Power system harmonic detection method based on hybrid convolution window

Abstract

The invention discloses an electric power system harmonic detection method based on a hybrid convolution window, and relates to the field of electric power system signal detection, and the method comprises the steps: carrying out the discrete sampling of an electric power signal of an electric power system, obtaining an original discrete input signal, carrying out the hybrid convolution construction through a Hanning window and an MSD window, and obtaining a hybrid convolution window; and performing windowing processing on the original input signal by using the hybrid convolution window to obtain truncated windowing signal data. And performing all-phase fast Fourier transform on the windowed signal data to obtain an all-phase amplitude spectrum, determining a target peak spectral line of each harmonic according to the amplitude spectrum, further determining k observation spectral lines of each harmonic, and performing detection by using the observation spectral lines to obtain each harmonic signal in the original discrete input signal. Harmonic signals are detected by constructing a hybrid convolution window in combination with all-phase fast Fourier transform, the influence of spectrum leakage and fence effect brought by asynchronous sampling can be optimized, and the detection precision is effectively improved.

Description

Technical Field

[0001] The present application relates to the field of power system signal detection, and in particular to a power system harmonic detection method based on a hybrid convolution window. Background Art

[0002] Harmonics refer to voltage or current components in the power system whose frequency is an integer multiple of the fundamental frequency. Harmonics often cause damage to the power system and related equipment, affecting the stability and efficiency of the power system, while causing energy waste and reducing the service life of the equipment. Therefore, accurately detecting the harmonic signals generated by nonlinear loads during the operation of the power system is of great significance to the safe and stable operation of the power system.

[0003] Harmonic detection is based on traditional Fourier transform, which separates the fundamental wave and different harmonic components in the power signal by transforming the power system's power signal in the time-frequency domain. However, traditional Fourier transform and many other improved Fourier transforms are prone to defects such as spectrum leakage and fence phenomenon when detecting power grid harmonics, resulting in low accuracy and precision of harmonic detection. Summary of the invention

[0004] In view of the above problems and technical requirements, this application proposes a power system harmonic detection method based on a hybrid convolution window. The technical solution of this application is as follows:

[0005] A method for detecting harmonics in a power system based on a hybrid convolution window comprises the following steps:

[0006] Perform N-point discrete sampling on the power signal of the power system to obtain the original discrete input signal;

[0007] Using the mixed convolution window w MH (n) Windowing the original discrete input signal to obtain the windowed signal data after truncating the original discrete input signal, and the mixed convolution window w MH (n) is constructed by performing a mixed convolution of a Hanning window with a length of N points and an MSD window with a length of N points. The mixed convolution window w MH The length of (n) is 2N-1, where n and N are integer parameters;

[0008] Performing full-phase fast Fourier transform on the windowed signal data to obtain a full-phase amplitude spectrum;

[0009] Determine the target peak spectrum line of each harmonic according to the full phase amplitude spectrum, and determine k observation spectrum lines of each harmonic according to the target peak spectrum line of each harmonic, and the integer parameter k≥2;

[0010] The k observed spectral lines of each harmonic in the full phase amplitude spectrum are used to detect the harmonic signals in the original discrete input signal.

[0011] A further technical solution is to determine the k observed spectral lines of each harmonic, including:

[0012] The full-phase amplitude spectrum is divided into H sub-amplitude spectra in sequence along the frequency direction, and the h-th sub-amplitude spectrum corresponding to the frequency interval from small to large contains the part of the full-phase amplitude spectrum whose corresponding frequency interval is within [h×f1-Δf, h×f1+Δf]; wherein f1 is the fundamental frequency of the original discrete input signal, and Δf is the frequency interval parameter;

[0013] Determine that the h-th sub-amplitude spectrum with a corresponding frequency interval from small to large corresponds to the h-th harmonic signal, and the k spectral lines in the h-th sub-amplitude spectrum that are symmetrical on both sides of the target peak spectral line of the h-th sub-amplitude spectrum are the k observed spectral lines of the h-th harmonic signal; integer parameter H≥2, integer parameter h∈[1,H].

[0014] A further technical solution is that the h-th harmonic signal is obtained by detecting k observed spectral lines of the h-th harmonic signal, including:

[0015] The interpolation coefficient β is determined according to the amplitude of k observed spectral lines of the h-th harmonic signal, and the correction parameter α is obtained by fitting the interpolation coefficient β using a polynomial fitting method;

[0016] The h-th harmonic signal in the original discrete input signal is calculated based on the correction parameter α combined with the amplitude and frequency of the k observed spectral lines of the h-th harmonic signal.

[0017] Its further technical solution is that k=4, the k observation spectral lines of the h-th harmonic signal include the second largest observation spectral line L1 on the left side of the target peak spectral line of the h-th sub-amplitude spectrum, the largest observation spectral line L2 on the left side of the target peak spectral line, the largest observation spectral line L3 on the right side of the target peak spectral line, and the second largest observation spectral line L4 on the right side of the target peak spectral line; the formula for determining the interpolation coefficient β according to the amplitude of the k observation spectral lines of the h-th harmonic signal is:

[0018]

[0019] Among them, y 11 is the amplitude of the observed spectrum line L1, y 22 is the amplitude of the observed spectrum line L2, y 33 is the amplitude of the observed spectral line L3, y 44 is the amplitude of the observed spectral line L4.

[0020] A further technical solution is that the hth harmonic signal in the original discrete input signal is calculated and obtained, including:

[0021] The amplitude A of the hth harmonic signal is calculated according to the following formula: h The expression is:

[0022]

[0023] The frequency f of the hth harmonic signal is calculated according to the following formula h The expression is:

[0024]

[0025] The phase of the hth harmonic signal is calculated according to the following formula: The expression is:

[0026]

[0027] Among them, y 11 is the amplitude of the second largest observed spectrum line L1 on the left side of the target peak spectrum line in the hth sub-amplitude spectrum, y 22 is the amplitude of the largest observed spectrum line L2 on the left side of the target peak spectrum line in the hth sub-amplitude spectrum, y 33 is the amplitude of the largest observed spectrum line L3 on the right side of the target peak spectrum line in the hth sub-amplitude spectrum, y 44 is the amplitude of the second largest observed spectrum line L4 on the right side of the target peak spectrum line in the hth sub-amplitude spectrum; k2 is the frequency of the observed spectrum line L2; X w represents Fourier transform, arg is the principal value of the complex argument, f s It is the sampling frequency when N-point discrete sampling is performed on the power signal of the power system.

[0028] A further technical solution is to use a polynomial fitting method to fit the interpolation coefficient β to obtain the expression of the correction parameter α:

[0029]

[0030] Its further technical solution is to use a mixed convolution window The pth windowed signal data x is obtained by windowing the original discrete input signal w (p) = x(p)·w MH (p), 1≤p≤N.

[0031] Its further technical solution is to mix the convolution window w MH (n) is constructed by mixing the N-point Hanning window and the N-point six-term MSD window through convolution. The N-point six-term MSD window w M The expression of (n) is:

[0032]

[0033] A further technical solution is that the N-point long Hanning window

[0034] A further technical solution is to perform full-phase fast Fourier transform on the windowed signal data to obtain a full-phase amplitude spectrum including:

[0035] The windowed signal data is divided into equal intervals according to the number of sampling points N, and two adjacent data after the division are added to obtain full-phase data, and the full-phase data is subjected to fast Fourier transform to obtain a full-phase amplitude spectrum.

[0036] The beneficial technical effects of this application are:

[0037] The present application proposes a power system harmonic detection method based on a hybrid convolution window. By constructing a hybrid convolution window of an MSD window (Maximum Sidelobe Decay window) and a Hanning window, the original discrete input signal containing the harmonic signal is windowed and shortened. This method fully combines the advantages of the narrow main lobe width of the Hanning window and the fast sidelobe attenuation speed of the six-item MSD window, optimizes the spectrum leakage caused by asynchronous sampling, and improves the detection accuracy of the harmonic signal.

[0038] By combining the hybrid convolution window and the all-phase FFT (Allphase Fast Fourier Transform) with phase invariance and excellent spectrum suppression characteristics, the sidelobe spectrum lines in the transformed spectrum decay at a square rate, and the main spectrum lines can be displayed more prominently. The component parameters of the harmonic signal are calculated by combining the spectrum line interpolation method, which effectively optimizes the error caused by the fence effect, especially for the case where the harmonic signal is more complex or weak, and can provide more accurate detection accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the power system harmonic detection method of the present application.

[0040] Figure 2 It is a power signal diagram of the power system.

[0041] Figure 3 It is a local schematic diagram of the full phase amplitude spectrum in an example.

[0042] Figure 4 It is a comparison chart of harmonic signal amplitude error detection.

[0043] Figure 5 It is a comparison chart of harmonic signal frequency error detection.

[0044] Figure 6 It is a comparison chart of harmonic signal phase error detection. DETAILED DESCRIPTION

[0045] The specific implementation of the present application is further described below in conjunction with the accompanying drawings.

[0046] This application proposes a power system harmonic detection method based on a hybrid convolution window, please refer to Figure 1 The flowchart shown in the figure has the following specific steps:

[0047] Step 1: Use HIoki PW3198 power quality analyzer to collect power signals from the power system. The collected power signals are as follows: Figure 2 As shown, the power signal of the power system is discretely sampled at N points to obtain the original discrete input signal.

[0048] Step 2: Use the mixed convolution window w MH (n) Windowing the original discrete input signal to obtain the windowed signal data after truncating the original discrete input signal, and the mixed convolution window w MH (n) is constructed by performing a mixed convolution of a Hanning window with a length of N points and an MSD window with a length of N points. The mixed convolution window w MH The length of (n) is 2N-1, where n and N are integer parameters.

[0049] The MSD window is a window function designed to minimize the spectral sidelobes, aiming to achieve lower spectral leakage. The Hanning window is a window function with good spectral suppression characteristics. Its main lobe is narrow, which can effectively reduce spectral leakage and provide smooth boundary transition. It is suitable for signal processing tasks that need to reduce spectral leakage and maintain spectral clarity. Mixing the MSD window and the Hanning window for convolution, and fully combining their respective advantages to optimize spectral performance, can obtain a clear spectrum and highlight the main lobe spectral line characteristics of the spectrum, which is conducive to accurate analysis of the spectrum and improve detection accuracy.

[0050] The hybrid convolution window constructed by hybrid convolution of N-point Hanning window and N-point MSD window can be expressed as

[0051] In one embodiment, the MSD window used to construct the hybrid convolution window adopts a six-term MSD window. The six-term MSD window is a type of MSD window, which is composed of six sine or cosine functions, and can make the hybrid convolution window have more excellent characteristics in both time domain and frequency domain.

[0052] Six-term MSD window w with N points M The expression of (n) is:

[0053]

[0054] N-point long Hanning window

[0055] The pth windowed signal data x is obtained by windowing the original discrete input signal w (p) = x(p)·w MH (p), 1≤p≤N.

[0056] Step 3: Perform full-phase fast Fourier transform on the windowed signal data to obtain a full-phase amplitude spectrum. The full-phase fast Fourier transform has phase invariance. After the full-phase fast Fourier transform, the side lobes of the full-phase amplitude spectrum decay at a square rate, thereby highlighting the main spectrum line.

[0057] In one embodiment, the windowed signal data is divided into equal intervals according to the number of sampling points N, and two adjacent data after the division are added to obtain full-phase data, and the full-phase data is subjected to fast Fourier transform to obtain a full-phase amplitude spectrum. The full-phase amplitude spectrum has frequency as the horizontal coordinate and the amplitude of the signal as the vertical coordinate, and the full-phase amplitude spectrum includes a plurality of spectral lines, each of which has a corresponding frequency and amplitude.

[0058] Step 4: determine the target peak spectrum line of each harmonic according to the full-phase amplitude spectrum, and determine k observation spectrum lines of each harmonic according to the target peak spectrum line of each harmonic, and the integer parameter k≥2.

[0059] The full-phase amplitude spectrum contains multiple sub-amplitude spectra of harmonic signals. In one embodiment, the full-phase amplitude spectrum is first divided into H sub-amplitude spectra in the frequency direction, and the corresponding frequency intervals from small to large, the hth sub-amplitude spectrum, contain the corresponding frequency intervals in the full-phase amplitude spectrum within [h×f1-Δf, h×f1+Δf]. Among them, f1 is the fundamental frequency of the original discrete input signal. In the power system, the fundamental frequency f1 of the original discrete input signal is generally set to 50Hz. Δf is a frequency interval parameter, which can be customized, for example, set to 25Hz.

[0060] Determine that the h-th sub-amplitude spectrum with the corresponding frequency interval from small to large corresponds to the h-th harmonic signal, and define the spectrum line with the largest amplitude in the h-th sub-amplitude spectrum as the target peak spectrum line of the h-th sub-amplitude spectrum. Then, the k spectrum lines in the h-th sub-amplitude spectrum that are symmetrical on both sides of the target peak spectrum line of the h-th sub-amplitude spectrum are the k observed spectrum lines of the h-th harmonic signal. Integer parameter H ≥ 2, integer parameter h∈[1, H].

[0061] Step 5, using k observed spectral lines of each harmonic in the full phase amplitude spectrum to detect each harmonic signal in the original discrete input signal. In one embodiment, the specific method of using k observed spectral lines of the hth harmonic signal to detect the hth harmonic signal is:

[0062] (1) The interpolation coefficient β is determined according to the amplitudes of the k observed spectral lines of the h-th harmonic signal, and the correction parameter α is obtained by fitting the interpolation coefficient β using a polynomial fitting method.

[0063] (2) The h-th harmonic signal in the original discrete input signal is calculated based on the correction parameter α and the amplitude and frequency of the k observed spectral lines of the h-th harmonic signal.

[0064] Under asynchronous sampling, since the actual spectrum is not at an observable discrete frequency point, the present application considers the comprehensive excellent effects of low computational complexity and high interpolation accuracy of four-line interpolation, and selects four spectral lines near the target peak spectrum line for interpolation calculation. In one embodiment, k=4, and the k observed spectral lines of the hth harmonic signal include the second largest observed spectral line L1 on the left side of the target peak spectrum line of the hth sub-amplitude spectrum, the largest observed spectral line L2 on the left side of the target peak spectrum line, the largest observed spectral line L3 on the right side of the target peak spectrum line, and the second largest observed spectral line L4 on the right side of the target peak spectrum line. In the hth sub-amplitude spectrum, the frequency corresponding to L1 is k1, the frequency corresponding to L2 is k2, the frequency corresponding to L3 is k3, the frequency corresponding to L4 is k4, and the frequency corresponding to the target peak spectrum line is k0. For example Figure 3 The target peak spectrum line of some subharmonics and four observed spectrum lines are shown in a local schematic diagram of the full-phase amplitude spectrum in an example. The target peak spectrum line in the second sub-amplitude spectrum with a corresponding frequency range from small to large is at 100 Hz, and the four observed spectrum lines L1, L2, L3, and L4 are respectively shown in the figure.

[0065] The formula for determining the interpolation coefficient β based on the amplitude of the k observed spectral lines of the hth harmonic signal is:

[0066]

[0067] Among them, y 11 is the amplitude of the observed spectrum line L1, y 22 is the amplitude of the observed spectrum line L2, y 33 is the amplitude of the observed spectral line L3, y 44 is the amplitude of the observed spectral line L4.

[0068] The expression of the correction parameter α obtained by fitting the interpolation coefficient β using the polynomial fitting method is:

[0069]

[0070] According to the correction parameter α, the hth harmonic signal in the original discrete input signal can be calculated, and the amplitude A of the hth harmonic signal can be calculated according to the following formula: h The expression is:

[0071]

[0072] The frequency f of the hth harmonic signal is calculated according to the following formula h The expression is:

[0073]

[0074] The phase of the hth harmonic signal is calculated according to the following formula: The expression is:

[0075]

[0076] Among them, y 11 is the amplitude of the second largest observed spectrum line L1 on the left side of the target peak spectrum line in the hth sub-amplitude spectrum, y 22 is the amplitude of the largest observed spectrum line L2 on the left side of the target peak spectrum line in the hth sub-amplitude spectrum, y 33 is the amplitude of the largest observed spectrum line L3 on the right side of the target peak spectrum line in the hth sub-amplitude spectrum, y 44 is the amplitude of the second largest observed spectrum line L4 on the right side of the target peak spectrum line in the hth sub-amplitude spectrum; k2 is the frequency of the observed spectrum line L2; X w represents Fourier transform, arg is the principal value of the complex argument, f s It is the sampling frequency when N-point discrete sampling is performed on the power signal of the power system.

[0077] Therefore, it can be considered that any p-th original discrete input signal x(p) obtained by sampling is obtained by superposition of H harmonic signals and expressed as:

[0078]

[0079] Among them, f s is the sampling frequency when the power signal of the power system is sampled at N points discretely, f1 is the base frequency, A h is the amplitude of the hth harmonic signal, is the phase of the hth harmonic signal, f h is the frequency of the hth harmonic signal, p is an integer parameter and 1≤p ≤N .

[0080] The detection results of the power system harmonic detection method proposed in this application are compared with the detection methods of the prior art. The detection results of the harmonic signal amplitude error are compared. Figure 4 As shown in the figure, the harmonic signal frequency error detection results are compared. Figure 5 As shown in Figure 2, the harmonic signal phase error detection results are compared. Figure 6As shown. Among them, FIMWAF is the power system harmonic detection method of this application, NCAFI is based on Nuttall self-convolution window full-phase FFT interpolation algorithm, NDAF is based on Nuttall double-window full-phase FFT algorithm, OCCSC is based on optimized combination of cosine self-convolution window and interpolation DFT algorithm. According to the comparison results, it can be seen that the power system harmonic detection method of this application has better detection accuracy for amplitude, frequency and phase.

[0081] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present application.

Claims

1. A method for detecting harmonics in a power system based on a hybrid convolution window, characterized in that: The power system harmonic detection method comprises: Perform N-point discrete sampling on the power signal of the power system to obtain the original discrete input signal; Using the mixed convolution window w MH (n) performing windowing processing on the original discrete input signal to obtain windowed signal data after truncating the original discrete input signal, the mixed convolution window w MH (n) is constructed by performing a mixed convolution operation on a Hanning window of N points and an MSD window of N points. The mixed convolution window w MH The length of (n) is 2N-1, where n and N are integer parameters; Performing full-phase fast Fourier transform on the windowed signal data to obtain a full-phase amplitude spectrum; Determine the target peak spectrum line of each harmonic according to the full phase amplitude spectrum, and determine k observation spectrum lines of each harmonic according to the target peak spectrum line of each harmonic, and the integer parameter k≥2; The k observed spectral lines of each harmonic in the full phase amplitude spectrum are used to detect each harmonic signal in the original discrete input signal.

2. The power system harmonic detection method according to claim 1, characterized in that: The k observed spectral lines for each harmonic are determined as follows: The full-phase amplitude spectrum is divided into H sub-amplitude spectra in sequence along the frequency direction, and the h-th sub-amplitude spectrum corresponding to the frequency interval from small to large contains the part of the full-phase amplitude spectrum whose corresponding frequency interval is within [h×f1-Δf, h×f1+Δf]; wherein f1 is the fundamental frequency of the original discrete input signal, and Δf is the frequency interval parameter; Determine that the h-th sub-amplitude spectrum with a corresponding frequency interval from small to large corresponds to the h-th harmonic signal, and the k spectral lines in the h-th sub-amplitude spectrum that are symmetrical on both sides of the target peak spectral line of the h-th sub-amplitude spectrum are the k observed spectral lines of the h-th harmonic signal; integer parameter H≥2, integer parameter h∈[1,H].

3. The power system harmonic detection method according to claim 2, characterized in that: The h-th harmonic signal is obtained by detecting the k observed spectral lines of the h-th harmonic signal, including: Determine an interpolation coefficient β according to the amplitudes of k observed spectral lines of the h-th harmonic signal, and obtain a correction parameter α by fitting the interpolation coefficient β using a polynomial fitting method; The hth harmonic signal in the original discrete input signal is obtained by calculating the correction parameter α in combination with the amplitude and frequency of k observed spectral lines of the hth harmonic signal.

4. The power system harmonic detection method according to claim 3, characterized in that: k=4, the k observation spectral lines of the h-th harmonic signal include the second largest observation spectral line L1 on the left side of the target peak spectral line of the h-th sub-amplitude spectrum, the largest observation spectral line L2 on the left side of the target peak spectral line, the largest observation spectral line L3 on the right side of the target peak spectral line, and the second largest observation spectral line L4 on the right side of the target peak spectral line; the formula for determining the interpolation coefficient β according to the amplitudes of the k observation spectral lines of the h-th harmonic signal is: Among them, y 11 is the amplitude of the observed spectrum line L1, y 22 is the amplitude of the observed spectrum line L2, y 33 is the amplitude of the observed spectral line L3, y 44 is the amplitude of the observed spectral line L4.

5. The power system harmonic detection method according to claim 3, characterized in that: Calculating the hth harmonic signal in the original discrete input signal includes: The amplitude A of the hth harmonic signal is calculated according to the following formula: h The expression is: The frequency f of the hth harmonic signal is calculated according to the following formula h The expression is: The phase of the hth harmonic signal is calculated according to the following formula: The expression is: Among them, y 11 is the amplitude of the second largest observed spectrum line L1 on the left side of the target peak spectrum line in the hth sub-amplitude spectrum, y 22 is the amplitude of the largest observed spectrum line L2 on the left side of the target peak spectrum line in the hth sub-amplitude spectrum, y 33 is the amplitude of the largest observed spectrum line L3 on the right side of the target peak spectrum line in the hth sub-amplitude spectrum, y 44 is the amplitude of the second largest observed spectrum line L4 on the right side of the target peak spectrum line in the hth sub-amplitude spectrum; k2 is the frequency of the observed spectrum line L2; X w represents Fourier transform, arg is the principal value of the complex argument, f s It is the sampling frequency when N-point discrete sampling is performed on the power signal of the power system.

6. The power system harmonic detection method according to claim 3, characterized in that: The expression of the correction parameter α obtained by fitting the interpolation coefficient β using a polynomial fitting method is:

7. The power system harmonic detection method according to claim 1, characterized in that: Mixed convolution windows The pth windowed signal data x is obtained by windowing the original discrete input signal w (p) = x(p)·w MH (p), 1≤p≤N.

8. The power system harmonic detection method according to claim 7, characterized in that: The mixed convolution window w MH (n) is constructed by mixing the N-point Hanning window and the N-point six-term MSD window through convolution. The N-point six-term MSD window w M The expression of (n) is:

9. The power system harmonic detection method according to claim 7, characterized in that: N-point long Hanning window 10. The power system harmonic detection method according to claim 1, characterized in that: The performing full-phase fast Fourier transform on the windowed signal data to obtain a full-phase amplitude spectrum comprises: The windowed signal data is divided into equal intervals according to the number of sampling points N, and two adjacent data after the division are added to obtain full-phase data, and the full-phase data is subjected to fast Fourier transform to obtain the full-phase amplitude spectrum.

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