CN103792433B - With the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device - Google Patents

Abstract

A kind of with the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device, utilize portable impact current feedback circuit as signal output source, earthing device is arranged with three grades of method metering systems, use uninterrupted power source is powered, dash current is injected from earthing pole, calculate the spark factor alpha of earthing device place soil, according to calculated spark factor alpha, to the initial impact stake resistance R that convolutional calculation obtains _crevise.Impulse earthed resistance under the present invention adopts convolutional calculation and spark leveling factor method to obtain standard lightning current, effectively can consider the inductive effect of earthing device and the spark discharge of soil, revised impulse earthed resistance is more close to the actual conditions that transmission line of electricity is struck by lightning.This method solving prior art can only adopt power frequency earthing resistance to carry out approximate estimation, can not carry out the problem of in-site measurement.

Description

With the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device

Technical field

The present invention relates to power transmission line lightning shielding protection field, is a kind of low amplitude value impulse resistance measuring method specifically.

Background technology

Electric power line pole tower earthing device impulse earthed resistance is the major influence factors of transmission line of electricity lightning withstand level, Measurement accuracy tower grounding device impulse earthed resistance can provide reliable foundation for transmission line of electricity lightning Protection Design, improves the safety operation level of transmission line of electricity.

Tower grounding device impulse earthed resistance refers to that tower grounding device is under lightning current effect, the ratio of the lightning current peak value flow through in the voltage peak that earthing device bears and earthing device:

$R_{ch}=\frac{U_m}{I_m}$

In formula: U _mfor lightning voltage peak value on earthing device, I _mfor the lightning current peak value flow through in earthing device.

Due to inductive effect and the soil spark discharge of earthing device, carry out measurement to the impulse resistance of earthing device in the lab to need to adopt jumbo impulse current generator, because the jumbo impulse current generator in laboratory is bulky, be subject to the restriction of site contour, make the impulse resistance not having effective method in-site measurement earthing device in practical implementation.

When carrying out the design of power transmission line lightning shielding protection, the general power frequency earthing resistance that adopts is estimated in conjunction with coefficient of impact.But coefficient of impact is theory speculates, with the earthing device of different size in different soil environments, coefficient of impact is widely different, thus the method that this employing power frequency earthing resistance of prior art carries out estimating can produce very large error, can not meet actual demands of engineering, the low amplitude value impulse resistance at present for earthing device is measured or the blank in industry.

Summary of the invention

Technical matters to be solved by this invention fills up the blank of prior art on earthing device impulse resistance is measured, there is provided a kind of with the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device, adopt low amplitude value impulse current generator in conjunction with spark leveling factor method, measure the impulse earthed resistance of electric power line pole tower earthing device.

Described with the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device, it is characterized in that: utilize portable impact current feedback circuit as signal output source, the dash current that described portable impact current feedback circuit produces is required to meet: amplitude within the scope of 5A ~ 50A, two exponential waves of wave head time 1.0 μ s ~ 5.0 μ s; Survey calculation is carried out according to following steps:

One), the shunting of portable impact current feedback circuit is connected digital oscillographic two autonomous channels respectively with dividing potential drop output terminal, earthing device is arranged with three electrode method metering system, use uninterrupted power source is powered, inject dash current from earthing pole, record the data of response voltage U (t) in dash current I (t) data and earthing pole that impulse current generator produces with oscillographic two autonomous channels of multi-channel digital simultaneously;

Two), set sampling interval Δ t, sample, the sample sequence of standard lightning current is i _std(n), wherein: n=1,2,3 ..., time t meets: t=Δ t × n; One by one convolutional calculation is carried out to the sample sequence of each standard lightning current, obtain the response voltage u after convolutional calculation _std(n); According to the initial impact grounding resistance R that formula (1) calculates under the effect of standard lightning current _c:

$R_c=\frac{max\left(u_{std}\right(n\left)\right)}{m\mathrm{\α}\left(i_{std}\right(n\left)\right)}---\left(1\right);$

Wherein, max (i _std(n)) represent maximal value in standard lightning current sample sequence, max (u _std(n)) represent the response voltage value of corresponding described standard lightning current sample sequence maximal value after convolutional calculation;

Three), calculate the spark factor alpha of earthing device place soil, calculation procedure is as follows:

Four), according to calculated spark factor alpha, to the initial impact stake resistance R that convolutional calculation obtains _crevise, calculate the impulse earthed resistance R under the effect of standard lightning current, computing formula is:

R＝α·R _c(2)。

Described spark factor alpha adopts the earthing device impulse earthed resistance frequency domain value simulation algorithm of Electromagnetic field to calculate, and calculation procedure is as follows:

A), structure, the dimensional parameters of input grounding pole in impulse earthed resistance Numeral Emulation System, soil parameters, iteration error ε, subdivision is carried out according to conductor subdivision length Δ l, conductor hop count after subdivision is p, node number is q, carries out modeling according to π shape equivalent electrical circuit to the earthing device after subdivision;

B), to standard lightning current I _stdt () carries out Fast Fourier Transform (FFT), Fourier transform sampling period T=300 μ s, harmonic order N=20, obtains the standard lightning current I of N order harmonic components _f, fundamental frequency f ₁=1/T=3333Hz, i.e. first harmonic frequency, the i-th subfrequency f _i=f ₁* i;

C), according to the model of earthing device, the nodal method of analysis is adopted to set up equation as follows:

$\left\{\begin{array}{c}{\mathrm{AI}}_b=\left[\begin{array}{c}-I_{dis}\\ I_f\end{array}\right]---\left(3\right);\\ Z_{dis}{I}_{dis}={\mathrm{\Φ}}_{dis}---\left(4\right);\\ Z_b{I}_b=A^T\left[\begin{array}{c}{\mathrm{\Φ}}_{dis}\\ {\mathrm{\Φ}}_n\end{array}\right]---\left(5\right);\end{array}\right.$

Wherein: equation (3) is node KCL equation, and wherein A is incidence matrix, I _bthe axial current of subdivision conductor segment, I _dissubdivision conductor segment mid point earth leakage current, I _fit is the standard lightning current injected;

Equation (4) is mid point diffusing equation of constraint over the ground, is obtained according to the foundation of Electromagnetic Field theory by " model of field " in institute's modeling, in formula, and Φ _disthe mid-point voltage of subdivision conductor segment, z _dis it is diffusing matrix over the ground;

The KVL equation of constraint that equation (5) is subdivision conductor segment, is obtained according to Circuit theory foundation by " model on road " in institute's modeling, in formula, and Z _bthe self-impedance matrix of subdivision conductor segment, mutual inductance matrix, A ^tthe transposed matrix of incidence matrix A, Φ _nit is node voltage;

The matrix of diffusing over the ground Z in equation (4) _discalculate according to formula (6):

$Z_{dis}(i,j)=\frac{1}{4{\mathrm{\π\ρ}}_o+{\mathrm{j\ω\ϵ}}_r}\·\frac{1}{L_i{L}_j}\·{\∫}_{L_i}{\∫}_{L_j}\frac{1}{r^{\′}}{\mathrm{dl}}_j{\mathrm{dl}}_i---\left(6\right);$

In formula: L _iand L _jbe i-th section with the length of j section two sections of conductors, r' is the distance between the point on two sections of conductive surfaces, ρ _othe conductivity of soil, ε _rthe specific inductive capacity of soil, ω=2 π * f _i, f _iit is the i-th subfrequency;

Self-impedance matrix, the mutual inductance matrix Z of subdivision conductor segment in equation (5) _bcalculate according to formula (7):

$\left\{\begin{array}{c}{Z}_{ii}=z_{ii}+{\mathrm{j\ωM}}_{ii}\\ Z_{ij}={\mathrm{j\ωM}}_{ij}\end{array}\right.---\left(7\right);$

Wherein: Z _iiand Z _ijfor matrix element, ω=2 π * f _i, z _iifor self-impedance, M _iifor outer self-induction, M _ijfor mutual inductance, z _iicalculate according to formula (8):

$z_{ii}=\frac{{\mathrm{j\ω\μ}}_c}{2\mathrm{\π}r\sqrt{{\mathrm{j\ω\μ}}_c{\mathrm{\σ}}_c}}\frac{I_0\left(r\sqrt{{\mathrm{j\ω\μ}}_c{\mathrm{\σ}}_c}\right)}{I_1\left(r\sqrt{{\mathrm{j\ω\μ}}_c{\mathrm{\σ}}_c}\right)}---\left(8\right);$

Wherein: ω=2 π * f _i, μ _cthe magnetic permeability of conductor, σ _cbe the conductivity of conductor, r is the radius of cylindrical conductor, I ₀and I ₁the first kind zeroth order and single order Bessel function revised respectively;

M _iicalculate according to formula (9):

$M_{ii}=\frac{{\mathrm{\μ}}_0\·l_o}{2\mathrm{\π}}(ln\frac{2l_o}{r}-1)---\left(9\right);$

Wherein: l _othe length of conductor segment, μ ₀it is the magnetic permeability in vacuum;

M _ijcalculate according to formula (10):

$M_{ij}=\frac{{\mathrm{\μ}}_0}{4\mathrm{\π}}{\∫}_{l_i}{\∫}_{l_j}\frac{1}{r^{\′}}{\mathrm{dl}}_j\·{\mathrm{dl}}_i---\left(10\right);$

Wherein: l _iand l _jbe i-th section with the length of j section two sections of conductors, r' is the distance between the point on two sections of conductive surfaces, μ ₀it is the magnetic permeability in vacuum;

D), according to formula (11) computing node voltage Φ _nwith mid-point voltage Φ _dis:

$\left[\begin{array}{c}{\mathrm{\Φ}}_{dis}\\ {\mathrm{\Φ}}_n\end{array}\right]={\[\[{\mathrm{AZ}}_b^{-1}{A}^T\]+\[\begin{array}{cc}{Z}_{dis}^{-1}& 0\\ 0& 0\end{array}\]\]}^{-1}.\left[\begin{array}{c}0\\ I_f\end{array}\right]---\left(11\right);$

In formula, the implication of each symbol is the same;

Mid point earth leakage current I is tried to achieve according to equation (4) _dis, try to achieve subdivision conductor segment axial current I according to equation (3) _b;

E) the impulse earthed resistance R' not considering soil spark discharge, is calculated _c: when not considering the spark discharge of soil, the node voltage in soil spark discharge situation is not considered in direct calculating;

F) the impulse earthed resistance R considering soil spark discharge, is calculated _i: when considering the spark discharge of soil, calculate the equivalent redius r of subdivision conductor according to formula (12) _eq:

$r_{eq}=\frac{{\mathrm{\ρI}}_{dis}}{2{\mathrm{\π\ΔlE}}_c}---\left(12\right);$

In formula: ρ is soil resistivity, I _disfor subdivision conductor segment mid point earth leakage current, Δ l is conductor subdivision length, E _cfor the critical breakdown strength of soil,

E _ccalculate according to formula (13):

E _c＝241ρ ^0.215(13)；

Equivalent redius is adopted to replace conductor radius r, by r=r _eqsubstitute into (a)-(d) and carry out loop iteration, until meet △ r _eqstop iteration during < ε, ε is iteration error, calculates the node voltage in consideration soil spark discharge situation; Wherein: Δ r _eqbe the equivalent redius difference calculated for twice, get 1/10 ~ 1/5 of conductor radius r;

G), according under the lightning current effect of N order harmonic components, the node voltage Φ under each harmonic component that step (c) ~ (f) is calculated _ncarry out Fast Fourier Transform Inverse (FFTI), obtain time domain interior joint voltage according to standard lightning current I _finjection sequence number i, extract the node voltage at Current injection points place formula (14) is adopted to calculate the impulse earthed resistance of earthing device:

Formula (14) obtains, in formula according to the defined formula of impulse earthed resistance: max (I _std(t)) for injecting the maximal value of the standard lightning current of earthing pole, for the maximal value of Current injection points place response voltage;

H), according to step (a)-(g), the impulse earthed resistance R' not considering spark discharge is calculated respectively _cand consider the impulse earthed resistance R of spark discharge _i; Spark factor alpha is calculated according to formula (15):

$\mathrm{\&alpha;}=\frac{R_i}{R_c^{\&prime;}}---\left(15\right).$

The step of described convolutional calculation is:

1. network function R (s) of system is: the ratio of image function U (s) of response voltage U (t) of zero condition and image function I (s) of exciting current I (t) in frequency domain, that is:

$R\left(s\right)=\frac{U\left(s\right)}{I\left(s\right)}---\left(16\right);$

2. under the effect of standard lightning current, the network function of image function is:

$R_{std}\left(s\right)=\frac{U_{std}\left(s\right)}{I_{std}\left(s\right)}---\left(17\right);$

In formula: I _stds () is standard lightning current I _stdthe image function of (t), U _stds () is standard lightning current I _stdthe lower response voltage U of (t) effect _stdthe image function of (t),

For linear time invariant system, network function R (s) of system immobilizes, namely

R(s)＝R _std(s)(18)；

3. calculate convolution, obtain standard lightning current i according to the RESPONSE CALCULATION under driving source different in time domain _stdresponse voltage u under (n) _std(n):

u _std(n)＝u(n)*i _std(n)/i(n)(19)；

In formula, u (n) and i (n) represents voltage and current Variables Sequence respectively;

Standard lightning current I _stdt () is selected according to electric system lightning Protection Design standard, parameter is: amplitude is determined according to the lightning withstand level of connection electric transmission line, and scope is at 10kA ~ 150kA, and to be the standard lightning current of two exponential waves of 2.6/40 μ s be waveform:

$I_{std}\left(t\right)=I_m\&times;(e^{-t/T_1}-e^{-t/T_2}),---\left(20\right);$

Wherein: T ₁for constant: T ₁=50e ^-6, T ₂for constant: T ₂=1e ^-6, sample according to sampling interval Δ t, its sample sequence is i _std(n), wherein: n=1,2,3 ..., meet t=Δ t × n, obtain standard lightning current i _stdresponse voltage u under (n) _std(n).

The arrangement that described three electrode method is measured is:

Injection Current forms current return by the current line between earthing pole G and electric current pole C and the earth, and voltage pole P is arranged in zero-potential point, for measuring the response voltage on grounding body, adopts angle wire laying mode: the length d of current line _gCwith the length d of pressure-wire _gPidentical or close, get 3l ~ 10l, l is the diagonal length of earthing device, and current line and pressure-wire are arranged in an angle, and angle is chosen in the scope of 30 ° to 180 °.

Or the arrangement adopting three electrode method to measure is:

Injection Current forms current return by the current line between earthing pole G and electric current pole C and the earth, voltage pole P is arranged in zero-potential point, adopt straight-line method wire laying mode: tested tower grounding pole G, voltage pole P and electric current pole C on the same line, wherein: the length d of current line _gC>=4l, wherein: l is the diagonal length of earthing device, voltage pole is routed in the zero-potential point place between electric current pole and earthing pole, the length d of pressure-wire _gP=0.618d _gCtime voltage pole be positioned at zero-potential point.

The invention has the beneficial effects as follows: due under lightning current effect, soil can discharge by flashing, and arc channel accelerates releasing of lightning current, and the impulse earthed resistance under lightning current is wanted significantly lower than power frequency earthing resistance.Adopt power frequency earthing resistance to replace impulse earthed resistance, obviously do not meet actual conditions.Adopt power frequency earthing resistance to carry out approximate estimation, there is error comparatively large, there is no the problem of general formula.The present invention proposes on the basis that low amplitude value impulse current generator carries out in-site measurement, impulse earthed resistance under adopting convolutional calculation and spark leveling factor method to obtain standard lightning current, effectively can consider the inductive effect of earthing device and the spark discharge of soil, revised impulse earthed resistance is more close to the actual conditions that transmission line of electricity is struck by lightning.This method solving prior art can only adopt power frequency earthing resistance to carry out approximate estimation, can not carry out the problem of in-site measurement.In the lightning protection of transmission line of electricity and power equipment, the impulse earthed resistance of its earthing device of in-site measurement can provide reference for the calculating of the lightning withstand level of equipment.

In addition, when current power frequency earthing resistance adopts straight-line method to connect up, according to Theory of Electromagnetic Field, zero-potential point is selected at 0.618 place, but under dash current effect, straight line can be adopted to connect up, the position of zero-potential point when adopting straight line wiring, there is no correlative study and test figure.The present invention is according to simulation and experimental study, determine when low amplitude value measures impulse earthed resistance, because soil does not have flashing to discharge, the response of earthed system is linear time invariant system, when impulse earthed resistance is measured in straight line wiring, 0.618 position of zero-potential point between earthing pole and electric current pole, i.e. d _gP=0.618d _gC, when solving in-site measurement earthing device impulse earthed resistance, straight-line method can be adopted to connect up, and determine zero potential, to actual measurement of engineering, there is directive significance.

Accompanying drawing explanation

Fig. 1 is the straight-line method in-site measurement wiring method schematic diagram of three electrode method;

Fig. 2 is the angle-off set in-site measurement wiring method schematic diagram of three electrode method;

Fig. 3 is grounding device constructions and diagonal length schematic diagram;

In figure, l _afor the length of side of earthing device, l _sfor the ray length of earthing device, l is the diagonal length of earthing device.

Fig. 4 standard lightning current waveform schematic diagram;

The waveform of standard lightning current is 2.6/40 μ s, and in figure, current peak is with I _m=10kA is example;

The π shape equivalent electrical circuit of Fig. 5 subdivision conductor segment;

The modeling of earthing device in Fig. 6 frequency domain value simulated program;

Carry out modeling according to Circuit theory, set up branch impedance matrix, comprise the self-impedance of conductor segment, transimpedance; Carry out modeling by Electromagnetic Field theory, set up diffusing impedance matrix over the ground, comprise the transimpedance between the self-impedance of diffusing over the ground of conductor segment and conductor segment; Current injection points is that square frame edge injects;

Fig. 7 earthing device impact characteristics frequency domain value simulated program process flow diagram;

Fig. 8 low amplitude value dash current and response voltage in-site measurement oscillogram;

Upper figure: in-site measurement obtains the low amplitude value impulse current waveform that earthing device injects;

Figure below: in-site measurement obtains the response voltage waveform at Current injection points place;

Earthing device response voltage oscillogram under the effect of Fig. 9 standard lightning current;

In figure: " o " represents that in-site measurement obtains the response voltage waveform at Current injection points place;

Under " * " represents that convolutional calculation obtains the effect of standard lightning current, the waveform of earthing device response voltage.

Embodiment

Be described in more detail embodiments of the invention below in conjunction with accompanying drawing, but the present embodiment is not limited to the present invention, the characteristic parameter that every employing the present invention is identical and evaluation method, all should list protection scope of the present invention in.

As shown in figures 1 to 9, the excitation of described measuring method is provided by portable impact current feedback circuit, and its dash current produced requires: amplitude is within the scope of 5A ~ 50A, and the wave head time meets two exponential waves of 1.0 μ s ~ 5.0 μ s; Measuring system is: multi-channel digital oscillograph, and the shunting of impulse current generator and dividing potential drop output terminal are connected respectively to passage 1 and the passage 2 of digital oscilloscope by concentric cable.

The impulse earthed resistance measuring method of small area analysis adopts three electrode method to measure, as Fig. 1, shown in Fig. 2, namely Injection Current forms current return by the current line between earthing pole G and electric current pole C and the earth, voltage pole P is arranged in zero-potential point, for measuring the response voltage on grounding body, wiring method is shown in Fig. 1, 2, dash current I (t) of oscillograph recording impulse current generator generation and the data of response voltage U (t) on grounding body, sample according to sampling interval Δ t, its sample sequence is respectively i (n) and U (n), n=1, 2, 3 meet t=Δ t × n.According to the condition of in-site measurement, angle can be selected to connect up for three electrode method and straight line connects up:

A) angle cabling requirement: the length d of current line _gCwith the length d of pressure-wire _gPlength is identical or close, generally gets 4l ~ 5l, and l is the diagonal length of earthing device, sees Fig. 3, the words d of conditions permit _gCand d _gP10l can be got.Current line and pressure-wire are arranged in an angle, and angle is chosen in the scope of 30 ° to 180 °, as Fig. 2.

B) straight-line method cabling requirement: tested tower grounding pole G, voltage pole P and electric current pole C on the same line, are shown in Fig. 1, wherein: d _gC>=4l, voltage pole is routed in the zero-potential point place between electric current pole and earthing pole, according to numerical simulation and field test research, meets d _gP=0.618d _gCtime voltage pole be positioned at zero-potential point.

Due to the inductive effect of earthing device, under needing that the response voltage under small magnitude dash current is converted to standard lightning current.Less owing to injecting dash current amplitude, not there is nonlinear ionization in soil, the shock response of earthing device belongs to linear time invariant system, and convolutional calculation method can be adopted to convert.According to the response voltage after convolutional calculation, calculate the impulse earthed resistance R under the effect of standard lightning current _c=U _m/ I _m, wherein: the step of convolutional calculation is as follows:

1. network function R (s) of define system is: the ratio of image function U (s) of response voltage U (t) of zero condition and image function I (s) of exciting current I (t) in frequency domain, that is:

$R\left(s\right)=\frac{U\left(s\right)}{I\left(s\right)}---\left(16\right);$

2. standard lightning current I _stdresponse voltage U under (t) effect _stdt (), image function is I _std(s) and U _std(s) its network function R _stds () asks for according to formula (1), namely

$R_{std}\left(s\right)=\frac{U_{std}\left(s\right)}{I_{std}\left(s\right)}---\left(17\right);$

For linear time invariant system, network function R (s) of system immobilizes, namely

R(s)＝R _std(s)(18)；

3., by convolutional calculation, the response in time domain under different driving source meets following computing formula, can calculate standard lightning current i _stdresponse voltage u under (n) _std(n):

u _std(n)＝u(n)*i _std(n)/i(n)(19)；

Standard lightning current I _stdt () is selected according to electric system lightning Protection Design standard, parameter is: amplitude is determined according to the lightning withstand level of connection electric transmission line, and scope is at 10kA ~ 150kA, and to be the standard lightning current of two exponential waves of 2.6/40 μ s be waveform:

$I_{std}\left(t\right)=I_m\&times;(e^{-t/T_1}-e^{-t/T_2}),$

As Fig. 4, wherein: constant T ₁=50e ^-6, constant T ₂=1e ^-6.Sample according to sampling interval Δ t, its sample sequence is i _std(n), wherein: n=1,2,3 ..., meet t=Δ t × n.

The determined standard lightning current of lightning withstand level due to transmission line of electricity, its amplitude is very large, earthing device is after flowing through very large lightning current, soil can ionize, need to adopt spark coefficient to revise, spark coefficient adopts the earthing device impulse earthed resistance frequency domain value simulation algorithm of Electromagnetic field to calculate, and calculation procedure is as follows:

A), in impulse earthed resistance numerical simulation program inputthe structure of earthing pole, dimensional parameters, soil parameters, iteration error ε.Carry out subdivision according to conductor subdivision length Δ l, the conductor hop count after subdivision is p, and node number is q, according to π shape equivalent electrical circuit, as Fig. 5, carries out modeling to the earthing device after subdivision;

B), to standard lightning current I _stdt () carries out Fast Fourier Transform (FFT), standard lightning current is as Fig. 4, and Fourier transform sampling period T=300 μ s, harmonic order N=20, obtain the standard lightning current I of N order harmonic components _f, fundamental frequency f ₁=1/T=3333Hz, i.e. first harmonic frequency, the i-th subfrequency f _i=f ₁* i;

C), according to the model of earthing device, harmonic frequency is respectively f _i=f ₁~ f _n, adopt the nodal method of analysis to set up equation as follows:

$\left\{\begin{array}{c}{\mathrm{AI}}_b=\left[\begin{array}{c}-I_{dis}\\ I_f\end{array}\right]---\left(3\right);\\ Z_{dis}{I}_{dis}={\mathrm{\&Phi;}}_{dis}---\left(4\right);\\ Z_b{I}_b=A^T\left[\begin{array}{c}{\mathrm{\&Phi;}}_{dis}\\ {\mathrm{\&Phi;}}_n\end{array}\right]---\left(5\right);\end{array}\right.$

Wherein: equation (3) is node KCL equation, and A is incidence matrix, I _bbeing the axial current of subdivision conductor segment, is amount to be asked, I _disbeing midpoint node earth leakage current, is amount to be asked, I _fbeing the standard lightning current injected, is known driving source;

Equation (4) is mid point diffusing equation of constraint over the ground, as Fig. 6 dotted line frame outer " model of field ", sets up obtain according to Electromagnetic Field theory.Z _disfor the subdivision conductor segment self-impedance of diffusing and mutual resistance matrix over the ground, Φ _disbeing the mid-point voltage of subdivision conductor segment, is amount to be asked; Wherein diffusing matrix Z over the ground _discalculate according to formula (6):

$Z_{dis}(i,j)=\frac{1}{4{\mathrm{\&pi;\&rho;}}_o+{\mathrm{j\&omega;\&epsiv;}}_r}\&CenterDot;\frac{1}{L_i{L}_j}\&CenterDot;{\&Integral;}_{L_i}{\&Integral;}_{L_j}\frac{1}{r^{\&prime;}}{\mathrm{dl}}_j{\mathrm{dl}}_i---\left(6\right);$

In formula: L _iand L _jbe i-th section with the length of j section two sections of conductors, r' is the distance between the point on two sections of conductive surfaces, ρ _othe conductivity of soil, ε _rthe specific inductive capacity of soil, ω=2 π * f _i.

The KVL equation of constraint that equation (5) is subdivision conductor segment, as " model on road " in Fig. 6 dotted line frame, sets up according to Circuit theory and obtains.Z _bthe self-impedance matrix of subdivision conductor segment, mutual inductance matrix, Φ _nbeing node voltage, is amount to be asked; Wherein self-impedance matrix, the mutual inductance matrix Z of subdivision conductor segment _bcalculate according to formula (7):

$\left\{\begin{array}{c}{Z}_{ii}=z_{ii}+{\mathrm{j\&omega;M}}_{ii}\\ Z_{ij}={\mathrm{j\&omega;M}}_{ij}\end{array}\right.---\left(7\right);$

Wherein: ω=2 π * f _i, the self-impedance z in formula 7 _ii, outer self-induction M _ii, mutual inductance M _ijcalculate according to formula 8 ~ 10:

$z_{ii}=\frac{{\mathrm{j\&omega;\&mu;}}_c}{2\mathrm{\&pi;}r\sqrt{{\mathrm{j\&omega;\&mu;}}_c{\mathrm{\&sigma;}}_c}}\frac{I_0\left(r\sqrt{{\mathrm{j\&omega;\&mu;}}_c{\mathrm{\&sigma;}}_c}\right)}{I_1\left(r\sqrt{{\mathrm{j\&omega;\&mu;}}_c{\mathrm{\&sigma;}}_c}\right)}---\left(8\right);$

Wherein: ω=2 π * f _i, μ _cthe magnetic permeability of conductor, σ _cbe the conductivity of conductor, r is the radius of cylindrical conductor, I ₀and I ₁the first kind zeroth order and single order Bessel function revised respectively.

$M_{ii}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;l_o}{2\mathrm{\&pi;}}(ln\frac{2l_o}{r}-1)---\left(9\right);$

Wherein: l _othe length of conductor segment, μ ₀it is the magnetic permeability in vacuum.

$M_{ij}=\frac{{\mathrm{\&mu;}}_0}{4\mathrm{\&pi;}}{\&Integral;}_{l_i}{\&Integral;}_{l_j}\frac{1}{r^{\&prime;}}{\mathrm{dl}}_j\&CenterDot;{\mathrm{dl}}_i---\left(10\right);$

Wherein: l _iand l _jbe i-th section with the length of j section two sections of conductors, r' is the distance between the point on two sections of conductive surfaces, μ ₀it is the magnetic permeability in vacuum.

D), solution node voltage equation, according to formula (11) computing node voltage Φ _nwith mid-point voltage Φ _dis:

$\left[\begin{array}{c}{\mathrm{\&Phi;}}_{dis}\\ {\mathrm{\&Phi;}}_n\end{array}\right]={\&lsqb;\&lsqb;{\mathrm{AZ}}_b^{-1}{A}^T\&rsqb;+\&lsqb;\begin{array}{cc}{Z}_{dis}^{-1}& 0\\ 0& 0\end{array}\&rsqb;\&rsqb;}^{-1}.\left[\begin{array}{c}0\\ I_f\end{array}\right]---\left(11\right);$

Mid point earth leakage current I is tried to achieve according to equation (4) _dis, try to achieve subdivision conductor segment axial current I according to equation (5) _b;

E) the impulse earthed resistance R' not considering soil spark discharge, is calculated _c: as Fig. 7 program circuit, when not considering the spark discharge of soil, zone bit Flag=0, simulated program judges that spark discharge zone bit is N, and the node voltage in soil spark discharge situation is not considered in direct calculating.According to step (g), calculate the impulse earthed resistance R' not considering spark discharge _c;

F) the impulse earthed resistance R considering soil spark discharge, is calculated _i: as Fig. 7 program circuit, when considering the spark discharge of soil, zone bit Flag=1, simulated program judges that spark discharge zone bit is Y, then consider the spark discharge of soil: the equivalent redius r calculating subdivision conductor according to formula (12) _eq:

$r_{eq}=\frac{{\mathrm{\&rho;I}}_{dis}}{2{\mathrm{\&pi;\&Delta;lE}}_c}---\left(12\right);$

In formula: ρ for soil resistivity, I _disfor the earth leakage current of subdivision conductor segment, Δ l is conductor subdivision length, E _cfor the critical breakdown strength of soil, calculate according to formula (13):

E _c＝241ρ ^0.215(13)；

Equivalent redius is adopted to replace conductor radius r, by r=r _eqsubstitute into (b)-(d) and carry out loop iteration, until meet △ r _eqstop iteration during < ε, calculate the node voltage in consideration soil spark discharge situation.Wherein: Δ r _eqbe the equivalent redius difference calculated for twice, ε is iteration error, generally gets 1/10 ~ 1/5 of conductor radius r.According to step (g), calculate the impulse earthed resistance R' considering spark discharge _c.

G), according under the lightning current effect of N order harmonic components, the node voltage Φ under each harmonic component that step (c) ~ (f) is calculated _ncarry out Fast Fourier Transform Inverse (FFTI), obtain time domain interior joint voltage according to standard lightning current I _finjection sequence number i, extract the node voltage at Current injection points place formula (14) is adopted to calculate the impulse earthed resistance of earthing device.

Formula (14) obtains, in formula according to the defined formula (explanation see background technology) of impulse earthed resistance: max (I _std(t)) for injecting the maximal value of the standard lightning current of earthing pole, for the maximal value of Current injection points place response voltage.

H), according to step (a)-(g), the impulse earthed resistance R' not considering spark discharge is calculated respectively _cand consider the impulse earthed resistance R of spark discharge _i; Spark factor alpha is calculated according to formula (15):

$\mathrm{\&alpha;}=\frac{R_i}{R_c^{\&prime;}}---\left(15\right);$

The modification method of earthing device impulse earthed resistance under standard lightning current: adopt the impulse earthed resistance R that spark factor alpha obtains convolutional calculation _crevise, calculate the impulse earthed resistance R under the effect of standard lightning current, computing formula is:

R＝α·R _c(16)；

The in-site measurement of low amplitude value dash current: in-site measurement object is Xianning section ± 800kV DC bipolar transmission line of electricity No. 2125 towers, residing for measuring object, environmental selection wire laying mode is angle-off set, field wiring is carried out according to Fig. 2, electric current pole and voltage pole angle α are 100 degree, and length of arrangement wire is 100m.Portable impact current feedback circuit can produce the dash current of 5A ~ 50A, the wave head time is 3.5 μ s, impulse current generator voltage divider exports with shunting and accesses digital oscilloscope, the waveform that oscillograph recording obtains as shown in Figure 8, wherein: upper figure is that shunt exports, figure below is that voltage divider exports, and the ohmically voltage of 0.2 Ω measured by shunt, and the intrinsic standoff ratio of voltage divider is 88:1.Read the data shown in Fig. 7, calculate virtual voltage and current peak in conjunction with intrinsic standoff ratio and shunt resistance, obtaining impulse earthed resistance is R _ch=5.59 Ω, concrete data are in table 1.

Table 1 earthing device impulse earthed resistance field measurement data

Standard lightning current waveform gets two exponential waves of 2.6/40 μ s, and as Fig. 4, amplitude increases gradually from 10kA to 150kA.

According to convolutional calculation method, by the voltage responsive convolutional calculation under the effect of low amplitude value dash current under standard lightning current, obtain waveform as Fig. 9, the amplitude U of response voltage _m=57.31kV, impulse earthed resistance R _c=5.73 Ω.

Tower grounding device impact characteristics numerical simulation program is adopted to calculate, earthing device size and measurand consistent size: square frame-shaped earthing pole length of side l _a=6m, conductor radius r=0.01m, ray length l _s=6m, buried depth h=0.8m, as Fig. 3, iteration error ε=0.002.Emulation obtains spark coefficient under the different current amplitude of 10 ~ 150kA in " the spark coefficient " in table 2.According to spark leveling factor method, carry out revising later resistance value in " modified value " in table 2 to convolutional calculation value, under different dash current amplitude can be obtained, the impulse earthed resistance of tower grounding device, its scope is in 4.44 ~ 5.45 Ω, and the design of electric power line pole tower lightning protection can be selected according to the lightning withstand level of circuit.

The modified value of earthing device Transient grounding resistance under the different current amplitude of table 2

Claims (4)

1. one kind with the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device, it is characterized in that: utilize portable impact current feedback circuit as signal output source, the dash current that described portable impact current feedback circuit produces is required to meet: amplitude within the scope of 5A ~ 50A, two exponential waves of wave head time 1.0 μ s ~ 5.0 μ s; Survey calculation is carried out according to following steps:

One), the shunting of portable impact current feedback circuit is connected digital oscillographic two autonomous channels respectively with dividing potential drop output terminal, earthing device is arranged with three electrode method metering system, use uninterrupted power source is powered, inject dash current from earthing pole, record the data of response voltage U (t) in dash current I (t) data and earthing pole that impulse current generator produces with oscillographic two autonomous channels of multi-channel digital simultaneously;

Two), set sampling interval Δ t, sample, the sample sequence of standard lightning current is i _std(n), wherein: n=1,2,3 ..., time t meets: t=Δ t × n; One by one convolutional calculation is carried out to the sample sequence of each standard lightning current, obtain the response voltage u after convolutional calculation _std(n); According to the initial impact grounding resistance R that formula (1) calculates under the effect of standard lightning current _c:

Wherein, max (i _std(n)) represent maximal value in standard lightning current sample sequence, max (u _std(n)) represent the response voltage value of corresponding described standard lightning current sample sequence maximal value after convolutional calculation;

Three), calculate the spark factor alpha of earthing device place soil, calculation procedure is as follows:

The earthing device impulse earthed resistance frequency domain value simulation algorithm of Electromagnetic field is adopted to calculate,

A), structure, the dimensional parameters of input grounding pole in impulse earthed resistance Numeral Emulation System, soil parameters, iteration error ε, subdivision is carried out according to conductor subdivision length Δ l, conductor hop count after subdivision is p, node number is q, carries out modeling according to π shape equivalent electrical circuit to the earthing device after subdivision;

B), to standard lightning current I _stdt () carries out Fast Fourier Transform (FFT), Fourier transform sampling period T=300 μ s, harmonic order N=20, obtains the standard lightning current I of N order harmonic components _f, fundamental frequency f ₁=1/T=3333Hz, i.e. first harmonic frequency, the i-th subfrequency f _i=f ₁* i;

C), according to the model of earthing device, the nodal method of analysis is adopted to set up equation as follows:

Wherein: equation (3) is node KCL equation, and wherein A is incidence matrix, I _bthe axial current of subdivision conductor segment, I _dissubdivision conductor segment mid point earth leakage current, I _fit is the standard lightning current injected;

Equation (4) is mid point diffusing equation of constraint over the ground, is obtained, Φ in formula by " model of field " in institute's modeling according to the foundation of Electromagnetic Field theory _disthe mid-point voltage of subdivision conductor segment, Z _disit is diffusing matrix over the ground;

The matrix of diffusing over the ground Z in equation (4) _discalculate according to formula (6):

In formula: L _iand L _jbe i-th section with the length of j section two sections of conductors, r' is the distance between the point on two sections of conductive surfaces, ρ _othe conductivity of soil, ε _rthe specific inductive capacity of soil, ω=2 π * f _i, f _iit is the i-th subfrequency;

The KVL equation of constraint that equation (5) is subdivision conductor segment, is obtained according to Circuit theory foundation by " model on road " in institute's modeling, in formula, and Z _bthe self-impedance matrix of subdivision conductor segment, mutual inductance matrix, A ^tthe transposed matrix of incidence matrix A, Φ _nit is node voltage;

Self-impedance matrix, the mutual inductance matrix Z of subdivision conductor segment in equation (5) _bcalculate according to formula (7):

Wherein: Z _iiand Z _ijfor matrix element, ω=2 π * f _i, z _iifor self-impedance, M _iifor outer self-induction, M _ijfor mutual inductance, z _iicalculate according to formula (8):

Wherein: ω=2 π * f _i, μ _cthe magnetic permeability of conductor, σ _cbe the conductivity of conductor, r is the radius of cylindrical conductor, I ₀and I ₁the first kind zeroth order and single order Bessel function revised respectively;

M _iicalculate according to formula (9):

Wherein: l _othe length of conductor segment, μ ₀it is the magnetic permeability in vacuum;

M _ijcalculate according to formula (10):

Wherein: l _iand l _jbe i-th section with the length of j section two sections of conductors, r' is the distance between the point on two sections of conductive surfaces, μ ₀it is the magnetic permeability in vacuum;

D), according to formula (11) computing node voltage Φ _nwith mid-point voltage Φ _dis:

In formula, the implication of each symbol is the same;

Mid point earth leakage current I is tried to achieve according to equation (4) _dis, try to achieve subdivision conductor segment axial current I according to equation (3) _b;

E) the impulse earthed resistance R' not considering soil spark discharge, is calculated _c: when not considering the spark discharge of soil, the node voltage in soil spark discharge situation is not considered in direct calculating;

F) the impulse earthed resistance R considering soil spark discharge, is calculated _i: when considering the spark discharge of soil, calculate the equivalent redius r of subdivision conductor according to formula (12) _eq:

In formula: ρ is soil resistivity, I _disfor subdivision conductor segment mid point earth leakage current, Δ l is conductor subdivision length, E _cfor the critical breakdown strength of soil,

E _ccalculate according to formula (13):

E _c＝241ρ ^0.215(13)；

Equivalent redius is adopted to replace conductor radius r, by r=r _eqsubstitute into (b)-(d) and carry out loop iteration, until meet △ r _eqstop iteration during < ε, ε is iteration error, calculates the node voltage in consideration soil spark discharge situation; Wherein: Δ r _eqbe the equivalent redius difference calculated for twice, get 1/10 ~ 1/5 of conductor radius r;

G), according under the lightning current effect of N order harmonic components, the node voltage Φ under each harmonic component that step (c) ~ (f) is calculated _ncarry out Fast Fourier Transform Inverse (FFTI), obtain time domain interior joint voltage according to standard lightning current I _finjection sequence number i, extract the node voltage at Current injection points place formula (14) is adopted to calculate the impulse earthed resistance of earthing device:

Formula (14) obtains, in formula according to the defined formula of impulse earthed resistance: max (I _std(t)) for injecting the maximal value of the standard lightning current of earthing pole, for the maximal value of Current injection points place response voltage;

H), according to step (a)-(g), the impulse earthed resistance R' not considering spark discharge is calculated respectively _cand consider the impulse earthed resistance R of spark discharge _i; Spark factor alpha is calculated according to formula (15):

Four), according to calculated spark factor alpha, to the initial impact stake resistance R that convolutional calculation obtains _crevise, calculate the impulse earthed resistance R under the effect of standard lightning current, computing formula is:

R＝α·R _c(2)。

2. according to claim 1 with the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device, it is characterized in that: the step of described convolutional calculation is:

A), network function R (s) of system is: the ratio of image function U (s) of response voltage U (t) of zero condition and image function I (s) of exciting current I (t) in frequency domain, that is:

B), under the effect of standard lightning current, the network function of image function is:

In formula: I _stds () is standard lightning current I _stdthe image function of (t), U _stds () is standard lightning current I _stdthe lower response voltage U of (t) effect _stdthe image function of (t),

For linear time invariant system, network function R (s) of system immobilizes, namely

R(s)＝R _std(s)(18)；

C), calculate convolution, obtain standard lightning current i according to the RESPONSE CALCULATION under driving source different in time domain _stdresponse voltage u under (n) _std(n):

u _std(n)＝u(n)*i _std(n)/i(n)(19)；

In formula, u (n) and i (n) represents voltage and current sample sequence respectively;

Standard lightning current I _stdt () is selected according to electric system lightning Protection Design standard, parameter is: amplitude is determined according to the lightning withstand level of connection electric transmission line, and scope is at 10kA ~ 150kA, and to be the standard lightning current of two exponential waves of 2.6/40 μ s be waveform:

Wherein: T ₁for constant: T ₁=50e ^-6, T ₂for constant: T ₂=1e ^-6, sample according to sampling interval Δ t, its sample sequence is i _std(n), wherein: n=1,2,3 ..., meet t=Δ t × n, obtain standard lightning current i _stdresponse voltage u under (n) _std(n).

3. according to claim 1 with the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device, it is characterized in that: the arrangement that described three electrode method is measured is:

Injection Current forms current return by the current line between earthing pole G and electric current pole C and the earth, and voltage pole P is arranged in zero-potential point, for measuring the response voltage on grounding body, adopts angle wire laying mode: the length d of current line _gCwith the length d of pressure-wire _gPidentical or close, get 3l ~ 10l, l is the diagonal length of earthing device, and current line and pressure-wire are arranged in an angle, and angle is chosen in the scope of 30 ° to 180 °.

4. according to claim 1 with the low amplitude value impulse resistance measuring method of spark coefficient correction tower grounding device, it is characterized in that: the arrangement that described three electrode method is measured is:

Injection Current forms current return by the current line between earthing pole G and electric current pole C and the earth, voltage pole P is arranged in zero-potential point, adopt straight-line method wire laying mode: tested tower grounding pole G, voltage pole P and electric current pole C on the same line, wherein: the length d of current line _gC>=4l, wherein: l is the diagonal length of earthing device, voltage pole is routed in the zero-potential point place between electric current pole and earthing pole, the length d of pressure-wire _gP=0.618d _gCtime voltage pole be positioned at zero-potential point.