DE102022211090A1 - Determining a frequency spectrum of an electric current - Google Patents

Abstract

The invention relates to a method for determining a frequency spectrum of an electric current. In the method, a current measurement signal is recorded at equidistant, successive measurement 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. A Fourier vector is calculated from the measurement signal vector using a Fourier matrix. An updated Fourier vector is formed from the previous Fourier vector by adding to the previous Fourier vector the product of the column of the Fourier matrix that 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.

Description

The invention relates to a method and a current analysis device for determining a frequency spectrum of an electric current.

For current measuring devices 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 systems. In general, a long time range is required for frequency analysis for a 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 evaluation systems currently available.

Currently, in the state of the art, the frequency distribution in a current measurement signal is usually determined by a so-called fast Fourier transform (FFT), which is an efficient calculation of a so-called discrete Fourier transform (DFT). Since the complete calculation of a fast Fourier transform is time-consuming, it usually cannot be carried out after each current measurement, although this would be desirable from a signal processing perspective. Therefore, the frequency amplitude is only calculated for selected frequencies, for example. 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 transformation is currently calculated using a so-called FPGA (abbreviation for Field Programmable Gate Array). The necessary arithmetic operations for a fast Fourier transformation scale with nolog(n), where n is the number of frequency support points in the calculation. Compared to the calculation of a normal discrete Fourier transformation, which requires n ² arithmetic operations, this is already an advantage. However, even this implementation has limits in the time and frequency domain. In order to reduce the noise in the measurement signals, analog or digital filters in the time domain are usually applied to the measurement signal.

The invention is based on the object of providing an improved method and an improved current analysis device for determining a frequency spectrum of an electric current.

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.

Advantageous embodiments of the invention are the subject of the subclaims.

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. 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 the column of the Fourier matrix that 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.

wobei (M_1k,...,M_nk) die k-te Spalte der Fourier-Matrix, als Zeilenvektor geschrieben, bezeichnet.In order to explain the method according to the invention in detail, let W(t ₁ )=(w ₁ ,..., w _k ,..., w _n ) denote the measurement signal vector which is formed from the n most recent current measurement signals w ₁ , ..., w _n recorded up to a measurement time t ₁ (including the measurement time t ₁ ), where the k-th component w _k is the oldest current measurement signal contained in the measurement signal vector W(t ₁ ). The Fourier vector formed from W(t ₁ ) is denoted by X (t ₁ ) = (x ₁ ,..., x _n ). Let w ₀ denote the current measurement signal measured at the measurement time t ₂ following the measurement time t ₁ . The Fourier vector X(t ₂ ) for the measurement time t ₂ is calculated according to the invention from the Fourier vector X(t ₁ ) as follows: $$\text{X}\left({\text{t}}_2\right)=\text{X}\left({\text{t}}_1\right)+\left({\text{M}}_{1\text{k}},\dots ,{\text{M}}_{\text{nk}}\right)\cdot \left({\text{w}}_0-{\text{w}}_{\text{k}}\right),$$

where (M _1k ,...,M _nk ) denotes the k-th column of the Fourier matrix, written as a row vector.

The method according to the invention therefore provides for the Fourier vector of a discrete Fourier transformation for a measurement time from the previous Fourier vector, that is, from the Fourier vector for the previous measurement time, to be determined according to the rule described above. calculate. 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 transformation, the number of arithmetic operations of which 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 point in time does not provide for a 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.

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 a light guide arranged near the current conductor, which 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 strength of the current flowing in the current conductor, the current strength 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 light guide is passed through a polarizer, for example, and a light intensity of the light transmitted by the polarizer is detected.

In a further embodiment of the method according to the invention, 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.

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. This embodiment of the method according to the invention takes advantage of the fact that large temporal changes in the Fourier vector can indicate, for example, fault currents or damage to an electrical switchgear.

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.

• - eine Strommessvorrichtung, die eingerichtet ist, zu zeitlich äquidistant aufeinander folgenden Messzeitpunkten jeweils ein Strommesssignal zu erfassen, und
• - eine Auswerteeinheit, die eingerichtet ist,
• - aus den jeweils n jüngsten Strommesssignalen einen Messsignalvektor zu bilden, wobei n eine vorgegebene Anzahl von Strommesssignalen ist, und
• - aus dem Messsignalvektor mittels einer Fourier-Matrix einen Fouriervektor zu bilden, der eine diskrete Fourier-Transformation des Messsignalvektors ist, wobei
• - ein aktualisierter Fouriervektor aus dem vorhergehenden Fouriervektor gebildet wird, indem zu dem vorhergehenden Fouriervektor das Produkt derjenigen Spalte der Fourier-Matrix, die zu dem ältesten in dem vorhergehenden Messsignalvektor enthaltenen Strommesssignal korrespondiert, und der Differenz des jeweils jüngsten Strommesssignals und des ältesten in dem vorhergehenden Messsignalvektor enthaltenen Strommesssignals addiert wird.

A current analysis device according to the invention for determining a frequency spectrum of an electric current comprises

• - a current measuring device which is designed to record a current measuring signal at equidistantly successive measuring times, and
• - an evaluation unit that 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.

A current analysis device according to the invention enables the method according to the invention to be carried out. 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 mentioned embodiments of the method according to the invention.

In one embodiment of a current analysis device according to the invention, the current measuring device has at least one optical current transformer.

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.

In a further embodiment of a current analysis device according to the invention, the evaluation unit is set up 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.

In a further embodiment of a current analysis device according to the invention, the evaluation unit is set up to set the components of each Fourier vector that fall below a threshold value to zero. For example, the evaluation unit is set up to calculate the threshold value as the product of a predetermined factor and an average value of the components of the Fourier vector.

• 1 ein Blockdiagramm eines Ausführungsbeispiels einer Stromanalysevorrichtung zum Ermitteln eines Frequenzspektrums eines elektrischen Stroms,
• 2 ein Ablaufdiagramm eines Ausführungsbeispiels eines Verfahrens zum Ermitteln eines Frequenzspektrums eines elektrischen Stroms.
• 1 (1) zeigt ein Blockdiagramm eines Ausführungsbeispiels einer Stromanalysevorrichtung 1 zum Ermitteln eines Frequenzspektrums eines elektrischen Stroms. Die Stromanalysevorrichtung 1 umfasst eine Strommessvorrichtung 3 und eine Auswerteeinheit 5.

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 embodiments, which are explained in more detail in connection with the drawings, in which:

• 1 a block diagram of an embodiment of a current analysis device for determining a frequency spectrum of an electrical current,
• 2 a flow chart of an embodiment of a method for determining a frequency spectrum of an electric current.
• 1 ( 1 ) shows a block diagram of an embodiment of a current analysis device 1 for determining a frequency spectrum of an electric current. The current analysis device 1 comprises a current measuring device 3 and an evaluation unit 5.

The current measuring device 3 is designed to record a current measuring signal at equidistantly spaced measuring times. For example, the current measuring device 3 has at least one optical current transformer.

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. The evaluation unit 5 is also set up 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. 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 the column of the Fourier matrix that 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.

The evaluation unit 5 can also be configured to set the components of a Fourier vector that fall below a threshold value to zero. 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.

2 ( 2 ) shows a flow chart of an embodiment of the method according to the invention for determining a frequency spectrum of an electric current. The method is carried out using a 1 described current analysis device 1.

In a first method step 11, a current measurement signal is recorded at n consecutive measurement times using the current measuring device 3. A first measurement signal vector is formed from these current measurement signals by the evaluation unit 5. A first Fourier vector is calculated from this measurement signal vector by the evaluation unit 5 by matrix multiplication with a Fourier matrix.

After the first method step 11, a second method step 12 is carried out.

In the second method step 12, a further current measurement signal is detected using the current measuring device 3.

After the second method step 12, a third method step 13 is carried out.

In the third method step 13, the previous Fourier vector is updated. The evaluation unit 5 generates an updated Fourier vector formed 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.

After the third method step 13, the second method step 12 is carried out again.

In method steps 11 and 13, it can also be provided that the evaluation unit 5 sets the components of the respective Fourier vector to zero 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.

Although the invention has been illustrated and described in detail by means of preferred embodiments, the invention is not limited to 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 (12)

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 successive measurement 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, wherein - an updated Fourier vector is formed from the previous Fourier vector by adding to the previous Fourier vector the product of the column of the Fourier matrix that 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. Procedure according to Claim 1 , wherein the current measuring device (3) has at least one optical current transformer. Procedure according to Claim 1 or 2 , where the Fourier vector is a frequency vector. 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. 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. Procedure according to Claim 5 , where the threshold is calculated as the product of a given factor and an average of the components of the Fourier vector. Current analysis device (1) for determining a frequency spectrum of an electric current, comprising - a current measuring device (3) which is set up to record a current measurement signal at equidistantly successive measurement 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 by means of 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 the 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. Current analysis device (1) according to Claim 7 , wherein the current measuring device (3) has at least one optical current transformer. Current analysis device (1) according to Claim 7 or 8th , where the Fourier vector is a frequency vector. Current analysis device (1) according to one of the Claims 7 until 9 , wherein the evaluation unit (5) is arranged to continuously calculate a temporal change of the Fourier vector, to calculate a stabilization value from the temporal change of the Fourier vector To calculate the stability value and to use the stability value to control a protective device of an electrical switchgear. Current analysis device (1) according to one of the Claims 7 until 10 , wherein the evaluation unit (5) is arranged to set to zero the components of each Fourier vector which fall below a threshold value. Current analysis device (1) according to Claim 11 , wherein the evaluation unit (5) is arranged to calculate the threshold value as the product of a predetermined factor and a mean value of the components of the Fourier vector.

Images