Method for optimally calculating transient current in GIS (Geographic Information System) based on radiation field

Abstract

The invention discloses a method for optimally calculating transient current in a GIS (Geographic Information System) based on a radiation field, which comprises the following steps of: 1, enabling the GIS to be equivalent to a nonlinear system on a time domain, then constructing a GIS electromagnetic radiation model, and establishing a coefficient matrix T of excitation current and a radiation field magnetic field at a characteristic frequency point of the model; 2, for any excitation current source of the GIS electromagnetic radiation model, calculating the frequency domain waveform of the excitation current source by measuring the radiation field combination coefficient matrix T of the external fixed position of the GIS electromagnetic radiation model; and step 3, calculating the current waveform according to the frequency domain waveform of the current source, and obtaining the transient current in the GIS. According to the method, the precision of the transient current is greatly improved, and a simulation arc model can be accurately established.

Description

Technical Field

[0001] The present invention relates to the technical field of current measurement, in particular to a method for optimizing the calculation of transient current in GIS based on a radiation field. Background Art

[0002] When a gas insulated switchgear (GIS) operates a disconnector, especially when switching an open bus, a very fast transient over-voltage (VFTO) and a very fast transient current (VFTC) with a large amplitude and a high frequency will be generated. VFTO and VFTC are ultra-high frequency transient phenomena, affected by many factors, and are difficult to measure and test. Therefore, simulation calculation is the main means to study VFTO and VFTC. However, due to the lack of experimental support, there are still many problems that need further research. In the simulation calculation, the arc model at the moment of breakdown of the disconnector gap is one of the key factors for the accuracy of the simulation results. At present, the arcs in the simulation calculation mostly adopt a constant value resistance model or a time-varying resistance model. However, due to the lack of measurement results of VFTC, the arc characteristics generated when the disconnector operates cannot be studied in depth, and thus an accurate simulation arc model cannot be established.

[0003] One of the methods for measuring transient current in a power system studied in China at present is to surround a certain number of micro-magnetic sensors around the busbar to be measured, and then calculate the busbar current by inversion according to Ampere's loop law. [1～3] This method requires a linear proportional relationship between the current to be measured and the generated magnetic field, and this linear relationship does not change violently with the change of frequency. However, for the transient current in GIS, due to the multiple reflections and refractions of the electromagnetic field in GIS, the magnetic field outside GIS and the current to be measured are no longer a simple linear proportional relationship, so the transient current in GIS cannot be measured by a magnetic array. The second method for measuring transient current is to use a broadband Rogowski coil as a sensor. For the measurement of transient current in GIS, the prior art has a method of installing the sensor on the static contact on the power supply side of the disconnector. However, since the upper limit of the broadband of a large-sized Rogowski coil is generally low, in order to meet the measurement frequency band, the static contact of the disconnector in GIS needs to be modified to make the diameter of a section of conductor smaller, and then transmitted to the measurement device outside GIS through an optical fiber. Installing the Rogowski coil in this way not only changes the internal structure of GIS, but also is not conducive to checking and replacing the Rogowski coil.

[0004] Whether it is a magnetic array or a Rogowski coil to measure transient current, it is based on the linear relationship between the current to be measured and the generated magnetic field. However, for a closed structure such as GIS, the magnetic field outside the GIS and the transient current inside the GIS do not have a simple linear relationship, resulting in a large measurement error. Summary of the Invention

[0005] The object of the present invention is to overcome the disadvantage that the existing methods for measuring transient current are all based on the linear relationship between the current to be measured and the generated magnetic field, resulting in a large measurement error, and to provide a method for optimizing the calculation of transient current in GIS based on the radiation field.

[0006] The object of the present invention is achieved by the following technical solutions: A method for optimizing the calculation of transient current in GIS based on the radiation field includes the following steps: Step 1: Equivalent the GIS to a nonlinear system in the time domain, then construct an electromagnetic radiation model of the GIS, and establish a coefficient matrix T of the excitation current and the magnetic field of the radiation field at the characteristic frequency points of the model; Step 2: For any excitation current source of the electromagnetic radiation model of the GIS, calculate the frequency-domain waveform of the excitation current source by measuring the radiation field at a fixed position outside the electromagnetic radiation model of the GIS and combining with the coefficient matrix T; Step 3: Calculate the current waveform according to the frequency-domain waveform of the current source to obtain the transient current in the GIS.

[0007] When the disconnector in the GIS operates, on the one hand, it will generate fast transient overvoltage and fast transient overcurrent, and on the other hand, it will radiate high-frequency electromagnetic fields into space. The electromagnetic field radiates from the GIS busbar to point A outside, and most of it has to pass through at least three media: SF6 inside the GIS, the GIS shell, and the air outside the GIS. The path of the electromagnetic field radiating from the GIS busbar to point A is equivalent to a "black box", without paying attention to how the electromagnetic field propagates inside it, only paying attention to the input and output of this "black box". The input is the transient current flowing through the disconnector when the disconnector in the GIS operates, and the output is the radiation field at point A.

[0008] Equivalent the above "black box" to a nonlinear system in the time domain, establish the matrix relationship between the input and output of this "black box" in the frequency domain, and represent it with the matrix T. Then, according to the measured radiation field data and the matrix T, the input of the "black box" can be obtained. Finally, the time-domain waveform of the input can be obtained by using frequency-domain interpolation and IFFT. The radiation field can be any one component of the electric field and the magnetic field. Here, the magnetic field component is selected, that is, the output of the "black box" is the magnetic field component.

[0009] Preferably, in step 1, establishing the coefficient matrix T of the excitation current and the magnetic field of the radiation field at the characteristic frequency points of the model specifically includes: The magnetic field at a point outside the GIS in the direction of the GIS busbar hammer is selected as the radiation field research component H z , excitation current input is I exc Indicates that the established matrix relationship is as follows: In the formula, H zfi It means that under the input signal, the magnetic field in the Z direction of a certain point in space is at a frequency of f i The weight on I excfi The input signal is at a frequency of f i The weight on 11 to T NN It represents the linear relationship between the excitation source current and the external magnetic field of GIS in the frequency domain, re represents the real part, and im represents the imaginary part; Therefore, the coefficient matrix T in T ij It can be found by the following formula: Where: T ij Indicates that when except I excfj When all inputs except z f i Frequency Components and I excfj The coefficient matrix T is determined by numerical simulation method.

[0010] Preferably, the numerical simulation method is to determine the coefficient matrix T through the CST model and the MATALB program, specifically: Enter the simulation start frequency, end frequency and frequency interval; Calculate the current simulation frequency f, modify the excitation source in the CST model, and update the calculation model for simulation calculation; The simulation results and excitation sources are stored in the specified table to determine whether the simulation termination frequency has been reached. If the simulation termination frequency has been reached, MATLAB is called to process the simulation results to obtain the coefficient matrix T. If the simulation termination frequency has not been reached, the current simulation results are deleted and the next simulation is prepared.

[0011] Preferably, in step 2, by measuring the radiation field combination coefficient matrix T at a fixed position outside the GIS electromagnetic radiation model, the formula for calculating the frequency domain waveform of the excitation current source is: I excf =T -1 H zf All elements in the formula are complex numbers, which can be decomposed into real and imaginary components for algebraic operations: In the formula, the superscript re represents taking the real part of it, and im represents taking the imaginary part of it.

[0012] Preferably, in step 3, calculating the current waveform according to the frequency-domain waveform of the current source specifically includes: Using frequency-domain interpolation to obtain the frequency-domain data of the input signal in the system response frequency range, and then using the IFFT transform to obtain its time-domain waveform.

[0013] Preferably, the method for optimizing the calculation of the transient current in the GIS based on the radiation field also estimates the relative error of the algebraic operation: In the formula, is the relative residual, ||T||||T -1 || is the condition number of matrix T. When the condition number of T is smaller, the relative error of the approximate solution is smaller. On the contrary, the relative error of the approximate solution may be larger.

[0014] Preferably, the accuracy of the back-calculation result is improved by increasing the number of frequency points for calculation.

[0015] The beneficial effects of the present invention are as follows: The present invention transforms the time-domain non-linear relationship between the surrounding radiation field and the current inside the GIS into the frequency domain for calculation, uses the CST simulation software to obtain the relationship between the magnetic field and the current at the characteristic frequency, thereby establishing the coefficient matrix T in the frequency domain. Finally, the transient current value inside the GIS can be obtained by measuring the magnetic field in a fixed surrounding direction. The method of the present invention greatly improves the accuracy of the transient current and can accurately establish a simulation arc model. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a flowchart of the present invention; Figure 2 is a flowchart for calculating the coefficient matrix T in the present invention; Figure 3 is a schematic diagram of the electromagnetic radiation path of the GIS; Figure 4 is a schematic diagram of the current excitation source waveform; Figure 5 is a comparison diagram of the frequency-domain waveform obtained by back-calculation and the frequency-domain waveform of the excitation source. Figure 5a is the real part, Figure 5b is the imaginary part; Figure 6 is a time-domain comparison diagram of the back-calculated waveform and the excitation source waveform; Figure 7 is Figure 6 a waveform schematic diagram of the first 2 us. DETAILED DESCRIPTION OF THE INVENTION

[0017] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this application will be more complete and comprehensive, and will fully convey the concept of the example embodiments to those skilled in the art.

[0018] In addition, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of the embodiments of this application. However, those skilled in the art will realize that the technical solutions of this application can be practiced without one or more of the specific details, or other methods, components, devices, steps, etc. may be used. In other cases, well-known methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of this application.

[0019] The flowcharts shown in the accompanying drawings are merely illustrative and not necessarily include all content and operations / steps, nor are they necessarily executed in the described order. For example, some operations / steps can be decomposed, while some operations / steps can be combined or partially combined, so the actual execution order may change according to the actual situation.

[0020] Embodiment: A method for optimizing the calculation of transient current in GIS based on the radiation field, as Figure 1 shown, includes the following steps: Step 1, equivalent the GIS to a nonlinear system in the time domain, then construct an electromagnetic radiation model of the GIS, and establish a coefficient matrix T of the excitation current and the radiation field magnetic field at the characteristic frequency points of the model; Step 2, for any excitation current source of the GIS electromagnetic radiation model, calculate the frequency-domain waveform of the excitation current source by measuring the radiation field at a fixed position outside the GIS electromagnetic radiation model and combining with the coefficient matrix T; Step 3, calculate the current waveform according to the frequency-domain waveform of the current source to obtain the transient current in the GIS.

[0021] When the disconnector in the GIS operates, on the one hand, it will generate fast transient overvoltage and fast transient overcurrent, and on the other hand, it will radiate high-frequency electromagnetic fields into space. The electromagnetic field radiates from the GIS busbar to point A, and most of it has to pass through at least three media: SF6 in the GIS, the GIS shell, and the air outside the GIS. The path of the electromagnetic field radiating from the GIS busbar to point A is equivalent to a "black box", without paying attention to how the electromagnetic field propagates inside it, only paying attention to the input and output of this "black box". The input is the transient current flowing through the disconnector when the disconnector in the GIS operates, and the output is the radiation field at point A.

[0022] The above-mentioned "black box" is equivalent to a nonlinear system in the time domain. The matrix relationship between the input and output of this "black box" is established in the frequency domain and represented by matrix T. Then, based on the radiation field data of point A measured in Figure 3 and combined with matrix T, the input of the "black box" can be obtained. Finally, the time-domain waveform of the input can be obtained by using frequency-domain interpolation and IFFT. The radiation field can be any component of the electric field and the magnetic field. Here, the magnetic field component is selected, that is, the output of the "black box" is the magnetic field component.

[0023] In step 1 described above, the coefficient matrix T of the excitation current and the magnetic field of the radiation field is established at the characteristic frequency points of the model. Specifically: Select the magnetic field at a certain point in the outer space of the GIS in the direction of the hammer of the GIS busbar as the research component H of the radiation field z , and the magnetic field value in this direction is theoretically the largest and is relatively easy to measure. The excitation current input is represented by I exc , and the established matrix relationship is as follows: In the formula, H zfi represents the component of the magnetic field in the Z direction at a certain point in space at frequency f i under the input signal, I excfi is the component of the input signal at frequency f i , and T 11 to T NN represent the linear relationship between the excitation source current and the external magnetic field of the GIS in the frequency domain. re represents the real part, and im represents the imaginary part; Therefore, T ij in the coefficient matrix T can be obtained by the following formula: In the formula: T ij represents the ratio of the frequency component of the response H excfj at frequency f z to I i when all inputs except I excfj are 0; Therefore, for the "black box", it is necessary to first estimate the approximate range of the system response frequency, determine a set of so-called "concerned frequency points f" of the system, that is, characteristic frequency points, then use the sine of this set of frequencies as the excitation source input respectively, and finally the value of the matrix T of the system can be obtained according to the above formula.

[0024] The matrix T can be obtained by the experimental method and the numerical simulation method. The experimental method is accurate, but the cost is high. Standard reference currents of various frequencies are required. To ensure that an accurate radiation field can be measured, the reference current cannot be too small, and a lot of manpower and time are also required for the experiment. Therefore, the numerical simulation method is selected, that is, the coefficient matrix T is determined by the CST WMS and MATLAB programs. For exampleFigure 2 As shown in Figure 2 , the calculation process of the coefficient matrix T is specifically as follows: Input the starting frequency, ending frequency, and frequency interval of the simulation; Calculate the current simulation frequency f, modify the excitation source in the CST model, and update the calculation model for simulation calculation; Store the simulation results and the excitation source in a specified table, and determine whether the ending frequency of the simulation is reached. If the ending frequency of the simulation is reached, call MATLAB to process the simulation results to obtain the coefficient matrix T. If the ending frequency of the simulation is not reached, delete the current simulation results and prepare for the next simulation.

[0025] In step 2 described above, the formula for calculating the frequency-domain waveform of the excitation current source by measuring the radiation field at a fixed external position of the GIS electromagnetic radiation model and combining the coefficient matrix T is: I excf = T -1 H zf All elements in the formula are complex numbers. Decompose them into real and imaginary components and then perform algebraic operations: In the formula, the superscript re represents taking the real part of it, and im represents taking the imaginary part of it.

[0026] In step 3 described above, the specific calculation of the current waveform based on the frequency-domain waveform of the current source is as follows: Use frequency-domain interpolation to obtain the frequency-domain data of the input signal in the system response frequency range, and then use the IFFT transform to find its time-domain waveform.

[0027] The method for optimizing the calculation of the transient current in the GIS based on the radiation field also estimates the relative error of the algebraic operation: In the formula, is the relative residual, ||T||||T -1 || is the condition number of the matrix T. When the condition number of T is smaller, the relative error of the approximate solution is smaller. On the contrary, the relative error of the approximate solution may be larger.

[0028] The following is an example analysis of transient current calculation based on the radiation field of a certain GIS. For the actual model of a 220kV GIS, referring to the structural parameters, an electromagnetic field radiation model was established using CST MWS. The radial direction along the GIS shell is the X direction, the axial direction is the Y direction, and the axial direction along the bushing is the Z direction. The overhead lines with wave impedances equal to those at both ends of the bushing of the established GIS model are replaced by concentrated resistors. The transient current flowing through the disconnector in the GIS generated by switch operation, obtained by simulating with ATP software, is used as the excitation source, and the waveform is as shown in the waveform of Figure 5. At a position 0.7m in the X direction from the GIS busbar at the same height as the GIS model, an electric field three-dimensional probe and a magnetic field three-dimensional probe are respectively placed. The green one is the electric field probe, and the blue one is the magnetic field probe. Take the magnetic field H in the Z direction z as the radiation field for research.

[0029] According to the characteristics of the GIS model and the transient current to be calculated, during verification, the excitation source of CST is controlled to simulate in the range of 0.5 - 50 MHz, with a frequency interval of 0.5 MHz, and MATLAB is called to extract the coefficient matrix T of the GIS model. The fast transient current flowing through the disconnector in the GIS generated by switch operation, obtained by simulating with ATP software, is used as the excitation source, and the waveform is as Figure 4 shown in the waveform. Take the electric field H in the Z direction at a position 0.7m in the X direction from the GIS busbar at the same height as the GIS model z as the radiation field for research. Import the radiation field data obtained by simulation into the MATLAB program, calculate the frequency-domain waveform of the excitation source at the characteristic frequency points, as shown in Figure 5, and the inverse transform to the time-domain waveform is shown in Figure 6 . Figure 5 shows the comparison of the waveform obtained by inverse calculation and the excitation source waveform in the frequency domain. The red dashed line is the frequency-domain waveform of the excitation source, and the blue thin line is the frequency-domain waveform obtained by inverse calculation. Figure 6 Figure [X] shows the comparison of the waveform obtained by inverse calculation and the excitation source waveform in the time domain. The black dashed line is the actual excitation source waveform, the red thin line is the interpolated inverse calculation waveform, the blue thin line is the non-interpolated inverse calculation waveform, and the green thin line is the time-domain waveform of the 0.5 - 50 MHz frequency component of the excitation source waveform.

[0030] From Figure 6 the frequency-domain waveforms of the two, the frequency-domain waveform obtained by inverse calculation and the frequency-domain waveform of the excitation source have the largest error at around 8 MHz, and there is a spike in the waveform obtained by inverse calculation. Analyzing the reason for the error, the resonant frequency of the established GIS model is around 8 MHz. Since the characteristic frequencies taken in this example are 0.5 - 50 MHz with an interval of 0.5 MHz, the resonant frequency point of the model may not be taken. Near the resonant point, the response changes very sensitively, resulting in a large error in the obtained matrix T near the resonant frequency.

[0031] Since the frequency interval obtained by back-calculation is 0.5 MHz, the time length of the time-domain waveform without interpolation is 2 us (see Figure 6 the blue line). After frequency-domain interpolation, the frequency interval becomes 0.25 MHz, and the length of the time-domain waveform obtained by back-calculation becomes 4 us (see Figure 6 the red line), which is equal to the time length of the excitation source waveform. From Figure 6 the time-domain waveforms, the length of the time-domain waveform becomes 4 us (see Figure 6 the red line), which is equal to the time length of the excitation source waveform. From Figure 6 the overall view of the time-domain waveforms, the following conclusions can be drawn: Before 2 us, the waveforms obtained by back-calculation (see Figure 6 the blue and red lines in ) are basically consistent with the excitation waveform, except that there is a downward offset relative to the overall excitation waveform, which is because the DC component of the excitation waveform is not considered; The time-domain waveforms obtained by back-calculation are distorted at the end, which is caused by truncating the frequency-domain signal;

[0032] Since 0 - 2 us is the effective time length of back-calculation and the excitation signal has basically decayed at 2 us, the first 2 us of the waveform is intercepted for local analysis (see Figure 6 ). It can be observed that the blue and green lines match well before 1.2 us, with only a small part of floating. Figure 7 )

[0033] For this example, the maximum condition number of the T matrix is Cond1(T) = 98.14. The number of calculated characteristic frequency points is not enough. Comparing Figure 7 the blue and green lines in

[0034] it can be seen that when the calculated frequency range is consistent with the frequency range of the excitation waveform, the results obtained by back-calculation are still relatively good. Therefore, increasing the number of calculated frequency points can improve the accuracy of the back-calculation results.

[0035] Other errors: When calculating the elements of matrix T, sinusoids of different frequencies are required as excitation. However, there is no ideal sinusoidal excitation source in CST simulation software. Each sinusoid has a certain rise time (Trise) at the beginning. Therefore, an ideal single-frequency sinusoidal excitation cannot be achieved, which will introduce errors in the calculation of matrix T. If the selection of characteristic frequency points for matrix T is unreasonable, the resonant frequency points of this GIS model may not be included; the frequency points after FFT transformation cannot completely coincide with the characteristic frequencies, resulting in only approximate values being taken. For example, the frequency values after FFT are 0, 0.2778, 0.5556, 0.8334, 1.112… There are no frequency values of 0.5 MHz and 1 MHz. At this time, the Hz in matrix T is approximated by taking the frequency values of 0.5556 MHz and 1.112 MHz as the characteristic frequencies of 0.5 MHz and 1 MHz. In this way, 100 frequency points are obtained by this method, thus introducing errors to matrix T. In the above example, the frequency interval is 0.25 MHz, and this error basically does not exist and can be ignored. To avoid this error, the sampling time should be long enough to have a large frequency resolution. The inverse-calculated frequency interval should be at least twice the frequency resolution or more.

[0036] After considering the specification and practicing the disclosed embodiments herein, those skilled in the art will readily conceive of other embodiments of the present application. The present application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include known common knowledge or conventional technical means in the technical field not disclosed in the present application.

[0037] It should be understood that the present application is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present application is only limited by the appended claims.

Claims

1. A method for optimizing the calculation of transient current in GIS based on radiation field, characterized in that: The following steps are involved: Step 1: Equivalently treat GIS as a nonlinear system in the time domain, then construct a GIS electromagnetic radiation model, and establish the coefficient matrix T of the excitation current and the radiation field magnetic field at the characteristic frequency point of the model; Step 2, for any excitation current source of the GIS electromagnetic radiation model, the frequency domain waveform of the excitation current source is calculated by measuring the radiation field combination coefficient matrix T at a fixed position outside the GIS electromagnetic radiation model; Step 3: Calculate the current waveform according to the frequency domain waveform of the current source to obtain the transient current in the GIS.

2. The method for optimizing and calculating transient current in GIS based on radiation field according to claim 1 is characterized in that: In step 1, the coefficient matrix T of the excitation current and the radiation field magnetic field is established at the characteristic frequency point of the model, specifically: The magnetic field at a point outside the GIS in the direction of the GIS busbar hammer is selected as the radiation field research component H z , excitation current input is I exc Indicates that the established matrix relationship is as follows: In the formula, H zfi It means that under the input signal, the magnetic field in the Z direction of a certain point in space is at a frequency of f i The weight on I excfi The input signal is at a frequency of f i The weight on 11 to T NN It represents the linear relationship between the excitation source current and the external magnetic field of GIS in the frequency domain, re represents the real part, and im represents the imaginary part; Therefore, the coefficient matrix T in T ij It can be found by the following formula: Where: T ij Indicates that when except I excfj When all inputs except z f i Frequency Components and I excfj The ratio of The coefficient matrix T is determined by numerical simulation method.

3. The method for optimizing and calculating transient current in GIS based on radiation field according to claim 2 is characterized in that: The numerical simulation method is to determine the coefficient matrix T through the CST model and the MATALB program, specifically: Enter the simulation start frequency, end frequency and frequency interval; Calculate the current simulation frequency f, modify the excitation source in the CST model, and update the calculation model for simulation calculation; The simulation results and excitation sources are stored in the specified table to determine whether the simulation termination frequency has been reached. If the simulation termination frequency has been reached, MATLAB is called to process the simulation results to obtain the coefficient matrix T. If the simulation termination frequency has not been reached, the current simulation results are deleted and the next simulation is prepared.

4. The method for optimizing and calculating transient current in GIS based on radiation field according to claim 2 or 3 is characterized in that: In the step 2, by measuring the radiation field combination coefficient matrix T at a fixed position outside the GIS electromagnetic radiation model, the formula for calculating the frequency domain waveform of the excitation current source is: I excf =T -1 H zf All elements in the formula are complex numbers, which can be decomposed into real and imaginary components for algebraic operations: In the formula, the superscript re means taking the real part, and im means taking the imaginary part.

5. The method for optimizing and calculating transient current in GIS based on radiation field according to claim 4 is characterized in that: In step 3, the current waveform is calculated based on the frequency domain waveform of the current source, which is specifically: Frequency domain interpolation is used to obtain the frequency domain data of the input signal within the system response frequency range, and then IFFT transform is used to obtain its time domain waveform.

6. The method for optimizing and calculating transient current in GIS based on radiation field according to claim 4 is characterized in that: The relative error of the algebraic operation is also estimated: In the formula, is the relative residual, ||T||||T -1 || is the condition number of matrix T. When the condition number of T is smaller, the relative error of the approximate solution is smaller. Conversely, the relative error of the approximate solution may be larger.

7. The method for optimizing and calculating transient current in GIS based on radiation field according to claim 6 is characterized in that: The accuracy of the inverse calculation results can be improved by increasing the frequency of calculation points.

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