CN112327108A - Tank-type circuit breaker partial discharge ultrasonic signal denoising and time difference identification method - Google Patents
Tank-type circuit breaker partial discharge ultrasonic signal denoising and time difference identification method Download PDFInfo
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Abstract
The invention discloses a tank-type circuit breaker partial discharge ultrasonic signal denoising and time difference identification method, which comprises the following steps of 1) obtaining a tank-type circuit breaker partial discharge ultrasonic signal by using an ultrasonic sensor; 2) selecting an optimal wavelet function for analyzing the partial discharge ultrasonic signals of the tank type circuit breaker based on the cross-correlation coefficient, and realizing ultrasonic signal denoising by adopting signal decomposition, threshold processing and signal reconstruction based on discrete wavelet transform; 3) acquiring a PRPD map of the typical defect partial discharge ultrasound of the tank type circuit breaker by using the denoised signal; 4) and automatically calculating the ultrasonic signal energy by adopting an energy criterion method and extracting the signal time difference. The method selects db14 as the optimal wavelet function for analyzing the tank type circuit breaker partial discharge ultrasonic signals based on the cross-correlation coefficient, realizes the de-noising of the ultrasonic signals by adopting signal decomposition, threshold processing and signal reconstruction based on discrete wavelet transform, and automatically extracts the time difference of the ultrasonic signals by adopting an energy criterion method.
Description
Technical Field
The invention relates to a method for denoising and time difference identifying partial discharge ultrasonic signals of a tank-type circuit breaker.
Background
The tank-type circuit breaker is a circuit breaker with an arc extinguish chamber positioned in a grounded metal shell, mainly comprises a tank body, the arc extinguish chamber, an operating mechanism, an insulating sleeve, a mutual inductor, a wiring terminal and the like, can close, bear and break current in a loop under normal conditions, can close and open fault current under abnormal conditions such as short circuit and the like, and is important control and protection equipment [1-3] in a transformer substation and an electric power system. The tank type circuit breaker adopts sulfur hexafluoride as an insulating medium and an arc extinguishing medium, and has the advantages of compact structure, small occupied area, low equipment gravity center, stable structure, good anti-seismic performance, self-contained current transformer, strong pollution resistance, convenient maintenance and the like.
In the manufacturing, transporting, installing and operating processes of the tank type circuit breaker, insulation defects can be generated inside the tank type circuit breaker due to factors such as process, mechanical impact, opening and closing operation or electrical aging. Under the action of test voltage or rated voltage, when the electric field intensity concentrated at the insulation defect reaches the breakdown field intensity of the region, a partial discharge phenomenon occurs; partial discharge is a major cause of circuit breaker insulation degradation and also a precursor to circuit breaker insulation failure. Therefore, the on-line monitoring of the partial discharge signal can detect the insulation defect before the fault, and is an important means for ensuring the safe and stable operation of the ground tank type circuit breaker and the power system.
The method has the advantages that the insulation defect of the tank type circuit breaker can be found in time before the fault is detected by implementing the online monitoring of the partial discharge of the tank type circuit breaker, the important significance is realized on the improvement of the reliability of the circuit breaker and the whole power grid, the signal denoising and signal time difference automatic extraction technology in the partial discharge ultrasonic detection is researched, and the sensitivity and the accuracy of the online monitoring of the tank type circuit breaker can be improved.
Meanwhile, the discharge source positioning is helpful for the maintainers to quickly and accurately determine the fault position, so that the targeted equipment maintenance is facilitated, and the time and cost for maintenance are saved. The positioning of the discharge source mainly utilizes the time difference of signals received by different sensors, and the positioning mode can be divided into ultrasonic signal positioning based on relative time and acoustoelectric combined positioning based on absolute time. The sound and electricity joint positioning takes a partial discharge high-frequency or ultrahigh-frequency signal as a reference, the time delay of the electric signal from a discharge source to the sensor can be ignored, and therefore the time delay can be used as the starting time of discharge, and different time differences exist when the ultrasonic signal reaches the sensors at different positions. The method is characterized in that the intensity of discharge can be quantitatively determined by using an electric signal, but the time of the electric signal is sometimes difficult to determine due to the influence of electromagnetic interference, so that the accuracy of positioning is influenced.
Based on physical and chemical phenomena generated during discharge, the monitoring method of the partial discharge of the circuit breaker mainly comprises a pulse current method, an ultrasonic method, an ultrahigh frequency method and a decomposition gas detection method; however, the existing methods and methods are difficult to achieve complete ultrasonic signal denoising and fault location through time difference, so that a new method needs to be developed to solve the problems encountered at present.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for denoising and automatically identifying the time difference of the partial discharge ultrasonic signal of the tank type circuit breaker, which selects db14 as an optimal wavelet function for analyzing the partial discharge ultrasonic signal of the tank type circuit breaker based on the cross-correlation coefficient, realizes the denoising of the ultrasonic signal by adopting the signal decomposition, the threshold value processing and the signal reconstruction based on the discrete wavelet transform, and can automatically extract the time difference of the ultrasonic signal by adopting an energy criterion method, realize the automatic positioning of the internal discharge power supply of the tank type circuit breaker, has the advantages of quick and accurate positioning, and has practicability and wide application.
In order to solve the problems, the invention adopts the following technical scheme:
a method for denoising and time difference identifying partial discharge ultrasonic signals of a tank type circuit breaker comprises the following steps,
1) acquiring a partial discharge ultrasonic signal of the tank type circuit breaker by using an ultrasonic sensor;
2) selecting an optimal wavelet function for analyzing the partial discharge ultrasonic signals of the tank type circuit breaker based on the cross-correlation coefficient, and realizing ultrasonic signal denoising by adopting signal decomposition, threshold processing and signal reconstruction based on discrete wavelet transform;
3) acquiring a PRPD map of the typical defect partial discharge ultrasound of the tank type circuit breaker by using the denoised signal;
4) and automatically calculating the ultrasonic signal energy by adopting an energy criterion method and extracting the signal time difference.
Preferably, in step 2), the selection of the optimal wavelet function is completed by calculating the cross-correlation coefficient between the partial discharge ultrasonic signal pulse and each wavelet function, and the cross-correlation coefficient r is calculated according to the following formula:
wherein X (i) and Y (i) are partial discharge ultrasound signal pulses and wavelet functions, respectively,
and
is the average of the corresponding signals;the cross correlation coefficient is used for measuring the similarity degree of the two groups of signals, the range of the cross correlation coefficient is 0-1, and the larger the cross correlation coefficient is, the closer the two groups of signals are.
Preferably, in step 2), the discrete wavelet transform can be implemented by the following formula:
wherein f (t) is the original signal; a is a scale factor, and the frequency domain analysis of an original signal is realized by the expansion and contraction transformation of a wavelet function; b is a translation factor, and the time domain analysis of the original signal is realized by the translation transformation of the wavelet function in a time axis; m and n are positive integers.
Preferably, in step 3), after selecting the optimal wavelet function, 8 layers of decomposition are performed on the original ultrasonic signal to obtain detail components from the first layer to the eighth layer and approximate components of the eighth layer, after selecting a proper threshold function and threshold processing are performed on the wavelet coefficient obtained by decomposition, the detail coefficient is denoised, in order to overcome discontinuity of a hard threshold function and signal reconstruction errors of the soft threshold function, an improved threshold function is adopted,
wherein x is a wavelet coefficient without threshold processing, η (x) is a wavelet coefficient processed by a threshold function, and λ is a threshold.
Preferably, when the signal is denoised, the thresholds of different decomposition layers are selected differently, and the threshold should be relatively reduced along with the increase of the decomposition scale. Therefore, the threshold value is automatically selected according to the wavelet coefficient of each layer signal in the following way,
wherein λjIs the threshold value of the j-th layer, mjAnd njRespectively, the median of the wavelet coefficient of the layerAnd length, q is a constant.
Preferably, in step 4), an ultrasonic signal positioning mode based on relative time is adopted, the two ultrasonic sensors are respectively installed on two sides of the tank body of the circuit breaker, the discharge source positioning is realized according to the time difference of the ultrasonic signals received by the sensors, and the positioning principle is as follows:
wherein x is the fault location, L is the breaker tank length, Δ t is the signal time difference, and v is the ultrasonic wave propagation speed.
Preferably, the automatic positioning of the power supply in the tank type circuit breaker is realized by four methods of obtaining the ultrasonic signal time difference through an energy accumulation curve, an energy criterion, a red pool information quantity criterion and a related function, wherein the signal energy accumulation curve SiThe definition is as follows:
in the formula, xkFor the measured partial discharge ultrasonic signal, N is the sampling depth of the signal, and i is the sampling index value; wherein the signal energy criterion ECkIs defined as:
in the formula, SNFor the total energy of the measured ultrasonic signal, N is the sampling depth of the signal, i is the sampling index value, and α is a constant.
The invention has the beneficial effects that: the method comprises the steps that an optimal wavelet function suitable for partial discharge ultrasonic signal analysis of the tank-type circuit breaker is selected, and signal decomposition, threshold processing and signal reconstruction based on discrete wavelet transformation are adopted to achieve ultrasonic signal denoising; aiming at the denoised ultrasonic signals, an automatic signal time difference extraction algorithm of a signal energy accumulation curve, an energy criterion, a red pool information quantity criterion and a related function is researched and compared so as to realize accurate automatic positioning of a discharge source, and the method has practicability and application universality.
Drawings
In order to clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, but the protection scope of the present invention is not limited.
FIG. 1 is a schematic diagram of partial discharge ultrasonic signal pulses of the present invention;
FIG. 2 is a schematic of the cross-correlation coefficient calculation of the present invention;
FIG. 3 is a schematic diagram of an original signal before denoising an ultrasonic signal based on discrete wavelet transform according to the present invention;
FIG. 4 is a schematic diagram of a denoised signal after denoising an ultrasonic signal based on discrete wavelet transform according to the present invention;
fig. 5 is a diagram illustrating a PRPD pattern of a metallic protrusion on a surface of a conductor in a typical defect of the tank type circuit breaker according to the present invention;
fig. 6 is a diagram illustrating a PRPD pattern of a metallic protrusion on the surface of a ground case in a typical defect of the tank type circuit breaker according to the present invention;
FIG. 7 is a diagram illustrating a PRPD pattern of a gap inside a basin-type insulator in a typical defect of a tank-type circuit breaker according to the present invention;
fig. 8 is a schematic diagram of a PRPD pattern of free metal ions in a typical defect of the tank type circuit breaker according to the present invention;
FIG. 9 is a schematic illustration of an exemplary partial discharge ultrasonic signal of the present invention;
FIG. 10 is a schematic diagram of an energy accumulation curve in signal time difference extraction according to the present invention;
FIG. 11 is a schematic diagram of an energy criterion in signal time difference extraction according to the present invention;
Detailed Description
Referring to fig. 1 to 11, a method for removing noise and identifying time difference of partial discharge ultrasonic signals of a tank type circuit breaker includes the following steps,
1) acquiring a partial discharge ultrasonic signal of the tank type circuit breaker by using an ultrasonic sensor;
2) selecting an optimal wavelet function for analyzing the partial discharge ultrasonic signals of the tank type circuit breaker based on the cross-correlation coefficient, and realizing ultrasonic signal denoising by adopting signal decomposition, threshold processing and signal reconstruction based on discrete wavelet transform;
3) acquiring a PRPD map of the typical defect partial discharge ultrasound of the tank type circuit breaker by using the denoised signal;
4) and automatically calculating the ultrasonic signal energy by adopting an energy criterion method and extracting the signal time difference.
Further, in step 2), selecting a proper wavelet function is a key for realizing the denoising of the partial discharge ultrasonic signal, the optimal wavelet function can describe the frequency components of each layer after the decomposition of the original signal most appropriately, the selection of the optimal wavelet function is completed by calculating the cross-correlation coefficient of the pulse of the partial discharge ultrasonic signal and each wavelet function, and the calculation formula of the cross-correlation coefficient r is as follows:
wherein X (i) and Y (i) are partial discharge ultrasound signal pulses and wavelet functions, respectively,
and
is the average of the corresponding signals. The cross correlation coefficient is used for measuring the similarity degree of the two groups of signals, the range of the cross correlation coefficient is 0-1, and the larger the cross correlation coefficient is, the closer the two groups of signals are.
Partial discharge ultrasonic signal pulses are shown in fig. 1, and the results of cross-correlation coefficient calculation with a typical wavelet function are shown in fig. 2; the cross-correlation coefficient of the db14 wavelet function and the ultrasonic signal pulse is the largest, and db14 is selected as the denoising optimal wavelet function of the tank type circuit breaker partial discharge ultrasonic signal.
Further, in step 2), compared to fourier transform, wavelet transform realizes both time domain analysis and frequency domain analysis of the original signal by scaling and shifting of wavelet function [6 ]. The wavelet transform includes a continuous wavelet transform and a discrete wavelet transform, and the continuous wavelet transform has computation complexity and redundancy phenomena due to the computation of wavelet coefficients in each time scale. The discrete wavelet transform may be implemented by:
wherein f (t) is the original signal; a is a scale factor, and the frequency domain analysis of an original signal is realized by the expansion and contraction transformation of a wavelet function; b is a translation factor, and the time domain analysis of the original signal is realized by the translation transformation of the wavelet function in a time axis; m and n are positive integers; the multi-resolution analysis based on the discrete wavelet transform has the characteristics of low time resolution and high frequency resolution at the low frequency of the signal and low frequency resolution and high time resolution at the high frequency of the signal. Therefore, the wavelet transform is widely applied to the field of signal processing, and the denoising of the tank type circuit breaker partial discharge ultrasonic signal is realized by using the discrete wavelet transform technology.
Further, in step 3), after selecting the optimal wavelet function, 8-layer decomposition is carried out on the original ultrasonic signal to obtain detail components from the first layer to the eighth layer and approximate components of the eighth layer, denoising is carried out on detail coefficients after proper threshold functions and threshold processing are selected for the wavelet coefficients obtained by decomposition, in order to overcome discontinuity of hard threshold functions and signal reconstruction errors of soft threshold functions, improved threshold functions are adopted,
wherein x is a wavelet coefficient without threshold processing, η (x) is a wavelet coefficient processed by a threshold function, and λ is a threshold.
Furthermore, because each layer of signals after wavelet multiresolution decomposition has different time frequency and amplitude distribution, when the signals are denoised, the threshold values of different decomposition layers are selected differently, and the threshold values are relatively reduced along with the increase of the decomposition scale. Therefore, the threshold value is automatically selected according to the wavelet coefficient of each layer signal in the following way,
wherein λjIs the threshold value of the j-th layer, mjAnd njThe median and the length of the wavelet coefficient of the layer are respectively, and q is a constant.
After threshold processing is carried out on detail coefficients of each layer, reconstruction of signals can be achieved through inverse wavelet transform, and denoising signals are obtained. Fig. 3 and 4 show the denoising result of the ultrasonic signal based on discrete wavelet transform, in which the signal-to-noise ratio of the denoised signal is improved by 6.21dB compared with the original signal; meanwhile, the cross-correlation coefficient of the denoised signal and the original signal is 0.91, and the problems of waveform distortion and the like do not exist. The denoised ultrasonic signals can improve the accuracy of the discharge map and the fault source positioning, so that the online monitoring and fault diagnosis of the tank-type circuit breaker can be more effectively implemented. Typical defect PRPD patterns of the tank type circuit breaker applying ultrasonic partial discharge detection and discrete wavelet transform are shown in FIGS. 5 to 8.
Furthermore, in the step 4), the discharge source positioning is helpful for the maintainers to quickly and accurately determine the fault position, so that the targeted equipment maintenance is facilitated, and the time and cost for maintenance are saved. The positioning of the discharge source mainly utilizes the time difference of signals received by different sensors, and the positioning mode can be divided into ultrasonic signal positioning based on relative time and acoustoelectric combined positioning based on absolute time. The sound and electricity joint positioning takes a partial discharge high-frequency or ultrahigh-frequency signal as a reference, the time delay of the electric signal from a discharge source to the sensor can be ignored, and therefore the time delay can be used as the starting time of discharge, and different time differences exist when the ultrasonic signal reaches the sensors at different positions. The method is characterized in that the intensity of discharge can be quantitatively determined by using an electric signal, but the time of the electric signal is sometimes difficult to determine due to the influence of electromagnetic interference, so that the accuracy of positioning is influenced; adopt the ultrasonic signal location mode based on relative time, two ultrasonic sensor install respectively in circuit breaker jar body both sides, realize discharging the source location according to the time difference that the sensor received ultrasonic signal, the location principle as follows:
wherein x is the fault position, L is the length of the tank body of the circuit breaker, delta t is the signal time difference, v is the ultrasonic wave propagation speed, and the ultrasonic signal propagation speed in the sulfur hexafluoride is 136 m/s.
From the above formula, it can be seen that the accurate measurement of the time difference is the key to the accuracy of the positioning. FIG. 9 shows a typical ultrasonic signal after de-noising using discrete wavelet transform, with a signal time difference of 112 μ s. In general, a cursor is used to determine the arrival time of the signal, and the arrival times of different receiving points are subtracted to obtain a time difference. The method is simple and intuitive, but needs manual operation, and cannot realize automatic positioning of the discharge source. Therefore, four methods for acquiring ultrasonic signal time difference are researched and compared with a signal energy accumulation curve, an energy criterion, a red pool information quantity criterion and a related function, and automatic positioning of a power supply in the tank type circuit breaker is achieved.
Further, the automatic positioning of the power supply in the tank type circuit breaker is realized by four methods of obtaining the ultrasonic signal time difference through an energy accumulation curve, an energy criterion, a red pool information quantity criterion and a related function, wherein the signal energy accumulation curve SiThe definition is as follows:
in the formula, xkFor the measured partial discharge ultrasound signal, N is the sampling depth of the signal, and i is the sampling index value, as shown in fig. 10, the cumulative energy of the background noise is close to zero before the ultrasound signal arrives. After the ultrasonic signal arrives, the accumulated energy is continuously increased, the maximum value of the energy accumulation curve is the total energy of the signal, and the time difference of the signal is the difference value of the inflection points of the two signal energy accumulation curves;
wherein the signal energy criterion ECkIs defined as:
in the formula, SNThe total energy of the measured ultrasonic signal, N is the sampling depth of the signal, i is the sampling index value, alpha is a constant, and the energy criterion is the difference value between the signal energy accumulation curve and the trend based on the total energy of the signal; thus, as shown in FIG. 11, the time difference between the two signals is the difference between the minimum values of the energy criterion curves.
Fig. 10 and fig. 11 show the analysis results of four algorithms for automatically extracting the signal time difference. The time differences extracted using the signal energy accumulation curve, the energy criterion, the erythroid information criterion, and the correlation function are 105 μ s, 113 μ s, 96 μ s, and 132 μ s, respectively. When the energy criterion method is adopted, the time difference from manual calculation only has an error of 1 mu s. Therefore, the energy criterion method can be used for extracting the time difference of the ultrasonic signals and realizing the automatic positioning of the power supply in the tank type circuit breaker
The signal denoising and signal time difference automatic extraction technology in the tank-type circuit breaker partial discharge ultrasonic detection is researched, and the sensitivity and the accuracy of online monitoring are improved. And selecting db14 as the optimal wavelet function for analyzing the partial discharge ultrasonic signal of the tank type circuit breaker by calculating the cross-correlation coefficient of the partial discharge ultrasonic signal pulse and each wavelet function. The signal decomposition based on discrete wavelet multiresolution, the improved threshold function and the automatic threshold are adopted, the denoising of the ultrasonic signal is realized, and compared with the original signal, the signal-to-noise ratio of the denoised ultrasonic signal is improved by 6.21 db. The comparison of the signal energy accumulation curve, the energy criterion, the red pool information content criterion and the related function results shows that the signal time difference extracted based on the energy criterion method is close to an actual value and can be applied to automatic positioning of the discharge source in the tank type circuit breaker.
The above is only a specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that are not thought of through the inventive work should be included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope defined by the claims.
Claims (7)
1. A tank-type circuit breaker partial discharge ultrasonic signal denoising and time difference identification method is characterized in that: the method comprises the following steps:
1) acquiring a partial discharge ultrasonic signal of the tank type circuit breaker by using an ultrasonic sensor;
2) selecting an optimal wavelet function for analyzing the partial discharge ultrasonic signals of the tank type circuit breaker based on the cross-correlation coefficient, and realizing ultrasonic signal denoising by adopting signal decomposition, threshold processing and signal reconstruction based on discrete wavelet transform;
3) acquiring a PRPD map of the typical defect partial discharge ultrasound of the tank type circuit breaker by using the denoised signal;
4) and automatically calculating the ultrasonic signal energy by adopting an energy criterion method and extracting the signal time difference.
2. The tank circuit breaker partial discharge ultrasonic signal denoising and time difference identifying method as claimed in claim 1, wherein: in step 2), the selection of the optimal wavelet function is completed by calculating the cross-correlation coefficient of the partial discharge ultrasonic signal pulse and each wavelet function, wherein the cross-correlation coefficient r is calculated according to the following formula:
wherein X (i) and Y (i) are partial discharge ultrasound signal pulses and wavelet functions, respectively,
and
the cross correlation coefficient is an average value of corresponding signals and is used for measuring the similarity degree of the two groups of signals, the range of the cross correlation coefficient is 0-1, and the larger the cross correlation coefficient is, the closer the two groups of signals are.
3. The tank circuit breaker partial discharge ultrasonic signal denoising and time difference identifying method as claimed in claim 2, wherein: in step 2), the discrete wavelet transform can be implemented by the following formula:
wherein f (t) is the original signal; a is a scale factor, and the frequency domain analysis of an original signal is realized by the expansion and contraction transformation of a wavelet function; b is a translation factor, and the time domain analysis of the original signal is realized by the translation transformation of the wavelet function in a time axis; m and n are positive integers.
4. The tank circuit breaker partial discharge ultrasonic signal denoising and time difference identifying method as claimed in claim 2, wherein: in step 3), after selecting an optimal wavelet function, carrying out 8-layer decomposition on an original ultrasonic signal to obtain detail components from a first layer to an eighth layer and approximate components of the eighth layer, denoising the detail coefficients after selecting a proper threshold function and threshold processing for the wavelet coefficients obtained by decomposition, adopting an improved threshold function for overcoming discontinuity of a hard threshold function and signal reconstruction errors of a soft threshold function,
wherein x is a wavelet coefficient without threshold processing, η (x) is a wavelet coefficient processed by a threshold function, and λ is a threshold.
5. The tank circuit breaker partial discharge ultrasonic signal denoising and time difference identifying method as claimed in claim 4, wherein: when the signal is denoised, the threshold values of different decomposition layers are selected differently, and the threshold values are relatively reduced along with the increase of the decomposition scale; therefore, the threshold value is automatically selected according to the wavelet coefficient of each layer signal in the following way,
wherein λjIs the threshold value of the j-th layer, mjAnd njThe median and the length of the wavelet coefficient of the layer are respectively, and q is a constant.
6. The tank circuit breaker partial discharge ultrasonic signal denoising and time difference identifying method as claimed in claim 4, wherein: in the step 4), an ultrasonic signal positioning mode based on relative time is adopted, the two ultrasonic sensors are respectively installed on two sides of the tank body of the circuit breaker, the discharge source positioning is realized according to the time difference of the ultrasonic signals received by the sensors, and the positioning principle is as follows:
wherein x is the fault location, L is the breaker tank length, Δ t is the signal time difference, and v is the ultrasonic wave propagation speed.
7. The tank circuit breaker partial discharge ultrasonic signal denoising and time difference identifying method as claimed in claim 6, wherein: the automatic positioning of the power supply in the tank type circuit breaker is realized by four methods of obtaining ultrasonic signal time difference through an energy accumulation curve, an energy criterion, a red pool information content criterion and a related function, wherein the signal energy accumulation curve SiThe definition is as follows:
in the formula, xkFor the measured partial discharge ultrasonic signal, N is the sampling depth of the signal, and i is the sampling index value; wherein the signal energy criterion ECkIs defined as:
in the formula, SNFor the total energy of the measured ultrasonic signal, N is the sampling depth of the signal, i is the sampling index value, and α is a constant.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| DE102021206721A1 (en) | 2021-06-29 | 2022-12-29 | Siemens Aktiengesellschaft | Locating an arc |
| DE102021206719A1 (en) | 2021-06-29 | 2022-12-29 | Siemens Aktiengesellschaft | Locating an arc |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| DE102021206719A1 (en) | 2021-06-29 | 2022-12-29 | Siemens Aktiengesellschaft | Locating an arc |
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