CN112924758B - Different-frequency impedance-based impact grounding resistance measurement method - Google Patents
Different-frequency impedance-based impact grounding resistance measurement method Download PDFInfo
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Abstract
The invention relates to a method for measuring impulse grounding resistance based on different-frequency impedance, which belongs to the technical field of operation and management of power transmission and transformation equipment, and comprises the following steps: s1: selecting lightning current waveforms with different waveform parameters, researching the spectrum characteristics and the energy characteristics of the lightning current after periodic prolongation to obtain a spectrum diagram and an energy diagram of the lightning current, and determining the concentrated frequency range and the measurement frequency point of the lightning current amplitude and the energy; s2: the impedance response of the grounding electrode in the frequency range is researched, and the numerical value of the potential of the end part of the grounding electrode under different frequencies is obtained; s3: and providing a time domain response expression of the potential of the end part of the grounding electrode containing unknown characteristic parameters, carrying out forward Fourier transform on the time domain response expression to obtain an impedance response expression containing the unknown parameters, and determining the characteristic parameters in the expression according to a coefficient method to be determined. The invention can more accurately measure the impact grounding resistance, reduces the calculated amount and effectively realizes the accurate and efficient measurement of the impact grounding resistance of the tower.
Description
Technical Field
The invention belongs to the technical field of operation and management of power transmission and transformation equipment, and relates to an impact grounding resistance measurement method based on different-frequency impedance.
Background
The accurate measurement of the impact grounding resistance of the grounding device has important engineering significance for effective lightning protection of the transmission line towers. When lightning impulse current flows through the tower grounding device, a complex electromagnetic transient process is generated with the surrounding soil environment, and the grounding performance is difficult to evaluate by adopting a general expression. Thus, accurate measurement of the impulse ground resistance has been an important issue in the field of grounding.
At present, a great deal of researches are carried out on electromagnetic transient processes with complex surrounding space when impact current flows through a grounding electrode at home and abroad. And R.Gupta provides an empirical formula and a method for calculating the inductances of the square grounding grid center grounding grid and the angle grounding grid, and the effectiveness of the analysis method is verified through a model test. Velazquez evaluates the impact characteristics of the ground poles from a numerical analysis point of view by programming a relevant computer program. The electromagnetic transient program taking the mutual coupling effect between conductors of a grounding system into consideration is established by the M.I. Lorentzou, and the influence of the mutual coupling effect of the conductors on the system response is studied. Visacro proposes a method for measuring the change of the resistivity and the dielectric constant of soil in the frequency component range of typical lightning current, and the values of the resistivity and the dielectric constant of the soil are corrected. The Ramamotorty adopts the concept of complex resistivity, and the influence of the capacitance to ground on the high-frequency transient performance of the grounding network is researched by a moment method numerical calculation method. Hablanc carries out simulation modeling on a simple grounding system and a complex grounding system buried in uniform or non-uniform soil, and provides a simulation model based on a finite element method aiming at ionization phenomena of soil around the grounding system. The calculation method of the time domain finite difference value can accurately describe the transient process of the grounding electrode under the action of impact current by adopting a Maxwell equation set and a space-time variable resistivity function. A.C.view establishes a dynamic model for describing the characteristics of a plurality of concentrated grounding nonlinear surge currents, can more accurately describe the fluctuation behavior of soil under the action of high-frequency surge currents, and provides a theoretical basis for the surge suppression factors in the test process. The He Jinliang team considers the dynamic and nonlinear effects of soil ionization around the grounding electrode, builds a grounding electrode transient characteristic analysis model under the action of lightning impulse, and provides a calculation formula of the effective length of grounding electrode impulse. The Cao Xiao team researches the Fourier form of the lightning current waveform expression, loads the decomposed sine wave on a grounding device as excitation, and provides a thought of converting transient lightning impulse response into steady-state response.
The research is mainly focused on the electromagnetic transient process of the soil around the grounding electrode under the action of lightning impulse and the process of the forward Fourier change of lightning current, and the problems of the frequency range selection after the decomposition of the lightning current and the time-frequency response conversion of the grounding device are not solved. The existing impact grounding resistance measurement method mainly comprises an impact coefficient method and a field measurement method, wherein the impact coefficient method can not accurately reflect the impact characteristics of a pole tower grounding electrode under the action of lightning stroke, and the problems of inaccurate calculation results and the like are easily caused; the field measurement laws require that personnel carry an impulse current source, oversized power equipment and complex terrain environments add difficulty and labor cost to accurately measure the pole-tower impulse ground resistance.
Therefore, the impact grounding resistance measurement method with small calculated amount, high measurement precision and high environmental adaptability is provided as a problem to be solved urgently.
Disclosure of Invention
Therefore, the invention aims to obtain a narrow frequency range and a small number of measurement frequency points which characterize the amplitude and energy characteristics of lightning current by carrying out forward Fourier transform and energy analysis after the period extension of the lightning current waveform, measure the impedance response of a grounding electrode in the narrow frequency range, and determine characteristic parameters in an expression by adopting a coefficient to be determined method in combination with a grounding electrode end potential time domain expression containing unknown parameters, thereby providing a method for measuring impulse grounding resistance based on different frequency impedance and further obtaining a relatively accurate impulse grounding resistance value.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the method for measuring the impulse grounding resistance based on the different-frequency impedance comprises the following steps:
s1: selecting lightning current waveforms with different waveform parameters, researching the spectrum characteristics and the energy characteristics of the lightning current after periodic prolongation to obtain a spectrum diagram and an energy diagram of the lightning current, and determining the concentrated frequency range and the measurement frequency point of the lightning current amplitude and the energy;
s2: the impedance response of the grounding electrode in the frequency range is researched, and the numerical value of the potential of the end part of the grounding electrode under different frequencies is obtained;
s3: and providing a time domain response expression of the potential of the end part of the grounding electrode containing unknown characteristic parameters, carrying out forward Fourier transform on the time domain response expression to obtain an impedance response expression containing the unknown parameters, and determining the characteristic parameters in the expression according to a coefficient method to be determined.
Further, the soil resistivity was 150 Ω·m, the length of the ground electrode was 10m, the burial depth was 0.8m, and the radius of the ground electrode was 0.006m, and analysis was performed.
Further, the step S1 specifically includes the following steps:
s11: selecting lightning current with waveform parameters of 2.6/50 mu s and amplitude of 10kA, obtaining a double-exponential function representing the waveform parameters, and performing cycle extension to obtain a calculation model;
s12: according to the calculation model, obtaining the lightning current function period and the fundamental wave frequency; performing forward Fourier transform on the double-exponential function subjected to periodic continuation to obtain a discrete spectrogram of the lightning current function;
s13: according to the Paswal power conservation theorem, obtaining the lightning energy at different frequency points and solving the energy proportion distribution of different frequency ranges; and determining a concentrated frequency range and a small number of measurement frequency points of the lightning current amplitude and the energy according to the lightning current spectrogram and the energy duty ratio chart.
Further, the double exponential function of the waveform parameter in step S11 is:
I(t)＝10474×(e -14790t -e -1877833t ) (1)。
further, in step S12, forward fourier transform is performed on the bi-exponential function that is extended periodically, so as to obtain an expression of the dc component and the n-th harmonic component of the bi-exponential function with continuous period:
wherein I is m ＝1×10 4 α= -147900, β= -1877833, and carrying into the formula (2) (3) to obtain a discrete spectrum diagram of the lightning current; with harmonic frequency kf 0 The amplitude spectrum is continuously attenuated and finally goes to zero, namely the higher the frequency is, the more the current amplitude goes to zero.
Further, in step S13, the total energy of the lightning current is:
bringing the values of α, β and M into equation (4) gives the total energy of the lightning current: w=3.62×10 3 And carrying different frequency values into the energy values to obtain different frequencies, so as to obtain the energy proportion distribution in different frequency ranges.
Further, in the lightning current spectrogram and the energy duty ratio chart obtained in the step S1, the amplitude of the lightning current is mainly concentrated in the low-frequency part; 2.6/50 mu s of lightning current energy is mainly concentrated at 0-10 kHz, wherein the maximum lightning current energy in the frequency range of 0-10 kHz accounts for 90% of the total lightning current energy;
according to the fundamental frequencyOnly the frequency point f is measured in the low frequency range of 0-10 kHz 0 ～f 3 The frequency response of the grounding electrode, thereby achieving the purpose of accurately obtaining the time domain response expression of the grounding electrode end part.
Further, the step S2 specifically includes the following steps:
and measuring impedance responses of the grounding electrode at different measuring frequency points by using the obtained measuring frequency range and measuring frequency points by using a tripolar method to obtain the numerical value of the potential of the end part of the grounding electrode at the measuring frequency points.
Further, in step S2, the length of the grounding electrode is l=10m, and the linear distance L between the potential measuring electrode P and the tower foundation of the tower is measured PG Linear distance L of current pole C from tower foundation of pole tower=2.5l=25m CG ＝4L＝40m；
With infinity as a reference point, the potential of the ground electrode should be:
the potential difference generated by the ground bulk current I between the ground electrode G and the voltage electrode P is:
similarly, the potential difference generated between the ground G and the voltage pole P by the current I flowing through the recovery current pole C is:
the voltage between GPs obtained by the superposition theorem is:
further, the step S3 specifically includes the following steps:
proposing a time domain response expression of the ground terminal potential with unknown parameters, U (t) =a·e b·t +c·e d·t Performing forward Fourier transform on U (t) to obtain an impedance response expression containing unknown parameters, wherein the potential frequency domain response of the end part of the grounding electrode meets the formula U=Z.I, and the injection current amplitude is set to be 1A, so that the following equation is obtained:
solving the above equations simultaneously to obtain the numerical value of a, b, c, d, the impact grounding resistance is:
the invention has the beneficial effects that: compared with an impact coefficient method, the method provided by the invention can be used for measuring the impact grounding resistance more accurately, and selecting a low-frequency range and a small number of measurement frequency points, so that the calculated amount is greatly reduced. In addition, the field measurement method has the problems of overlarge equipment, poor environmental adaptability and the like, and the method can effectively realize accurate and efficient measurement of the pole tower impact grounding resistance.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is a graph of a lightning current time domain calculation model after periodic extension;
FIG. 2 is a graph of a lightning current dispersion spectrum at 2.6/50. Mu.s;
FIG. 3 is a graph of 2.6/50 μs lightning energy duty cycle;
fig. 4 is a general flow chart of the method of the present invention.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Wherein the drawings are for illustrative purposes only and are shown in schematic, non-physical, and not intended to limit the invention; for the purpose of better illustrating embodiments of the invention, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the size of the actual product; it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numbers in the drawings of embodiments of the invention correspond to the same or similar components; in the description of the present invention, it should be understood that, if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc., that indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but not for indicating or suggesting that the referred device or element must have a specific azimuth, be constructed and operated in a specific azimuth, so that the terms describing the positional relationship in the drawings are merely for exemplary illustration and should not be construed as limiting the present invention, and that the specific meaning of the above terms may be understood by those of ordinary skill in the art according to the specific circumstances.
As shown in FIG. 4, the invention provides a method for measuring impulse grounding resistance based on different frequency impedance, which selects soil resistivity of 150Ω.m, grounding electrode length of 10m, burial depth of 0.8m and grounding electrode radius of 0.006m for analysis according to the design requirements of DL/T5092-1999 '110-500 kV overhead power transmission line design technical specification', and comprises the following steps:
step 1: and selecting lightning current waveforms with different waveform parameters, researching the frequency spectrum characteristic and the energy characteristic of the lightning current after periodic prolongation to obtain a frequency spectrum chart and an energy spectrum chart of the lightning current, and determining the concentrated frequency range and the measuring frequency point of the lightning current amplitude and the energy.
Step 1, selecting a double-exponential function to represent the waveform characteristics of lightning current, and selecting the lightning current with the waveform parameter of 2.6/50 mu s and the amplitude of 10kA to obtain the double-exponential function representing the waveform parameter, wherein the double-exponential function is as follows:
I(t)＝10474×(e -14790t -e -1877833t ) (1)
the double-exponential function representing the lightning current characteristic is a non-periodic function, and periodic prolongation is carried out on the formula (1) to obtain the current amplitude values of the lightning current at different frequency points. The time value at which the apparent current amplitude is zero is one cycle, then t=400 μs, as shown in fig. 1. Performing forward Fourier transform on the double-exponential function subjected to period extension to obtain an expression of a direct current component and an n-order harmonic component of the continuous period double-exponential function:
wherein I is m ＝1×10 4 The discrete spectrum diagram of the lightning current can be obtained by taking the alpha= -147900 and beta= -1877833 into the formulas (2) and (3) as shown in figure 2. With harmonic frequency kf 0 The amplitude spectrum is increasingly attenuated and eventually goes to zero. I.e. the higher the frequency, the more zero the current amplitude. According to the forward decomposition Fourier series expression and the Paswal power conservation theorem, namely that the energy contained in the lightning current is equal to the sum of the energy of each component in the complete orthogonal function set, the total energy of the lightning current in the time domain is equal to the total energy in the frequency domain, and the total energy of the lightning current is obtained by:
bringing the values of α, β and M into equation (4) gives the total energy of the lightning current: w=3.62×10 3 The energy of different frequencies can be obtained by bringing different frequency values into the energy of different frequencies, so that the energy proportion distribution of different frequency ranges can be obtained.
TABLE 1 amplitude values of 2.6/50 mu s lightning current frequency component
And obtaining the energy distribution of the lightning current according to the forward decomposition Fourier series expression and the Paswal power conservation theorem.
TABLE 2 2.6/50 mu s lightning current energy distribution
| Frequency range/kHz | Angular frequency range/(rad/s) | (Energy) |
| 0～0.1 | 0 | 98.6 |
| 0.1～1 | 15708 | 834 |
| 1～10 | 31415.9 | 2180 |
| 10～100 | 47123.9 | 477 |
| 100～1000 | 62831.8 | 0.155 |
As can be seen from fig. 3, table 1 and table 2, the harmonic frequency kf 0 The amplitude spectrum is increasingly attenuated and eventually goes to zero. I.e. the higher the frequency, the more zero the current amplitude. 2.6/50 μs lightningThe energy of the current is mainly concentrated in 0-10 kHz, wherein the maximum energy of lightning current in the frequency range of 0-10 kHz accounts for 96.7% of the total energy of the lightning current.
From the analysis, it is known that the amplitude and energy of lightning current are mainly concentrated in the low frequency portion by studying the amplitude characteristic and energy characteristic of lightning current of 2.6/50. Mu.s. Analyzing the frequency domain response of the ground electrode according to the fundamental frequencyOnly the frequency point f is measured in the low frequency range of 0-10 kHz 0 ～f 3 The frequency response of the grounding electrode can achieve the purpose of accurately obtaining the time domain response expression of the grounding electrode end.
Step 2: and researching the impedance response of the grounding electrode in the frequency range to obtain the numerical value of the end potential of the grounding electrode at different frequencies.
The end electric potential of the grounding electrode at different frequency points can be measured by a tripolar method, and if the length of the grounding electrode is L=10m, the linear distance L of the electric potential measuring electrode P from the tower foundation of the tower is measured PG Linear distance L of current pole C from tower foundation of pole tower=2.5l=25m CG ＝4L＝40m。
With infinity as a reference point, the potential of the ground electrode should be:
the potential difference generated by the ground bulk current I between the ground electrode G and the voltage electrode P is:
similarly, the potential difference generated between the ground G and the voltage pole P by the current I flowing through the recovery current pole C is:
the voltage between GPs obtained by the superposition theorem is:
the end potential of the grounding electrode at different frequency points can be measured by a tripolar method. Current 1A injected into the grounding electrode with frequency f 0 ～f 3 Calculating U by combining the formulas (5) to (8) 0 ～U 3 。
Step 3: and providing a time domain response expression of the potential of the end part of the grounding electrode containing unknown characteristic parameters, carrying out forward Fourier transform on the time domain response expression to obtain an impedance response expression containing the unknown parameters, and determining the characteristic parameters in the expression according to a coefficient method to be determined.
The impulse ground resistance is the ratio of the maximum value of the ground potential to the peak value of the lightning current when the lightning current flows through the ground. Under the effect of complete lightning current impact, the change of the end potential of the grounding electrode accords with the characteristic of a double-exponential function, so that the time domain response expression of the end potential is U (t) =a.e b·t +c·e d·t . And performing forward Fourier transform on the U (t) to obtain an impedance response expression containing unknown parameters. The earth terminal potential frequency domain response satisfies the formula u=z·i, and the injection current amplitude is set to 1A, resulting in the following equation:
solving the above equations simultaneously can obtain the numerical value of a, b, c, d. a=2.24×10 5 ，b＝-1.54×10 4 ，c＝-2.25×10 5 ，d＝-2.53×10 6 . The expression of the time domain response of the ground terminal potential isSo the impact grounding resistance is:
finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (9)
1. The utility model provides a shock ground resistance measuring method based on different frequency impedance which characterized in that: the method comprises the following steps:
s1: selecting lightning current waveforms with different waveform parameters, researching the spectrum characteristics and the energy characteristics of the lightning current after periodic prolongation to obtain a spectrum diagram and an energy diagram of the lightning current, and determining the concentrated frequency range and the measurement frequency point of the lightning current amplitude and the energy;
s2: the impedance response of the grounding electrode in the frequency range is researched, and the numerical value of the potential of the end part of the grounding electrode under different frequencies is obtained;
s3: providing a time domain response expression of the potential of the end part of the grounding electrode containing unknown characteristic parameters, carrying out forward Fourier transform on the time domain response expression to obtain an impedance response expression containing the unknown parameters, and determining the characteristic parameters in the expression according to a coefficient method to be determined;
the step S3 specifically comprises the following steps:
proposing a time domain response expression of the ground terminal potential with unknown parameters, U (t) =a·e b·t +c·e d·t Performing forward Fourier transform on U (t) to obtain an impedance response expression containing unknown parameters, wherein the potential frequency domain response of the end part of the grounding electrode meets the formula U=Z.I, and the injection current amplitude is set to be 1A, so that the following equation is obtained:
solving the above equations simultaneously to obtain the numerical value of a, b, c, d, the impact grounding resistance is:
2. the method for measuring impulse ground resistance based on different frequency impedance according to claim 1, wherein: the soil resistivity is 150 Ω & m, the length of the grounding electrode is 10m, the burial depth is 0.8m, and the radius of the grounding electrode is 0.006m for analysis.
3. The method for measuring impulse ground resistance based on different frequency impedance according to claim 2, wherein: the step S1 specifically comprises the following steps:
s11: selecting lightning current with waveform parameters of 2.6/50 mu s and amplitude of 10kA, obtaining a double-exponential function representing the waveform parameters, and performing cycle extension to obtain a calculation model;
s12: according to the calculation model, obtaining the lightning current function period and the fundamental wave frequency; performing forward Fourier transform on the double-exponential function subjected to periodic continuation to obtain a discrete spectrogram of the lightning current function;
s13: according to the Paswal power conservation theorem, obtaining the lightning energy at different frequency points and solving the energy proportion distribution of different frequency ranges; and determining a concentrated frequency range and a small number of measurement frequency points of the lightning current amplitude and the energy according to the lightning current spectrogram and the energy duty ratio chart.
4. The method for measuring impulse ground resistance based on different frequency impedance according to claim 3, wherein: the double exponential function of the waveform parameter in step S11 is:
I(t)＝10474×(e -14790t -e -1877833t ) (3)。
5. the method for measuring impulse ground resistance based on different frequency impedance according to claim 4, wherein: in step S12, forward fourier transform is performed on the bi-exponential function that is extended periodically, so as to obtain an expression of the dc component and the n-th harmonic component of the bi-exponential function with continuous period:
wherein I is m ＝1×10 4 α= -147900, β= -1877833, and carrying into the formula (4) (5) to obtain a discrete spectrum diagram of the lightning current; as the harmonic frequency increases, the amplitude spectrum is continuously attenuated and eventually goes to zero, i.e., the higher the frequency, the more the current amplitude goes to zero.
6. The method for measuring impulse ground resistance based on different frequency impedance according to claim 5, wherein: in step S13, the total energy of the lightning current is:
bringing the values of α, β and M into equation (6) yields the total energy of the lightning current: w=3.62×10 3 And carrying different frequency values into the energy values to obtain different frequencies, so as to obtain the energy proportion distribution in different frequency ranges.
7. The method for measuring impulse ground resistance based on different frequency impedance according to claim 6, wherein: in the lightning current spectrogram and the energy duty ratio chart obtained in the step S1, the amplitude of the lightning current is mainly concentrated in a low-frequency part; 2.6/50 mu s of lightning current energy is mainly concentrated at 0-10 kHz, wherein the maximum lightning current energy in the frequency range of 0-10 kHz accounts for 90% of the total lightning current energy;
according to the fundamental frequencyOnly the frequency point f is measured in the low frequency range of 0-10 kHz 0 ～f 3 The frequency response of the grounding electrode, thereby achieving the purpose of accurately obtaining the time domain response expression of the grounding electrode end part.
8. The method for measuring impulse ground resistance based on different frequency impedance according to claim 2, wherein: the step S2 specifically comprises the following steps:
and measuring impedance responses of the grounding electrode at different measuring frequency points by using the obtained measuring frequency range and measuring frequency points by using a tripolar method to obtain the numerical value of the potential of the end part of the grounding electrode at the measuring frequency points.
9. The method for measuring impulse ground resistance based on different frequency impedance according to claim 8, wherein: in step S2, the length of the grounding electrode is l=10m, and the linear distance L between the potential measuring electrode P and the tower foundation of the tower is measured PG Linear distance L of current pole C from tower foundation of pole tower=2.5l=25m CG ＝4L＝40m；
With infinity as a reference point, the potential of the ground electrode should be:
the potential difference generated by the ground bulk current I between the ground electrode G and the voltage electrode P is:
similarly, the potential difference generated between the ground G and the voltage pole P by the current I flowing through the recovery current pole C is:
the voltage between GPs obtained by the superposition theorem is:
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