Determining a frequency spectrum of an electric current
Patent Information
- Application Number
- EP2023786001
- Authority / Receiving Office
- EP · EP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2022-10-19
- Filing Date
- 2023-10-02
- Publication Date
- 2025-08-27
AI Technical Summary
Current methods for determining the frequency spectrum of an electrical current in power protection technology are limited by high computational requirements, especially for high frequency resolution, which exceeds the computing speed of most evaluation systems, and often only allow for frequency amplitude calculation at selected frequencies without reverse transformation to the time domain.
A method that updates the Fourier vector by multiplying a column of the Fourier matrix with the difference between the newest and oldest current measurement signals, reducing arithmetic operations from n-log(n) to proportional to n, enabling faster calculation and noise reduction by setting components below a threshold to zero.
This approach allows for efficient calculation of the frequency spectrum with improved time and frequency resolution, enabling real-time analysis and noise suppression, and can be used to control protective devices for electrical switchgear.
Smart Images
Figure 1.1
Abstract
Description
[0001] Description
[0002] Determining a frequency spectrum of an electric current
[0003] The invention relates to a method and a current analysis device for determining a frequency spectrum of an electric current.
[0004] For current measuring devices, which are used in power protection technology, for example, it is necessary to reduce the noise in the measurement signal and to measure the frequency and phase of the measurement signal with a high frequency resolution and time resolution. If, for example, several lines are connected in parallel in a transmission network, a frequency or phase deviation between the lines could lead to high fault currents or damage to equipment. In general, a long time range for frequency analysis is required for high frequency resolution. Ideally, a frequency analysis would have to be carried out after each current measurement in order to obtain a frequency curve or a spectrum of the frequencies of a current measurement signal. However, this exceeds the computing speed of most currently available evaluation systems.
[0005] Currently, the state of the art usually determines the frequency distribution in a current measurement signal using a so-called fast Fourier transform (FFT for short), which is an efficient calculation of a so-called discrete Fourier transform (DFT for short). Since the complete calculation of a fast Fourier transform is time-consuming, it usually cannot be performed after every current measurement, although this would be desirable from a signal processing point of view. Therefore, the frequency amplitude, for example, is only calculated for selected frequencies. This may be sufficient for certain analysis purposes, but it does not allow a back transformation from the frequency domain to the time domain. A fast Fourier transform is currently calculated using a so-called FPGA (field programmable gate array).The computational operations required for a fast Fourier transform scale with n - log(n), where n is the number of frequency support points in the calculation. This compares to the calculation of a normal discrete Fourier transform, which uses n. 2 This is already an advantage if computational operations are required. However, even this implementation has limitations in the time and frequency domains. To reduce noise in the measurement signals, analog or digital time-domain filters are usually applied to the measurement signal.
[0006] The invention is based on the object of specifying an improved method and an improved current analysis device for determining a frequency spectrum of an electric current.
[0007] The object is achieved according to the invention by a method having the features of claim 1 and a current analysis device having the features of claim 7.
[0008] Advantageous embodiments of the invention are the subject of the dependent claims.
[0009] In the method according to the invention for determining a frequency spectrum of an electric current, a current measurement signal is recorded by means of a current measuring device at equidistant measuring times following one another. A measurement signal vector is formed from the n most recent current measurement signals, where n is a predetermined number of current measurement signals. A Fourier vector is calculated from the measurement signal vector using a Fourier matrix, which is a discrete Fourier transformation of the measurement signal vector. An updated Fourier vector is formed from the previous Fourier vector by adding to the previous Fourier vector the product of that column of the Fourier matrix which corresponds to the oldest current measurement signal contained in the previous measurement signal vector and the difference between the most recent current measurement signal and the oldest current measurement signal contained in the previous measurement signal vector.
[0010] To explain the method according to the invention in detail, denote W ( t2) = (w2, ..., w k , ..., w n ) the measurement signal vector consisting of the n most recent current measurement signals w2,...,w acquired up to a measurement time ti (including the measurement time ti) n is formed, where the k-th component w k is the oldest current measurement signal contained in the measurement signal vector W(t2). The Fourier vector formed from W(t2) is X ( t2) = (x2, ..., x n ). Let w0 denote the current measurement signal measured at the measurement time t2 following the measurement time t2. The Fourier vector X(t2) for the measurement time t2 is calculated according to the invention from the Fourier vector X(t2) as follows:
[0011] X(t2) = X(t2) + (M lk , ...,M nk ) - (w0-w k ) , where (M lk , ...,M nk ) is the k-th column of the Fourier matrix, written as a row vector.
[0012] The method according to the invention therefore provides for calculating the Fourier vector of a discrete Fourier transform for a measurement time from the previous Fourier vector, i.e. from the Fourier vector for the previous measurement time, according to the rule described above. The arithmetic operations to be carried out for this rule are proportional to the number n of components of the measurement signal vector and thus enable a more effective (faster) calculation of the Fourier vector than a conventional fast Fourier transform, whose number of arithmetic operations scales with n-log(n). This is made possible by the fact that the method according to the invention for calculating the Fourier vector for a measurement time does not provide for matrix multiplication of the Fourier matrix with the complete current measurement signal vector.Instead, the method according to the invention provides for an update of the previous Fourier vector, which only requires a multiplication of a column of the Fourier matrix with the difference between the most recent current measurement signal and the oldest current measurement signal contained in the previous measurement signal vector and the addition of the result of this multiplication to the previous Fourier vector.
[0013] In one embodiment of the method according to the invention, the current measuring device has at least one optical current transformer. An optical current transformer is understood here to be an optical measuring device for measuring an electric current flowing in a current conductor, which is based on the magneto-optical Faraday effect. This effect is understood to be the rotation of the polarization direction of a linearly polarized electromagnetic wave in a medium by a magnetic field parallel to the direction of propagation of the wave. The rotation of the polarization direction is proportional to the magnetic flux density of the magnetic field. In an optical current transformer, linearly polarized light is sent through an optical fiber arranged near the current conductor, which fiber optic cable exhibits the Faraday effect. The magnetic field generated by the current in the current conductor causes a rotation of the polarization direction of the light.Since the magnetic flux density of the magnetic field depends on the current flowing in the conductor, the current can be measured by detecting the rotation of the polarization direction of the light. To detect the rotation of the polarization direction, the light emitted by the optical fiber is passed through a polarizer, for example, and the light intensity of the light transmitted by the polarizer is measured.
[0014] In a further embodiment of the inventive
[0015] In this method, the Fourier vector is a frequency vector whose components are amplitudes of the current measurement signal as a function of frequencies of the current measurement signal.
[0016] In a further embodiment of the method according to the invention, a temporal change in the Fourier vector is continuously calculated. A stability value is calculated from the temporal change in the Fourier vector, and the stability value is used to control a protective device of an electrical switchgear assembly. This embodiment of the method according to the invention exploits the fact that large temporal changes in the Fourier vector can indicate, for example, fault currents or damage to an electrical switchgear assembly.
[0017] In a further embodiment of the method according to the invention, the components of a Fourier vector that fall below a threshold value are set to zero. The threshold value is calculated, for example, as the product of a predetermined factor and an average value of the components of the Fourier vector. This embodiment of the method according to the invention advantageously enables suppression of the influence of noise contained in the current measurement signals on the Fourier vectors formed from the current measurement signals.
[0018] A current analysis device according to the invention for determining a frequency spectrum of an electric current comprises
[0019] - a current measuring device which is designed to record a current measuring signal at equidistant successive measuring times, and
[0020] - an evaluation unit which is set up,
[0021] - to form a measurement signal vector from the n most recent current measurement signals, where n is a predetermined number of current measurement signals, and
[0022] - to form a Fourier vector from the measurement signal vector using a Fourier matrix, which is a discrete Fourier transformation of the measurement signal vector, where
[0023] - an updated Fourier vector is formed from the previous Fourier vector by adding to the previous Fourier vector the product of that column of the Fourier matrix which corresponds to the oldest current measurement signal contained in the previous measurement signal vector and the difference between the respectively most recent current measurement signal and the oldest current measurement signal contained in the previous measurement signal vector.
[0024] A current analysis device according to the invention enables the implementation of the method according to the invention. The advantages of such a current analysis device therefore correspond to the above-mentioned advantages of the method according to the invention. The same applies to the following embodiments of a current analysis device according to the invention, which correspond to the above-mentioned embodiments of the method according to the invention.
[0025] In one embodiment of a current analysis device according to the invention, the current measuring device has at least one optical current transformer.
[0026] In a further embodiment of a current analysis device according to the invention, the Fourier vector formed by the evaluation unit is a frequency vector whose components are amplitudes of the current measurement signal as a function of frequencies of the current measurement signal.
[0027] In a further embodiment of a current analysis device according to the invention, the evaluation unit is designed to continuously calculate a temporal change of the Fourier vector, to calculate a stability value from the temporal change of the Fourier vector and to use the stability value to control a protective device of an electrical switchgear.
[0028] In a further embodiment of an inventive
[0029] In a current analysis device, the evaluation unit is configured to set to zero the components of each Fourier vector that fall below a threshold value. For example, the evaluation unit is configured to calculate the threshold value as the product of a predetermined factor and an average value of the components of the Fourier vector.
[0030] The above-described properties, features, and advantages of this invention, as well as the manner in which they are achieved, will become clearer and more readily understood in connection with the following description of exemplary embodiments, which are explained in more detail in conjunction with the drawings.
[0031] FIG 1 is a block diagram of an embodiment of a current analysis device for determining a frequency spectrum of an electrical current,
[0032] FIG 2 is a flow diagram of an embodiment of a method for determining a frequency spectrum of an electric current.
[0033] Figure 1 (FIG. 1) shows a block diagram of an exemplary embodiment of a current analysis device 1 for determining a frequency spectrum of an electrical current. The current analysis device 1 comprises a current measuring device 3 and an evaluation unit 5.
[0034] The current measuring device 3 is configured to detect a current measurement signal at equidistant, successive measurement times. For example, the current measuring device 3 comprises at least one optical current transformer.
[0035] The evaluation unit 5 is set up to form a measurement signal vector from the n most recent current measurement signals, where n is a predetermined number of current measurement signals. Furthermore, the evaluation unit 5 is set up to form a Fourier vector from the measurement signal vector by means of a Fourier matrix, which is a discrete Fourier transformation of the measurement signal vector. For this purpose, the evaluation unit 5 is set up to form an updated Fourier vector from the previous Fourier vector by adding to the previous Fourier vector the product of that column of the Fourier matrix which corresponds to the oldest current measurement signal contained in the previous measurement signal vector and the difference between the respective most recent current measurement signal and the oldest current measurement signal contained in the previous measurement signal vector.
[0036] The evaluation unit 5 can further be configured to set to zero the components of a Fourier vector that fall below a threshold value. The threshold value is calculated by the evaluation unit 5, for example, as the product of a predetermined factor and an average value of the components of the Fourier vector.
[0037] Figure 2 (FIG. 2) shows a flow diagram of an exemplary embodiment of the method according to the invention for determining a frequency spectrum of an electric current. The method is carried out using a current analysis device 1 described with reference to Figure 1.
[0038] In a first method step 11, a current measurement signal is acquired at n consecutive measurement times using the current measuring device 3. From these current measurement signals, a first measurement signal vector is formed by the evaluation unit 5. From this measurement signal vector, a first Fourier vector is calculated by the evaluation unit 5 by matrix multiplication with a Fourier matrix.
[0039] After the first method step 11, a second method step 12 is carried out.
[0040] In the second process step 12, the
[0041] Current measuring device 3 detects another current measurement signal. After the second method step 12, a third method step 13 is carried out.
[0042] In the third method step 13, the previous Fourier vector is updated. In this case, the evaluation unit 5 forms an updated Fourier vector from the previous (previous) Fourier vector by adding to the previous Fourier vector the product of that column of the Fourier matrix which corresponds to the oldest current measurement signal contained in the previous measurement signal vector and the difference between the current measurement signal acquired in the previous method step 12 (and thus most recent) and the oldest current measurement signal contained in the previous measurement signal vector.
[0043] After the third method step 13, the second method step 12 is carried out again.
[0044] In method steps 11 and 13, it can further be provided that the evaluation unit 5 sets to zero those components of the respective Fourier vector that fall below a threshold value. The threshold value is calculated by the evaluation unit 5, for example, as the product of a predetermined factor and an average value of the components of the Fourier vector.
[0045] Although the invention has been illustrated and described in detail by means of preferred embodiments, the invention is not limited by the disclosed examples and other variations can be derived therefrom by those skilled in the art without departing from the scope of the invention.
Claims
Patent claims 1 . Method for determining a frequency spectrum of an electric current, wherein - a current measurement signal is recorded by means of a current measuring device ( 3 ) at equidistantly spaced measuring times, - a measurement signal vector is formed from the n most recent current measurement signals, where n is a predetermined number of current measurement signals, and - a Fourier vector is calculated from the measurement signal vector using a Fourier matrix, which is a discrete Fourier transformation of the measurement signal vector, where - an updated Fourier vector is formed from the previous Fourier vector by adding to the previous Fourier vector the product of that column of the Fourier matrix which corresponds to the oldest current measurement signal contained in the previous measurement signal vector and the difference between the respectively most recent current measurement signal and the oldest current measurement signal contained in the previous measurement signal vector.
2. Method according to claim 1, wherein the current measuring device (3) comprises at least one optical current transformer.
3. Method according to claim 1 or 2, wherein the Fourier vector is a frequency vector.
4. Method according to one of the preceding claims, wherein a temporal change of the Fourier vector is continuously calculated, a stability value is calculated from the temporal change of the Fourier vector and the stability value is used to control a protective device of an electrical switchgear.
5. Method according to one of the preceding claims, wherein the components of a Fourier vector which fall below a threshold value are set to zero.
6. The method of claim 5, wherein the threshold value is calculated as the product of a predetermined factor and an average of the components of the Fourier vector.
7. Current analysis device (1) for determining a frequency spectrum of an electric current, comprising - a current measuring device (3) which is designed to detect a current measuring signal at equidistantly successive measuring times, and - an evaluation unit (5) which is set up, - to form a measurement signal vector from the n most recent current measurement signals, where n is a predetermined number of current measurement signals, and - to form a Fourier vector from the measurement signal vector using a Fourier matrix, which is a discrete Fourier transformation of the measurement signal vector, where - an updated Fourier vector is formed from the previous Fourier vector by adding to the previous Fourier vector the product of that column of the Fourier matrix which corresponds to the oldest current measurement signal contained in the previous measurement signal vector and the difference between the most recent current measurement signal and the oldest current measurement signal contained in the previous measurement signal vector.
8. Current analysis device (1) according to claim 7, wherein the current measuring device (3) comprises at least one optical current transformer.
9. Current analysis device (1) according to claim 7 or 8, wherein the Fourier vector is a frequency vector.
10. Current analysis device (1) according to one of claims 7 to 9, wherein the evaluation unit (5) is arranged to continuously calculate a temporal change of the Fourier vector, to calculate a stability value from the temporal change of the Fourier vector and to use the stability value to control a protective device of an electrical switchgear.
11. Current analysis device (1) according to one of claims 7 to 10, wherein the evaluation unit (5) is arranged to set to zero the components of each Fourier vector which fall below a threshold value.
12. Current analysis device (1) according to claim 11, wherein the evaluation unit (5) is configured to calculate the threshold value as the product of a predetermined factor and a mean value of the components of the Fourier vector.