Power system broadband component feature identification method based on ApFFT

Abstract

The invention discloses a power system broadband component feature identification method based on ApFFT, and relates to the technical field of power system broadband synchronous measurement, and the method comprises the steps: firstly, carrying out the sampling of a voltage and current broadband signal x (t) of a power system, and obtaining a discrete sampling sequence x (n); then, performing all-phase windowing zero padding preprocessing on the discrete sampling sequence x (n) to obtain a sequence x'ap (n); then, performing N'point fast Fourier transform on the sequence x'ap (n) to obtain an all-phase amplitude-frequency spectrum and a phase-frequency spectrum; and finally, searching a spectrum peak of the amplitude-frequency spectrum, and judging broadband component characteristics according to the spectrum peak and phases corresponding to the left and right spectrum lines. Therefore, by the adoption of the power system broadband component feature recognition method based on ApFFT, accurate recognition of static, dense and dynamic broadband components can be achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of broadband synchronous measurement of power systems, and in particular to an ApFFT-based method for identifying broadband component features of power systems. Background Art

[0002] With the rapid development of renewable energy, a large number of power electronic devices are connected to the power grid. The interactions between these devices and between them and the power grid have led to frequent broadband oscillations in power systems, seriously endangering the safe and stable operation of the system. Extensive field recordings have shown that broadband oscillation signals exhibit time-varying behavior, with numerous components and closely spaced frequencies, posing a challenge to existing algorithms.

[0003] Current broadband measurement methods can be primarily categorized into time-frequency domain methods and spectral estimation methods. Common time-frequency domain methods include FFT, wavelet transform, and HHT. FFT is the most widely used analysis method, characterized by fast computational speed and ease of engineering implementation. However, it suffers from issues such as spectrum leakage and picket fence effects, and has an averaging effect, making it less effective for dynamic signals. Wavelet transform is suitable for analyzing dynamic and transient signals, but suffers from wavelet aliasing and places high demands on the selection of the wavelet basis. Compared to wavelet transform, HHT has the advantage of being able to extract harmonic signals of any frequency, but suffers from reduced harmonic resolution. Spectral estimation methods such as Prony, Music, and ESPRIT typically have high frequency resolution and a high computational load. They can accurately calculate multiple frequency components with similar intervals, but only if the number of different frequency components contained in the signal is accurately estimated. These methods are also sensitive to noise and are currently primarily used to detect low-frequency oscillations below 300 Hz and sub- / supersynchronous oscillation components.

[0004] However, existing broadband measurement algorithms are unable to simultaneously meet the requirements of high frequency resolution and time-varying signal measurement capabilities, and are unable to provide effective data for broadband oscillation analysis. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for identifying broadband component features of power systems based on ApFFT, so as to accurately identify static, intensive and dynamic broadband signal components, thereby using different algorithms for targeted processing.

[0006] To achieve the above object, the present invention provides a method for identifying broadband component features of a power system based on ApFFT, comprising the following steps:

[0007] S1. Sample the power system voltage and current broadband signals x(t) to obtain a discrete sampling sequence x(n);

[0008] S2, perform full phase windowing and zero filling preprocessing on the discrete sampling sequence x(n) to obtain the sequence x'ap (n);

[0009] S3, for sequence x' ap (n) Performing N'-point fast Fourier transform to obtain the full phase amplitude spectrum and phase spectrum;

[0010] S4. Find the peak of the amplitude spectrum and determine the characteristics of the broadband component based on the phases corresponding to the peak and the two spectral lines on its left and right.

[0011] Furthermore, in S1, the power system voltage and current broadband signals are expressed as:

[0012]

[0013] Where x(t) represents the broadband signal at time t, A0(t), f0 and Represent the fundamental amplitude, frequency and phase angle respectively, M is the number of broadband components contained in the signal, A m (t), f m and represent the amplitude, frequency and phase angle of the mth broadband component respectively;

[0014] Discrete sampling of the broadband signal yields the sampling sequence x(n):

[0015]

[0016] Among them, f s is the sampling frequency, and 2N-1 sampling points [x(1-N),x(2-N),…,x(0),…,x(N-2),x(N-1)] are taken as the center with x(0).

[0017] Furthermore, S2 includes taking the number of FFT points as N', which is the smallest integer power of 2 that is not less than N, and the full-phase windowing and zero-padding preprocessing process is as follows:

[0018] x win (n) = x(n)·w CONV (n), n=-N+1,…,N-1;

[0019]

[0020] Where w CONV (n) represents the self-convolution of the window function with a length of N, x win (n) is the windowed sequence, x′ win (n) represents a symmetrical windowed zero-filled sequence, x′ ap (n) is the sequence after full-phase windowing and zero padding.

[0021] Furthermore, in S3, the phase of the full phase amplitude spectrum is the initial phase of the center point of the discrete sampling sequence x(n), which has phase invariance.

[0022] Furthermore, S4 includes recording the spectral line number of the spectral peak and its left and right spectral lines as k max , k max-1 and k max+1 ;

[0023] when When , it is considered that the full phase amplitude spectrum has dense components or dynamic components; otherwise, it is considered that the full phase amplitude spectrum is generated by static non-dense components.

[0024] Therefore, the present invention adopts the above-mentioned method for identifying broadband component features of power systems based on ApFFT, which has the following technical effects:

[0025] (1) The present invention proposes a full-phase windowing and zero-padding method, which solves the problem that it is difficult to process non-radix-2 integer power FFTs in hardware and is easy to implement in a chip-based measurement device;

[0026] (2) The present invention proposes a simple and practical method for distinguishing broadband component characteristics, which can adaptively identify dense components and dynamic components with large ApFFT measurement errors, facilitating subsequent processing.

[0027] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of a method for identifying broadband component characteristics of a power system based on ApFFT;

[0029] Figure 2 This is a schematic diagram of the principle of S4 in an embodiment of the method for identifying broadband component features of a power system based on ApFFT, where the blue line is the spectrum corresponding to component 1, the orange line is the spectrum corresponding to component 2, and the black line is the actual spectrum formed by adding the two together;

[0030] Figure 3 The present invention is a comparison diagram of the windowed zero-filled ApFFT amplitude spectrum of the signal fundamental frequency part and the non-zero-filled and direct zero-filled ApFFT amplitude spectrum in an embodiment of the power system broadband component feature recognition method based on ApFFT;

[0031] Figure 4 The figure shows the signal ApFFT spectrum and recognition results in an embodiment of the power system broadband component feature recognition method based on ApFFT, where the blue line is the amplitude spectrum and the orange line is the phase spectrum. DETAILED DESCRIPTION

[0032] The present invention can be explained in more detail by the following examples. The purpose of disclosing the present invention is to protect all changes and improvements within the scope of the present invention. The present invention is not limited to the following examples.

[0033] Example 1

[0034] like Figure 1 As shown, the present invention provides a method for identifying broadband component features of a power system based on ApFFT, comprising the following steps:

[0035] S1. Sample the power system voltage and current broadband signals x(t) to obtain a discrete sampling sequence x(n). The power system voltage and current broadband signals x(t) are expressed as:

[0036]

[0037] Where x(t) represents the broadband signal at time t, A0(t), f0 and Represent the fundamental amplitude, frequency and phase angle respectively, M is the number of broadband components contained in the signal, A m (t), f m and represent the amplitude, frequency, and phase angle of the mth broadband component respectively.

[0038] Discrete sampling of the broadband signal yields:

[0039]

[0040] Among them, f s is the sampling frequency, and 2N-1 sampling points [x(1-N),x(2-N),…,x(0),…,x(N-2),x(N-1)] are taken as the center with x(0), that is, n=1-N,2-N,…,0,…,N-2,N-1.

[0041] S2. The existing full-phase preprocessing process is:

[0042] Form N N-dimensional sequences X from the sampling sequence:

[0043]

[0044] Shift and align each sequence with x(0) as the center to obtain the sequence X':

[0045]

[0046] Sum and average the corresponding bits in turn to obtain a new N-dimensional sequence x'(n):

[0047]

[0048] The sampling rate of a broadband measurement device is usually set to 12.8kHz. According to the above full-phase preprocessing process, when the sampling data of a 1s time window is selected for analysis, the number of FFT points required is 6400, which is not an integer power of base-2 FFT, which brings difficulties to hardware implementation; directly padding x'(n) to 8192 (i.e. 2 13 ) number of FFT will result in errors; while reducing the time window length to match the number of FFT points will result in a decrease in frequency resolution. To this end, this embodiment proposes a full-phase windowing and zero-filling method, which is equivalent to the formation process of x'(n) in the full-phase preprocessing process to the convolution of x(n) with a rectangular convolution window Rect of length N. CONV (n) and add the parts separated by interval N, that is:

[0049] x win (n) = x(n)·Rect CONV (n), n=-N+1,…,N-1;

[0050]

[0051] Based on the above content, this embodiment takes the number of FFT points as N', which is the smallest integer power of 2 that is not less than N, and performs full-phase windowing and zero-filling preprocessing on the discrete sampling sequence x(n) to obtain a new sequence x' ap (n) as follows:

[0052] x win (n) = x(n)·w CONV (n), n=-N+1,…,N-1;

[0053]

[0054] Where w CONV (n) represents the self-convolution of a window function of length N. The window function can be selected from the Hanning window, Blackman window, etc. with excellent performance; x win (n) is the windowed sequence, x′ win (n) represents a symmetrical windowed zero-padded sequence.

[0055] S3, for sequence x' ap (n) Perform N'-point fast Fourier transform to obtain the full phase-amplitude spectrum Y ap (k) and phase spectrum k = [0, 1, ..., N'] is the spectral line number of the spectrum. Among them, a single broadband component can be expressed in the form of a complex exponential:

[0056]

[0057] It can be shown that the single-frequency complex exponential signal The windowed ApFFT spectrum Y apFFT (k) and the traditional windowed FFT spectrum Y FFT The expression of (k) is as follows:

[0058]

[0059]

[0060] Where w(n) is the time domain expression of the window function, W() is its corresponding amplitude spectrum; k m f m The corresponding spectral line number. It can be seen that the phase of the ApFFT spectrum is the initial phase of the sequence center point x(0). It has phase invariance.

[0061] S4. Assume that the signal contains two broadband components and According to the superposition of Fourier transform, its ApFFT spectrum is:

[0062]

[0063] Due to spectrum leakage and fence effect, the spectrum obtained by ApFFT is a cluster of spectral lines corresponding to the main lobe of the window function frequency domain. After addition, if the frequency interval of the two components is lower than the frequency resolution of ApFFT, main lobe interference will occur, and ApFFT will not be able to accurately distinguish the two components, resulting in large measurement errors, such as Figure 2 As shown in the figure, due to the mutual interference between the two, the phases of the spectra in the main lobe are no longer equal, and the phases of the spectral lines that are farther apart are greatly affected, which can be used as a basis for determining the presence of dense components.

[0064] For dynamic modulation components, they are essentially the superposition of multiple static components of different frequencies. Taking amplitude modulation as an example, its broadband signal model is:

[0065]

[0066] Where a am is the modulation depth, f am is the modulation frequency, is the initial phase angle of the modulation part.

[0067] By converting the product and difference of trigonometric functions, we can get:

[0068]

[0069] Therefore, the amplitude modulated signal can be regarded as f m 、f m -f am 、f m +f amWhen the frequency resolution of ApFFT is higher than the modulation frequency, the three static components can be accurately obtained; when the frequency resolution of ApFFT is lower than the modulation frequency, the main lobe interference can be identified as a dynamic component by the phase spectrum.

[0070] Based on the above principle, this embodiment proposes a simple and practical method for distinguishing broadband component features, which can adaptively identify dense components and dynamic components with large ApFFT measurement errors, facilitating subsequent processing. Specifically, find the full phase amplitude spectrum Y ap (k) The spectral peak and its left and right spectral lines are denoted by the spectral line numbers k max , k max-1 and k max+1 , judge the characteristics of the broadband component according to the phase corresponding to the spectrum peak and its left and right two spectrum lines:

[0071] when When , it is considered that the full phase amplitude spectrum has dense components or dynamic components; otherwise, it is considered that the full phase amplitude spectrum is generated by static non-dense components.

[0072] Example 2

[0073] To verify the effectiveness of the proposed method, this example selected a broadband signal containing static, dense, and dynamic components as the analysis object. The signal sampling rate was 12.8kHz, where a 106Hz interharmonic existed near the 104Hz interharmonic, and the fifth harmonic was amplitude modulated. Figure 3 The amplitude spectrum of the ApFFT with windowing and zero padding for the fundamental frequency portion of the broadband signal is compared with that of the ApFFT without zero padding and with the ApFFT with direct zero padding. It can be seen that the main lobe spectrum is more concentrated after full-phase windowing and zero padding, which improves the frequency resolution. Figure 4 The ApFFT spectrum and identification result of the broadband signal are shown in FIG. 1 . The method of this embodiment achieves accurate identification of broadband component features.

[0074] Therefore, the present invention adopts the above-mentioned method for identifying the characteristics of wide-band components of power systems based on ApFFT. Through the full-phase windowing and zero-padding method, it overcomes the problem that it is difficult to process non-radix-2 integer power FFTs in hardware, and is easy to implement in a chip-based measurement device. At the same time, through the wide-band component characteristic discrimination method, it can adaptively identify dense components and dynamic components with large ApFFT measurement errors, which is convenient for subsequent processing.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. 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 method for identifying broadband component features of a power system based on ApFFT, characterized in that: The following steps are involved: S1. Sample the power system voltage and current broadband signals x(t) to obtain a discrete sampling sequence x(n); S2, perform full phase windowing and zero filling preprocessing on the discrete sampling sequence x(n) to obtain the sequence x' ap (n); S3, for sequence x' ap (n) Performing N'-point fast Fourier transform to obtain the full phase amplitude spectrum and phase spectrum; S4. Find the peak of the full phase amplitude spectrum and determine the characteristics of the broadband component based on the phases corresponding to the peak and the two spectral lines on its left and right.

2. The method for identifying broadband component features of a power system based on ApFFT according to claim 1, characterized in that: In S1, the power system voltage and current broadband signals are expressed as: Where x(t) represents a broadband signal, A0(t), f0 and Represent the fundamental amplitude, frequency and phase angle respectively, M is the number of broadband components contained in the signal, A m (t), f m and represent the amplitude, frequency and phase angle of the mth broadband component respectively; Discrete sampling of the broadband signal yields the sampling sequence x(n): Among them, f s is the sampling frequency, and 2N-1 sampling points [x(1-N),x(2-N),…,x(0),…,x(N-2),x(N-1)] are taken as the center with x(0).

3. The method for identifying broadband component features of a power system based on ApFFT according to claim 1, characterized in that: S2 includes taking the number of FFT points as N', which is the smallest integer power of 2 that is not less than N. The full-phase windowing and zero-padding preprocessing process is as follows: x win (n)=x(n)·w CONV (n),n=-N+1,…,N-1; Where w CONV (n) represents the self-convolution of the window function with a length of N, x win (n) is the windowed sequence, x′ win (n) represents a symmetrical windowed zero-filled sequence, x′ ap (n) is the sequence after full-phase windowing and zero padding.

4. The method for identifying broadband component features of a power system based on ApFFT according to claim 1, characterized in that: In S3, the phase of the full phase amplitude spectrum is the initial phase of the center point of the discrete sampling sequence x(n), which has phase invariance.

5. The method for identifying broadband component features of a power system based on ApFFT according to claim 1, characterized in that: S4 includes recording the spectral line number of the spectral peak and its left and right spectral lines as k max , k max-1 and k max+1 ; when When , it is considered that there are dense components or dynamic components in the full phase amplitude spectrum; Otherwise, the full phase-amplitude spectrum is considered to be generated by static non-dense components.

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