] ;

[0091] Considering the slow rate of change of the dynamic component, the second-order expansion term can well approximate the signal within the calculation window. N T arrive N T of Downsampling points, N T is the half-width of the Taylor expansion window. Substituting the Taylor expansion into the dynamic signal model, we get:

[0092] ;

[0093] in, is the dynamic phasor column vector, ; The center frequency is Matrix of is a column vector of downsampled values, ;

[0094] .

[0095] but The least squares estimate of

[0096] ;

[0097] Essentially, it can be considered as the center frequency The filtering performance of the filter bank can be improved by using a weighted diagonal matrix, that is, . Remember the last two lines 、 ,but

[0098] ;

[0099] ;

[0100] Since the frequency of the frequency-shifted component is close to the fundamental frequency, we can make , calculate the filter group coefficients offline to reduce the amount of real-time calculation. , .at this time, The passband is approximately 1 Hz, which meets the needs of dynamic component measurement.

[0101] The amplitude, phase, and frequency of the dynamic component before frequency shifting are given by:

[0102] ;

[0103] ;

[0104] .

[0105] The advantages and positive effects of the high-frequency resolution dynamic broadband measurement method described in the present invention are: the present invention conducts a preliminary analysis of broadband electrical quantities through the phase invariance of the full-phase FFT, and proposes a simple and practical identification method, which can accurately identify dense components and dynamic components with poor full-phase FFT measurement accuracy; according to the identification results, the sampling sequence is pre-processed by frequency shifting and resampling, which reduces the mutual interference between components, improves the stability of the improved matrix bundle method, and greatly reduces the computational burden; a second-order Taylor expansion model is established, and the Taylor filter coefficients are calculated offline using the known frequency range after frequency shifting, which simplifies the calculation steps and ultimately realizes real-time measurement of broadband dense components and dynamic components.

[0106] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 This is a flow chart of an embodiment of a high frequency resolution dynamic broadband measurement method of the present invention;

[0108] Figure 2 This is a comparison diagram of interharmonic adjacent fundamental wave analysis errors of an embodiment of a high frequency resolution dynamic broadband measurement method of the present invention, wherein APTFT is the method of this embodiment;

[0109] Figure 3This is a comparison diagram of interharmonic and adjacent harmonic analysis errors of an embodiment of a high-frequency resolution dynamic broadband measurement method of the present invention, wherein APTFT is the method of this embodiment;

[0110] Figure 4 It is an experimental platform for an embodiment of a high-frequency resolution dynamic broadband measurement method of the present invention. DETAILED DESCRIPTION

[0111] 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 art to which this application belongs. In the event of any inconsistency, the meaning described in this specification or the meaning derived from the contents recorded in this specification shall prevail. In addition, the terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0112] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0113] Example

[0114] like Figure 1 The high frequency resolution dynamic broadband measurement method includes the following steps:

[0115] S1. Discretely sample the broadband voltage and current electrical quantities of the power system to obtain a discrete sequence of sampled values.

[0116] Power system broadband voltage and current electrical quantities Expressed as:

[0117] ;

[0118] in, represents the fundamental amplitude, represents the fundamental frequency, represents the fundamental phase angle, W is the number of broadband components contained in the signal, Indicates the The amplitude of the broadband component, Indicates the The frequency of the broadband component, Indicates the The phase angle of the broadband component, Indicates time;

[0119] Sample value for:

[0120] ;

[0121] in, is the sampling point, Fs is the sampling frequency. Centered 2 N -1 sampling point constitutes a sampling sequence .

[0122] S2. Perform full-phase FFT transformation on the discrete sampling value sequence to obtain full-phase amplitude spectrum and phase spectrum.

[0123] The sample value With Hanning self-convolution window Multiply and space the sampling points as The data are added two by two to obtain the full-phase FFT window sequence ,

[0124] ;

[0125] Where, is the time domain expression of the Hanning window, ;

[0126] superscript Indicates full phase, subscript represents the Hanning window function;

[0127] Full-phase FFT windowing sequence do Point FFT transformation to obtain the full phase amplitude spectrum Sum and phase spectrum , is the index number corresponding to the spectrum.

[0128] S3. Find the peak of the amplitude spectrum and identify the broadband component characteristics based on the phase of the phase spectrum corresponding to the three spectral lines with the largest amplitudes.

[0129] Finding the Amplitude Spectrum If and , then it is judged that there is a spectrum peak at this location, and this I indivual( I ≤ W ) for .

[0130] Through the phase spectrum Perform feature identification, if , then it is considered that there is no dense component or dynamic component, and the solution is obtained through step S4. Otherwise, the solution is obtained through steps S5-S7.

[0131] S4. If the spectrum peak is a static non-dense component, the frequency and amplitude of the static non-dense component are corrected by the three-spectrum ratio method.

[0132] The amplitudes of the three spectral lines with the largest amplitudes in the peak are y 1, y 2 and y 3. Assume the frequency correction amount is ,but

[0133] ;

[0134] The component frequency correction value is:

[0135] ;

[0136] Similarly, the amplitude correction value can be obtained as

[0137] ;

[0138] The phase angle is the spectral line with the maximum amplitude The corresponding phase , no correction is needed.

[0139] S5. If the spectrum peak is composed of a dynamic component with time-varying parameters or the superposition of multiple dense components of different frequencies, the frequency, amplitude and phase angle of the component are calculated using the matrix bundle method.

[0140] For sample values Perform frequency shift downsampling preprocessing:

[0141] ;

[0142] ;

[0143] in, for The corresponding frequency, for The low-pass filter coefficients of order are obtained by offline design; is the low-pass filter coefficient after frequency shift, is the length The down-sampling sequence, for The largest integer, Indicates the half width of the downsampling window, downsampling is the downsampling frequency. The frequency of the low-pass filter is 200Hz, and the equiripple method is used to design the low-pass filter. After processing, other components are filtered out and the positive frequency part of the component to be measured is moved to the vicinity of the fundamental frequency.

[0144] S52, using a simplified matrix bundle model to distinguish frequency-dense components;

[0145] If the spectrum peak exists after frequency shift downsampling preprocessing M dense components, ignoring the exponential decay term, the sampling value expression is

[0146] ;

[0147] in, For the The amplitude of the dense component, For the The frequency of the dense components, For the k The phase angle of the dense component, is the downsampling interval.

[0148] make , ,but

[0149] ;

[0150] Construct the Hankel matrix from the downsampled values:

[0151] ;

[0152] Where, L For the number of columns, select the appropriate L Can improve noise, usually take .from Winning as follows

[0153] ;

[0154] Matrix bundle The generalized eigenvalue of is calculated as follows:

[0155] ;

[0156] Find After that, the parameters It is derived from the following formula:

[0157] ;

[0158] Thus, the frequency, amplitude and phase of the dense component after frequency shift are obtained as shown in the following formula: That is the frequency of each component before frequency shift.

[0159] ;

[0160] ;

[0161] .

[0162] S6. Calculate the calibration coefficient and determine whether it is a dynamic component.

[0163] Calibration coefficient for:

[0164] ;

[0165] It is reconstructed based on the calculation results of S5. Its expression is as follows:

[0166] ;

[0167] in, is the estimated value of the downsampled value; For the An estimate of the magnitude of the dense component, For the The estimated values ​​of the frequencies of dense components, For the The estimated value of the phase angle of the dense component; when When , there is an error caused by the dynamic component.

[0168] 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.

[0169] For the dynamic component, a dynamic signal model is established:

[0170] ;

[0171] in, , , represents a dynamic broadband phasor, Represents the frequency complex exponential factor; unlike the matrix bundle model, the amplitude and phase contained in this model are time-varying quantities. Reflects the dynamic changes of amplitude, Represents the time-varying behavior of the phase;

[0172] Will exist Perform a second-order Taylor expansion at:

[0173] ;

[0174] Considering the slow rate of change of the dynamic component, the second-order expansion term can well approximate the signal within the calculation window. N T arrive N T of Downsampling points, N Tis the half-width of the Taylor expansion window. Substituting the Taylor expansion into the dynamic signal model, we get:

[0175] ;

[0176] in, is the dynamic phasor column vector, ; The center frequency is Matrix of is a column vector of downsampled values, ;

[0177] .

[0178] but The least squares estimate of

[0179] ;

[0180] Essentially, it can be considered as the center frequency The filtering performance of the filter bank can be improved by using a weighted diagonal matrix, that is, . Remember the last two lines 、 ,but

[0181] ;

[0182] ;

[0183] Since the frequency of the frequency-shifted component is close to the fundamental frequency, we can make , calculate the filter group coefficients offline to reduce the amount of real-time calculation. , .at this time, The passband is approximately 1 Hz, which meets the needs of dynamic component measurement.

[0184] The amplitude, phase, and frequency of the dynamic component before frequency shifting are given by:

[0185] ;

[0186] ;

[0187] .

[0188] In order to illustrate the technical effect 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.

[0189] 1. Frequency resolution

[0190] Comparing with IpFFT and K-ESPRIT, the simulation signal is set to

[0191] ;

[0192] Where, is the sampling interval, is the fundamental frequency, is the interharmonic frequency, 、 、 are the initial phase angles of the fundamental frequency, interharmonics, and harmonics, respectively. In the simulation test, Ts = 1 / 12.8ms, white noise is added, and SNR = 60dB.

[0193] Keeping the fundamental frequency at 50Hz, the interharmonic frequency is set to decrease from 58Hz to 50.5Hz in steps of 2Hz. When the interval between the fundamental frequency and the interharmonic is 6Hz, the frequency, amplitude and phase errors of the interharmonic calculated by IpFFT are 0.002Hz, 2.99% and 1.4° respectively. When the frequency interval is 4Hz, the two signals cannot be distinguished, so the simulation results are not given here. The simulation results of this embodiment and K-ESPRIT are shown in Figure 1. Figure 2 As shown in the figure, 、 、 、 Respectively represent the analysis results of the method on the fundamental wave and interharmonics.

[0194] Keep the harmonic frequency at 150Hz, and set the interharmonic frequency to increase from 142Hz to 149.5Hz in steps of 2Hz. The simulation results of this embodiment and ESPRIT are as follows: Figure 3 As shown in the figure, 、 、 、 They represent the analysis results of the method on interharmonics and harmonics respectively.

[0195] Depend on 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 regardless of 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 is slightly increased, not exceeding 0.3%.

[0196] 2. Dynamic analysis capabilities

[0197] Set the simulation signal to

[0198] ;

[0199] Where, is the sampling interval, is the fundamental frequency, is the interharmonic frequency, 、 、 are the initial phase angles of fundamental frequency, interharmonics and harmonics respectively. A linear change in amplitude occurs, and interharmonics and The fifth harmonic undergoes phase modulation for adjacent components of equal amplitude separated by 0.2 Hz. The fundamental frequency is set to 50.5 Hz, the amplitude variation rate is 10%, the modulation frequency is 0.3 Hz, white noise is added, and the SNR is set to 60 dB. The simulation results of this embodiment, IpFFT, and K-ESPRIT are shown in Table 1.

[0200] Table 1 Dynamic signal analysis error

[0201] ;

[0202] For the dynamic components of interharmonic 1 and harmonics, IpFFT analysis errors are large due to averaging effects. The ESPRIT signal model considers the amplitude as a decaying exponential function, resulting in small errors when the amplitude changes slightly. For interharmonic components 2 and 3, which have similar frequency intervals, the IpFFT spectrum has only one peak. Due to the similar signal subspaces, ESPRIT cannot distinguish them and calculates them as a single dynamic component, resulting in large measurement errors. The method described in this embodiment achieves high measurement accuracy under both dense and dynamic conditions.

[0203] 3. Broadband measurement capability

[0204] Build relevant test platforms, such as Figure 4 As shown in the figure, an OMICRON signal generator is used to generate the signal to be measured. This signal is then transmitted to a broadband measurement device for analysis using the proposed algorithm. The amplitude, frequency, and phase information of each component of the broadband signal are obtained. Finally, the host computer reads the data and analyzes the error.

[0205] The test examples are shown in Table 2. Component 3 undergoes amplitude modulation with a modulation frequency of 3 Hz and a modulation depth of 10%, while component 4 undergoes a linear amplitude change, increasing from 1.5 V to 3.0 V at a rate of 20% per second.

[0206] Table 2 Test cases

[0207] ;

[0208] Due to hardware sampling and environmental noise, the measurement accuracy of each method was reduced, as shown in Table 3. For static, non-dense components, the measurement errors of the three algorithms were similar. However, for dense components 5 and 6, IpFFT and K-ESPRIT were unable to distinguish them. For dynamic components 3 and 4, the method described in this example significantly outperformed IpFFT and K-ESPRIT, demonstrating its effectiveness. While some accuracy loss is unavoidable in a practical device, its frequency error remains below 0.05 Hz and its amplitude error below 0.3%, meeting the requirements for broadband oscillation monitoring and suppression.

[0209] Table 3 Experimental test results

[0210] ;

[0211] Therefore, the high-frequency resolution dynamic broadband measurement method described in the present invention can accurately and in real time measure broadband electrical quantities with time-varying parameters and multi-component superposition, and can restore the actual situation of on-site electrical quantities to a large extent, which has certain engineering application value.

[0212] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A high frequency resolution dynamic broadband measurement method, characterized in that: The following steps are involved: S1. Discretely sample the broadband voltage and current electrical quantities of the power system to obtain a discrete sequence of sampled values; S2. Perform full-phase FFT transformation on the discrete sampling value sequence to obtain full-phase amplitude spectrum and phase spectrum; S3. Find the peak of the amplitude spectrum and identify the broadband component characteristics based on the phase of the phase spectrum corresponding to the three spectral lines with the largest amplitudes; S4. If the spectrum peak is a static non-dense component, correct the frequency and amplitude of the static non-dense component by using the three-spectrum ratio method; S5. If the spectrum peak is composed of a dynamic component with time-varying parameters or a superposition of multiple dense components of different frequencies, the frequency, amplitude and phase angle of the component are calculated by the matrix bundle 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 the second-order Taylor expansion model.

2. The high frequency resolution dynamic broadband measurement method according to claim 1, characterized in that: In S1, the power system broadband voltage and current electrical quantities Expressed as: ； in, represents the fundamental amplitude, represents the fundamental frequency, represents the fundamental phase angle, W is the number of broadband components contained in the signal, Indicates the The amplitude of the broadband component, Indicates the The frequency of the broadband component, Indicates the The phase angle of the broadband component, Indicates time; Sample value for: ； in, is the sampling point, F s is the sampling frequency.

3. The high frequency resolution dynamic broadband measurement method according to claim 2, characterized in that: In S2, the full-phase FFT transformation is specifically: The sample value With Hanning self-convolution window Multiply and space the sampling points as The data are added two by two to obtain the full-phase FFT window sequence , ； Where, is the time domain expression of the Hanning window, ; superscript Indicates full phase, subscript represents the Hanning window function; Full-phase FFT windowing sequence do Point FFT transformation to obtain the full phase amplitude spectrum Sum and phase spectrum , is the index number corresponding to the spectrum.

4. The high frequency resolution dynamic broadband measurement method according to claim 3, characterized in that: In the S3, the phase spectrum The identification of broadband component characteristics is specifically as follows: Using the phase invariance of the full-phase FFT, if the sum of the absolute differences between the phase angles corresponding to the three spectral lines with the largest amplitudes in a spectral peak is less than or equal to 0.5°, the spectral peak is considered to have no dense or dynamic components and is a static non-dense component. The solution is obtained by performing step S4. Otherwise, the solution is obtained by performing steps S5-S7.

5. The high frequency resolution dynamic broadband measurement method according to claim 4, characterized in that: In S4, the frequency and amplitude of the static non-dense component are corrected by the three-spectrum ratio method as follows: The amplitudes of the three spectral lines with the largest amplitudes in the peak are 、 and ,remember , let the correction amount be , ； The component frequency correction value is: ； The component amplitude correction value is: ； Where, is the index of the spectral line with the maximum amplitude.

6. The high frequency resolution dynamic broadband measurement method according to claim 5, characterized in that: In S5, the frequency, amplitude and phase angle of the components are calculated by the matrix bundle method as follows: S51, performing frequency shift downsampling preprocessing on the sampled values: ； ； in, is the frequency corresponding to the maximum amplitude spectrum line of the spectrum peak with dense components or dynamic components, for The low-pass filter coefficients of order are obtained by offline design; is the low-pass filter coefficient after frequency shift, is the length The down-sampling sequence, for The largest integer, represents the half-width of the downsampling window, is the downsampling frequency; S52, using a simplified matrix bundle model to distinguish frequency-dense components; If the spectrum peak exists after frequency shift downsampling preprocessing M dense components, ignoring the exponential decay term, the sampling value expression is ； in, For the The amplitude of the dense component, For the The frequency of the dense components, For the The phase angle of the dense component, is the downsampling interval.

7. The high frequency resolution dynamic broadband measurement method according to claim 6, characterized in that: In S6, the calibration coefficient for: ； ； in, is the estimated value of the downsampled value; For the An estimate of the magnitude of the dense component, For the The estimated values ​​of the frequencies of dense components, For the The estimated value of the phase angle of the dense component; when There is a dynamic component.

8. The high frequency resolution dynamic broadband measurement method according to claim 7, characterized in that: In S7, the dynamic signal model is: ； in, , ; Reflects the dynamic changes of amplitude, Represents the time-varying behavior of the phase; represents a broadband dynamic phasor, represents the frequency complex exponential factor; Will exist Perform a second-order Taylor expansion at: ； Pick- N T arrive N T of Downsampling points, N T is the half-width of the Taylor expansion window; Substituting the Taylor expansion into the dynamic signal model, we get: ； in, is the dynamic phasor column vector, ; The center frequency is Matrix, set = ; is a column vector of downsampled values, ; 。

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