CN105486929A - Impulse grounding resistance calculation method considering spark discharge effect - Google Patents

Impulse grounding resistance calculation method considering spark discharge effect Download PDF

Info

Publication number
CN105486929A
CN105486929A CN201410483980.5A CN201410483980A CN105486929A CN 105486929 A CN105486929 A CN 105486929A CN 201410483980 A CN201410483980 A CN 201410483980A CN 105486929 A CN105486929 A CN 105486929A
Authority
CN
China
Prior art keywords
conductor
node
conductor segment
resistance
current
Prior art date
Application number
CN201410483980.5A
Other languages
Chinese (zh)
Inventor
吴锦鹏
张波
段舒宁
Original Assignee
国家电网公司
中国电力科学研究院
国网山东省电力公司
清华大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 国家电网公司, 中国电力科学研究院, 国网山东省电力公司, 清华大学 filed Critical 国家电网公司
Priority to CN201410483980.5A priority Critical patent/CN105486929A/en
Publication of CN105486929A publication Critical patent/CN105486929A/en

Links

Abstract

The invention relates to an impulse grounding resistance calculation method considering a spark discharge effect. The method comprises the following steps: respectively determining relations among leakage current, axial current, and node potential of a grounding body conductor; determining the leakage current, axial current, and node potential of the grounding body conductor; determining an equivalent radius of a grounding body conductor segment; determining axial resistance, self-inductance, and frequency-dependent property of the grounding body conductor; determining self-resistance of the grounding body conductor over ground, mutual resistance among conductors, and time-variant characteristic; and determining the relation of the leakage current of the node of the grounding body conductor and the equivalent radius of the conductor segment. An analytical method of combining an electromagnetic field with a circuit is used, an electromagnetic field method is used to solve conductor parameters, and a circuit method is used to solve transient response. The method can adapt to grounding bodies in complex shapes, and can give comprehensive consideration to conditions which may occur in spark discharge effect, inductive effect, potential shielding effect, and other impulse heavy current conditions. Compared with a conventional calculation method, the method is closer to volt-ampere characteristics of a grounding device under an impact condition.

Description

A kind of impulse earthed resistance computing method considering spark discharge effect
Technical field:
The present invention relates to a kind of impulse earthed resistance computing method, more specifically relate to a kind of impulse earthed resistance computing method considering spark discharge effect.
Background technology:
Ground connection being of electric system is directly connected to the major issue of the person, equipment and security of system.The accuracy that Resistance of Grounding Grids is measured is directly connected to and correctly judges whether the construction quality of grounded screen and operating grounded screen conform with construction quality requirement.
Solve in the method for impulse earthed resistance resistance in tradition, transmission line method is when solving horizontal grounding conductor transient characterisitics, better effects can be obtained, but for the grounding body that the shapes such as tower grounding device are more complicated, or vertical grounding electrode, transmission line method solves transient characterisitics certain difficulty.
And electromagnetic method generally all needs to carry out subdivision to conductor region, computing velocity is slow, and algorithm also may not be restrained.If employing Finite Difference Time Domain, then to labyrinth conductor dyscalculia; If adopt finite element scheduling algorithm, then need time domain lightning current first to transform to frequency domain, after each frequency tries to achieve transient response in inverse fourier transform to frequency domain, not only computing velocity is slowly, but also has end reforming phenomena.At consideration time-varying characteristics, such as also there is very large difficulty during spark discharge in electromagnetic method.
Therefore propose a kind ofly to consider that the impulse earthed resistance computing method of spark discharge effect are to overcome above-mentioned shortcoming.
Summary of the invention:
The object of this invention is to provide a kind of impulse earthed resistance computing method considering spark discharge effect, the method can adapt to the grounding body of complicated shape, more close to the volt-ampere characteristic of earthing device under impact conditions.
For achieving the above object, the present invention is by the following technical solutions: a kind of impulse earthed resistance computing method considering spark discharge effect, comprise the following steps:
(1) leakage current of grounding body conductor, axial current and node potential relation is each other determined respectively;
(2) leakage current of described grounding body conductor, axial current and node potential is determined;
(3) grounding body conductor segment equivalent redius is determined;
(4) the axial resistance of grounding body conductor, self-induction and frequency dependent characteristic is determined;
(5) mutual resistance and time-varying characteristics between the self-resistance over the ground of grounding body conductor, conductor are determined;
(6) relation of grounding body conductor node Leakage Current and conductor segment equivalent redius is determined.
A kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, the leakage current in described step (1) and the relation between axial current are determined by following formula:
A n × b I b a + E n × n I n l = I n f
In formula, b is the number of conductor segment, is also branch road number, and n is node number, the axial current of branch road or conductor segment, the leakage current of each node, the Injection Current of each node, A n × bthe incidence matrix between node and branch road, E n × nit is unit matrix.
A kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, the leakage current in described step (1) and the relation between node potential are determined by following formula:
Φ n = Z n × n m I n l
In formula, Φ neach node potential, the mutual resistance capacitive reactance between each conductor segment, for the leakage current of each node.
Another preferred a kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, the axial current in described step (1) and the relation between node potential are determined by following formula:
A n × b T Φ n = Z n × n m I n l
In formula, for being the incidence matrix between node and branch road, Φ nfor each node potential, the mutual resistance capacitive reactance between each conductor segment, for the leakage current of each node.
The preferred a kind of impulse earthed resistance computing method considering spark discharge effect more provided by the invention, the leakage current of described step (2), axial current and node potential are determined by the relational expression in step described in simultaneous (1), are:
A n × b E n × n 0 n × n 0 n × n Z n × n m - E n × n Z b × b a 0 b × n - ( A n × b ) T I b a I n l Φ n = I n f 0 0 .
Another preferred a kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, the conductor segment equivalent redius in described step (3) is by the leakage current of every strip conductor section in t determine; Described leakage current determined by following formula:
I b l ( t ) = N n × b T · I n l ( t )
In formula, N n × bfor weight coefficient matrix, i.e. the relational matrix of node and conductor segment; for the node Leakage Current of branch road;
Suppose the length of the leakage current of certain node according to connected conductor segment, be uniformly distributed in the conductor segment that is connected with this node, then described weight coefficient matrix N n × bfor:
In formula, l ijfor the length of the conductor segment that this node is connected, L kfor the length of kth bar branch road, q is the branch road number associated with node i, L pfor the length of branch road p associated with node i.
Another preferred a kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, the axial resistance of the grounding body conductor in described step (4) is by the self-impedance Z of each conductor segment of each moment cconversion is determined; Described self-impedance Z cdetermined by following formula:
Z c = jω μ c 2 πa jω σ c μ c · I 0 ( a jω σ c μ c ) I 1 ( a jω σ c μ c )
In formula, σ cand μ cbe respectively conductivity and the magnetic permeability of conductor material therefor, a is the equivalent redius of cylindrical conductor, I 0and I 1be respectively first kind zeroth order and the first-order bessel function of correction;
The self-induction L of described grounding body conductor is determined by following formula:
L=L e+L c
In formula, L efor the outer self-induction of cylindrical conductor section, L cfor the self-inductance of conductor segment everywhere;
Described self-inductance L cby the self-impedance Z of each conductor segment of each moment cconversion is determined; Described outer self-induction L edetermined by following formula:
L e = μ 4 π ∫ l ∫ l ′ 1 r dl ′ dl ≈ μ 4 π ( ln l a - 1 )
In formula, μ is the magnetic permeability of conductor material, l and l' is the path being in conductor segment axis He being in conductor segment surface respectively, and r is the distance of source point and field point;
The frequency dependent characteristic of described grounding body conductor is determined by following formula:
w = arccos ( I light ( t - Δt ) + I light ( t + Δt ) 2 × I li ght ( t ) )
In formula, w is cosine wave frequency, is also the equivalent frequency of t lightning current; I light(t-Δ t), I light(t) what I light(t+ Δ t) is respectively three thunder and lightning flow valuves in t-Δ t, t and t+ Δ t, and regards the value in 0 moment on cosine alternating current respectively as;
No matter how frequency and initial phase change, as long as curve average is 0, the equivalent frequency in each moment accurately can be calculated; If the average of curve is not 0, then equivalent frequency is just no longer stabilized in a frequency.
Another preferred a kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, the self-resistance over the ground of described step (5) grounding body conductor is determined by following formula:
When the vertical buried depth of grounding body is in h soil, described self-resistance is over the ground:
R = ρ 2 πl [ ln 2 l a - 1 + 1 2 ln 2 h + 3 2 l + ( 2 h + 3 2 l ) 2 + a 2 2 h + 1 2 l + ( 2 h + 1 2 l ) 2 + a 2 ]
When the horizontal buried depth of grounding body is in h soil, described self-resistance is over the ground:
R = ρ 2 πl [ 2 h + a l + ln l + l 2 + a 2 a - 1 + ( a l ) 2 + ln l + l 2 + 4 h 2 2 h - 1 + ( 2 h l ) 2 ]
In formula, ρ is soil resistivity, and l is conductor segment length, and h is the buried depth of grounding body vertically in soil, and a is the equivalent redius after spark discharge;
Between the conductor of described grounding body conductor, mutual resistance is determined by following formula:
R ij = ρ 4 π · 1 l i l j · ( ∫ l i ∫ l j 1 D ij dl j dl i + ∫ l i ′ ∫ l j 1 D i ′ j dl j dl i ′ )
In formula, l irepresent the path of integration of i-th conductor segment, l jrepresent the path of integration of jth root conductor segment, l i' represent the path of integration of i-th conductor segment mirror image in atmosphere, D ijrepresent the segment dl respectively on conductor segment i and conductor segment j two path of integration iand dl jbetween distance, D i'jrepresent the segment dl respectively in the air of conductor segment i on mirror image and conductor segment j two path of integration i' and dl jbetween distance;
Under lightning current effect, flashing electric discharge around conductor, the equivalent redius a being equivalent to conductor increases, therefore, in conductor section over the ground between self-resistance and conductor segment when mutual resistance, need to determine according to described equivalent redius a; Because equivalent redius a is time-varying parameter, the mutual resistance over the ground between self-impedance and conductor of conductor is also time-varying parameter.
Another preferred a kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, the Leakage Current of the node i in described step (6) in conductor segment (k) +the current potential of upper generation for:
φ ( k ) + = R ( k - 2 ) - , ( k ) + mc R ( k - 1 ) - , ( k ) + mc R ( k ) - , ( k ) + mc T · I ( k - 2 ) - n I ( k - 1 ) + n I ( k ) - n = R ( k - 2 ) - , ( k ) + mc R ( k - 1 ) - , ( k ) + mc R ( k ) - , ( k ) + mc T · L k - 2 L k - 2 + L k - 1 + L k L k - 1 L k - 2 + L k - 1 + L k L k L k - 2 + L k - 1 + L k · I i l
with be respectively the conductor segment be connected in node i to have in kth-2, k-1 and k section (k-2) -, (k-1) +(k) -duan Yu (k) +mutual resistance between section; L k-2, L k-1, L kthe length of the conductor segment be connected with node i; with the electric current that the conductor segment be connected in node i has kth-2, k-1 and k section is revealed respectively; Half section that in conductor segment, branch current points to is "+", and half section that leaves is "-";
The voltage of described node j be multiplied by corresponding conductor length weight according to the length of connected conductor segment to determine:
φ j = L k L k + L k + 1 + L k + 2 L k + 1 L k + L k + 1 + L k + 2 L k + 2 L k + L k + 1 + L k + 2 T · φ ( k ) + φ ( k + 1 ) + φ ( k + 2 ) -
Wherein, with be respectively (k-2) -, (k-1) +(k) -current potential in section;
For whole grounding body, each node potential Φ nmatrix form be:
Φ n = ( N n × 2 b · R 2 b × 2 b mc · N n × 2 b T ) · I n l
Wherein, for the node Leakage Current of branch road; for the mutual resistance matrix between conductor segment, represent after all former conductor segment are divided into two from mid point, the mutual resistance between all new conductor segment; N n × 2bfor weight coefficient matrix, i.e. the relational matrix of node and new conductor segment;
Then internodal mutual resistance matrix, namely impulse earthed resistance is:
R n × n m = N n × 2 b · R 2 b × 2 b mc · N n × 2 b T
Due to conductor segment mutual resistance matrix change along with conductor equivalent redius, and conductor equivalent redius is relevant with amplitude of lightning current and time, therefore impulse earthed resistance also be time dependent.
Another preferred a kind of impulse earthed resistance computing method considering spark discharge effect provided by the invention, due to described in determining over the ground self-impedance time use equivalent redius, then when determining conductor self and radial mutual resistance, current source is assumed to be electric line source, but affected point can not be equivalent to a line again, and be a face of cylinder, after mutual resistance is tried to achieve to each point on this face of cylinder, then to the mutual resistance that whole Line Integral obtains between two conductors be:
R ij = ρ 4 π · 1 l i l j · ( ∫ l i ∫ ∫ S j 1 D ij d S j dl i + ∫ l i ′ ∫ ∫ S j 1 D ij d S j dl i ′ )
Wherein, S jfor the equivalent cross-section of jth root conductor segment.
With immediate prior art ratio, the invention provides technical scheme and there is following excellent effect
1, the present invention adopts the analytic approach that electromagnetic field is combined with circuit, solves conductor parameter, solve transient response with circuit methods with electromagnetic method, can adapt to the grounding body of complicated shape;
2, the present invention considers issuable situation in the heavy impulse current situations such as spark discharge effect, inductive effect, potential screen effect, compares traditional computing method more close to the volt-ampere characteristic of earthing device under impact conditions;
3, the present invention can measure impulse earthed resistance resistance by efficiently and accurately;
4, method computing velocity of the present invention is fast, uncomplicated and without reforming phenomena;
5, the present invention correctly judges whether the construction quality of grounded screen and operating grounded screen conform with construction quality and require to lay a good foundation.
Accompanying drawing explanation
Fig. 1 is the inventive method process flow diagram;
Fig. 2 is conductor node leakage current of the present invention and axial current;
Fig. 3 is the circular rod electrode in infinitely great homogeneous medium of the present invention;
Fig. 4 is transimpedance between solution node of the present invention.
Embodiment
Below in conjunction with embodiment, the invention will be described in further detail.
Embodiment 1:
As Figure 1-4, the inventive method of this example comprises the following steps:
Relation between 1 leakage current and axial current
For the grounding body structure of complexity, Nodes meets Kirchhoff's current law (KCL)---and the inflow current total amount of a node equals to flow out electric current total amount.The electric current flowed in whole conductor and peripheral region is illustrated in fig. 2 shown below.
If represent the leakage current in node i; represent from node i to node j axial current, have between node i to node j and only have a conductor segment they to be associated; the Injection Current of each node i, I on lightning current decanting point fequal the lightning current injected, I on non-Current injection points fbe zero.
According to KCL equation, their relation can be listed for node i:
I i l - I i - 1 , i a + I i , i + 1 a + I i , i + 2 a = I i f - - - ( 1 )
Wherein, for the axial current from node i-1 to node i, for the axial current from node i to node i between+1 and for the axial current from node i to node i between+2.
For whole grounding body, the relation matrix representation of all conductor segment axial currents and node leakage current, Injection Current is:
A n × b I b a + E n × n I n l = I n f - - - ( 2 )
In formula, b is the number of conductor segment, is also branch road number, and n is node number, branch current, the leakage current of each node, the Injection Current of each node, A n × bthe incidence matrix between node and branch road, E n × nit is unit matrix.
Relation between leakage current and node potential
Node potential on conductor and also there is the relation of mutual resistance between leakage current.When each conductor segment is to its surrounding diffusing, due to the existence of the mutual resistance between self-resistance and conductor segment, self with the outside surface of other conductor segment on all can produce the rising of current potential.Because the leakage current of all nodes has contribution, then node i outside surface current potential φ for the outside surface current potential of conductor residing for node i i' equal:
φ i ′ = Σ j = 1 n Z j , i m I j l - - - ( 3 )
In formula, for the leakage current on node j; As j=i, for the self-impedance of node i infinite point over the ground, as j ≠ i, for node j is for the transimpedance of node i.
According to gauss flux theorem, the current potential φ of conductor segment inside surface iequal the current potential φ of conductor segment outside surface i'.Because the resistivity of conductor is very little, so the voltage drop of the Leakage Current of Nodes on cross-sectional area of conductor is very little, therefore can be similar to and think that the node of conductor segment junction is an equipotential surface, the current potential of conductor outside surfaces just equals the current potential at kernel of section place.The current potential of node cross-section center equals:
φ i = Σ j = 1 n Z j , i m I j l - - - ( 4 )
For whole grounding body, being write as matrix form is:
Φ n = Z n × n m I n l - - - ( 5 )
In formula, Φ neach node potential, it is the mutual resistance capacitive reactance between each conductor segment. for the leakage current of each node.
The conductor of specifying Nodes is an equipotential surface, and conductor outside surfaces current potential equals conductor central potential is very important.Because when considering spark discharge effect, the equivalent redius of conductor can expand a lot, the distance of shaft centers of conductor is no longer the distance of the mm magnitude of conductor metal radius from the border of discharging, and tens cm may be expanded to, if now do not suppose that conductors cross is equipotential surface, then solve in conductor segment mutual resistance process can exist " two conductor distance " be distance region of discharge boundary or distance conductor axle center place difference.Therefore, after this specify that the position of node potential, the position at center just in calculating afterwards, is only considered.Otherwise after also needing to try to achieve mutual resistance to outside surface each point, line integral goes out overall mutual resistance again, adds the difficulty of calculating.
Relation between axial current and node potential
The model of grounding body of the present invention is not equipotential model, and the current potential namely between each node not etc., does not need self-impedance and the mutual inductance of considering conductor, can obtain the voltage drop on conductor segment k according to Ohm law with the relation of axial current:
U k a = Σ p = 1 b Z p , k a I p a - - - ( 6 )
In formula, it is the axial current of p article of branch road; As p=k, for the self-impedance on kth bar branch road, as p ≠ k, for the mutual inductance between k, p two branch roads resists.
For whole grounding body, being write as matrix form is:
U b a = Z b × b a I b a - - - ( 7 )
In formula, it is the axial impedance induction reactance matrix of conductor segment branch road.
Again due to each node potential Φ nwith each conductor segment voltage drop between there is relation:
U b a = A n × b T Φ n - - - ( 8 )
So known:
A n × b T Φ n = Z n × n m I n l - - - ( 9 )
Wherein, for the incidence matrix between node and branch road.
2 determine the leakage current of described grounding body conductor, axial current and node potential by solving equation in time domain
Simultaneous formula (2), formula (5) and formula (9), obtain:
A n × b E n × n 0 n × n 0 n × n Z n × n m - E n × n Z b × b a 0 b × n - ( A n × b ) T I b a I n l Φ n = I n f 0 0 - - - ( 10 )
First equation is the KCL equation of node, and second equation is the equation of constraint of mutual resistance, and the 3rd equation is the equation of constraint of branch road, and automatically meets KVL equation.One total 2n+b unknown number and 2n+b independent equation, therefore can obtain each conductor segment leakage current, axial current and each node potential.With branch current for unknown number, abbreviation equation is:
( Z b × b a + A n × b T Z n × n m A n × b ) I b a = A n × b T Z n × n m I n f - - - ( 11 )
Through grounding body flow into the earth total current be by conduction current and displacement current dimerous.Judge that ground is conductor or semiconductor or dielectric, be decided by the conduction current density of same point and the ratio of displacement current density in ground.In exchange current field, the ratio of conduction current density and displacement current density absolute value is:
K = 1 ω ϵ r ϵ 0 ρ - - - ( 12 )
In formula, ω=2 π f is electric current angular frequency (rad), ε 0it is the specific inductive capacity (8.85 × 10 in vacuum -12f/m), ε rbe the relative dielectric constant of soil relative vacuum, ρ is soil resistivity (Ω m).
Majority of case, the relative dielectric coefficient ε on ground rin the scope of 5 ~ 50.Only in very high resistivity area, just need the impact counting displacement current.During impulse grounding, in general resistivity area, only need consider the effect of conduction current.Such as: soil resistivity 1000 Ω m, DIELECTRIC CONSTANT ε r=9, getting lightning current wave head is half cosine-shaped, and the wave head time is 3 μ s, therefore the equivalent angular frequency of lightning current wave head is ω=π/3 × 10 6(rad), calculate to obtain K=12, namely conduction current is 12 times of displacement current.In fact, at general lightning current equivalent frequency, when resistivity is 2000 Ω m, the impact of displacement current (i.e. capacity effect) can be disregarded.
Ignoring the electric capacity effect between conductor segment herein when calculating shaft tower impact characteristics, therefore calculating and greatly simplifying.Formula (11) becomes:
( A n × b T R n × n m A n × b + Z b × b a ) I b a = A n × b T R n × n m I n f - - - ( 13 )
In formula, represent the mutual resistance between conductor segment.
Formula (13) is expressed as in the time domain:
A n × b T R n × n m A n × b I b a + ( R b × b a + L b × b a d dt ) I b a = A n × b T R n × n m I n f - - - ( 14 )
Injecting the time domain response after earthing device to emulate lightning current, to need formula (14) according to trapezoidal integration formula discretize:
A n × b T R n × n m A n × b I b a ( t ) + I b a ( t - Δt ) 2 + R b × b a I b a ( t ) + I b a ( t - Δt ) 2 + L b × b a I a a ( t ) - I b a ( t - Δt ) Δt = A n × b T R n × n I n f ( t ) + I n f ( t - Δt ) 2 - - - ( 15 )
Order S b × b al = 2 L b × b a Δt + R b × b a , S b × b a 2 = - 2 L b × b a Δt + R b × b a , Then can obtain:
I b a ( t ) = ( S b × b a 1 + A n × b T R n × n m A n × b ) - 1 A n × b T R n × n m ( I n f ( t ) + I n f ( t - Δt ) ) - ( S b × b a 2 + A n × b T R n × n m A n × n ) I b a ( t - Δt ) - - - ( 16 )
In formula, each moment a n × bwith all known parameters, with the lightning current injection value of this moment t and a upper moment t-Δ t each point respectively, for each branch current value of a upper moment t-Δ t.Therefore the branch current of moment t can be obtained for mutual inductance between conductor segment.
3 conductor equivalent redius
Formula (16) A n × brepresenting the topological structure of grounding body, is constant; Lightning current with determined by the external world, for the result of calculation of previous step, it is known quantity.Therefore calculative parameter is the axial resistance of conductor, inductance, mutual inductance and the mutual resistance over the ground between self-resistance and conductor.
The branch current of known moment t through type (10) learns the node Leakage Current of branch road
I n l ( t ) = I n f ( t ) - I n l ( t - Δt ) - A n × b ( I b a ( t ) + I b a ( t - Δt ) ) - - - ( 17 )
And the node leakage current of trying to achieve in formula (17) can not calculate the leakage current density of each conductor segment connecting this node, the equivalent redius of each conductor segment therefore can not be extrapolated.We suppose the length of the leakage current of this point according to connected conductor segment for this reason, are uniformly distributed in the conductor segment that is connected with node, for the conductor structure in Fig. 1, and the earial drainage of node i to the current contribution of conductor segment k, k+1 and k+2 respectively:
I i n · L k L k + L k + 1 + L k + 2 , I i n · L k + 1 L k + L k + 1 + L k + 2 , I i n · L k + 2 L k + L k + 1 + L k + 2
In order to represent the allocation proportion of this node to connected conductor segment, introduce weight coefficient matrix N herein n × bconcept, be similar to incidence matrix, N n × bfor the relational matrix of node and conductor segment, unlike: related position no longer represents with 1, and instead of being connected in any this conductor segment length ratio.
Contrast incidence matrix obtains
Weight coefficient matrix N n × bfor:
In formula, l ijfor the length of the conductor segment that this node is connected, L kfor the length of kth bar branch road, q is the branch road number associated with node i, L pfor the length of branch road p associated with node i.
Therefore every strip conductor section is at the leakage current of moment t for:
I b l ( t ) = N n × b T · I n l ( t ) - - - ( 20 )
Try to achieve the equivalent redius of each conductor segment again
The axial resistance of 6 conductors, self-induction and frequency dependent characteristic
The axial resistance of conductor describe the inhibition of conductor for axial conduction current.When spark discharge, although the equivalent redius of conductor expands, axial current remains and flows in metallic conductor, instead of flows in the soil in spark discharge region.Even if because consider the skin effect of conductor, the resistivity that metallic conductor presents, be still far smaller than the resistivity in ionization soil, axial current remains and flows in metallic conductor, and spark discharge region only has radial Leakage Current.So the axial resistance of calculating conductor and self-induction, mutual inductance time, still calculate with the radius of metallic conductor.
For same section of conductor, when flowing through high-frequency current, skin effect makes electric current flow along conductive surface, and conductor central current is little, and the sectional area being equivalent to conductor reduces, axial resistance become large; And when flowing through low-frequency current, skin effect is little, the cross-sectional area of conductor of equivalence is long-pending large, axial resistance diminish, therefore axial resistance is frequency variable element.Because the frequency spectrum of lightning current is very wide, therefore when different when, conductor can present different axial resistance.In like manner can learn that the interior self-induction of conductor is also frequently become.
The self-impedance of conductor can be tried to achieve by formula (21):
Z l=Z cl+jωL(21)
In formula, Z cfor the long interior self-impedance of the conductor unit determined by conductor segment own material, l is the length of conductor segment, and L is the outer self-induction of conductor segment.For cylindrical conductor section, self-impedance Z in its unit head ccan be expressed as:
Z c = jω μ c 2 πa jω σ c μ c · I 0 ( a jω σ c μ c ) I 1 ( a jω σ c μ c ) - - - ( 22 )
In formula, σ cand μ cbe respectively conductivity and the magnetic permeability of conductor material therefor, a is the equivalent redius of cylindrical conductor, I 0and I 1be respectively first kind zeroth order and the first-order bessel function of correction.
What more than try to achieve is the self-impedance in frequency domain, and algorithm need solve in the time domain herein, therefore needs the self-impedance in frequency domain to be converted into resistance in time domain and internal inductance.
Self-impedance Z cequal Z c=R a+ j ω L cas long as therefore know that frequencies omega just can know the internal inductance in time domain.And ω in lightning current along with time variations, when wave head, rising edge is steep, and ω is larger; When wave rear declines, ω is less, therefore utilizes the way approximate treatment of sine curve fitting to go out the angular frequency of lightning current every bit herein.
The frequency of time domain waveform each point is asked to can be understood as: the speed of time domain waveform change can affect the skin effect of conductor.When rate of change is fast, in conductor, magnetic hysteresis and eddy effect can hinder the curent change in conductor, and skin effect is large; When waveform rate of change is slow, in conductor magnetic hysteresis and eddy current effect little, skin effect is little.Therefore the speed of waveform change can wait to a certain extent and be all a frequency, and the two makes conductor present identical skin effect.And this frequency just thinks the frequency of this point in time domain waveform, namely waveform rate of change is equivalent to this dot frequency.
If calculate the equivalent frequency of t lightning current, concrete method is: suppose three the thunder and lightning flow valuves I respectively in t-Δ t, t, t+ Δ t light(t-Δ t), I light(t), I light(t+ Δ t) regards the value in 0 moment on cosine alternating current as, the corresponding cosine alternating current-Δ t of t-Δ t, t corresponding cosine alternating current 0 moment, and t+ Δ t corresponding cosine alternating current Δ t, therefore can obtain system of equations:
A cos ( - wΔt + θ 0 ) = I light ( t - Δt ) A cos ( θ 0 ) = I light ( t ) A cos ( wΔt + θ 0 ) = I light ( t + Δt ) - - - ( 23 )
In formula, A is the maximum amplitude of cosine alternating current, θ 0be the initial phase of cosine wave (CW), w is cosine wave frequency, and namely lightning current is at the equivalent frequency of this moment point.Can be solved by (23) system of equations:
w = arccos ( I light ( t - Δt ) + I light ( t + Δt ) 2 × I light ( t ) ) - - - ( 24 )
Calculating shows, though frequency why, initial phase, as long as curve average is 0, then this method accurately can calculate the equivalent frequency in each moment.If the average of curve is not 0, then equivalent frequency is just no longer stabilized in a frequency.Known as calculated, frequency jitter is maximum differs from 10 times, if frequency is 50Hz, then calculating minimum frequency may be 5Hz, and maximum frequency may be 500Hz.Therefore be necessary to calculating curve obtained take certain mathematical smoothing technique, make frequency be basically stable at the actual frequency at this place, and be also conducive to the frequency of consecutive point on curve be unlikely to difference too large.
Calculating shows, adopts after smoothing action, institute a little distance equivalent frequency point all within 3 times.In grounding body calculates, it is be negligible on the impact of overall calculation result that conductor longitudinal electrical resistance and internal inductance change in 3 times.The equivalent frequency w in each moment on lightning current can be estimated.Through type (22) calculates the self-impedance Z of each conductor segment of each moment thus c, and the axial resistance R of the conductor segment everywhere of converting awith self-inductance L c.
The outer self-induction L of cylindrical conductor section equals to be in the mutual inductance between the fine rule section of conductor segment axis and the fine rule section being in conductor segment surface, owing to solving middle magnetic linkage and whole electric current interlinkage, therefore the change of skin depth is on external inductance without any impact, can think external inductance L etime-independent.Can be calculated by formula (25).
L e = μ 4 π ∫ l ∫ l ′ 1 r dl ′ dl ≈ μ 4 π ( ln l a - 1 ) - - - ( 25 )
In formula, μ is the magnetic permeability of conductor material, l and l' is the path being in conductor segment axis He being in conductor segment surface respectively, and r is the distance of source point and field point.
Just the self-induction L of whole conductor segment can be calculated thus:
L=L e+L c(26)
7 conductors are mutual resistance and time-varying characteristics between self-resistance, conductor over the ground
The leakage current of a conductor segment, will inevitably produce current potential on the conductor of self.Conductor segment resistance certainly has over the ground showed the leakage current of a conductor to the impact of self current potential.
Because grounding body is divided into very little conductor segment, thus hypothesis in the conductor segment that each is little, Leakage Current all along the even diffusing of conductor segment, and suppose leakage current all from axis to surrounding diffusing, then along the diffusing density δ=I/l of conductor segment axis.The total current that I reveals for this conductor segment, l is conductor segment length.
For the conductor segment in Fig. 3, under can obtaining cylindrical-coordinate system (r, θ, z), soil resistivity is the current potential (r of any point N in the soil of ρ n, θ, z n), now the region of soil is infinitely great:
V N = ρ 4 π ∫ 0 l δdz ( z N - z ) 2 + r N 2 = ρδ 4 π ln z N + z N 2 + r N 2 z N - l + ( z N - l ) 2 + r N 2 - - - ( 27 )
Suppose that pole radius is a, conductor current potential gets the average potential of each point, and its Chinese style gets r in (27) n=a, then conductor current potential V afor:
V a = δρ 4 πl ∫ 0 l ( sh - 1 z a - sh - 1 z - l a ) dz = ρI 2 πl [ a l + sh - 1 l a - 1 + ( a l ) 2 ] = ρI 2 πl [ a l + ln l + l 2 + a 2 a - 1 + ( a l ) 2 ] ≈ ρI 2 πl ( ln 2 l a - 1 ) - - - ( 28 )
Grounding body resistance to earth in infinitely great soil of gained is:
R = V a I = ρ 2 πl ( ln 2 l a - 1 ) - - - ( 29 )
Be the Grounding Grids of h for buried depth in soil, because now soil is not infinitely-great region, need to consider the impact of mirror image in air when therefore calculating, can obtain self-resistance is over the ground:
R = ρ 2 πl [ ln 2 l a - 1 + 1 2 ln 2 h + 3 2 l + ( 2 h + 3 2 l ) 2 + a 2 2 h + 1 2 l + ( 2 h + 1 2 l ) 2 + a 2 ] - - - ( 30 )
Be the horizontal grounding objects of h for buried depth, consider the impact of mirror image in air, can obtain self-resistance is over the ground:
R = ρ 2 πl [ 2 h + a l + ln l + l 2 + a 2 a - 1 + ( a l ) 2 + ln l + l 2 + 4 h 2 2 h - 1 + ( 2 h l ) 2 ] - - - ( 31 )
Mutual resistance between two conductors is:
R ij = ρ 4 π · 1 l i l j · ( ∫ l i ∫ l j 1 D ij dl j dl i + ∫ l i ′ ∫ l j 1 D i ′ j dl j dl i ′ ) - - - ( 32 )
In formula, l irepresent the path of integration of i-th conductor segment, l jrepresent the path of integration of jth root conductor segment, l i' represent the path of integration of i-th conductor segment mirror image in atmosphere, D ijrepresent the segment dl respectively on conductor segment i and conductor segment j two path of integration iand dl jbetween distance, D i'jrepresent the segment dl respectively in the air of conductor segment i on mirror image and conductor segment j two path of integration i' and dl jbetween distance.
Under lightning current effect, can flashing electric discharge around conductor, the equivalent redius being equivalent to conductor increases, therefore in conductor section over the ground between self-resistance and conductor segment when mutual resistance, need to ask according to equivalent redius.Because equivalent redius is time-varying parameter, the mutual resistance over the ground between self-impedance and conductor of conductor is also time-varying parameter.The equivalent redius that what a in formula (30), (31) referred to is exactly after spark discharge, the over the ground self-resistance of a to conductor segment self has the greatest impact, and therefore must use equivalent redius calculating self-impedance over the ground.
After using equivalent redius, distance between mirror image in conductor self and its air and the distance between conductor segment may not be far longer than equivalent redius a, therefore when calculating conductor self is with radial mutual resistance, current source still can be assumed to be electric line source, but affected point can not be equivalent to a line again, and should be a face of cylinder, after mutual resistance is tried to achieve to each point on this face of cylinder, then the mutual resistance between two conductors is obtained to whole Line Integral.Formula (32) becomes:
R ij = ρ 4 π · 1 l i l j · ( ∫ l i ∫ ∫ S j 1 D ij d S j dl i + ∫ l i ′ ∫ ∫ S j 1 D ij d S j dl i ′ ) - - - ( 33 )
Wherein, S jfor the equivalent cross-section of jth root conductor segment.
8 node Leakage Currents associate with conductor segment equivalent redius
Mutual resistance in formula (16) for node and internodal mutual resistance, because the Leakage Current of each conductor calculating gained is not identical, thus same node the equivalent redius of each conductor segment be also not quite similar, the mutual resistance matrix between computing node time just there is contradiction.So herein in calculating try to achieve not by internodal current potential impact, but try to achieve according to mutual resistance between the conductor segment be connected with node, formula (33) is also the mutual resistance between the conductor segment of calculating.
In the diagram, the conductor segment be connected in node i has kth-2, k-1 and k section, and the conductor segment be connected on node j has kth, k+1 and k+2 section.Obtain kth-2, k-1 and k section successively to the mutual resistance between kth, k+1 and k+2 section, then they are added according to the weight of conductor segment length and internodal mutual resistance matrix can be obtained.
For avoiding the difficulty that between one section of conductor two ends end points, mutual resistance calculates, in calculating, every section of conductor is divided into two from mid point.Half section that in definition conductor segment, branch current points to is "+", and half section that leaves is "-".In figure when computing node i and node j mutual resistance, then only need calculate (k-2) -, (k-1) +(k) -section is to (k) +, (k+1) +(k+2) -mutual resistance between section, does not just have identical conductor between such two nodes, more conveniently can calculate mutual resistance.
If (k-2) -, (k-1) +(k) -duan Yu (k) +mutual resistance between section is respectively with then the Leakage Current of node i is in conductor segment (k) +the current potential of upper generation for:
φ ( k ) + = R ( k - 2 ) - , ( k ) + mc R ( k - 1 ) - , ( k ) + mc R ( k ) - , ( k ) + mc T · I ( k - 2 ) - n I ( k - 1 ) + n I ( k ) - n = R ( k - 2 ) - , ( k ) + mc R ( k - 1 ) - , ( k ) + mc R ( k ) - , ( k ) + mc T · L k - 2 L k - 2 + L k - 1 + L k L k - 1 L k - 2 + L k - 1 + L k L k L k - 2 + L k - 1 + L k · I i l - - - ( 34 )
In formula, L k-2, L k-1, L kthe length of the conductor segment be connected with node i.Consider that the Leakage Current of node i is according to the uniform length diffusing of connected conductor segment, needs to be multiplied by weight coefficient matrix; with the electric current that the conductor segment be connected in node i has kth-2, k-1 and k section is revealed respectively.
The voltage of node j can get the current potential of connected arbitrary conductor segment, but is more accurately be multiplied by according to the length of the conductor segment that is connected the voltage that corresponding conductor length weight obtains node j with the way of algorithm convergence of being more convenient for.So
φ j = L k L k + L k + 1 + L k + 2 L k + 1 L k + L k + 1 + L k + 2 L k + 2 L k + L k + 1 + L k + 2 T · φ ( k ) + φ ( k + 1 ) + φ ( k + 2 ) - - - - ( 35 )
Wherein, with be respectively (k-2) -, (k-1) +(k) -current potential in section;
For whole grounding body, being write as matrix form is:
Φ n = ( N n × 2 b · R 2 b × 2 b mc · N n × 2 b T ) · I n l - - - ( 36 )
Internodal mutual resistance matrix is:
R n × n m = N n × 2 b · R 2 b × 2 b mc · N n × 2 b T - - - ( 37 )
Mutual resistance matrix between conductor segment represent that after all former conductor segment being divided into two from mid point, the mutual resistance between all new conductor segment, both sides obtain internodal mutual resistance matrix after being multiplied by weight matrix.
Due to conductor segment mutual resistance matrix change along with conductor radius, and conductor equivalent redius and amplitude of lightning current and time correlation, therefore impulse earthed resistance also be time dependent.
Finally should be noted that: above embodiment is only in order to illustrate that technical scheme of the present invention is not intended to limit; although those of ordinary skill in the field are to be understood that with reference to above-described embodiment: still can modify to the specific embodiment of the present invention or equivalent replacement; these do not depart from any amendment of spirit and scope of the invention or equivalent replacement, are all applying within the claims of the present invention awaited the reply.

Claims (10)

1. consider impulse earthed resistance computing method for spark discharge effect, it is characterized in that: comprise the following steps:
(1) leakage current of grounding body conductor, axial current and node potential relation is each other determined respectively;
(2) leakage current of described grounding body conductor, axial current and node potential is determined;
(3) grounding body conductor segment equivalent redius is determined;
(4) the axial resistance of grounding body conductor, self-induction and frequency dependent characteristic is determined;
(5) mutual resistance and time-varying characteristics between the self-resistance over the ground of grounding body conductor, conductor are determined;
(6) relation of grounding body conductor node Leakage Current and conductor segment equivalent redius is determined.
2. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 1, is characterized in that: the leakage current in described step (1) and the relation between axial current are determined by following formula:
A n × b I b a + E n × n I n l = I n f
In formula, b is the number of conductor segment, is also branch road number, and n is node number, the axial current of branch road or conductor segment, the leakage current of each node, the Injection Current of each node, A n × bthe incidence matrix between node and branch road, E n × nit is unit matrix.
3. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 2, is characterized in that: the leakage current in described step (1) and the relation between node potential are determined by following formula:
Φ n = Z n × n m I n l
In formula, Φ neach node potential, the mutual resistance capacitive reactance between each conductor segment, for the leakage current of each node.
4. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 3, is characterized in that: the axial current in described step (1) and the relation between node potential are determined by following formula:
A n × b T Φ n = Z n × n m I n l
In formula, for the incidence matrix between node and branch road, Φ nfor each node potential, the mutual resistance capacitive reactance between each conductor segment, for the leakage current of each node.
5. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 4, it is characterized in that: the leakage current of described step (2), axial current and node potential are determined by the relational expression in step described in simultaneous (1), are:
A n × b E n × n 0 n × n 0 n × n Z n × n m - E n × n Z b × b a 0 b × n - ( A n × b ) T I b a I n l Φ n = I n f 0 0 .
6. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 5, is characterized in that: the conductor segment equivalent redius in described step (3) is by the leakage current of every strip conductor section in t determine; Described leakage current determined by following formula:
I b l ( t ) = N n × b T · I n l ( t )
In formula, N n × bfor weight coefficient matrix, i.e. the relational matrix of node and conductor segment; for the node Leakage Current of branch road;
Suppose the length of the leakage current of certain node according to connected conductor segment, be uniformly distributed in the conductor segment that is connected with this node, then described weight coefficient matrix N n × bfor:
In formula, l ijfor the length of the conductor segment that this node is connected, L kfor the length of kth bar branch road, q is the branch road number associated with node i, L pfor the length of branch road p associated with node i.
7. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 1, is characterized in that: the axial resistance of the grounding body conductor in described step (4) is by the self-impedance Z of each conductor segment of each moment cconversion is determined; Described self-impedance Z cdetermined by following formula:
Z c = jω μ c 2 πa jω σ c μ c · I 0 ( a jω σ c μ c ) I 1 ( a jω σ c μ c )
In formula, σ cand μ cbe respectively conductivity and the magnetic permeability of conductor material therefor, a is the equivalent redius of cylindrical conductor, I 0and I 1be respectively first kind zeroth order and the first-order bessel function of correction;
The self-induction L of described grounding body conductor is determined by following formula:
L=L e+L c
In formula, L efor the outer self-induction of cylindrical conductor section, L cfor the self-inductance of conductor segment everywhere;
Described self-inductance L cby the self-impedance Z of each conductor segment of each moment cconversion is determined; Described outer self-induction L edetermined by following formula:
L e = μ 4 π ∫ l ∫ l ′ 1 r dl ′ dl ≈ μ 4 π ( ln l a - 1 )
In formula, μ is the magnetic permeability of conductor material, l and l' is the path being in conductor segment axis He being in conductor segment surface respectively, and r is the distance of source point and field point;
The frequency dependent characteristic of described grounding body conductor is determined by following formula:
w = arccos ( I light ( t - Δt ) + I light ( t + Δt ) 2 × I li ght ( t ) )
In formula, w is cosine wave frequency, is also the equivalent frequency of t lightning current; I light(t-Δ t), I light(t) what I light(t+ Δ t) is respectively three thunder and lightning flow valuves in t-Δ t, t and t+ Δ t, and regards the value in 0 moment on cosine alternating current respectively as;
No matter how frequency and initial phase change, as long as curve average is 0, the equivalent frequency in each moment accurately can be calculated; If the average of curve is not 0, then equivalent frequency is just no longer stabilized in a frequency.
8. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 1, is characterized in that: the self-resistance over the ground of described step (5) grounding body conductor is determined by following formula:
When the vertical buried depth of grounding body is in h soil, described self-resistance is over the ground:
R = ρ 2 πl [ ln 2 l a - 1 + 1 2 ln 2 h + 3 2 l + ( 2 h + 3 2 l ) 2 + a 2 2 h + 1 2 l + ( 2 h + 1 2 l ) 2 + a 2 ]
When the horizontal buried depth of grounding body is in h soil, described self-resistance is over the ground:
R = ρ 2 πl [ 2 h + a l + ln l + l 2 + a 2 a - 1 + ( a l ) 2 + ln l + l 2 + 4 h 2 2 h - 1 + ( 2 h l ) 2 ]
In formula, ρ is soil resistivity, and l is conductor segment length, and h is the buried depth of grounding body vertically in soil, and a is the equivalent redius after spark discharge;
Between the conductor of described grounding body conductor, mutual resistance is determined by following formula:
R ij = ρ 4 π · 1 l i l j · ( ∫ l i ∫ l j 1 D ij dl j dl i + ∫ l i ′ ∫ l j 1 D i ′ j dl j dl i ′ )
In formula, l irepresent the path of integration of i-th conductor segment, l jrepresent the path of integration of jth root conductor segment, l i' represent the path of integration of i-th conductor segment mirror image in atmosphere, D ijrepresent the segment dl respectively on conductor segment i and conductor segment j two path of integration iand dl jbetween distance, D i'jrepresent the segment dl respectively in the air of conductor segment i on mirror image and conductor segment j two path of integration i' and dl jbetween distance;
Under lightning current effect, flashing electric discharge around conductor, the equivalent redius a being equivalent to conductor increases, therefore, in conductor section over the ground between self-resistance and conductor segment when mutual resistance, need to determine according to described equivalent redius a; Because equivalent redius a is time-varying parameter, the mutual resistance over the ground between self-impedance and conductor of conductor is also time-varying parameter.
9. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 6, is characterized in that: the Leakage Current of the node i in described step (6) in conductor segment (k) +the current potential of upper generation for:
φ ( k ) + = R ( k - 2 ) - , ( k ) + mc R ( k - 1 ) - , ( k ) + mc R ( k ) - , ( k ) + mc T · I ( k - 2 ) - n I ( k - 1 ) + n I ( k ) - n = R ( k - 2 ) - , ( k ) + mc R ( k - 1 ) - , ( k ) + mc R ( k ) - , ( k ) + mc T · L k - 2 L k - 2 + L k - 1 + L k L k - 1 L k - 2 + L k - 1 + L k L k L k - 2 + L k - 1 + L k · I i l
with be respectively the conductor segment be connected in node i to have in kth-2, k-1 and k section (k-2) -, (k-1) +(k) -duan Yu (k) +mutual resistance between section; L k-2, L k-1, L kthe length of the conductor segment be connected with node i; with the electric current that the conductor segment be connected in node i has kth-2, k-1 and k section is revealed respectively; Half section that in conductor segment, branch current points to is "+", and half section that leaves is "-";
The voltage of described node j be multiplied by corresponding conductor length weight according to the length of connected conductor segment to determine:
φ j = L k L k + L k + 1 + L k + 2 L k + 1 L k + L k + 1 + L k + 2 L k + 2 L k + L k + 1 + L k + 2 T · φ ( k ) + φ ( k + 1 ) + φ ( k + 2 ) -
Wherein, with be respectively (k-2) -, (k-1) +(k) -current potential in section;
For whole grounding body, each node potential Φ nmatrix form be:
Φ n = ( N n × 2 b · R 2 b × 2 b mc · N n × 2 b T ) · I n l
Wherein, for the node Leakage Current of branch road; for the mutual resistance matrix between conductor segment, represent after all former conductor segment are divided into two from mid point, the mutual resistance between all new conductor segment; N n × 2bfor weight coefficient matrix, i.e. the relational matrix of node and new conductor segment;
Then internodal mutual resistance matrix, namely impulse earthed resistance is:
R n × n m = N n × 2 b · R 2 b × 2 b mc · N n × 2 b T
Due to conductor segment mutual resistance matrix change along with conductor equivalent redius, and conductor equivalent redius is relevant with amplitude of lightning current and time, therefore impulse earthed resistance also be time dependent.
10. a kind of impulse earthed resistance computing method considering spark discharge effect as claimed in claim 8, it is characterized in that: due to described in determining over the ground self-impedance time use equivalent redius, then when determining conductor self and radial mutual resistance, current source is assumed to be electric line source, but affected point can not be equivalent to a line again, and be a face of cylinder, after mutual resistance is tried to achieve to each point on this face of cylinder, then to the mutual resistance that whole Line Integral obtains between two conductors be:
R ij = ρ 4 π · 1 l i l j · ( ∫ l i ∫ ∫ S j 1 D ij d S j dl i + ∫ l i ′ ∫ ∫ S j 1 D ij d S j dl i ′ )
Wherein, S jfor the equivalent cross-section of jth root conductor segment.
CN201410483980.5A 2014-09-19 2014-09-19 Impulse grounding resistance calculation method considering spark discharge effect CN105486929A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201410483980.5A CN105486929A (en) 2014-09-19 2014-09-19 Impulse grounding resistance calculation method considering spark discharge effect

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201410483980.5A CN105486929A (en) 2014-09-19 2014-09-19 Impulse grounding resistance calculation method considering spark discharge effect

Publications (1)

Publication Number Publication Date
CN105486929A true CN105486929A (en) 2016-04-13

Family

ID=55674043

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201410483980.5A CN105486929A (en) 2014-09-19 2014-09-19 Impulse grounding resistance calculation method considering spark discharge effect

Country Status (1)

Country Link
CN (1) CN105486929A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110889225A (en) * 2019-11-28 2020-03-17 贵州电网有限责任公司 Method for calculating grounding resistance of artificial grounding body

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101819233A (en) * 2010-05-10 2010-09-01 中国人民解放军理工大学 Impact grounding impedance measuring system and measuring method thereof
CN101900764A (en) * 2009-05-26 2010-12-01 上海市电力公司 Method for measuring grounded resistance of grounded screen by short range measuring method
DE102009050279A1 (en) * 2009-10-21 2011-05-05 Metrawatt International Gmbh Method for testing resistance of electrical ground connection of electrical load, involves producing cleaning power by discharge of capacitor, and charging capacitor by testing current generator producing testing current
CN103293451A (en) * 2013-05-24 2013-09-11 华南理工大学 Method of estimating lightning protection of high-voltage transmission line pole/tower earthing device
CN103792433A (en) * 2014-02-21 2014-05-14 国家电网公司 Measuring method using spark coefficient for correcting low-amplitude value impact resistance of tower grounding device
CN103901328A (en) * 2014-03-26 2014-07-02 国家电网公司 Method suitable for calculating transmission line pole tower grounding body lightning impulse characteristics

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101900764A (en) * 2009-05-26 2010-12-01 上海市电力公司 Method for measuring grounded resistance of grounded screen by short range measuring method
DE102009050279A1 (en) * 2009-10-21 2011-05-05 Metrawatt International Gmbh Method for testing resistance of electrical ground connection of electrical load, involves producing cleaning power by discharge of capacitor, and charging capacitor by testing current generator producing testing current
CN101819233A (en) * 2010-05-10 2010-09-01 中国人民解放军理工大学 Impact grounding impedance measuring system and measuring method thereof
CN103293451A (en) * 2013-05-24 2013-09-11 华南理工大学 Method of estimating lightning protection of high-voltage transmission line pole/tower earthing device
CN103792433A (en) * 2014-02-21 2014-05-14 国家电网公司 Measuring method using spark coefficient for correcting low-amplitude value impact resistance of tower grounding device
CN103901328A (en) * 2014-03-26 2014-07-02 国家电网公司 Method suitable for calculating transmission line pole tower grounding body lightning impulse characteristics

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
何金良等: "考虑火花放电的杆塔冲击接地特性计算方法", 《高电压技术》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110889225A (en) * 2019-11-28 2020-03-17 贵州电网有限责任公司 Method for calculating grounding resistance of artificial grounding body
CN110889225B (en) * 2019-11-28 2020-10-09 贵州电网有限责任公司 Method for calculating grounding resistance of artificial grounding body

Similar Documents

Publication Publication Date Title
Liu et al. An improved transmission-line model of grounding system
Mousavi-Seyedi et al. Parameter estimation of multiterminal transmission lines using joint PMU and SCADA data
de Lieto Vollaro et al. Thermal analysis of underground electrical power cables buried in non-homogeneous soils
Lorentzou et al. Time domain analysis of grounding electrodes impulse response
Viljanen et al. Continental scale modelling of geomagnetically induced currents
Liu et al. An engineering model for transient analysis of grounding system under lightning strikes: Nonuniform transmission-line approach
Ye et al. An improved fault-location method for distribution system using wavelets and support vector regression
Bernadić et al. Fault location in power networks with mixed feeders using the complex space-phasor and Hilbert–Huang transform
Martinez et al. Parameter determination for modeling system transients-Part I: Overhead lines
Mamiş et al. Transmission lines fault location using transient signal spectrum
Zhang et al. Diagnosis of breaks in substation's grounding grid by using the electromagnetic method
Wait Geo-electromagnetism
Silvester et al. Exterior finite elements for 2-dimensional field problems with open boundaries
Rüdenberg Grounding principles and practice I—Fundamental considerations on ground currents
Paolone et al. Lightning induced disturbances in buried cables-part II: experiment and model validation
Cooray et al. Lightning-induced overvoltages in power lines: Validity of various approximations made in overvoltage calculations
Zheng et al. Effects of geophysical parameters on GIC illustrated by benchmark network modeling
CN101788603B (en) VFTO measuring system
CN103279601A (en) Method for simulating wide-band electromagnetic scattering property of conductor target
Çapar et al. A performance oriented impedance based fault location algorithm for series compensated transmission lines
Zhao et al. Improved GPS travelling wave fault locator for power cables by using wavelet analysis
CN103412199B (en) A kind of computational methods of same many back transmission lines of tower degree of unbalancedness
Yin et al. Finite volume-based approach for the hybrid ion-flow field of UHVAC and UHVDC transmission lines in parallel
Patel et al. MoM-SO: a complete method for computing the impedance of cable systems including skin, proximity, and ground return effects
CN106202610B (en) A kind of overhead line radial temperature field emulation mode based on ANSYS CFX

Legal Events

Date Code Title Description
PB01 Publication
C06 Publication
SE01 Entry into force of request for substantive examination
C10 Entry into substantive examination
RJ01 Rejection of invention patent application after publication

Application publication date: 20160413

RJ01 Rejection of invention patent application after publication