Ultrahigh-order harmonic detection method based on compressed sensing and window function

Abstract

The invention discloses an ultra-high-order harmonic detection method based on compressed sensing and a window function, and the method comprises the following steps: S1, building an ultra-high-order harmonic compressed sensing model, and carrying out the spectrum analysis of an original ultra-high-order harmonic signal, and obtaining an ultra-high-order harmonic data set; s2, generating an FIR window function filter bank based on the ultra-high-order harmonic frequency set; s3, performing amplitude detection on the original ultra-high-order harmonic signal by using an FIR window function filter bank; s4, correcting the amplitude detection result according to the passband gain of the FIR window function filter; and S5, restoring and combining the detected ultrahigh harmonic amplitude, frequency and phase. According to the method, the ultra-high harmonic frequency is detected based on the compressed sensing algorithm, and the estimation precision of the ultra-high harmonic amplitude is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing and data analysis, and in particular to a super-high harmonic detection method based on compressed sensing and window function. Background Art

[0002] In recent years, with the extensive use of power electronic devices and nonlinear devices, the high-frequency harmonic problem brought by new energy stations has become increasingly serious, and the harmonic content of distribution network signals with a frequency higher than 2 kHz has continued to increase. In 2015, international organizations such as the International Electrotechnical Commission (IEC), the International Conference on Large Electric Systems (CIGRE) and the European Committee for Electrotechnical Standardization (CENELEC) expanded the high-frequency harmonics higher than 2kHz to 2 kHz~150 kHz and named them ultra-high-order harmonics. For ultra-high-order harmonics, although the amplitude generated by each device itself is not large, the harmonic currents generated by different devices are injected into the power grid and superimposed at the common connection point, resulting in relatively serious high-frequency voltage distortion. The superimposed ultra-high-order harmonics will cause electromagnetic interference to other electrical equipment connected to the power grid and power line communications, affecting the normal operation of various electrical equipment, and even posing a hidden danger to the stable and economic operation of the entire power system.

[0003] The relevant international standards that can be used for ultra-high harmonic measurement are IEC 61000-4-7, IEC 61000-4-30 and CISPR 16-2-2. IEC 61000-4-7 and IEC 61000-4-30 are power quality measurement standards. Both of them put forward ultra-high harmonic measurement recommendations in the appendix, but they are not clearly specified. CISPR 16-2-2 is an equipment electromagnetic compatibility test standard, which is of reference significance for ultra-high harmonic measurement in power systems. The frequency resolution of the CISPR 16-2-1 method and the IEC 61000-4-7 method is 200 Hz, and the detection amplitude is the same in most cases. However, the amount of data processed by these two methods is more than 10 times that of the IEC 61000-4-30 method. The disadvantage of the IEC 61000-4-30 method is that the frequency resolution is 2 kHz, and this method only analyzes 8% of the measurement data. Based on the above research summary of the measurement standard recommendation method, the existing standard test methods have their own advantages and disadvantages, and more suitable measurement methods are still needed to meet the needs of ultra-high harmonic measurement. Summary of the invention

[0004] In order to solve the problems existing in the above-mentioned existing ultra-high-order harmonic measurement methods, the present invention proposes an ultra-high-order harmonic detection method based on compressed sensing and window function to solve the above-mentioned problems.

[0005] The present application discloses a method for detecting ultra-high harmonics based on compressed sensing and window function, comprising the following steps: S1. Establish an ultra-high harmonic compressed sensing model, and use the orthogonal matching pursuit compressed sensing algorithm to analyze the original ultra-high harmonic signal to obtain an ultra-high harmonic data set; S2, generating a FIR window function filter bank based on the ultra-high harmonic frequency set; S3, using the FIR window function filter group to detect the amplitude of the original ultra-high harmonic signal; S4, correcting the amplitude detection result obtained in S3 according to the passband gain of the FIR window function filter; S5. Restore and combine the detected ultra-high harmonic amplitude and ultra-high harmonic frequency.

[0006] Preferably, the S1 comprises the following steps: The ultra-high harmonic signal is:

[0007] in, is the ultra-high harmonic amplitude, is the ultra-high harmonic frequency, is the ultra-high harmonic phase, is the sampling interval, For ultra-high harmonic order, is the total number of ultra-high harmonic content, is the sampling point number, is the maximum number of samples.

[0008] The ultra-high-order harmonic compression sensing model uses 400 sets of 0.5ms sampling data to achieve ultra-high-order harmonic detection and achieve a frequency resolution of 200Hz. The established ultra-high-order harmonic compression sensing model is as follows:

[0009] in, The spectrum analysis results of 400 sets of 0.5ms data are used as column vectors. is the ultra-high harmonic vector matrix with a frequency resolution of 200 Hz, is the noise matrix, is the observation matrix; Observation Matrix The composition element expression is:

[0010] in, , is the interpolation coefficient, and are the rotor numbers of the observation matrix, The value is 0, 1, 2, ..., , The value is 0, 1, 2, ..., ; The ultra-high harmonic compressed sensing model is solved by the orthogonal matching pursuit compressed sensing algorithm to estimate the ultra-high harmonic frequency set matrix , at this time there is .

[0011] Preferably, S2 comprises the following steps: The FIR window function filter used for ultra-high harmonic signal amplitude estimation is:

[0012] Among them, the ultra-high harmonic frequency Corresponding to the center frequency of the FIR window function filter, represents the Kaiser window function; The estimated value of the ultra-high harmonic amplitude obtained by solving the FIR window function filter is:

[0013] Simultaneously solve the ultra-high harmonic frequency set matrix The amplitude of all ultra-high harmonics contained in the 200Hz frequency band is estimated, and the ultra-high harmonic frequency set matrix is ​​obtained. The FIR window function filter bank at all frequencies in is:

[0014] in, is a FIR window function filter bank.

[0015] Preferably, the amplitude detection formula in S3 is:

[0016] in, is the estimated value of the ultra-high harmonic amplitude.

[0017] Preferably, S4 comprises the following steps: The ultra-high harmonic amplitude is corrected by the following formula:

[0018] in, is the amplitude-frequency response of the FIR window function filter; The expression of the amplitude-frequency response of the FIR window function filter is:

[0019] in,

[0020] is a constant, Is a positive integer.

[0021] Preferably, the detected ultra-high harmonic amplitude and ultra-high harmonic frequency are restored and combined as follows:

[0022] in, is the estimated value of the restored ultra-high harmonic time domain signal.

[0023] Beneficial effects of the present invention: The present invention detects ultra-high harmonic frequencies based on a compressed sensing algorithm, designs a multi-band pass window function filter with a bandwidth of 200Hz and a center frequency of the ultra-high harmonic frequency to estimate the amplitude of ultra-high harmonics. Compared with the traditional frequency domain method for estimating the amplitude of ultra-high harmonics, the method of the present invention also only uses data of 0.5ms time length, but can detect ultra-high harmonics within the 200Hz frequency band. Through simulation and experimental verification, the method has significantly improved the amplitude estimation accuracy compared with the least squares method. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a flow chart of a method for detecting ultra-high harmonics based on compressed sensing and window function according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the 2000Hz-2200Hz amplitude measurement results of an embodiment of the present invention; Figure 3 This is a schematic diagram of the 149800Hz-150000Hz amplitude measurement results of an embodiment of the present invention; Figure 4 This is a schematic diagram of the 74000Hz-76000Hz amplitude measurement results of an embodiment of the present invention; Figure 5 1 is a waveform analysis result of the photovoltaic inverter according to an embodiment of the present invention. DETAILED DESCRIPTION

[0025] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0026] The embodiment of the present application discloses a method for detecting ultra-high harmonics based on compressed sensing and window function, comprising the following steps: S1. Establishment of ultra-high-order harmonic compressed sensing model: Establish an ultra-high-order harmonic compressed sensing model, and use the orthogonal matching pursuit (OMP) compressed sensing algorithm to analyze the original ultra-high-order harmonic signal to obtain an ultra-high-order harmonic data set.

[0027] The ultra-high harmonic signal for ultra-high harmonic frequency detection is:

[0028] in, is the ultra-high harmonic amplitude, is the ultra-high harmonic frequency, is the ultra-high harmonic phase, is the sampling interval, For ultra-high harmonic order, is the total number of ultra-high harmonic content, is the sampling point number, is the maximum number of samples.

[0029] The ultra-high-order harmonic compression sensing model uses 400 sets of 0.5ms sampling data to achieve ultra-high-order harmonic detection and achieve a frequency resolution of 200Hz. The established ultra-high-order harmonic compression sensing model is as follows:

[0030] in, The frequency detection results of 400 sets of 0.5ms data are used as column vectors. is the ultra-high harmonic vector matrix with a frequency resolution of 200 Hz, is the noise matrix, is the observation matrix; Observation Matrix The composition element expression is:

[0031] in, , is the interpolation coefficient, and are the rotor numbers of the observation matrix, The value is 0, 1, 2, ..., , The value is 0, 1, 2, ..., ; The ultra-high harmonic frequency set matrix is ​​estimated through the orthogonal matching pursuit compressed sensing algorithm. , at this time there is .

[0032] S2. Generation of ultra-high harmonic window function filters: Generate an FIR window function filter group based on an ultra-high harmonic frequency set.

[0033] The FIR window function filter used for ultra-high harmonic signal amplitude estimation is:

[0034] Among them, the ultra-high harmonic frequency Corresponding to the center frequency of the FIR window function filter, represents the Kaiser window function; Although the amplitude and phase of the ultra-high harmonics may be time-varying, they can be assumed to be constants within a short observation window. The estimated value of the ultra-high harmonic amplitude obtained by solving the FIR window function filter is:

[0035] After obtaining the ultra-high harmonic frequency set of the original ultra-high harmonic signal using the ultra-high harmonic compressed sensing model, the ultra-high harmonic frequency set matrix is ​​solved at the same time The amplitude of all ultra-high harmonics contained in the 200Hz frequency band is estimated, and the ultra-high harmonic frequency set matrix is ​​obtained. The FIR window function filter bank at all frequencies in is:

[0036] in, is a FIR window function filter bank.

[0037] S3, FIR window function amplitude detection: Use the FIR window function filter group to perform amplitude detection on the original ultra-high harmonic signal.

[0038] The ultra-high harmonic amplitude at this time can be obtained through the original ultra-high harmonic signal and the FIR window function filter group:

[0039] in, is the estimated value of the ultra-high harmonic amplitude. In this embodiment, the original ultra-high harmonic signal with a window length of 0.5 ms and the FIR window function filter bank are used to estimate the amplitude.

[0040] S4, amplitude correction: correct the amplitude detection result obtained in S3 according to the passband gain of the FIR window function filter.

[0041] The obtained ultra-high harmonic amplitude needs to be corrected according to the passband gain of the FIR window function filter. The ultra-high harmonic amplitude is corrected by the following formula:

[0042] in, is the amplitude-frequency response of the FIR window function filter.

[0043] The expression is:

[0044] In this embodiment, the Kaiser window function is used for ultra-high harmonic vector amplitude analysis. The expression of the window function is as follows:

[0045] in,

[0046] In summary, the expression of the amplitude-frequency response of the FIR window function filter is:

[0047] in, is a constant, and in this implementation the value is 5.6533. is a positive integer, then the window function can be implemented as The 200Hz bandpass filtering effect is the center frequency, so the ultra-high-order harmonics at the frequency obtained by the ultra-high-order harmonic compression sensing model can be filtered out. The 200Hz filter bandwidth makes the filtering result include all ultra-high-order harmonic broadband and narrowband emissions in this frequency band, which meets the frequency resolution requirements in IEC 61000-4-7 and CISPR 16-1-1, and can be compared with the electromagnetic compatibility limits.

[0048] S5. Ultra-high harmonic signal restoration: restore and combine the detected ultra-high harmonic amplitude and ultra-high harmonic frequency.

[0049] The detected ultra-high harmonic amplitude and ultra-high harmonic frequency are restored and combined as follows:

[0050] in, The estimated value of the restored ultra-high-order harmonic time domain signal can be compared with the original ultra-high-order harmonic signal.

[0051] In a specific embodiment, for a single-frequency test signal, superharmonic signals at three frequency bands of 2000-2200 Hz, 74000-76000 Hz and 149800-150000 Hz are used for testing, and the measurement results of equal amplitude signals in the three frequency bands by the method proposed in the present application and the comparison algorithm are compared.

[0052] like Figure 2-Figure 4 The results show the calculation results of the ultra-high harmonic amplitudes in three frequency bands. Figure 2-Figure 4 It can be seen that as the signal frequency changes, although the frequency values ​​detected by different measurement algorithms are the same, there are differences in the amplitudes.

[0053] like Figure 2As shown, in the 2000-2200 Hz frequency band, the accuracy of the method proposed in this application and the IEC 61000-4-7 algorithm are basically consistent, and the accuracy of the MMV-OMP algorithm and the IEC 61000-4-30 algorithm decreases as the signal frequency shifts by 2000 Hz.

[0054] like Figure 3 As shown in the figure, in the frequency band of 149800 Hz-150 000 Hz, the accuracy of the method proposed in this application and the IEC 61000-4-7 algorithm remains consistent, and the accuracy of the MMV-OMP algorithm and the IEC 61000-4-30 algorithm increases as the signal frequency approaches 150 000 Hz. By comparing the measurement results of the two 200 Hz frequency bands, it can be seen that when the four algorithms measure signals of 2 000 Hz and its multiple frequencies, the amplitude error is small, but as the signal frequency changes, the amplitude measurement error of the MMV-OMP algorithm and the IEC 61000-4-30 algorithm increases. Therefore, in order to explore the amplitude measurement effect of the algorithm in the 2 000 Hz frequency band, the 74 000 Hz-76 000 Hz frequency band was selected for simulation.

[0055] like Figure 4 As shown in the figure, within the 2 000 Hz frequency band, the amplitude measurement result of IEC 61000-4-7 remains stable at 1, while the amplitude detection results of IEC 61000-4-30 and MMV-OMP algorithms have a tendency to increase and then decrease. This phenomenon is caused by the IEC 61000-4-30 algorithm using 0.5 ms time length measurement data. Since the amplitude detection result of the MMV-OMP algorithm is based on the IEC 61000-4-30 result for perception and least square calculation, the change pattern of its amplitude detection result is the same as that of the IEC 61000-4-30 algorithm. The method proposed in this application also uses 0.5 ms calculated data for compressed sensing. However, after obtaining the ultra-high harmonic frequency, the ultra-high harmonic frequency is used as the center frequency of the Kaiser window function filter with a bandwidth of 200 Hz to perform windowing on the 0.5 ms data and then calculate the ultra-high harmonic amplitude. Therefore, the ultra-high harmonics in the 200 Hz frequency band can be detected, achieving an effect close to the calculation result of IEC61000-4-7 using 200 ms data, which proves the amplitude detection accuracy of the compressed sensing algorithm.

[0056] In another specific embodiment, in order to highlight the detection performance of the algorithm, the estimation accuracy of the algorithm for the signal component is evaluated. In order to simulate the influence of the fluctuation of the switching frequency during the actual operation of the photovoltaic inverter on the ultra-high harmonic measurement results, the test signal model is amplitude modulated, that is:

[0057] in, , , , , , , , , , , , .

[0058] Figure 5 The measurement effect of the method proposed in this application and the MMV-OMP algorithm on amplitude modulated signals is shown. Since the results of the IEC61000-4-7 and IEC 61000-4-30 methods are calculated using the entire 200 ms data, they do not reflect the sensitive detection of amplitude changes. Therefore, only the algorithms using 0.5 ms data for detection are compared to reflect the measurement effect of the algorithms on amplitude modulated signals. Figure 5 The measurement results of the ultra-high-order harmonic amplitude with the amplitude change center at 0.6 A and a frequency of 30.2 kHz are given. The calculation results of the two algorithms can reflect the amplitude change of the simulated signal, but the amplitude change amplitude of the ultra-high-order harmonic detection method based on compressed sensing and window function proposed in this application is closer to the amplitude change amplitude of the actual simulated signal.

[0059] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for detecting ultra-high harmonics based on compressed sensing and window function, characterized in that: The following steps are involved: S1. Establish an ultra-high harmonic compressed sensing model, and use the orthogonal matching pursuit compressed sensing algorithm to analyze the original ultra-high harmonic signal to obtain an ultra-high harmonic data set; S2, generating a FIR window function filter bank based on the ultra-high harmonic frequency set; S3, using the FIR window function filter group to detect the amplitude of the original ultra-high harmonic signal; S4, correcting the amplitude detection result obtained in S3 according to the passband gain of the FIR window function filter; S5. Restore and combine the detected ultra-high harmonic amplitude and ultra-high harmonic frequency.

2. The ultra-high harmonic detection method based on compressed sensing and window function according to claim 1 is characterized in that: The S1 comprises the following steps: The ultra-high harmonic signal is: in, is the amplitude of ultra-high harmonics, is the ultra-high harmonic frequency, is the ultra-high harmonic phase, is the sampling interval, For ultra-high harmonic order, is the total number of ultra-high harmonic content, is the sampling point number, is the maximum number of samples; The ultra-high-order harmonic compression sensing model uses 400 sets of 0.5ms sampling data to achieve ultra-high-order harmonic detection and achieve a frequency resolution of 200Hz. The established ultra-high-order harmonic compression sensing model is as follows: in, The spectrum analysis results of 400 sets of 0.5ms data are used as column vectors. is the ultra-high harmonic vector matrix with a frequency resolution of 200 Hz, is the noise matrix, is the observation matrix; Observation Matrix The composition element expression is: in, , is the interpolation coefficient, and are the rotor numbers of the observation matrix, The value is 0, 1, 2, ..., , The value is 0, 1, 2, ..., ; The ultra-high harmonic frequency set matrix is ​​estimated through the orthogonal matching pursuit compressed sensing algorithm. , at this time there is .

3. The ultra-high harmonic detection method based on compressed sensing and window function according to claim 2 is characterized in that: The S2 comprises the following steps: The FIR window function filter used for ultra-high harmonic signal amplitude estimation is: Among them, the ultra-high harmonic frequency Corresponding to the center frequency of the FIR window function filter, represents the Kaiser window function; The estimated value of the ultra-high harmonic amplitude obtained by solving the FIR window function filter is: Simultaneously solve the ultra-high harmonic frequency set matrix The amplitude of all ultra-high harmonics contained in the 200Hz frequency band is estimated, and the ultra-high harmonic frequency set matrix is ​​obtained. The FIR window function filter bank at all frequencies in is: in, is a FIR window function filter bank.

4. The ultra-high harmonic detection method based on compressed sensing and window function according to claim 3 is characterized in that: The amplitude detection formula in S3 is: in, is the estimated value of the ultra-high harmonic amplitude.

5. The ultra-high harmonic detection method based on compressed sensing and window function according to claim 4 is characterized in that: The S4 comprises the following steps: The ultra-high harmonic amplitude is corrected by the following formula: in, is the amplitude-frequency response of the FIR window function filter; The expression of the amplitude-frequency response of the FIR window function filter is: in, is a constant, Is a positive integer.

6. The ultra-high harmonic detection method based on compressed sensing and window function according to claim 5 is characterized in that: The detected ultra-high harmonic amplitude and ultra-high harmonic frequency are restored and combined as follows: in, is the estimated value of the restored ultra-high harmonic time domain signal.

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