CN103792433A - Measuring method using spark coefficient for correcting low-amplitude value impact resistance of tower grounding device - Google Patents

Abstract

Provided is a measuring method using a spark coefficient for correcting low-amplitude value impact resistance of a tower grounding device. A portable impulse current generator is used as a signal output source, a three-level measuring mode is adopted to arrange the grounding device, an UPS is used for supplying power to inject impulse currents from a grounding electrode, a spark coefficient alpha of soil where the grounding device located is calculated, and initial impulse grounding resistance Rc obtained through convolution calculation is corrected according to the spark coefficient alpha obtained through calculation. According to the measuring method using the spark coefficient for correcting the low-amplitude value impact resistance of the tower grounding device, standard impulse grounding resistance under lightning currents is obtained by adopting the convolution calculation and a spark coefficient modification method, the inductive effect of the grounding device and spark discharge of the soil can be taken into consideration effectively, the corrected impulse grounding resistance is more similar to practical situations when electric transmission lines are struck by lightning. The measuring method using the spark coefficient for correcting the low-amplitude value impact resistance of the tower grounding device solves the problems that only power frequency grounding resistance can be adopted to carry out approximate estimation and field measurement cannot be carried out in the prior art are solved.

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 flowing through in the voltage peak that earthing device bears and earthing device:

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

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

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

In the time carrying out the design of power transmission line lightning shielding protection, generally adopt power frequency earthing resistance to estimate in conjunction with coefficient of impact.But coefficient of impact is theoretical supposition, in different soil environments with the earthing device of different size, coefficient of impact is widely different, thereby the method that this employing power frequency earthing resistance of prior art is estimated can produce very large error, can not meet actual demands of engineering, at present for the blank in the measurement of low amplitude value impulse resistance or the industry of earthing device.

Summary of the invention

Technical matters to be solved by this invention is to fill up the blank of prior art on earthing device impulse resistance is measured, a kind of low amplitude value impulse resistance measuring method with spark coefficient correction tower grounding device is provided, 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.

The described low amplitude value impulse resistance measuring method with spark coefficient correction tower grounding device, it is characterized in that: utilize portable impulse current generator as signal output source, the dash current that described portable impulse current generator 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; Measure calculating according to following steps:

One), the shunting of portable impulse current generator is connected respectively digital oscillographic two autonomous channels with dividing potential drop output terminal, arrange earthing device with three grades of method metering systems, the power supply of use uninterrupted power source, inject dash current from earthing pole, record the data of response voltage U (t) on dash current I (t) data that impulse current generator produces and earthing pole 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 is natural number, time t meets: t=Δ t × n; One by one the sample sequence of each standard lightning current is carried out to convolutional calculation, obtain the response voltage u after convolutional calculation _std(n); Calculate the initial impact grounding resistance R under the effect of standard lightning current according to formula (1) _c:

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

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

Three), calculate the spark factor alpha of earthing device place soil;

Four), according to calculated spark factor alpha, the initial impact stake resistance R that convolutional calculation is obtained _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 a road combination to calculate, and calculation procedure is as follows:

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

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

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

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

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

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

Equation (5) is the KVL equation of constraint of subdivision conductor segment, sets up and obtains according to Circuit theory by " model on road " in institute's modeling, and in formula, Z _bself-impedance matrix, the mutual inductance matrix of subdivision conductor segment, 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):

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

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

Self-impedance matrix Z in equation (5) _bcalculate according to formula (7):

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

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):

$z_{\mathrm{ii}}=\frac{\mathrm{j\&omega;}{\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000468107270000021.png,HDA0000468107270000041.png"\; state="\{\{state\}\}">c</figure-callout>}}}{2\mathrm{\&pi;r}\sqrt{\mathrm{j\&omega;}{\mathrm{\&mu;}}_c{\mathrm{\&sigma;}}_c}}\frac{I_0\left(r\sqrt{\mathrm{j\&omega;}{\mathrm{\&mu;}}_c{\mathrm{\&sigma;}}_c}\right)}{I_1\left(r\sqrt{\mathrm{j\&omega;}{\mathrm{\&mu;}}_c{\mathrm{\&sigma;}}_c}\right)}---\left(8\right);$

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 ₁respectively first kind zeroth order and the single order Bessel function of revising;

M _iicalculate according to formula (9):

$M_{\mathrm{ii}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000468107270000021.png,HDA0000468107270000041.png"\; state="\{\{state\}\}">l</figure-callout>}}{2\mathrm{\&pi;}}(\ln \frac{2l}{r}-1)---\left(9\right);$

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

M _ijcalculate according to formula (10):

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

Wherein: l _iand l _jbe the length of i section and two sections of conductors of j section, 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:

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

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

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

E), calculate the impulse earthed resistance R' that does not consider soil spark discharge _c: in the time not considering the spark discharge of soil, directly the node voltage in soil spark discharge situation is not considered in calculating;

F), calculate the impulse earthed resistance R that considers soil spark discharge _i: in the time considering the spark discharge of soil, calculate the equivalent redius r of subdivision conductor according to formula (12) _eq:

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

In formula: ρ is 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,

E _ccalculate according to formula (13):

E _c=241ρ ^0.215 (13)；

Adopt equivalent redius to replace conductor radius r, by r=r _eqsubstitution (a)-(d) carry out loop iteration, until meet Δ r _eqwhen < ε, stop iteration, ε is iteration error, calculates the node voltage of considering in soil spark discharge situation; Wherein: Δ r _eqbe the equivalent redius difference calculating for twice, get 1/10～1/5 of conductor radius r;

G), according under the lightning current effect of N order harmonic components, to the node voltage Φ under each harmonic component of step (c)～(f) calculate _ncarry out Fast Fourier Transform Inverse (FFTI), obtain node voltage in time domain

according to standard lightning current I _finjection sequence number i, extract the node voltage at electric current decanting point place

adopt formula (14) to calculate the impulse earthed resistance of earthing device:

Formula (14) obtains according to the defined formula of impulse earthed resistance, in formula: max (I _std(t)) be the maximal value of injecting the standard lightning current of earthing pole,

for the maximal value of electric current decanting point place response voltage;

H), according to step (a)-(g), the impulse earthed resistance R' of spark discharge is not considered in calculating respectively _cand the impulse earthed resistance R of consideration spark discharge _i; Calculate spark factor alpha according to formula (15):

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

The step of described convolutional calculation is:

1. the network function R (s) of system is: the ratio of the image function U (s) of the response voltage U (t) of zero condition and the 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:

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

In formula: I _std(s) be standard lightning current I _std(t) image function, U _std(s) be standard lightning current I _std(t) the lower response voltage U of effect _std(t) image function,

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

R(s)=R _std(s) (18)；

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

u _std（n）=u（n）*i _std（n）/i（n） (19)；

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

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

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

The arrangement that described three grades of methods are measured is:

Injection Current forms current return by the electric current line between earthing pole G and electric current utmost point 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 electric current line _gClength d with pressure-wire _gPidentical or close, get 3l～10l, the diagonal angle length that l is earthing device, electric current line and pressure-wire arrange in an angle, angle is chosen in the scope of 30 ° to 180 °.

Or the arrangement that adopts three grades of methods to measure is:

Injection Current forms current return by the electric current line between earthing pole G and electric current utmost point C and the earth, voltage pole P is arranged in zero-potential point, adopt straight-line method wire laying mode: tested tower grounding body G, voltage pole P and electric current utmost point C are on same straight line, wherein: the length d of electric current line _gC>=4l, voltage pole is routed in the zero-potential point place between the electric current utmost point 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 flashing electric discharge, arc channel has been accelerated releasing of lightning current, makes the impulse earthed resistance under lightning current will be 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, exist error larger, there is no the problem of general formula.The present invention proposes to carry out on the basis of in-site measurement at low amplitude value impulse current generator, adopt convolutional calculation and spark leveling factor method to obtain the impulse earthed resistance under standard lightning current, can effectively consider the inductive effect of earthing device and the spark discharge of soil, revised impulse earthed resistance approaches the actual conditions that transmission line of electricity is struck by lightning more.The method has solved prior art and 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 power frequency earthing resistance adopts straight-line method to connect up at present, according to Theory of Electromagnetic Field, zero-potential point is chosen in 0.618 place, but under dash current effect, can the position of the zero-potential point adopt straight line wiring, the wiring of employing straight line time, do not have correlative study and test figure.The present invention is according to simulation and experimental study, determine in the time that low amplitude value is measured impulse earthed resistance, because soil does not have flashing electric 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 the electric current utmost point, i.e. d _gP=0.618d _gC, while having solved in-site measurement earthing device impulse earthed resistance, can adopt straight-line method to connect up, and determine zero potential actual measurement of engineering to be had to 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 earthing device structure and diagonal angle length schematic diagram;

In figure, l _afor the length of side of earthing device, l _sfor the ray length of earthing device, the diagonal angle length that l is 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 self-impedance, the transimpedance of conductor segment; 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 and the conductor segment of conductor segment; Electric current decanting point 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 electric current decanting point 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 electric current decanting point place;

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

Embodiment

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

As shown in Fig. 1-9, the excitation of described measuring method is provided by portable impulse current generator, and the dash current of its generation 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, is connected respectively to the shunting of impulse current generator and dividing potential drop output terminal the passage 1 and passage 2 of digital oscilloscope by concentric cable.

The impulse earthed resistance measuring method of little electric current adopts three electrode method to measure, as Fig. 1, shown in Fig. 2, be that electric current line and the earth that Injection Current passes through between earthing pole G and electric current utmost point C forms current return, 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, the data of response voltage U (t) on the dash current I (t) that oscillograph recording impulse current generator produces and grounding body, according to sampling interval Δ, t samples, 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, three electrode method can be selected angle wiring and straight line wiring:

A) angle cabling requirement: the length d of electric current line _gClength d with pressure-wire _gPlength is identical or close, generally gets 4l～5l, and the diagonal angle length that l is earthing device, is shown in Fig. 3, the words d of conditions permit _gCand d _gPcan get 10l.Electric current line and pressure-wire arrange 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 body G, voltage pole P and electric current utmost point C, on same straight line, are shown in Fig. 1, wherein: d _gC>=4l, voltage pole is routed in the zero-potential point place between the electric current utmost point and earthing pole, according to numerical simulation and experimental study, meets d _gP=0.618d _gCtime voltage pole be positioned at zero-potential point.

Due to the inductive effect of earthing device, the response voltage under small magnitude dash current need to be converted under standard lightning current.Owing to injecting, dash current amplitude is less, and nonlinear ionization does not occur soil, and the shock response of earthing device belongs to linear time invariant system, can adopt convolutional calculation method 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. the network function R (s) of define system is: the ratio of the image function U (s) of the response voltage U (t) of zero condition and the 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 _std(t) the response voltage U under effect _std(t), image function is I _stdand U (s) _std(s) its network function R _std(s) ask for according to formula (1),

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

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

R(s)=R _std(s) (18)；

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

u _std（n）=u（n）*i _std（n）/i（n） (19)；

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

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

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

Due to the determined standard lightning current of lightning withstand level of transmission line of electricity, its amplitude is very large, earthing device is flowing through after very large lightning current, soil can ionize, need to adopt spark coefficient to revise, the earthing device impulse earthed resistance frequency domain value simulation algorithm of spark coefficients by using field road combination calculates, 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.According to conductor subdivision length Δ, l carries out subdivision, and the conductor hop count after subdivision is p, and node number is q, according to π shape equivalent electrical circuit, as Fig. 5, the earthing device after subdivision is carried out to modeling;

B), to standard lightning current I _std(t) carry out Fast Fourier Transform (FFT), standard lightning current is as Fig. 4, Fourier transform sampling period T=300 μ s, and harmonic wave order N=20, obtains N order harmonic components I _f, fundamental frequency f ₁=1/T=3333Hz, i.e. first harmonic frequency, i 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:

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

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 mid point node earth leakage current, is amount to be asked, I _fbeing the standard lightning current injecting, is known driving source;

Equation (4) is mid point diffusing equation of constraint over the ground, and as outer in Fig. 6 dotted line frame " model of field ", obtains according to theoretical foundation of Electromagnetic Field.Z _disfor subdivision conductor segment self-impedance and the mutual resistance matrix of diffusing 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):

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

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

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

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

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:

$z_{\mathrm{ii}}=\frac{\mathrm{j\&omega;}{\mathrm{\&mu;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000468107270000021.png,HDA0000468107270000041.png"\; state="\{\{state\}\}">c</figure-callout>}}}{2\mathrm{\&pi;r}\sqrt{\mathrm{j\&omega;}{\mathrm{\&mu;}}_c{\mathrm{\&sigma;}}_c}}\frac{I_0\left(r\sqrt{\mathrm{j\&omega;}{\mathrm{\&mu;}}_c{\mathrm{\&sigma;}}_c}\right)}{I_1\left(r\sqrt{\mathrm{j\&omega;}{\mathrm{\&mu;}}_c{\mathrm{\&sigma;}}_c}\right)}---\left(8\right);$

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 ₁respectively first kind zeroth order and the single order Bessel function of revising.

$M_{\mathrm{ii}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000468107270000021.png,HDA0000468107270000041.png"\; state="\{\{state\}\}">l</figure-callout>}}{2\mathrm{\&pi;}}(\ln \frac{2l}{r}-1)---\left(9\right);$

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

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

Wherein: l _iand l _jbe the length of i section and two sections of conductors of j section, 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:

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

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

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

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

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

In formula: ρ is 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)；

Adopt equivalent redius to replace conductor radius r, by r=r _eqsubstitution (b)-(d) carry out loop iteration, until meet Δ r _eqwhen < ε, stop iteration, calculate the node voltage of considering in soil spark discharge situation.Wherein: Δ r _eqbe the equivalent redius difference calculating 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' that considers spark discharge _c.

G), according under the lightning current effect of N order harmonic components, to the node voltage Φ under each harmonic component of step (c)～(f) calculate _ncarry out Fast Fourier Transform Inverse (FFTI), obtain node voltage in time domain

according to standard lightning current I _finjection sequence number i, extract the node voltage at electric current decanting point place

adopt formula (14) to calculate the impulse earthed resistance of earthing device.

Formula (14) obtains according to the defined formula (seeing the explanation of background technology) of impulse earthed resistance, in formula: max (I _std(t)) be the maximal value of injecting the standard lightning current of earthing pole,

for the maximal value of electric current decanting point place response voltage.

H), according to step (a)-(g), the impulse earthed resistance R' of spark discharge is not considered in calculating respectively _cand the impulse earthed resistance R of consideration spark discharge _i; Calculate spark factor alpha 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: the impulse earthed resistance R that adopts spark factor alpha to obtain 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 No. 2125 towers of Xianning section ± 800kV DC bipolar transmission line of electricity, be angle-off set according to measuring object environmental selection wire laying mode of living in, carry out field wiring according to Fig. 2, the electric current utmost point and voltage pole angle α are 100 degree, and length of arrangement wire is 100m.Portable impulse current generator can produce the dash current of 5A～50A, the wave head time is 3.5 μ s, impulse current generator voltage divider and shunting output access digital oscilloscope, the waveform that oscillograph recording obtains as shown in Figure 8, wherein: upper figure is shunt output, figure below is voltage divider output, and shunt is measured the ohmically voltage of 0.2 Ω, 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 in-site measurement data

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

Adopt tower grounding device impact characteristics numerical simulation program 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 amplitudes of 10～150kA in " spark coefficient " in table 2.According to spark leveling factor method, convolutional calculation value is revised to later resistance value in " modified value " in table 2, can obtain under different dash current amplitudes, 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 impulse grounding impedance under the different current amplitudes of table 2

Claims (4)

1. the low amplitude value impulse resistance measuring method with spark coefficient correction tower grounding device, it is characterized in that: utilize portable impulse current generator as signal output source, the dash current that described portable impulse current generator 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; Measure calculating according to following steps:

One), the shunting of portable impulse current generator is connected respectively digital oscillographic two autonomous channels with dividing potential drop output terminal, arrange earthing device with three grades of method metering systems, the power supply of use uninterrupted power source, inject dash current from earthing pole, record the data of response voltage U (t) on dash current I (t) data that impulse current generator produces and earthing pole 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 is natural number, time t meets: t=Δ t × n; One by one the sample sequence of each standard lightning current is carried out to convolutional calculation, obtain the response voltage u after convolutional calculation _std(n); Calculate the initial impact grounding resistance R under the effect of standard lightning current according to formula (1) _c:

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

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

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

Adopt the earthing device impulse earthed resistance frequency domain value simulation algorithm of a road combination to calculate:

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

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

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

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

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

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

Equation (5) is the KVL equation of constraint of subdivision conductor segment, sets up and obtains according to Circuit theory by " model on road " in institute's modeling, and in formula, Z _bself-impedance matrix, the mutual inductance matrix of subdivision conductor segment, 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):

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

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

Self-impedance matrix Z in equation (5) _bcalculate according to formula (7):

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

Wherein: Z _iiand Zi _jfor 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):

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

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 ₁respectively first kind zeroth order and the single order Bessel function of revising;

M _iicalculate according to formula (9):

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

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

M _ijcalculate according to formula (10):

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

Wherein: l _iand l _jbe the length of i section and two sections of conductors of j section, 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:

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

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

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

E), calculate the impulse earthed resistance R' that does not consider soil spark discharge _c: in the time not considering the spark discharge of soil, directly the node voltage in soil spark discharge situation is not considered in calculating;

F), calculate the impulse earthed resistance R that considers soil spark discharge _i: in the time considering the spark discharge of soil, calculate the equivalent redius r of subdivision conductor according to formula (12) _eq:

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

In formula: ρ is 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,

E _ccalculate according to formula (13):

E _c=241ρ ^0.215 (13)；

Adopt equivalent redius to replace conductor radius r, by r=r _eqsubstitution (b)-(d) carry out loop iteration, until meet Δ r _eqwhen < ε, stop iteration, ε is iteration error, calculates the node voltage of considering in soil spark discharge situation; Wherein: Δ r _eqbe the equivalent redius difference calculating for twice, get 1/10～1/5 of conductor radius r;

G), according under the lightning current effect of N order harmonic components, to the node voltage Φ under each harmonic component of step (c)～(f) calculate _ncarry out Fast Fourier Transform Inverse (FFTI), obtain node voltage in time domain

according to standard lightning current I _finjection sequence number i, extract the node voltage at electric current decanting point place

adopt formula (14) to calculate the impulse earthed resistance of earthing device:

Formula (14) obtains according to the defined formula of impulse earthed resistance, in formula: max (I _std(t)) be the maximal value of injecting the standard lightning current of earthing pole,

for the maximal value of electric current decanting point place response voltage;

H), according to step (a)-(g), the impulse earthed resistance R' of spark discharge is not considered in calculating respectively _cand the impulse earthed resistance R of consideration spark discharge _i; Calculate spark factor alpha according to formula (15):

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

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

R=α·R _c （2）。

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

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

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

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

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

In formula: I _std(s) be standard lightning current I _std(t) image function, U _std(s) be standard lightning current I _std(t) the lower response voltage U of effect _std(t) image function,

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

R(s)=R _std(s) (18)；

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

u _std(n)=u(n)*i _std(n)/i(n) (19)；

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

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

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

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

Injection Current forms current return by the electric current line between earthing pole G and electric current utmost point 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 electric current line _gClength d with pressure-wire _gPidentical or close, get 3l～10l, the diagonal angle length that l is earthing device, electric current line and pressure-wire arrange in an angle, angle is chosen in the scope of 30 ° to 180 °.

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

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

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