A waveform correction method for short-circuit current measurement of Rogowski coil based on FFT
Through the FFT-based correction method, the influence of the DC attenuation component in the short-circuit current measurement of Rochester coil is eliminated, and the problem of large measurement errors in the prior art is solved, and higher measurement accuracy and accuracy are achieved.
Patent Information
- Application Number
- CN202210383283.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-04-13
- Publication Date
- 2025-05-13
- Estimated Expiration
- 2042-04-13
AI Technical Summary
When using Rochester coils to measure short circuit current, the measurement results are disturbed due to the existence of the DC attenuation component, and the error is large, making it difficult to accurately extract the key parameters of the short circuit current.
The FFT-based correction method is adopted, and the effect of the DC attenuation component in the short-circuit current is eliminated and the short-circuit current waveform is accurately corrected.
It effectively eliminates the impact of the DC attenuation component on short-circuit current measurement, improves measurement accuracy, reduces principle errors, and can accurately determine key parameters such as the system short-circuit impact coefficient.
Smart Images
Figure CN114814703B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a correction method, in particular to a correction method for measuring a short-circuit current of a Rogowski coil based on FFT. Background Art
[0002] The Rogowski coil is a device for measuring periodic current waveforms. However, due to the existence of the DC attenuation component, when the Rogowski coil is directly used to measure the short-circuit current waveform, the measured short-circuit current waveform is equivalent to a corresponding change in the direction of the DC component attenuation. In addition, due to the influence of the integrator time constant of the Rogowski coil itself, the measured short-circuit current waveform is also affected by the Rogowski coil itself, which makes it difficult to extract the key parameters of the short-circuit current.
[0003] like Figure 1 As shown in the figure, the short-circuit current waveform is a composite waveform of the DC decay component and the periodic component. When measuring the short-circuit current, the DC decay component interferes with the short-circuit current waveform measured by the Rogowski coil. Therefore, when using the uncorrected short-circuit current waveform to calculate the impact coefficient, decay time constant, etc., it will lead to large errors and it is difficult to meet the actual application requirements. Summary of the invention
[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a Rogowski coil short-circuit current measurement waveform correction method based on FFT, which can eliminate the influence of the DC attenuation component in the short-circuit current through the filtering effect of fast Fourier transform, can accurately correct the short-circuit current waveform, and can provide a basis for determining key parameters such as the system short-circuit impact coefficient.
[0005] According to the technical solution provided by the present invention, a Rogowski coil short-circuit current measurement waveform correction method based on FFT, the correction method comprises the following steps:
[0006] Step 1: providing a short-circuit current to be corrected based on Rogowski coil measurement, and discretizing the provided short-circuit current to be corrected to obtain a discrete short-circuit current;
[0007] Step 2: For the above discrete short-circuit current, construct an expression for the discrete short-circuit current, then:
[0008]
[0009] Where i(k) is the short-circuit current value to be corrected at sampling point number k, f is the fundamental frequency, N is the number of samplings within the fundamental period, h is the harmonic number, is the short-circuit initial phase angle of the periodic component, τ is the time constant of the DC decay component, A e is the initial value coefficient matrix of the DC attenuation component, Aj is the initial value coefficient matrix of the periodic component, k is the sampling point number during discretization, and m is the total number of sampling points during discretization;
[0010] Step 3: construct and determine a filter vector for filtering out periodic components, and use the determined filter vector to eliminate the periodic components in the above discrete short-circuit current to obtain a DC attenuation filter amount; the DC attenuation filter amount is:
[0011]
[0012] Among them, I α is the DC attenuation filter amount, α k is the kth filter value in the filter vector, and the filter vector is α=[α1…α m-1 ] T ;
[0013] Step 4: According to the DC attenuation filter amount obtained above, the DC attenuation filter amount corresponding to any two sampling points is used to determine the time constant τ of the DC attenuation component and the initial value coefficient matrix A of the DC attenuation component. e , according to the determined time constant τ of the DC attenuation component and the initial value coefficient matrix A of the DC attenuation component e Get the DC attenuation component i of the short-circuit current to be corrected y ;
[0014] Step 5: Subtract the DC attenuation component i determined above from the short-circuit current to be corrected provided above y , so as to realize the correction of the short-circuit current to be corrected.
[0015] In step 1, the short-circuit current to be corrected is provided, and the waveform of the short-circuit current to be corrected at least includes the short-circuit waveform of the period where the peak current is located after the short circuit starts and more than three periods thereafter.
[0016] In step 3, for the constructed filter vector α, a filter characteristic parameter matrix B is constructed according to the characteristics of the periodic component, and then an identity is constructed according to the relationship between the filter vector α and the periodic component. The constructed identity is: Bα=0, so that the constructed filter vector α is determined by using the constructed identity;
[0017] Among them, the constructed filter characteristic parameter matrix B is:
[0018]
[0019] For the DC attenuation filtering amount at the kth sampling point and the DC attenuation filtering amount at the k+λth sampling point, according to the filter component ratio β corresponding to the DC attenuation filtering amount at the k+λth sampling point and the DC attenuation filtering amount at the kth sampling point, the time constant τ of the DC attenuation component is determined according to the filter component ratio β, and:
[0020]
[0021] Among them, λ is the difference between the numbers of two sampling points.
[0022] Determine the initial value coefficient matrix A of the DC attenuation component e for:
[0023]
[0024] For the corrected short-circuit current, after determining the fundamental frequency f, Fourier series expansion is performed at the fundamental frequency f to determine basic parameters corresponding to the fundamental and harmonic components, wherein the basic parameters include amplitude, phase and / or frequency.
[0025] The advantages of the present invention are as follows: through the filtering effect of fast Fourier transform, the influence of the DC attenuation component in the short-circuit current can be eliminated, the short-circuit current waveform can be accurately corrected, the interference of the principle error based on the Rogowski coil measurement on the short-circuit current measurement is reduced, the accuracy of short-circuit current acquisition is improved, and a basis can be provided for determining key parameters such as the system short-circuit impact coefficient. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] Figure 1 Schematic diagram of the short-circuit current to be corrected.
[0027] Figure 2 It is a schematic diagram of the present invention when correcting the short-circuit current to be corrected.
[0028] Figure 3 It is a flow chart of the present invention. DETAILED DESCRIPTION
[0029] The present invention will be further described below in conjunction with specific drawings and embodiments.
[0030] like Figure 3 As shown: In order to accurately correct the short-circuit current waveform, the present invention provides a Rogowski coil short-circuit current measurement waveform correction method based on FFT (Fast Fourier Transform). Specifically, the correction method includes the following steps:
[0031] Step 1: providing a short-circuit current to be corrected based on Rogowski coil measurement, and discretizing the provided short-circuit current to be corrected to obtain a discrete short-circuit current;
[0032] Specifically, the short-circuit current to be corrected is measured by a Rogowski coil using an existing commonly used measurement method. The specific method and process of using the Rogowski coil to measure the short-circuit current to be corrected are consistent with the existing ones. In an embodiment of the present invention, the short-circuit current to be corrected is provided, and the waveform of the short-circuit current to be corrected at least includes the short-circuit waveform of the period where the peak current is located after the short circuit starts and more than three periods thereafter. Specifically, after the short circuit occurs, the short-circuit current in the first period is the largest, and the peak current can be obtained; the waveform of the short-circuit current to be corrected needs to include a short-circuit waveform of more than three periods after the period where the peak current is located, mainly to ensure that the short-circuit current can basically reach stability.
[0033] In an embodiment of the present invention, for the short-circuit current measured by the Rogowski coil, it is necessary to sample the current to be corrected. According to the sampling frequency, the short-circuit current value corresponding to each sampling moment can be obtained, that is, according to the sampled short-circuit current value, the discretization of the short-circuit current to be corrected is realized. After the sampling discretization, the corresponding discrete short-circuit current is obtained. In specific implementation, the obtained discrete short-circuit current is used as the basis for subsequent correction processing.
[0034] It is known to those skilled in the art that, since the short-circuit current waveform measured based on the Rogowski coil can be regarded as the superposition of the steady-state short-circuit current and the impulse short-circuit current, the expression of the short-circuit current to be corrected must consist of a trigonometric function expression (periodic component) and an exponential function with a natural number as the base (DC attenuation component), and this characteristic is still retained after discrete processing, that is, the expression of the discrete short-circuit current must contain a periodic component and a DC attenuation component.
[0035] Step 2: For the above discrete short-circuit current, construct an expression for the discrete short-circuit current, then:
[0036]
[0037] Where i(k) is the short-circuit current value to be corrected at sampling point number k, f is the fundamental frequency, N is the number of samplings within the fundamental period, h is the harmonic number, is the short-circuit initial phase angle of the periodic component, τ is the time constant of the DC decay component, A e is the initial value coefficient matrix of the DC attenuation component, A j is the initial value coefficient matrix of the periodic component, k is the sampling point number during discretization, and m is the total number of sampling points during discretization;
[0038] Specifically, since the short-circuit current collected based on the Rogowski coil only contains the amplitude information of the short-circuit current waveform, and it can be seen from the process description of obtaining the discrete short-circuit current by the above discretization processing that the discrete short-circuit data is the corresponding relationship between the sampling point number (k) and the amplitude of the short-circuit current to be corrected, therefore, in order to obtain the corresponding relationship between the amplitude and time of the waveform at a certain time point after the starting moment of the short-circuit current, it is necessary to write the t at this moment in the form of the product of the sampling point number (which data after the starting point of the short-circuit current) k and the sampling time interval (Δt), t=kΔt, and the time t of the collected amplitude data relative to the moment when the short circuit occurs can be determined.
[0039] Since the short-circuit current can be regarded as the superposition of the steady-state short-circuit current and the transient short-circuit current, the expansion expression of the short-circuit current waveform based on Fourier transform can be obtained, which is:
[0040]
[0041] In the formula, A e is the initial value of the DC attenuation component obtained after Fourier expansion, A j is the initial value of the fundamental component (j=1) and the initial value of each harmonic component (j≥2) obtained by Fourier transform, ω is the fundamental angular frequency, and for the initial phase angle of the periodic component, when j=1, it is the initial phase angle of the fundamental wave; when j≥2, The method and process of expanding the short-circuit current based on Fourier transform to obtain the expanded expression are consistent with the prior art, and the specific transformation process is well known to those skilled in the art and will not be described here.
[0042] Assuming that the fundamental frequency is f, when the discretization process is performed, the number of short-circuit current samples in one fundamental cycle is N, and the sampling time interval is: Δt=1 / Nf. Therefore, by substituting Δt=1 / Nf into the above formula (2), the above formula (1) can be obtained, that is, the expression of discrete short-circuit current is constructed.
[0043] Step 3: construct and determine a filter vector for filtering out periodic components, and use the determined filter vector to eliminate the periodic components in the above discrete short-circuit current to obtain a DC attenuation filter amount, wherein the DC attenuation filter amount is:
[0044]
[0045] Among them, I α is the DC attenuation filter amount, α k is the kth filter value in the filter vector, and the filter vector is α=[α1…α m-1 ] T ;
[0046] In a specific implementation, for constructing the filter vector α, a filter characteristic parameter matrix B is constructed according to the characteristics of the periodic component, and then an identity is constructed according to the relationship between the filter vector α and the periodic component. The constructed identity is: Bα=0, so that the constructed filter vector α is determined by using the constructed identity;
[0047] Since the filtering effect of the filter vector α is independent of the initial phases of the fundamental and harmonic components, the constructed filter characteristic parameter matrix B is:
[0048]
[0049] In specific implementation, the specific value of the harmonic order h can be selected and determined according to needs, such as the harmonic order h can be determined according to the object measured by the Rogowski coil. After the harmonic order h is determined, since the entire periodic component needs to be removed, the filter characteristic parameter matrix B can be constructed according to the commonly used Fourier coefficient solution method. After determining the total number of sampling points m during discretization processing and the number of sampling times N in the fundamental wave period, the constructed filter characteristic parameter matrix B can be determined.
[0050] Therefore, from the above description, we can see that the constructed identity is:
[0051]
[0052] Therefore, according to the above constructed identity, the filter vector α can be determined.
[0053] Since the filtering effect of the filter vector α is independent of the initial value of the periodic component, the filter vector α is multiplied by the short-circuit current in the above formula (1) to obtain
[0054]
[0055] Step 4: According to the DC attenuation filter amount obtained above, the DC attenuation filter amount corresponding to any two sampling points is used to determine the time constant τ of the DC attenuation component and the initial value coefficient matrix A of the DC attenuation component. e , according to the determined time constant τ of the DC attenuation component and the initial value coefficient matrix A of the DC attenuation component e Get the DC attenuation component i of the short-circuit current to be corrected y ;
[0056] Specifically, for the DC attenuation filtering amount at the kth sampling point and the DC attenuation filtering amount at the k+λth sampling point, according to the filter component ratio β corresponding to the DC attenuation filtering amount at the k+λth sampling point and the DC attenuation filtering amount at the kth sampling point, the time constant τ of the DC attenuation component is determined according to the filter component ratio β, and there is:
[0057]
[0058] Among them, λ is the difference between the numbers of two sampling points.
[0059] As can be seen from the above description, since the expression of the DC attenuation filter component is an exponential function with a natural number as the base, for the exponential function, the proportional relationship of its value within a certain period of time can be determined, that is, for a fixed time interval t (after the time interval t is fixed, since the sampling time interval Δt is fixed, the difference λ between the data numbers of the two sampling points is also fixed), the filter component ratio β corresponding to the DC attenuation filter amount of the k+λth sampling point and the DC attenuation filter amount of the kth sampling point can be determined. In specific implementation, after the filter vector α is determined, the DC filter attenuation of any sampling point can be obtained by filtering the discrete short-circuit current of any sampling point using the filter vector α, that is, the DC attenuation filter amount of the k+λth sampling point and the DC attenuation filter amount of the kth sampling point can be directly determined. After the filter component ratio β is determined, the time constant τ of the DC attenuation component can be determined according to the above formula (4) and formula (5).
[0060] After determining the time constant τ of the DC attenuation component, determine the initial value coefficient matrix A of the DC attenuation component e , where, according to the above formula (4) and formula (5), the initial value coefficient matrix A of the DC attenuation component can be determined e for:
[0061]
[0062] It is known to those skilled in the art that the time constant τ of the DC decay component and the initial value coefficient matrix A of the DC decay component are determined by e After that, according to the expression of the DC attenuation component in the short-circuit current, the DC attenuation component i can be determined. y , where the DC attenuation component i y for:
[0063] Step 5: Subtract the DC attenuation component i determined above from the short-circuit current to be corrected provided above y , so as to realize the correction of the short-circuit current to be corrected.
[0064] Specifically, after obtaining the complete DC attenuation component i y After that, as long as the DC attenuation component of the corresponding sampling point number is subtracted from the above discrete short-circuit current, a short-circuit current waveform containing only the periodic component can be obtained. That is, the short-circuit current measured based on the Rogowski coil can be corrected by the above method to eliminate the influence of the DC attenuation component on the measured steady-state short-circuit current waveform. The specific correction method is as follows: Figure 2 shown.
[0065] Further, for the corrected short-circuit current, after determining the fundamental frequency f, Fourier series expansion is performed at the fundamental frequency f to determine basic parameters corresponding to the fundamental and harmonic components, wherein the basic parameters include amplitude, phase and / or frequency.
[0066] In a specific implementation, the original short-circuit current waveform data is subtracted from the DC attenuation component value corresponding to the DC attenuation component expression obtained above at the same sampling time to obtain data containing only the steady-state short-circuit current waveform.
[0067]
[0068] Among them, i T (k) is the corrected short-circuit current, “~” is the estimated value, i(k) is the discrete short-circuit current at sampling point number k, is the DC attenuation component correction amount.
[0069] For the actual short-circuit current waveform, its fundamental frequency is known (such as the power frequency of China's power grid is 50Hz). Therefore, the Fourier series expansion is performed on the corrected steady-state short-circuit current waveform at the fundamental frequency. From the expression of each frequency signal of the Fourier series expansion, the basic information such as the amplitude, phase, frequency, etc. corresponding to the fundamental and harmonic components can be obtained.
[0070] In summary, after obtaining the discrete short-circuit current, the FFT method is used to process the discrete short-circuit current to obtain the DC attenuation component i y That is, the above steps 2 to 5 are based on FFT processing, which subtracts the DC attenuation component i of the corresponding sampling point from the discrete short-circuit current. y The short-circuit current correction based on the Rogowski coil can be achieved.
Claims
1. A Rogowski coil short-circuit current measurement waveform correction method based on FFT, characterized in that: The calibration method includes the following steps: Step 1: providing a short-circuit current to be corrected based on Rogowski coil measurement, and discretizing the short-circuit current to be corrected to obtain a discrete short-circuit current; Step 2: For the discrete short-circuit current, construct the expression of the discrete short-circuit current, then: Where i(k) is the short-circuit current value to be corrected at sampling point number k, f is the fundamental frequency, N is the number of samplings in the fundamental period, h is the harmonic number, is the short-circuit initial phase angle of the periodic component, τ is the time constant of the DC decay component, A e is the initial value coefficient matrix of the DC attenuation component, A j is the initial value coefficient matrix of the periodic component, k is the sampling point number during discretization, and m is the total number of sampling points during discretization; Step 3: construct and determine a filter vector, and use the determined filter vector to eliminate the periodic component in the discrete short-circuit current to obtain a DC attenuation filter amount; the DC attenuation filter amount is: Among them, I α is the DC attenuation filter amount, α k is the kth filter value in the filter vector, and the filter vector is α=[α1…α m-1 ] T ; For the constructed filter vector α, a filter characteristic parameter matrix B is constructed according to the characteristics of the periodic component, and then an identity is constructed according to the relationship between the filter vector α and the periodic component. The constructed identity is: Bα=0, so that the constructed filter vector α is determined by using the constructed identity; Among them, the constructed filter characteristic parameter matrix B is: Step 4: According to the DC attenuation filtering amount, use the DC attenuation filtering amounts corresponding to any two sampling points to determine the time constant τ of the DC attenuation component and the initial value coefficient matrix A of the DC attenuation component. e , according to the determined time constant τ of the DC attenuation component and the initial value coefficient matrix A of the DC attenuation component e Get the DC attenuation component i of the short-circuit current to be corrected y ; Step 5: Subtract the DC attenuation component i determined above from the short-circuit current to be corrected y , in order to achieve the correction of the short-circuit current to be corrected.
2. The FFT-based Rogowski coil short-circuit current measurement waveform correction method according to claim 1 is characterized by: In step 1, the short-circuit current to be corrected is provided, and the waveform of the short-circuit current to be corrected at least includes the short-circuit waveform of the period where the peak current is located after the short circuit starts and more than three periods thereafter.
3. The Rogowski coil short-circuit current measurement waveform correction method based on FFT according to any one of claims 1 to 2, characterized in that: For the DC attenuation filtering amount at the kth sampling point and the DC attenuation filtering amount at the k+λth sampling point, according to the filter component ratio β corresponding to the DC attenuation filtering amount at the k+λth sampling point and the DC attenuation filtering amount at the kth sampling point, the time constant τ of the DC attenuation component is determined according to the filter component ratio β, and: Among them, λ is the difference between the numbers of two sampling points.
4. The FFT-based Rogowski coil short-circuit current measurement waveform correction method according to claim 3 is characterized in that: Determine the initial value coefficient matrix A of the DC attenuation component e for:
5. The Rogowski coil short-circuit current measurement waveform correction method based on FFT according to any one of claims 1 to 2, characterized in that: For the corrected short-circuit current, after determining the fundamental frequency f, Fourier series expansion is performed at the fundamental frequency f to determine basic parameters corresponding to the fundamental and harmonic components, wherein the basic parameters include amplitude, phase and / or frequency.