Short-circuit current zero crossing point prediction method and system based on vacuum switch

By analyzing the spectrum characteristics of historical short-circuit current waveform samples, predicting the zero crossing point of the short-circuit current in the power system, the problem of low prediction accuracy in the existing technology is solved, and more accurate fault handling and improved operating efficiency of the power system is achieved.

CN119249276APending Publication Date: 2025-01-03STATE GRID HUNAN ELECTRIC POWER COMPANY LIMITED +2
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Patent Information

Application Number
CN202411355673.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-27
Publication Date
2025-01-03

AI Technical Summary

Technical Problem

The existing short-circuit current zero-crossing prediction method has low prediction accuracy and cannot effectively cope with the complexity and variability of short-circuit faults in power systems.

Method used

By obtaining multiple historical short-circuit current waveform samples, extracting spectrum characteristics and comparing them with real-time current data, selecting the historical spectrum characteristics with the highest similarity to predict the zero crossing point of the next cycle, and using Fourier transform to obtain fundamental waves, harmonics and The interharmonic content is calculated to determine the most similar historical samples.

Benefits of technology

Improves the accuracy of short-circuit current zero crossing prediction, ensures that the fast vacuum switch operates at the optimal moment, and reduces arc duration and system impact.

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Abstract

The invention discloses a short-circuit current zero crossing point prediction method and system based on a vacuum switch. The method comprises the following steps: acquiring a period sample set of a plurality of historical short-circuit current waveform samples with complete periods; associating and numbering the historical short-circuit current period samples in each period sample set according to a time sequence, and extracting historical spectrum characteristics and zero crossing point time of each historical short-circuit current period sample; comparing the to-be-detected spectrum features with historical spectrum features, and selecting a historical current period sample corresponding to the historical spectrum feature with the highest similarity as a reference short-circuit current period sample; and setting the historical short-circuit current period sample located at the next serial number of the reference short-circuit current period sample as a prediction period short-circuit current, and predicting the zero-crossing point time of the next period of the to-be-detected short-circuit current based on the zero-crossing point time corresponding to the prediction period short-circuit current. The method can improve the prediction accuracy through a spectrum feature matching method.
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Description

Technical Field

[0001] The present invention relates to the technical field of power protection, and in particular to a method and system for predicting a short-circuit current zero-crossing point based on a vacuum switch. Background Art

[0002] In the power system, short-circuit fault is a common power accident, which may cause serious equipment damage and power supply interruption. In order to effectively control and protect the power system, it is necessary to quickly cut off the part that generates short-circuit current. Fast vacuum switches are widely used in the protection of power systems due to their high-speed disconnection capability and good electrical performance. Fast vacuum switches are designed with high-speed action characteristics and can act quickly after detecting short-circuit current, thereby quickly isolating the fault point. Since the current value of the short-circuit current is large, if it is cut off when the short-circuit current is large, a high-temperature arc will be generated at the disconnection point, causing damage to the contacts of the fast vacuum switch. When the current passes through the zero point, the instantaneous value of the current is zero. At this time, disconnecting the circuit can avoid or significantly reduce the formation of arcs, thereby protecting the contacts of the switch from high temperature and arc erosion.

[0003] Fast vacuum switches have extremely high disconnection speeds and excellent arc extinguishing capabilities. In a vacuum environment, the conditions for the generation and maintenance of arcs are extremely harsh. Therefore, by predicting and accurately controlling the switch action when the current passes through zero, this advantage of the vacuum switch can be fully utilized to achieve almost arc-free disconnection operations. Therefore, by real-time monitoring and predicting the zero-crossing point of the short-circuit current, the operation of the fast vacuum switch can be more effectively coordinated, achieving rapid response and precise control of short-circuit faults, and improving the fault handling capability and operating efficiency of the entire power system.

[0004] The existing short-circuit current zero-crossing point prediction method mainly predicts the zero-crossing point through simple waveform analysis. However, since the waveform analysis is mainly aimed at the current short-circuit current situation for prediction, that is, only the law of the zero-crossing point of the current when the short-circuit fault occurs is analyzed to make a prediction. However, the main difficulty in predicting the short-circuit current zero point is that there will be many other current waveforms superimposed inside the short-circuit current, so it is not a very strict periodic signal. Moreover, this method has high requirements on the waveform of the short-circuit current, and the prediction accuracy is not high in practical applications. Because the existing technology does not fully consider the complexity and variability of short-circuit faults in the power system when designing, therefore, a more advanced and flexible method is needed to improve the accuracy of short-circuit current zero-crossing point prediction. Summary of the invention

[0005] The present invention provides a short-circuit current zero-crossing point prediction method and system based on a vacuum switch, which are used to solve the technical problem that the prediction accuracy of the existing short-circuit current zero-crossing point prediction method is low.

[0006] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0007] A method for predicting a short-circuit current zero-crossing point based on a vacuum switch, comprising:

[0008] Obtain complete historical short-circuit current waveform samples for multiple cycles;

[0009] Dividing each historical short-circuit current waveform sample into a plurality of historical short-circuit current cycle samples according to each historical short-circuit current waveform sample current cycle; obtaining a cycle sample set of each historical short-circuit current waveform sample;

[0010] The historical short-circuit current cycle samples in each cycle sample set are associated and numbered in chronological order, and the historical spectrum characteristics and zero-crossing time of each historical short-circuit current cycle sample are extracted;

[0011] Acquire current cycle data of the short-circuit current to be measured, extract the frequency spectrum features to be measured of the current cycle data, compare the frequency spectrum features to be measured with the historical frequency spectrum features respectively, and select the historical current cycle samples corresponding to the historical frequency spectrum features with the highest similarity as reference short-circuit current cycle samples;

[0012] A historical short-circuit current cycle sample that belongs to the same cycle sample set as the reference short-circuit current cycle sample and is located at the next number of the reference short-circuit current cycle sample is set as the predicted cycle short-circuit current, and the zero-crossing time of the next cycle of the short-circuit current to be measured is predicted based on the zero-crossing time corresponding to the predicted cycle short-circuit current.

[0013] Preferably, the complete historical short-circuit current waveform sample includes: a current waveform including a positive half-cycle and a negative half-cycle, wherein the positive half-cycle is that the current starts from zero, rises to the maximum positive value and then drops back to zero, and the negative half-cycle is that the current or voltage starts from zero, drops to the maximum negative value, and then rises back to zero.

[0014] Preferably, when each historical short-circuit current waveform sample is divided into multiple historical short-circuit current cycle samples according to each historical short-circuit current waveform sample current cycle, the cycle starting point is the point where the current waveform passes through zero from a negative value or zero value to a positive value, and the cycle end point is the point where the historical short-circuit current waveform starts from the cycle starting point and returns to zero after a positive half cycle and a negative half cycle in sequence, and the zero-crossing point is the point where the waveform passes through zero from a negative value or positive value to the opposite value.

[0015] Preferably, the spectrum characteristics include fundamental wave content, harmonic content and interharmonic content;

[0016] and / or

[0017] The zero-crossing time of each historical short-circuit current cycle sample is the time length of each zero-crossing point in each historical short-circuit current cycle sample relative to the starting point;

[0018] and / or

[0019] The current cycle data of the short-circuit current to be measured is the current waveform data from the fault start phase to the end of the cycle in which it is located.

[0020] Preferably, the fundamental wave content includes the phase and amplitude of the fundamental wave, the harmonic content includes the phase and amplitude of the harmonic, and the interharmonic content includes the phase and amplitude of the interharmonic; extracting the spectrum features includes:

[0021] Performing Fourier transform on historical short-circuit current cycle samples or current cycle data, transforming the historical short-circuit current cycle samples or current cycle data into the form of a sum of a series of complex numbers through Fourier transform, each complex number represents a frequency component, the imaginary part of the frequency component is represented as the phase of the corresponding frequency component, and the real part is represented as the amplitude of the corresponding frequency component, and the frequency corresponding to each frequency component is determined using the parameters of Fourier transform;

[0022] The frequency component with the largest amplitude value is set as the frequency component of the fundamental wave, the frequency component with an integer multiple of the fundamental wave frequency is set as the frequency component of the harmonic, and the frequency component with a non-integer multiple of the fundamental wave frequency is set as the frequency component of the interharmonic. The fundamental wave content, harmonic content and interharmonic content are obtained according to the fundamental wave, harmonic and interharmonic frequency components, respectively.

[0023] Preferably, obtaining the current cycle data of the short-circuit current to be measured includes:

[0024] Assume that the sampling frequency is set to K, sample the real-time current data of the vacuum switch outlet, and calculate the current change rate between adjacent sampling time points. If the current change rate exceeds the current growth threshold, it is determined that a short circuit fault occurs. The formula is:

[0025]

[0026] Among them, I j represents the current value at the jth sampling time point, I j+1 represents the current value at the j+1th sampling time point, Iz y represents the current growth threshold, and the time interval between the jth sampling time point and the j+1th sampling time point is 1 / K;

[0027] After determining that the j+1th sampling time point is the fault starting point, the starting phase of the current data at this point is obtained and calibrated as the fault starting phase. The current cycle data is the current waveform timing data from the fault starting point to the end of the current cycle where the current fault occurs.

[0028] Preferably, the historical short-circuit current cycle samples in each cycle sample set are associated and numbered in chronological order, specifically:

[0029] For the historical short-circuit current cycle samples in the cycle sample set, the timestamp corresponding to the cycle start point and the timestamp corresponding to the cycle end point of each historical short-circuit current cycle sample are recorded, and according to the timestamp of each historical short-circuit current cycle sample, they are sorted in the order of the actual occurrence time, and the historical short-circuit current cycle sample with the earliest timestamp corresponding to the cycle start point is arranged at the front, and then the timestamp corresponding to the cycle start point of the next historical short-circuit current cycle sample is the timestamp corresponding to the cycle end point of the previous historical short-circuit current cycle sample;

[0030] The sorted historical short-circuit current cycle samples are numbered to identify their positions in the same group of short-circuit current waveform samples, and the numbers are incremented in sequence.

[0031] Preferably, the similarity is calculated in the following manner:

[0032] The similarity index between the spectrum feature to be tested and each history is calculated by:

[0033]

[0034] Wherein, Sd(i,j) represents the similarity index between the frequency spectrum feature j to be measured and the historical frequency spectrum feature of the mth short-circuit current cycle sample in the cycle sample set of the i-th historical short-circuit current waveform sample, and They respectively represent the frequency components of the fundamental wave content, average harmonic content and average interharmonic content in the spectrum characteristics to be measured, i is the number of the short-circuit current waveform sample, and m is the number of the historical short-circuit current cycle sample; and Respectively represent the frequency components of the fundamental wave content, the average harmonic content and the average interharmonic content in the reference spectrum characteristics of the mth historical short-circuit current cycle sample in the cycle sample set of the i-th historical short-circuit current waveform sample;

[0035] The short-circuit current cycle sample corresponding to the smallest similarity index is selected as the historical current cycle sample with the highest similarity.

[0036] Preferably, the method for generating the frequency component of the average harmonic content is: respectively superimposing the real and imaginary parts of all the harmonic frequency components within the same spectrum feature, and then calculating the average, and using the averaged real and imaginary parts as the real and imaginary parts of the frequency component of the average harmonic content; the method for generating the frequency component of the average interharmonic content is: respectively superimposing the real and imaginary parts of all the interharmonic frequency components within the same spectrum feature, and then calculating the average, and using the averaged real and imaginary parts as the real and imaginary parts of the frequency component of the average interharmonic content.

[0037] A computer system comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the steps of the above method are implemented when the processor executes the computer program.

[0038] The present invention has the following beneficial effects:

[0039] 1. The present invention establishes a rich data set by collecting and analyzing multiple groups of historical short-circuit current waveform data. These data contain current waveform characteristics under various short-circuit conditions. By eliminating incomplete data, the quality of the analyzed samples is ensured, providing a reliable basis for subsequent predictions. Based on the above data set, the present invention extracts spectral features and compares the spectral features of real-time fault samples with the reference spectral features of historical samples. It can identify the most similar historical short-circuit current cycle samples. By finding the most similar historical samples, the characteristics of the real-time fault can be inferred, thereby predicting the zero-crossing point of the next cycle. The matching method of spectral features greatly improves the accuracy of the prediction, and quickly and accurately predicts the zero-crossing point of the short-circuit current, which can provide a reference for the fast vacuum switch to operate at the optimal time.

[0040] 2. In the preferred solution, by extracting key spectral features such as fundamental content, harmonic content and interharmonic content, high-precision prediction can be achieved with fewer data features.

[0041] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0043] Figure 1 It is a schematic diagram of the overall method flow of the present invention;

[0044] Figure 2 It is a schematic diagram of the short-circuit current waveform collected in the present invention;

[0045] Figure 3 It is a schematic diagram of predicting the zero-crossing time in the present invention;

[0046] Figure 4 It is a schematic diagram of the overall system structure of the present invention. DETAILED DESCRIPTION

[0047] The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0048] Embodiment 1:

[0049] See also Figures 1 to 3 , the present invention provides a technical solution:

[0050] A method for predicting a short-circuit current zero-crossing point based on a fast vacuum switch, the specific steps comprising:

[0051] Step 1: For the outgoing cabinet equipped with a fast vacuum switch, collect multiple sets of short-circuit current waveforms at the outgoing terminals of the vacuum fast switch, remove the current waveform data with incomplete periods in the short-circuit current waveform, and obtain the short-circuit current waveform samples.

[0052] In this embodiment, the short-circuit current waveform of each group of vacuum fast switch outlets is the current waveform time series data recorded when a short-circuit fault occurs at the vacuum fast switch outlet. The start timestamp of the current waveform time series data is the moment when the short-circuit fault occurs, and the end timestamp is the moment when the short-circuit fault is isolated or cleared and the current returns to a normal level.

[0053] The outgoing line cabinet is an important component of the power distribution system, usually located in a substation or distribution room. Its main function is to distribute electricity from the high-voltage side to the low-voltage side. The outgoing line cabinet contains circuit breakers, disconnectors, current transformers and other equipment. The fast vacuum switch is a special type of circuit breaker. The high-voltage busbar of the outgoing line cabinet is electrically connected to the input end of the fast vacuum switch, and the output end is generally connected to a transformer. A current transformer is set at the output end to measure the current. The current waveform data at the outlet end of the vacuum fast switch in this embodiment are all collected through the secondary side of the current transformer. Since the vacuum fast switch generally controls the on and off of multi-phase currents, the current waveform data in this embodiment are all single-phase current working data.

[0054] The short-circuit current waveforms of multiple groups of vacuum fast switch outlets are all historical short-circuit current waveform data. Potential failure modes and trends can be identified through the historical short-circuit current waveform data, thereby realizing failure prediction and prevention.

[0055] Furthermore, the current waveform data with a complete cycle includes the current waveforms of the positive half cycle and the negative half cycle, wherein the positive half cycle is that the current starts from zero, rises to the positive maximum value and then drops back to zero, and the negative half cycle is that the current or voltage starts from zero, drops to the negative maximum value, and then rises back to zero, and the current waveform data with an incomplete cycle is that the current waveform data is truncated in the positive half cycle and the negative half cycle, resulting in the cycle not starting from zero and ending from zero.

[0056] A complete cycle of current waveform data includes a complete sinusoidal wave cycle, which consists of a positive half-cycle and a negative half-cycle. The current starts from zero, gradually rises to the positive maximum value, and then drops back to zero. This process corresponds to the rising part of the sine wave. The negative half-cycle current starts from zero, drops to the negative maximum value, and then rises back to zero. This process corresponds to the falling part of the sine wave. A complete cycle means that the current waveform starts from zero, passes through the positive half-cycle and the negative half-cycle, and finally returns to zero to form a complete sinusoidal waveform. A complete cycle of the waveform of a current short-circuit fault means that the current waveform starts from zero, passes through the positive half-cycle and the negative half-cycle. In the case of a short-circuit fault, the current waveform will show abnormalities and is no longer a standard sinusoidal waveform.

[0057] For example, at the moment of short circuit, the current will quickly rise to a very high peak value, which is much higher than the current value during normal operation. This initial impact current is usually caused by the system voltage suddenly applied to the short circuit point, resulting in a rapid increase in current. After the initial impact current, the current may undergo an attenuated oscillation process, which is due to the inductance and capacitance effects in the system. In this process, the current waveform may show multiple peaks, and the oscillation gradually decays over time until the current stabilizes at a lower level. During the attenuated oscillation process, the current waveform will pass through multiple zero crossings, but in essence, the waveform of the short-circuit fault current is still a sine waveform as a whole, but the peak value and period are no longer a standard sine waveform. A complete cycle of short-circuit current waveform data includes a complete sine wave cycle.

[0058] Current waveform data with incomplete cycles means that during the recording process, the current waveform is truncated in the positive half cycle or the negative half cycle, resulting in the cycle not starting from zero and ending at zero. For example, in the positive half cycle, the current may be truncated before rising to the maximum positive value, or it may not drop back to zero after reaching the peak value. In the negative half cycle, the current may be truncated before dropping to the maximum negative value, or it may not rise back to zero after reaching the peak value. The reason why the short-circuit current waveform contains an incomplete current waveform is that the start timestamp of the short-circuit current waveform is the moment when the short-circuit fault occurs, and the end timestamp is the moment when the short-circuit fault is isolated or cleared and the current returns to normal levels. The start timestamp and the end timestamp may not be the starting and end points of the current waveform cycle. The eliminated current waveform data is actually the data at the head and tail of the wave.

[0059] Therefore, when analyzing the short-circuit current waveform, the current waveform data with incomplete cycles is eliminated, so that the current waveforms within the short-circuit current waveform samples all have complete cycles, and focusing on the samples with complete cycles for analysis can better identify and classify the characteristics of short-circuit faults, because the current waveform data with complete cycles is closer to the ideal sinusoidal waveform, which can improve the accuracy and reliability of data analysis, and the waveform data with complete cycles are easier to analyze because they follow predictable patterns, ensuring that the short-circuit current waveform samples used for reference are more reliable.

[0060] Step 2: Divide all short-circuit current waveform samples into multiple short-circuit current cycle samples according to the current cycle, obtain the time length of each zero-crossing point relative to the starting point in each short-circuit current cycle sample, and associate and number the short-circuit current cycle samples corresponding to each group of short-circuit current waveform samples in chronological order.

[0061] In this embodiment, when all short-circuit current waveform samples are divided into multiple short-circuit current cycle samples according to the current cycle, the cycle starting point is the point where the current waveform passes through zero from a negative value or zero value to a positive value, and the cycle end point is the point where the short-circuit current waveform starts from the cycle starting point and returns to zero after a positive half cycle and a negative half cycle in sequence. The zero-crossing point is the point where the waveform passes through zero from a negative value or a positive value to the opposite value.

[0062] By defining clear cycle start and end points, it can be ensured that all analysis is based on a unified standard. This standardization helps improve the consistency and repeatability of the analysis, and can more accurately analyze the characteristics of the short-circuit current waveform, thereby improving the accuracy of fault analysis.

[0063] When obtaining the time length of each zero-crossing point in each short-circuit current cycle sample relative to the starting point, the cycle starting point of the short-circuit current cycle sample is used as the reference point for calculating the time length, and the specific timestamp of the cycle starting point is recorded. All zero-crossing points are identified in the current waveform. The zero-crossing point refers to the point where the current waveform passes from a positive value to a negative value, or from a negative value to a positive value. For each zero-crossing point, its specific timestamp is also recorded, and the difference between the specific time of each zero-crossing point and the specific timestamp of the cycle starting point is calculated. The obtained time difference is the time length of the zero-crossing point relative to the starting point.

[0064] For example, if the timestamp of the period start point is t 0 , the timestamp of a zero-crossing point is t 1 , then the time length of the zero crossing point relative to the starting point is t 1 -t 0 , record the calculated time length and use it for subsequent analysis.

[0065] Furthermore, the logic for associating and numbering the short-circuit current cycle samples corresponding to each group of short-circuit current waveform samples in chronological order is as follows:

[0066] For the short-circuit current cycle samples divided from the same group of short-circuit current waveform samples, the timestamp corresponding to the cycle start point and the timestamp corresponding to the cycle end point of each short-circuit current cycle sample are recorded, and according to the timestamp of each short-circuit current cycle sample, they are sorted in the order of actual occurrence, and the cycle sample with the earliest timestamp corresponding to the cycle start point is sorted first, and then the timestamp corresponding to the cycle start point of the next short-circuit current cycle sample is the timestamp corresponding to the cycle end point of the previous short-circuit current cycle sample;

[0067] The sorted period samples are numbered to identify their positions in the same group of short-circuit current waveform samples, and the numbering starts from 1 and increases in sequence.

[0068] For example, the current waveform in the i-th group of short-circuit current waveform samples has waveform signals of multiple cycles. When sorting, according to the time sequence, the waveform signal of the first cycle is marked as the first short-circuit current cycle sample, the waveform signal of the second cycle is marked as the second short-circuit current cycle sample, and so on.

[0069] During the sorting process, ensure that the cycle start point timestamp of each subsequent short-circuit current cycle sample is connected with the cycle end point timestamp of the previous short-circuit current cycle sample, ensuring the continuity and consistency of the time sequence between the cycle samples. The numbering starts from 1 and increases sequentially to ensure that each cycle sample has a unique number. The sorted and numbered cycle sample data is recorded for subsequent analysis.

[0070] Step 3: Perform Fourier transform on each short-circuit current cycle sample, obtain the spectrum characteristics corresponding to each short-circuit current cycle sample, and calibrate them as reference spectrum characteristics (i.e. historical spectrum characteristics), wherein the spectrum characteristics include fundamental wave content, harmonic content, and interharmonic content.

[0071] In this embodiment, the fundamental wave content includes the phase and amplitude of the fundamental wave, the harmonic content includes the phase and amplitude of the harmonic, and the interharmonic content includes the phase and amplitude of the interharmonic. When Fourier transform is performed on each short-circuit current cycle sample and current fault sample, the short-circuit current cycle sample and the current fault sample are transformed into the form of a sum of a series of complex numbers through Fourier transform, each complex number represents a frequency component, the imaginary part of the frequency component is represented as the phase of the corresponding frequency component, and the real part is represented as the amplitude of the corresponding frequency component. The frequency corresponding to each frequency component is determined using the parameters of Fourier transform;

[0072] The frequency component with the largest amplitude value is set as the frequency component of the fundamental wave, the frequency component with an integer multiple of the fundamental wave frequency is set as the frequency component of the harmonic, and the frequency component with a non-integer multiple of the fundamental wave frequency is set as the frequency component of the interharmonic. The fundamental wave content, harmonic content and interharmonic content are obtained according to the fundamental wave, harmonic and interharmonic frequency components, respectively.

[0073] The Fourier transform converts the short-circuit current cycle samples from the time domain to the frequency domain, and decomposes the data into a series of frequency components using a combination of sine waves of different frequencies. In the frequency domain, many natural signals tend to concentrate their energy, which means that a few frequency components can represent the original signal well, so the data can be analyzed more quickly and its basic characteristics can be understood. Therefore, through the Fourier transform, the characteristics of each short-circuit current cycle sample can be represented by the spectral characteristics.

[0074] Furthermore, the fundamental frequency component, harmonic frequency component and interharmonic frequency component all contain real and imaginary parts, so they can all be represented by vectors. The fundamental frequency usually refers to the standard frequency of the power grid, which is generally 50 Hz or 60 Hz. This frequency is generated by the generator and is the basic frequency for the design and operation of all electrical equipment in the power system.

[0075] Determining the frequency of a frequency component is accomplished by analyzing the results of Fourier transform. First, Fourier transform is performed on the signal to obtain an array of complex numbers, where each complex number represents a frequency component. The position of each complex number in the spectrum is associated with its corresponding frequency. The frequency can be calculated by multiplying the index by the frequency resolution. The frequency resolution is the sampling frequency divided by the number of sampling points. By detecting the peaks in the spectrum, significant frequency components can be identified. These peaks correspond to the main frequencies in the signal, such as fundamental waves, harmonics, etc. In this embodiment, a fast Fourier transform is used, and the result of the transformation is a complex number sequence, where each complex number represents a specific frequency component. These complex numbers can be expressed as:

[0076] X[z]=A[z]·e jφ[z]

[0077] Where X[z] is the complex representation of the zth frequency component, a[z] is its amplitude, φ[z] is its phase, and the frequency f of the frequency component is k It can be calculated by the following formula:

[0078]

[0079] Where z is the index of the frequency component, f s is the sampling frequency of the signal, N is the number of Fourier transform points, the sampling frequency of the signal and the number of Fourier transform points are inherent parameters of the fast Fourier transform. Therefore, the specific frequency, amplitude and phase of each frequency component can be determined through the result of the Fourier transform.

[0080] Step 4: Sample the real-time current data at the outlet of the vacuum fast switch and determine whether a short-circuit fault occurs. If a short-circuit fault occurs, identify the starting phase of the fault and collect the current waveform data from the starting phase of the fault to the end of the cycle in which it is located, and calibrate it as a current fault sample (i.e., the current cycle data of the short-circuit current to be measured).

[0081] In this embodiment, the method for sampling the real-time current data of the outlet terminal of the vacuum fast switch and determining whether a short circuit fault occurs is based on:

[0082] The sampling frequency is set to K, and the real-time current data of the outlet of the vacuum fast switch is sampled, and K = N*50Hz, N is a positive integer, representing the sampling multiple, N≥20, and the current change rate between adjacent sampling time points is calculated. If the current change rate exceeds the current growth threshold, it is determined that a short circuit fault occurs. The formula is:

[0083]

[0084] Among them, I j represents the current value at the jth sampling time point, Ij+1 represents the current value at the j+1th sampling time point, Iz y represents the current growth threshold, and the time interval between the jth sampling time point and the j+1th sampling time point is 1 / K;

[0085] After determining that the j+1th sampling time point is the fault starting point, the starting phase of the current data at this point is obtained and calibrated as the fault starting phase. The current fault sample is the current waveform timing data from the fault starting point to the end of the current cycle where the current fault occurs.

[0086] The sampling frequency is set to K, which is a multiple of the power grid frequency (50Hz), which helps to synchronize the analysis and reduce the analysis error caused by frequency asynchrony, forming a high-frequency sampling. High-frequency sampling can capture the instantaneous changes of current more accurately, achieve a rapid response to current changes, and detect abnormal conditions such as short circuits in a timely manner.

[0087] In the working system of the fast vacuum switch, the short circuit fault is accompanied by a sharp increase in current. This rapid increase in current is due to the sudden decrease in resistance in the circuit, which causes the current to increase without restriction. Therefore, by monitoring the rate of change of the current, this abnormal situation can be effectively detected.

[0088] When the rate of change of current exceeds the preset threshold, it can be determined that a short circuit fault may have occurred. This is because under normal operating conditions, the change of current should be smooth without sharp fluctuations, while a short circuit fault will cause the current to rise rapidly in a very short period of time, and this rate of increase far exceeds the current change rate during normal operation.

[0089] The logic for determining a short-circuit fault is as follows: through high-frequency sampling, the instantaneous change of the current can be captured, which is crucial for detecting a short-circuit fault that occurs quickly. The current change rate between adjacent sampling time points is calculated, which reflects the rate of change of the current over time. A current growth threshold is pre-set, which is determined based on the statistical data of the current change rate under normal operating conditions and engineering experience. The calculated current change rate is compared with the preset threshold. If the current change rate exceeds the threshold, it indicates that the current growth rate is abnormal and a short-circuit fault may have occurred. This embodiment utilizes the typical feature of a short-circuit fault—a sharp increase in current, and distinguishes between normal operation and potential fault states by setting a reasonable threshold.

[0090] Step 5: Perform Fourier transform on the current fault sample to obtain the spectrum characteristics in the current fault sample, calibrate them as sample spectrum characteristics (i.e., spectrum characteristics to be measured), traverse the reference spectrum characteristics corresponding to all short-circuit current cycle samples, screen out the short-circuit current cycle samples with the highest degree of similarity to the sample spectrum characteristics, and calibrate them as reference short-circuit current cycle samples.

[0091] The method of performing Fourier transform on the current fault sample to obtain the spectral characteristics within the current fault sample is consistent with the method of performing Fourier transform on each short-circuit current cycle sample to obtain the spectral characteristics corresponding to each short-circuit current cycle sample. The spectral characteristics within the current fault sample also include fundamental wave content, harmonic content and interharmonic content.

[0092] In the working system of the fast vacuum switch, the same type of short-circuit fault will produce specific spectral characteristics in the current signal. These characteristics are due to the nonlinear change and harmonic generation of the current when the fault occurs. Through Fourier transform, the current signal in the time domain can be converted into a spectrum in the frequency domain, thereby revealing these characteristics.

[0093] Each short-circuit fault has its own unique spectral characteristics, which are manifested in the frequency domain as specific frequency components and harmonics, such as fundamental content, harmonic content and interharmonic content. By performing Fourier transform on the current fault sample, the spectral characteristics of the fundamental content, harmonic content and interharmonic content can be extracted.

[0094] The extracted sample spectrum features are compared with the spectrum features of the known reference short-circuit current cycle samples, and the similarity between the sample spectrum features and each reference spectrum feature is calculated using a similarity metric. The reference short-circuit current cycle sample with the highest similarity is selected, which means that the sample is closest to the reference sample in terms of spectrum features.

[0095] The similarity of the spectral features reflects the degree of matching of the fault type. If the spectral features of a current fault sample are most similar to those of a reference short-circuit current cycle sample, it means that they have similar fault features and belong to the same type of short-circuit fault. The current zero-crossing point refers to the moment when the current waveform changes from a negative value to a positive value or from a positive value to a negative value. In the case of a short-circuit fault, although the current waveform may be distorted due to the fault, the basic periodic characteristics usually still exist.

[0096] Whether in normal operation or a short-circuit fault, the current signal is usually periodic, so even if a short-circuit fault occurs, the current waveform will still pass through zero in each cycle. If the current fault sample and the reference short-circuit current cycle sample belong to the same type of fault, their current waveforms may behave very similarly after the fault occurs. This similarity includes the time of the zero crossing. Although a short-circuit fault usually introduces additional frequency components into the current signal, the periodicity of these components is still related to the fundamental frequency. Therefore, even if the current waveform contains harmonics or other nonlinear components, the basic time pattern of the zero crossing may still remain consistent.

[0097] If the spectral characteristics of the current fault sample and the reference short-circuit current cycle sample are similar, then their current waveforms will also behave similarly after the fault occurs. By analyzing the zero-crossing time of the reference short-circuit current cycle sample, the zero-crossing time under the same type of fault can be predicted. The zero-crossing time of the reference short-circuit current cycle sample is based on historical data.

[0098] In this embodiment, the method for selecting the short-circuit current cycle sample with the highest similarity to the sample spectrum feature is:

[0099] The similarity index between the sample spectrum characteristics and the reference spectrum characteristics of each short-circuit current cycle sample is calculated. The formula for calculating the similarity index is:

[0100]

[0101] Wherein, Sd(i,j) represents the similarity index between the sample spectrum feature and the reference spectrum feature of the mth short-circuit current cycle sample in the i-th group of short-circuit current waveform samples, and Respectively represent the frequency components of the fundamental content, average harmonic content and average interharmonic content in the sample spectrum characteristics, i is the number of the short-circuit current waveform sample, and m is the number of the short-circuit current period sample;

[0102] and They respectively represent the frequency components of the fundamental content, the average harmonic content and the average interharmonic content in the reference spectrum characteristics of the mth short-circuit current cycle sample in the i-th group of short-circuit current waveform samples. When the similarity index is the smallest, the corresponding short-circuit current cycle sample is calibrated as the short-circuit current cycle sample with the highest similarity, that is, the short-circuit current cycle sample corresponding to the smallest similarity index is used as the reference short-circuit current cycle sample.

[0103] Furthermore, when calculating the similarity index, the frequency components of the fundamental content, the average harmonic content and the average interharmonic content are substituted as components of the vector. The calculation of the similarity index is based on the vector space model, and the similarity between two spectral feature vectors is evaluated by calculating their distance and directional similarity.

[0104] The formula on which the Euclidean distance part is based is: This part calculates the Euclidean distance between the sample spectrum features and the reference spectrum features in terms of fundamental content, average harmonic content and average interharmonic content. It measures the numerical difference between the two spectrum features, that is, the numerical difference between the sample spectrum features and the reference spectrum features in terms of fundamental content, average harmonic content and average interharmonic content. The smaller the distance, the closer the values ​​of the two spectrum features in these aspects, and thus the higher the similarity, and the more similar the current fault sample and the short-circuit current cycle sample.

[0105] The formula on which the cosine similarity part is based is:

[0106]

[0107] It measures the similarity of the directions of two spectral features, that is, the cosine value of their angle. Cosine similarity is used to evaluate whether the distribution trends of sample spectral features and reference spectral features in the spectral space are consistent. The closer the cosine similarity is to 1, the more consistent the directions of the two vectors are, that is, the more similar their spectral features are in distribution. -1 indicates that the distributions are completely opposite. In this embodiment, a constant 1 is added to the denominator, so the value range of the denominator is [0,1]. The larger the denominator, the more similar they are.

[0108] Therefore, when the Euclidean distance is smaller and the cosine similarity is larger, the similarity index is smaller, and the current fault sample and the short-circuit current cycle sample are more similar. When the denominator is 0, the similarity index is calibrated to infinity. When the Euclidean distance is larger and the cosine similarity is smaller, the similarity index is larger, and the current fault sample and the short-circuit current cycle sample are less similar.

[0109] This embodiment combines the Euclidean distance and the cosine similarity, taking into account both the numerical difference and the directional similarity of the spectral features, and can more comprehensively evaluate the similarity between two spectral features. The Euclidean distance and the cosine similarity provide complementary information. The Euclidean distance focuses on the numerical difference, while the cosine similarity focuses on the directional similarity. Both the numerical difference and the directional similarity of the spectral features are important, so combining these two metrics can provide a more accurate similarity evaluation.

[0110] Harmonics refer to sinusoidal components whose frequencies are integer multiples of the fundamental frequency. Due to the presence of nonlinear loads, the current waveform may contain multiple harmonic components. For example, if the fundamental frequency is 50Hz, then the frequency of the second harmonic will be 100Hz, and the frequency of the third harmonic will be 150Hz. Interharmonics refer to sinusoidal components whose frequencies are between the fundamental frequency and its integer multiples. Interharmonics are caused by imperfect control of specific power system equipment (such as certain types of transformers, arc furnaces, etc.) or power electronic equipment. Similar to harmonics, the current waveform may contain multiple interharmonic components, so all harmonic frequency components and interharmonic frequency components within the same spectrum feature often have multiple.

[0111] The method for generating the frequency component of the average harmonic content is as follows: the real part and the imaginary part of all the harmonic frequency components in the same spectrum feature are superimposed and the average is calculated, and the averaged real part and imaginary part are used as the real part and imaginary part of the frequency component of the average harmonic content.

[0112] The method for generating the frequency component of the average interharmonic content is: the real part and the imaginary part of all the interharmonic frequency components in the same spectrum feature are superimposed and the average is calculated, and the averaged real part and imaginary part are used as the real part and imaginary part of the frequency component of the average interharmonic content.

[0113] For each harmonic or interharmonic frequency component, its real part and imaginary part respectively represent the position of the component on the complex plane. The sum of these components can be obtained by superimposing the real and imaginary parts of all harmonic or interharmonic frequency components within the same spectral feature. The average of the superimposed real and imaginary parts is calculated, that is, the sum is divided by the number of components. This can be understood as the "average position" of all harmonic or interharmonic components. The averaged real and imaginary parts are used as the real and imaginary parts of the frequency components of the average harmonic content or the average interharmonic content. The frequency components obtained in this way represent the average characteristics of the harmonics or interharmonics, and the average harmonic content and the average interharmonic content are used to reflect the typical values ​​of the harmonic content and the interharmonic content.

[0114] Step 6: Set the short-circuit current cycle sample that is in the same group as the reference short-circuit current cycle sample and is located next to the reference short-circuit current cycle sample as the predicted cycle short-circuit current, and predict the zero-crossing time of the next cycle of the short-circuit current according to the time length of each zero-crossing point in the predicted cycle short-circuit current relative to the starting point.

[0115] In this embodiment, prediction is performed based on the principle of adjacent cycle correlation in time series analysis. In the working system of the fast vacuum switch, the periodic change of the short-circuit current often has a certain regularity and continuity, that is, there is a certain correlation between the characteristics of the current cycle and the characteristics of the adjacent cycle. Therefore, by analyzing the next short-circuit current cycle sample that is in the same group and adjacent to the reference short-circuit current cycle sample, the zero-crossing time of the next cycle of the current fault sample can be predicted.

[0116] A short-circuit current cycle sample that is in the same group as the reference short-circuit current cycle sample and is located at the next number is selected as the predicted sample, because adjacent short-circuit current cycle samples are closer in time. In essence, this embodiment predicts the current waveform of the next cycle of the current fault sample, and regards the predicted cycle short-circuit current as the current waveform of the next cycle of the current fault sample. Since the predicted cycle short-circuit current is a short-circuit current cycle sample in the historical data, the time of the zero-crossing point has been calibrated in step 2, so the time of the current zero-crossing point of the next cycle of the current fault sample can be predicted.

[0117] In this embodiment, when predicting the zero-crossing moment of the next cycle of the short-circuit current, the current waveform of the predicted cycle short-circuit current is used as the waveform to be generated in the next cycle of the short-circuit current and is calibrated as the predicted cycle current waveform. The starting point of the predicted cycle current waveform is the end point of the current waveform of the current fault sample. The zero-crossing moment of the next cycle of the short-circuit current is predicted based on the time length data of each zero-crossing point relative to the starting point in the reference short-circuit current cycle sample. If there is no short-circuit current cycle sample with the next number of the reference short-circuit current cycle sample, that is, there is no predicted cycle short-circuit current, then it is re-determined whether there is a short-circuit fault and re-predicted.

[0118] This embodiment establishes a rich data set by collecting and analyzing multiple sets of historical short-circuit current waveform data. These data contain current waveform characteristics under various short-circuit conditions. By eliminating incomplete data, the quality of the analyzed samples is ensured, providing a reliable basis for subsequent predictions.

[0119] This embodiment uses Fourier transform to convert the current waveform in the time domain into the spectrum characteristics in the frequency domain, and can extract the key spectrum characteristics such as fundamental wave content, harmonic content and interharmonic content. By comparing the spectrum characteristics of the real-time fault sample with the reference spectrum characteristics of the historical sample, the most similar historical short-circuit current cycle sample can be identified. By finding the most similar historical sample, the characteristics of the real-time fault can be inferred, thereby predicting the zero-crossing point of the next cycle;

[0120] This embodiment greatly improves the prediction accuracy through the matching method of spectrum characteristics, and quickly and accurately predicts the zero-crossing point of the short-circuit current, so that the fast vacuum switch can be operated at the optimal time, quickly cut off the short-circuit current, and reduce the arc duration and the impact on the system.

[0121] See also Figure 4 The present invention further provides a short-circuit current zero-crossing point prediction system based on a fast vacuum switch, wherein the short-circuit current zero-crossing point prediction system is used to execute the above-mentioned short-circuit current zero-crossing point prediction method, comprising:

[0122] The historical data acquisition module is used to collect multiple groups of short-circuit current waveforms of the outlet terminals of vacuum fast switches installed in the outlet cabinet, remove the current waveform data with incomplete periods in the short-circuit current waveform, and obtain short-circuit current waveform samples;

[0123] A historical data processing module is used to divide all short-circuit current waveform samples into multiple short-circuit current cycle samples according to the current cycle, obtain the time length of each zero-crossing point relative to the starting point in each short-circuit current cycle sample, and associate and number the short-circuit current cycle samples corresponding to each group of short-circuit current waveform samples in chronological order;

[0124] A historical data analysis module is used to perform Fourier transform on each short-circuit current cycle sample, obtain the frequency spectrum characteristics corresponding to each short-circuit current cycle sample, and calibrate them as reference frequency spectrum characteristics, wherein the frequency spectrum characteristics include fundamental wave content, harmonic content, and interharmonic content;

[0125] The fault current acquisition module is used to sample the real-time current data of the outlet end of the vacuum fast switch and determine whether a short-circuit fault occurs. If a short-circuit fault occurs, the fault start phase is identified and the current waveform data from the fault start phase to the end of the cycle is collected and marked as a current fault sample.

[0126] The fault current analysis module is used to perform Fourier transform on the current fault sample, obtain the spectrum characteristics in the current fault sample, calibrate them as sample spectrum characteristics, traverse the reference spectrum characteristics corresponding to all short-circuit current cycle samples, screen out the short-circuit current cycle sample with the highest similarity to the sample spectrum characteristics, and calibrate them as reference short-circuit current cycle samples;

[0127] The zero-crossing prediction module is used to set the short-circuit current cycle sample that is in the same group as the reference short-circuit current cycle sample and is located next to the reference short-circuit current cycle sample as the predicted cycle short-circuit current, and predict the zero-crossing moment of the next cycle of the short-circuit current according to the time length of each zero-crossing point in the predicted cycle short-circuit current relative to the starting point.

[0128] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0129] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting the zero-crossing point of short-circuit current based on a vacuum switch, characterized in that: include: Obtain complete historical short-circuit current waveform samples for multiple cycles; Dividing each historical short-circuit current waveform sample into a plurality of historical short-circuit current cycle samples according to each historical short-circuit current waveform sample current cycle; Obtaining a periodic sample set of each historical short-circuit current waveform sample; The historical short-circuit current cycle samples in each cycle sample set are associated and numbered in chronological order, and the historical spectrum characteristics and zero-crossing time of each historical short-circuit current cycle sample are extracted; Acquire current cycle data of the short-circuit current to be measured, extract the frequency spectrum features to be measured of the current cycle data, compare the frequency spectrum features to be measured with the historical frequency spectrum features respectively, and select the historical current cycle samples corresponding to the historical frequency spectrum features with the highest similarity as reference short-circuit current cycle samples; A historical short-circuit current cycle sample that belongs to the same cycle sample set as the reference short-circuit current cycle sample and is located at the next number of the reference short-circuit current cycle sample is set as the predicted cycle short-circuit current, and the zero-crossing time of the next cycle of the short-circuit current to be measured is predicted based on the zero-crossing time corresponding to the predicted cycle short-circuit current.

2. The short-circuit current zero-crossing point prediction method based on vacuum switch according to claim 1 is characterized in that: The complete historical short-circuit current waveform sample includes: a current waveform including a positive half-cycle and a negative half-cycle, wherein the positive half-cycle is that the current starts from zero, rises to the maximum positive value and then drops back to zero, and the negative half-cycle is that the current or voltage starts from zero, drops to the maximum negative value, and then rises back to zero.

3. The short-circuit current zero-crossing point prediction method based on vacuum switch according to claim 2 is characterized in that: When each historical short-circuit current waveform sample is divided into multiple historical short-circuit current cycle samples according to each historical short-circuit current waveform sample current cycle, the cycle starting point is the point where the current waveform passes through zero from a negative value or zero value to a positive value, and the cycle end point is the point where the historical short-circuit current waveform starts from the cycle starting point and returns to zero after a positive half cycle and a negative half cycle in sequence, and the zero crossing point is the point where the waveform passes through zero from a negative value or a positive value to the opposite value.

4. The method for predicting the zero-crossing point of short-circuit current based on a vacuum switch according to claim 3, characterized in that: The spectrum characteristics include fundamental wave content, harmonic content and interharmonic content; and / or The zero-crossing time of each historical short-circuit current cycle sample is the time length of each zero-crossing point in each historical short-circuit current cycle sample relative to the starting point; and / or The current cycle data of the short-circuit current to be measured is the current waveform data from the fault start phase to the end of the cycle in which it is located.

5. The short-circuit current zero-crossing point prediction method based on vacuum switch according to claim 4 is characterized in that: The fundamental wave content includes the phase and amplitude of the fundamental wave, the harmonic content includes the phase and amplitude of the harmonic, and the interharmonic content includes the phase and amplitude of the interharmonic; extracting the spectrum features includes: Performing Fourier transform on historical short-circuit current cycle samples or current cycle data, transforming the historical short-circuit current cycle samples or current cycle data into the form of a sum of a series of complex numbers through Fourier transform, each complex number represents a frequency component, the imaginary part of the frequency component is represented as the phase of the corresponding frequency component, and the real part is represented as the amplitude of the corresponding frequency component, and the frequency corresponding to each frequency component is determined using the parameters of Fourier transform; The frequency component with the largest amplitude value is set as the frequency component of the fundamental wave, the frequency component with an integer multiple of the fundamental wave frequency is set as the frequency component of the harmonic, and the frequency component with a non-integer multiple of the fundamental wave frequency is set as the frequency component of the interharmonic. The fundamental wave content, harmonic content and interharmonic content are obtained according to the fundamental wave, harmonic and interharmonic frequency components, respectively.

6. The method for predicting the zero-crossing point of short-circuit current based on a vacuum switch according to claim 4, characterized in that: The current cycle data of the short-circuit current to be measured is obtained by: Assume that the sampling frequency is set to K, sample the real-time current data of the vacuum switch outlet, and calculate the current change rate between adjacent sampling time points. If the current change rate exceeds the current growth threshold, it is determined that a short circuit fault occurs. The formula is: Among them, I j represents the current value at the jth sampling time point, I j+1 Indicates the current value at the j+1th sampling time point, Iz y represents the current growth threshold, and the time interval between the jth sampling time point and the j+1th sampling time point is 1 / K; After determining that the j+1th sampling time point is the fault starting point, the starting phase of the current data at this point is obtained and calibrated as the fault starting phase. The current cycle data is the current waveform timing data from the fault starting point to the end of the current cycle where the current fault occurs.

7. The method for predicting the short-circuit current zero-crossing point based on a vacuum switch according to claim 4, characterized in that: The historical short-circuit current cycle samples in each cycle sample set are associated and numbered in chronological order, specifically: For the historical short-circuit current cycle samples in the cycle sample set, the timestamp corresponding to the cycle start point and the timestamp corresponding to the cycle end point of each historical short-circuit current cycle sample are recorded, and according to the timestamp of each historical short-circuit current cycle sample, they are sorted in the order of the actual occurrence time, and the historical short-circuit current cycle sample with the earliest timestamp corresponding to the cycle start point is arranged at the front, and then the timestamp corresponding to the cycle start point of the next historical short-circuit current cycle sample is the timestamp corresponding to the cycle end point of the previous historical short-circuit current cycle sample; The sorted historical short-circuit current cycle samples are numbered to identify their positions in the same group of short-circuit current waveform samples, and the numbers are incremented in sequence.

8. The method for predicting the short-circuit current zero-crossing point based on a vacuum switch according to claim 7, characterized in that: The similarity is calculated in the following way: The similarity index between the spectrum feature to be tested and each history is calculated by: Wherein, Sd(i,j) represents the similarity index between the frequency spectrum feature j to be measured and the historical frequency spectrum feature of the mth short-circuit current cycle sample in the cycle sample set of the i-th historical short-circuit current waveform sample, and They respectively represent the frequency components of the fundamental wave content, average harmonic content and average interharmonic content in the spectrum characteristics to be measured, i is the number of the short-circuit current waveform sample, and m is the number of the historical short-circuit current cycle sample; and Respectively represent the frequency components of the fundamental wave content, the average harmonic content and the average interharmonic content in the reference spectrum characteristics of the nth historical short-circuit current cycle sample in the cycle sample set of the i-th historical short-circuit current waveform sample; The short-circuit current cycle sample corresponding to the smallest similarity index is selected as the historical current cycle sample with the highest similarity.

9. The method for predicting the zero-crossing point of short-circuit current based on a vacuum switch according to claim 8, characterized in that: The method for generating the frequency component of the average harmonic content is as follows: the real part and the imaginary part of all the harmonic frequency components in the same frequency spectrum feature are superimposed and the average is calculated, and the averaged real part and imaginary part are used as the real part and imaginary part of the frequency component of the average harmonic content; the method for generating the frequency component of the average interharmonic content is as follows: the real part and the imaginary part of all the interharmonic frequency components in the same frequency spectrum feature are superimposed and the average is calculated, and the averaged real part and imaginary part are used as the real part and imaginary part of the frequency component of the average interharmonic content.

10. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 9 are implemented.

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