CN103901328A - Method suitable for calculating transmission line pole tower grounding body lightning impulse characteristics - Google Patents

Abstract

The invention discloses a method suitable for calculating transmission line pole tower grounding body lightning impulse characteristics. By means of the method, formulas for calculating all basic parameters of a grounding body under the action of a lightning current impulse are determined on the basis of the circuit theory; nonlinear spark discharge is presented through a circuit parameter dynamic change calculation model on the basis of existing formulas and through the combination with the soil spark discharge theory; the calculation thought and method are put forward, and therefore the nonlinear relation between the current of each small section of the grounding conductor in the spark discharge process and the ground resistance, namely, the conductance, of the small section of the grounding conductor in the spark discharge process can be obtained, and the ground resistance is changed instantly according to the current of a branch circuit, and the inductance effect, the spark effect and the lightning current time-varying characteristics are taken into consideration at the same time; meanwhile, the calculation process is simple and visual, workloads are small, parameters can be flexibly changed, and a rapid means is provided for correctly researching the pole tower grounding body lightning impulse characteristics.

Description

A kind of computing method that are applicable to electric power line pole tower grounding body Lightning Characteristic

Technical field

The present invention relates to a kind of computing method that are applicable to electric power line pole tower grounding body Lightning Characteristic, belong to power technology field.

Background technology

Due to high-frequency and the high steepness of lightning current, make inductance important role in impact characteristics of grounding body, stop electric current to flow to a grounding body distant place, make impulse grounding coefficient be greater than 1, i.e. the inductive effect of lightning current; The amplitude of lightning current is very high, and then increase the electric field intensity in soil, in the time that being greater than the tolerance of soil, this electric field intensity just can there is non-linear puncturing, be equivalent to increase the effective dimensions of grounding body, now impulse earthed resistance is less than power frequency earthing resistance, and this feature is called the spark effect of lightning current; When lightning current injects when grounding body, just each branch's bamboo telegraph along grounding body with the form of ripple, in communication process the voltage and current ripple of each point can be with the difference in travel-time difference, i.e. the time-varying characteristics of lightning current.The calculating of grounding body Lightning Characteristic is not considered to inductive effect and spark effect both at home and abroad simultaneously, consider that inductive effect and spark effect can reflect the time-varying characteristics of grounding body impulse earthed resistance simultaneously.

At present mainly contain four about the theoretical system of Lightning Characteristic: Finite Element Method, transmission line theory, Theory of Electromagnetic Field and Circuit theory.Utilize finite element method matheematical equation, can solve engineering problem, but in impact characteristics numerical evaluation, finite element method thinks that the spark discharge of grounding body surrounding soil is uniformly approx, but in fact the power of spark effect is to change with the instantaneous size of dash current.The model of setting up according to transmission line theory and Theory of Electromagnetic Field can be considered the transient state process of impact characteristics, but two kinds of theories are not all considered the spark effect that grounding body presents under dash current; And Circuit theory can be calculated by setting up the model on road the transient characterisitics of grounding body, but need correct theoretical formula to derive, and non-linear spark discharge will be taken into account.

Summary of the invention

The deficiency existing for prior art, the object of the invention is to provide a kind of computing method that are applicable to electric power line pole tower grounding body Lightning Characteristic of simultaneously considering inductive effect and non-linear spark effect, computation process simple, intuitive, workload is little, parameter can change flexibly, for correct research tower grounding body impact characteristics provides quick means.

To achieve these goals, the present invention realizes by the following technical solutions:

Method of the present invention specifically comprises following step:

(1) the spark discharge region under dash current effect by grounding body, is subdivided into the cylindrical of some sections of different sizes; According to the non-homogeneous transmission line theory that damages, set up grounding body basic circuit model, wherein, R _0i, L _i, C _iand G _ibe respectively every section of grounding body self-resistance, inductance, ground capacitance and over the ground electricity lead;

The calculating that electricity is led over the ground of unit length grounding body

$G_0=\frac{2\mathrm{\π}}{\mathrm{\ρ}(\ln \frac{l^2}{2\mathrm{hr}}-0.61)}$

Wherein, h is the buried degree of depth of grounding body; ρ is grounding body soil resistivity around; R is grounding body radius, can be by the equivalent radius r including bloom in the time that flashing discharges _ireplace; L is grounding body length;

(2) calculate each section of columniform grounding body soil be critical around the current density, J while puncturing _cfor:

$J_c=\frac{E_c}{\mathrm{\ρ}}=\frac{i_i}{2\mathrm{\π}{\mathrm{al}}_i}$

Wherein:

E _c=241r ⁰. ²¹⁵

J _ccurrent density while puncturing for soil is critical, E _cfor soil critical breakdown strength, i _ibe the diffusing size of i section, l _ibe i segment length, a is grounding body original radius;

(3) critical current of calculating i section grounding body generation spark discharge is:

$i_c=\frac{482000\mathrm{\π}{\mathrm{al}}_i}{{\mathrm{\ρ}}^{0.785}}$

Work as i _i<i _ctime, not flashing electric discharge; Otherwise, flashing electric discharge;

(4) in the time that flashing discharges, its region of discharge is equivalent to good conductor, the equivalent redius of i section spark discharge is:

$r_i=\frac{{\mathrm{\&rho;i}}_i}{2\mathrm{\&pi;}{l}_i{E}_c}$

In formula, i _ichange along with the variation of time, thus equivalent redius also change along with the variation of time, each section of impulse earthed resistance nature temporal evolution;

(5) while calculating spark discharge, the resistance to earth of each section of grounding body is:

$\begin{array}{c}{R}_i=\frac{1}{G_i}=\frac{1}{l_i{G}_0}\\ =\frac{\mathrm{\&rho;}\left(\mathrm{In}\frac{l^2}{2{\mathrm{hr}}_i}\right)-0.61}{2\mathrm{\&pi;}{l}_i}\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\left(\mathrm{In}\frac{l^2\mathrm{\&pi;}{l}_i{E}_c}{\mathrm{\&rho;}{\mathrm{hi}}_i}\right)-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\left(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}{\mathrm{hi}}_i}\right)-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-{\mathrm{Ini}}_i-0.61]\end{array}$

$=\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-0.61)-\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}\mathrm{In}{i}_i$

If order $\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-0.61),b=\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i},$ :

R _i=1/G _i=a-bIn(i _i)

Electricity is led and is over the ground:

$G_i=\frac{1}{a-\mathrm{bIn}\left(i_i\right)}$

Wherein a, b is the undetermined coefficient that is greater than 0;

Thereby, determine that each section of grounding body is in spark discharge process, electric current and resistance to earth/nonlinear relationship between electric leading over the ground, utilizes this relation can realize the calculating of Lightning Characteristic.

In step (1), grounding body Parameter Calculation formula is as follows:

(1a) calculating of every section of grounding body self-resistance

$R_0=\frac{1}{2\mathrm{\&pi;r}}\sqrt{\frac{\mathrm{\&omega;\&mu;}}{2\mathrm{\&sigma;}}}$

R _oi=R _o*l _i

In formula, R _ofor unit length grounding body self-resistance, σ is the conductivity of grounding body own, the magnetic permeability that μ is grounding body, and ω is dash current equivalence angular frequency;

(2a) calculating of every section of grounding body inductance

$L_0=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}(\ln \frac{2l}{r}-1)$

L _i=L _o*l _i

In formula, L _ofor unit length grounding body inductance, μ ₀for permeability of vacuum;

(3a) calculating of every section of grounding body ground capacitance

C ₀=e ₀e _rrG ₀

C _i=C _o*l _i

In formula, C _ofor unit length grounding body ground capacitance, ε ₀for permittivity of vacuum, ε _rfor soil relative dielectric constant, ε ₀ε _rbe the specific inductive capacity that is filled in grounding body surrounding soil.

The present invention can truly reflect lightning current impact process on grounding body, comprises the time-varying characteristics of inductive effect, spark effect and impact characteristics; Meanwhile, this computation process simple, intuitive, workload is little, and parameter can change flexibly, for correct research tower grounding body impact characteristics provides quick means.

Brief description of the drawings

Fig. 1 is the spark discharge district schematic diagram of single horizontal grounding objects;

Fig. 2 is the isoboles in spark region;

Fig. 3 is the grounding body circuit model of considering transient process;

Fig. 4 is the circuit model of considering inductive effect and non-linear spark discharge.

Embodiment

For technological means, creation characteristic that the present invention is realized, reach object and effect is easy to understand, below in conjunction with embodiment, further set forth the present invention.

1, set up the equivalent-circuit model of non-linear spark discharge

Under lightning current impacts, the electric field intensity producing in soil can be calculated as follows:

E=ρJ （1）

Wherein ρ is the resistivity of soil of contacting with grounding body, and J is the diffusing density in soil.In the time that the field intensity of lightning current generation exceedes the withstand voltage of soil, grounding body soil around can puncture, and produces strong spark discharge, has been equivalent to increase the radius of grounding body, and diffusing effect is strengthened; The equivalent radius of transient state process of grounding body is taken as the equivalent radius at place place of spark discharge district.

The initial electric discharge field intensity of soil E _calong with the increase of soil resistivity increases, its data are well below the breakdown field strength of air.Adopt the initial breakdown field strength of soil of E.E.Oettle proposition and the relation of resistivity:

E _c=241r ⁰. ²¹⁵ （2）

In formula, the unit of Ec is kV/m, and the unit of ρ is Ω m.

The big or small time to time change of dash current causes the severe degree of spark discharge also to change along with the time, and the frequency of lightning current is very high in addition, and therefore conductor induction reactance is very large, hinders electric current wandering to other one end along grounding body.Earial drainage just because of each position along grounding body is inhomogeneous, and the equivalent radius of spark discharge in transient state process is just different, has maximum equivalent radius at grounding body electric current decanting point, along with larger from decanting point distance, equivalent radius is less, and whole breakdown area presents taper, as shown in Figure 1.In order to facilitate the calculating of circuit parameter, cremate district is subdivided into regular small cylindrical, as Fig. 2.In order to improve simulation nicety, segmentation hop count is abundant, and in figure, a is grounding body original radius, r _iit is the equivalent redius of i section.

Have for every a bit of cylindrical grounding body:

$J_c=\frac{E_c}{\mathrm{\&rho;}}=\frac{i_i}{2\mathrm{\&pi;}{\mathrm{al}}_i}---\left(3\right)$

Wherein J _ccurrent density while puncturing for soil is critical, E _cfor soil critical breakdown strength, i _ibe the diffusing size of i section, l _irefer to i segment length.Convolution (6) and (7) are tried to achieve i section grounding body and are produced the critical electric current value of spark discharge and be again:

$i_c=\frac{482000\mathrm{\&pi;}{\mathrm{al}}_i}{{\mathrm{\&rho;}}^{0.785}}$

（4）

Work as i _i<i _ctime, not flashing electric discharge; Otherwise, flashing electric discharge, and the equivalent redius of i section spark discharge is:

$r_i=\frac{{\mathrm{\&rho;i}}_i}{2\mathrm{\&pi;}{l}_i{E}_c}$

Because i _ichange along with the variation of time, thus equivalent redius also change along with the variation of time, impulse earthed resistance nature temporal evolution.

Unit length over the ground electricity is led formula and is:

$G_0=\frac{2\mathrm{\&pi;}}{\mathrm{\&rho;}(\ln \frac{l^2}{2\mathrm{hr}}-0.61)}$

（6）

The resistance to earth that simultaneous formula (2), (3), (5) and (6) can obtain i article of branch road with the variation pass of branch current is:

$\begin{array}{c}{R}_i=\frac{1}{G_i}=\frac{1}{l_i{G}_0}\\ =\frac{\mathrm{\&rho;}\left(\mathrm{In}\frac{l^2}{2{\mathrm{hr}}_i}\right)-0.61}{2\mathrm{\&pi;}{l}_i}\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\left(\mathrm{In}\frac{l^2\mathrm{\&pi;}{l}_i{E}_c}{\mathrm{\&rho;}{\mathrm{hi}}_i}\right)-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\left(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}{\mathrm{hi}}_i}\right)-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-{\mathrm{Ini}}_i-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-0.61)-\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}I{\mathrm{ni}}_i\end{array}$

If order $\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-0.61),b=\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i},$ :

R _i=1/G _i=a-bIn(i _i) （7）

Electricity is led and is over the ground:

$G_i=\frac{1}{a-\mathrm{bIn}\left(i_i\right)}$

Wherein a, b is the undetermined coefficient that is greater than 0; Determine that thus every a bit of earth conductor is in spark discharge process, the nonlinear relationship between this section of electric current and this section of resistance to earth (electricity is led).

In order to realize above nonlinear relationship, just need to calculate in each moment the new equivalent radius of each section of grounding body according to the current value of tried to achieve each node, can make the resistance to earth of this section by program means was a fixed value for this reason before critical current; And reaching critical current back-pushed-type (7) variation, thus be grounded the transient change of electrical resistance branch current, by inductive effect, the time varying characteristic of spark effect and lightning current is taken into account simultaneously.

For example in ATPDraw, introduce MODELS module, as Fig. 4.G in figure _iwith i _ivariation and the moment change, as long as collect i _isize, just can change the size of every section of grounding body resistance to earth, wherein MODELS embeds following program:

MODEL ModelDef

INPUT i1

OUTPUT o1

VAR o1

INIT

o1:=0

ENDINIT

EXEC

if i1>ic then

o1:=a-b*ln(i1)

else o1:=R(0)

endif

ENDEXEC

ENDMODEL

2, set up complete impact characteristics circuit model

As shown in Figure 3, under the effect of dash current, grounding body can be regarded the non-homogeneous transmission line that damages as, and grounding body is divided into a lot of segments, and each section of grounding body can be regarded as by R _0i, L _i, C _iand G _ithe equivalent circuit of composition; If spark effect is taken into account, obtain complete impact characteristics computation model, see Fig. 4.The Parameter Calculation formula of constituent parts length is as follows:

1) calculating of unit length grounding body self-resistance

The size of unit length grounding body resistance depends primarily on size and the conductor resistance rate of itself, with whether have spark effect irrelevant, but because lightning current equivalent frequency is very high, in the time flowing through grounding body, there is obvious skin effect on its surface, now the resistance of grounding body can become greatly, considers that the unit conductor resistance computing formula of lightning current high frequency characteristics has:

$R_0=\frac{1}{2\mathrm{\&pi;r}}\sqrt{\frac{\mathrm{\&omega;\&mu;\&rho;}}{2}}$

In formula, r is grounding body radius; R is the resistivity of metallic conductor own; M is the magnetic permeability of conductor; W is dash current equivalence angular frequency.To general iron and steel grounding body, test real side result between 0.04-0.05 Ω/m.

2) calculating of unit length grounding body inductance

Under lightning current percussive action, the inductance of magnetic linkage and current ratio is no longer a constant, but an amount with wave process dynamic change.In the process of propagating before wave direction, when the initial time that shock wave injects from conductor head end, conductor head end unit length dynamic inductance value is about stablizes 58% of inductance, and in the time that wave head arrives conductor ends, this value is close to 90%, and now dynamic inductance levels off to corresponding stable state inductance.The stable state inductance of unit length grounding body is calculated as follows:

$L_0=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}(\ln \frac{2l}{r}-1)$

3) the unit length grounding body calculating that electricity is led over the ground

Unit length over the ground electricity is led formula and is:

$G_0=\frac{2\mathrm{\&pi;}}{\mathrm{\&rho;}(\ln \frac{l^2}{2\mathrm{hr}}-0.61)}$

Wherein h is the buried degree of depth of grounding body, and ρ is grounding body soil resistivity around; R is grounding body radius, under large electric current, in soil, non-linear puncturing occurs, and considers that the pressure drop in arc discharge area and spark region is very little, and the radius r in this formula must replace with the equivalent radius including bloom.The lightning current instantaneous value that is strongly subject to of spark discharge must affect, so equivalent radius temporal evolution, to lead be also time dependent nonlinear parameter to electricity over the ground.

4) calculating of unit length grounding body ground capacitance

Under power frequency steady-state current, the calculating formula of unit length grounding body ground capacitance is as follows:

C ₀=e ₀e _rrG ₀

In formula, ε ₀for permittivity of vacuum; ε _rfor soil relative dielectric constant; ε ₀ε _rbe and be filled in grounding body

The specific inductive capacity of surrounding soil, general value is 9 × 8.86 × 10 ^-12.

In general soil (m), grounding body size is limited for ρ=10～1000 Ω,

$\frac{\mathrm{\&omega;}{C}_0}{G_0}=2\mathrm{\&pi;f\&epsiv;\&rho;}=\frac{2\mathrm{\&pi;}}{4\&times;2.6\&times;{10}^{-6}}\&times;9\&times;8.86\&times;{10}^{-12}\&times;(10~1000)\&ap;4.8\&times;{10}^{-4}~4.8\&times;{10}^{-2}$

Can be found out G completely by result of calculation ₀effect than C ₀effect much bigger, now can be by C ₀ignore over time.

More than show and described ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; that in above-described embodiment and instructions, describes just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.The claimed scope of the present invention is defined by appending claims and equivalent thereof.

Claims (2)

1. computing method that are applicable to electric power line pole tower grounding body Lightning Characteristic, is characterized in that, specifically comprise following step:

(1) the spark discharge region under dash current effect by grounding body, is subdivided into the cylindrical of some sections of different sizes; According to the non-homogeneous transmission line theory that damages, set up grounding body basic circuit model, wherein, R _0i, L _i, C _iand G _ibe respectively every section of grounding body self-resistance, inductance, ground capacitance and over the ground electricity lead;

The calculating that electricity is led over the ground of unit length grounding body

$G_0=\frac{2\mathrm{\&pi;}}{\mathrm{\&rho;}(\ln \frac{l^2}{2\mathrm{hr}}-0.61)}$

Wherein, h is the buried degree of depth of grounding body; ρ is grounding body soil resistivity around; R is grounding body radius, can be by the equivalent radius r including bloom in the time that flashing discharges _ireplace; L is grounding body length;

(2) current density, J while calculating each section of cylindrical grounding body and critical puncturing occurs in soil around _cfor:

$J_c=\frac{E_c}{\mathrm{\&rho;}}=\frac{i_i}{2\mathrm{\&pi;}{\mathrm{al}}_i}$

Wherein:

E _c=241r ⁰. ²¹⁵

J _ccurrent density while puncturing for soil is critical, E _cfor soil critical breakdown strength, i _ibe the diffusing size of i section, l _ibe i segment length, a is grounding body original radius;

(3) critical current of calculating i section grounding body generation spark discharge is:

$i_c=\frac{482000\mathrm{\&pi;}{\mathrm{al}}_i}{{\mathrm{\&rho;}}^{0.785}}$

Work as i _i<i _ctime, not flashing electric discharge; Otherwise, flashing electric discharge;

(4) in the time that flashing discharges, its region of discharge is equivalent to good conductor, the equivalent redius of i section spark discharge is:

$r_i=\frac{{\mathrm{\&rho;i}}_i}{2\mathrm{\&pi;}{l}_i{E}_c}$

In formula, i _ichange along with the variation of time, thus equivalent redius also change along with the variation of time, each section of impulse earthed resistance nature temporal evolution;

(5) while calculating spark discharge, the resistance to earth of each section of grounding body is:

$\begin{array}{c}{R}_i=\frac{1}{G_i}=\frac{1}{l_i{G}_0}\\ =\frac{\mathrm{\&rho;}\left(\mathrm{In}\frac{l^2}{2{\mathrm{hr}}_i}\right)-0.61}{2\mathrm{\&pi;}{l}_i}\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\left(\mathrm{In}\frac{l^2\mathrm{\&pi;}{l}_i{E}_c}{\mathrm{\&rho;}{\mathrm{hi}}_i}\right)-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\left(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}{\mathrm{hi}}_i}\right)-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}[\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-{\mathrm{Ini}}_i-0.61]\\ =\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-0.61)-\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}I{\mathrm{ni}}_i\end{array}$

If order $\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i}(\mathrm{In}\frac{241\mathrm{\&pi;}{l}^2{l}_i}{{\mathrm{\&rho;}}^{0.785}h}-0.61),b=\frac{\mathrm{\&rho;}}{2\mathrm{\&pi;}{l}_i},$ :

R _i=1/G _i=a-bIn(i _i)

Electricity is led and is over the ground:

$G_i=\frac{1}{a-\mathrm{bIn}\left(i_i\right)}$

Wherein a, b is the undetermined coefficient that is greater than 0;

Thereby, determine that each section of grounding body is in spark discharge process, electric current and resistance to earth/nonlinear relationship between electric leading over the ground, utilizes this relation can realize the calculating of Lightning Characteristic.

2. the computing method that are applicable to electric power line pole tower grounding body Lightning Characteristic according to claim 1, is characterized in that,

In step (1), grounding body Parameter Calculation formula is as follows:

(1a) calculating of every section of grounding body self-resistance

$R_0=\frac{1}{2\mathrm{\&pi;r}}\sqrt{\frac{\mathrm{\&omega;\&mu;}}{2\mathrm{\&sigma;}}}$

R _oi=R _o*l _i

In formula, R _ofor unit length grounding body self-resistance, σ is the conductivity of grounding body own, the magnetic permeability that μ is grounding body, and ω is dash current equivalence angular frequency;

(2a) calculating of every section of grounding body inductance

$L_0=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}(\ln \frac{2l}{r}-1)$

L _i=L _o*l _i

In formula, L _ofor unit length grounding body inductance, μ ₀for permeability of vacuum;

(3a) calculating of every section of grounding body ground capacitance

C ₀=e ₀e _rrG ₀

C _i=C _o*l _i

In formula, C _ofor unit length grounding body ground capacitance, ε ₀for permittivity of vacuum, ε _rfor soil relative dielectric constant, ε ₀ε _rbe the specific inductive capacity that is filled in grounding body surrounding soil.

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