CN105486929A  Impulse grounding resistance calculation method considering spark discharge effect  Google Patents
Impulse grounding resistance calculation method considering spark discharge effect Download PDFInfo
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 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
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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, selfinductance, and frequencydependent property of the grounding body conductor; determining selfresistance of the grounding body conductor over ground, mutual resistance among conductors, and timevariant 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 voltampere characteristics of a grounding device under an impact condition.
Description
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 timevarying 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 abovementioned 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 voltampere 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, selfinduction and frequency dependent characteristic is determined;
(5) mutual resistance and timevarying characteristics between the selfresistance 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:
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 × b}the incidence matrix between node and branch road, E
_{n × n}it 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:
In formula, Φ
_{n}each 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:
In formula,
for being the incidence matrix between node and branch road, Φ
_{n}for 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:
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:
In formula, N
_{n × b}for 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 × b}for:
In formula, l
_{ij}for the length of the conductor segment that this node is connected, L
_{k}for the length of kth bar branch road, q is the branch road number associated with node i, L
_{p}for 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 selfimpedance Z of each conductor segment of each moment
^{c}conversion is determined; Described selfimpedance Z
^{c}determined by following formula:
In formula, σ
_{c}and μ
_{c}be respectively conductivity and the magnetic permeability of conductor material therefor, a is the equivalent redius of cylindrical conductor, I
_{0}and I
_{1}be respectively first kind zeroth order and the firstorder bessel function of correction;
The selfinduction L of described grounding body conductor is determined by following formula:
L＝L
^{e}+L
^{c}
In formula, L
^{e}for the outer selfinduction of cylindrical conductor section, L
^{c}for the selfinductance of conductor segment everywhere;
Described selfinductance L
^{c}by the selfimpedance Z of each conductor segment of each moment
^{c}conversion is determined; Described outer selfinduction L
^{e}determined by following formula:
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:
In formula, w is cosine wave frequency, is also the equivalent frequency of t lightning current; I
_{light}(tΔ t), I
_{light}(t) what I
_{light}(t+ Δ t) is respectively three thunder and lightning flow valuves in tΔ 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 selfresistance 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 selfresistance is over the ground:
When the horizontal buried depth of grounding body is in h soil, described selfresistance is over the ground:
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:
In formula, l
_{i}represent the path of integration of ith conductor segment, l
_{j}represent the path of integration of jth root conductor segment, l
_{i}' represent the path of integration of ith conductor segment mirror image in atmosphere, D
_{ij}represent the segment dl respectively on conductor segment i and conductor segment j two path of integration
_{i}and dl
_{j}between distance, D
_{i'j}represent 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
_{j}between 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 selfresistance and conductor segment when mutual resistance, need to determine according to described equivalent redius a; Because equivalent redius a is timevarying parameter, the mutual resistance over the ground between selfimpedance and conductor of conductor is also timevarying 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:
with
be respectively the conductor segment be connected in node i to have in kth2, k1 and k section (k2)
^{}, (k1)
^{+}(k)
^{}duan Yu (k)
^{+}mutual resistance between section; L
_{k2}, L
_{k1}, L
_{k}the length of the conductor segment be connected with node i;
with
the electric current that the conductor segment be connected in node i has kth2, k1 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:
Wherein,
with
be respectively (k2)
^{}, (k1)
^{+}(k)
^{}current potential in section;
For whole grounding body, each node potential Φ
_{n}matrix form be:
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 × 2b}for weight coefficient matrix, i.e. the relational matrix of node and new conductor segment;
Then internodal mutual resistance matrix, namely impulse earthed resistance is:
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 selfimpedance 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:
Wherein, S
_{j}for the equivalent crosssection 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 voltampere 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 14, 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
^{f}equal the lightning current injected, I on nonCurrent injection points
^{f}be zero.
According to KCL equation, their relation can be listed for node i:
Wherein,
for the axial current from node i1 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:
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 × b}the incidence matrix between node and branch road, E
_{n × n}it 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 selfresistance 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:
In formula,
for the leakage current on node j; As j=i,
for the selfimpedance 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
_{i}equal 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 crosssectional 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 crosssection center equals:
For whole grounding body, being write as matrix form is:
In formula, Φ
_{n}each 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 selfimpedance 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:
In formula,
it is the axial current of p article of branch road; As p=k,
for the selfimpedance 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:
In formula,
it is the axial impedance induction reactance matrix of conductor segment branch road.
Again due to each node potential Φ
_{n}with each conductor segment voltage drop
between there is relation:
So known:
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:
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:
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:
In formula, ω=2 π f is electric current angular frequency (rad), ε
_{0}it is the specific inductive capacity (8.85 × 10 in vacuum
^{12}f/m), ε
_{r}be the relative dielectric constant of soil relative vacuum, ρ is soil resistivity (Ω m).
Majority of case, the relative dielectric coefficient ε on ground
_{r}in 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 cosineshaped, 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:
In formula,
represent the mutual resistance between conductor segment.
Formula (13) is expressed as in the time domain:
Injecting the time domain response after earthing device to emulate lightning current, to need formula (14) according to trapezoidal integration formula discretize:
Order
${S}_{b\×b}^{\mathrm{al}}=\frac{2{L}_{b\×b}^{a}}{\mathrm{\Δt}}+{R}_{b\×b}^{a},{S}_{b\×b}^{a2}=\frac{2{L}_{b\×b}^{a}}{\mathrm{\Δt}}+{R}_{b\×b}^{a},$ Then can obtain:
In formula, each moment
a
_{n × b}with
all known parameters,
with
the lightning current injection value of this moment t and a upper moment tΔ t each point respectively,
for each branch current value of a upper moment tΔ 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 × b}representing 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 selfresistance and conductor.
The branch current of known moment t
through type (10) learns the node Leakage Current of branch road
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:
In order to represent the allocation proportion of this node to connected conductor segment, introduce weight coefficient matrix N herein
_{n × b}concept, be similar to incidence matrix, N
_{n × b}for 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 × b}for:
In formula, l
_{ij}for the length of the conductor segment that this node is connected, L
_{k}for the length of kth bar branch road, q is the branch road number associated with node i, L
_{p}for the length of branch road p associated with node i.
Therefore every strip conductor section is at the leakage current of moment t
for:
Try to achieve the equivalent redius of each conductor segment again
The axial resistance of 6 conductors, selfinduction 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 selfinduction, mutual inductance time, still calculate with the radius of metallic conductor.
For same section of conductor, when flowing through highfrequency 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 lowfrequency current, skin effect is little, the crosssectional area of conductor of equivalence is longpending 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 selfinduction of conductor is also frequently become.
The selfimpedance of conductor can be tried to achieve by formula (21):
Z
^{l}＝Z
^{c}l+jωL(21)
In formula, Z
^{c}for the long interior selfimpedance of the conductor unit determined by conductor segment own material, l is the length of conductor segment, and L is the outer selfinduction of conductor segment.For cylindrical conductor section, selfimpedance Z in its unit head
^{c}can be expressed as:
In formula, σ
_{c}and μ
_{c}be respectively conductivity and the magnetic permeability of conductor material therefor, a is the equivalent redius of cylindrical conductor, I
_{0}and I
_{1}be respectively first kind zeroth order and the firstorder bessel function of correction.
What more than try to achieve is the selfimpedance in frequency domain, and algorithm need solve in the time domain herein, therefore needs the selfimpedance in frequency domain to be converted into resistance in time domain and internal inductance.
Selfimpedance Z
^{c}equal Z
^{c}=R
^{a}+ j ω L
^{c}as 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 tΔ t, t, t+ Δ t
_{light}(tΔ t), I
_{light}(t), I
_{light}(t+ Δ t) regards the value in 0 moment on cosine alternating current as, the corresponding cosine alternating currentΔ t of tΔ t, t corresponding cosine alternating current 0 moment, and t+ Δ t corresponding cosine alternating current Δ t, therefore can obtain system of equations:
In formula, A is the maximum amplitude of cosine alternating current, θ
_{0}be 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:
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 selfimpedance Z of each conductor segment of each moment thus
^{c}, and the axial resistance R of the conductor segment everywhere of converting
^{a}with selfinductance L
^{c}.
The outer selfinduction 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
^{e}timeindependent.Can be calculated by formula (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 selfinduction L of whole conductor segment can be calculated thus:
L＝L
^{e}+L
^{c}(26)
7 conductors are mutual resistance and timevarying characteristics between selfresistance, 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 cylindricalcoordinate 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:
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
_{a}for:
Grounding body resistance to earth in infinitely great soil of gained is:
Be the Grounding Grids of h for buried depth in soil, because now soil is not infinitelygreat region, need to consider the impact of mirror image in air when therefore calculating, can obtain selfresistance is over the ground:
Be the horizontal grounding objects of h for buried depth, consider the impact of mirror image in air, can obtain selfresistance is over the ground:
Mutual resistance between two conductors is:
In formula, l
_{i}represent the path of integration of ith conductor segment, l
_{j}represent the path of integration of jth root conductor segment, l
_{i}' represent the path of integration of ith conductor segment mirror image in atmosphere, D
_{ij}represent the segment dl respectively on conductor segment i and conductor segment j two path of integration
_{i}and dl
_{j}between distance, D
_{i'j}represent 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
_{j}between 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 selfresistance and conductor segment when mutual resistance, need to ask according to equivalent redius.Because equivalent redius is timevarying parameter, the mutual resistance over the ground between selfimpedance and conductor of conductor is also timevarying parameter.The equivalent redius that what a in formula (30), (31) referred to is exactly after spark discharge, the over the ground selfresistance of a to conductor segment self has the greatest impact, and therefore must use equivalent redius calculating selfimpedance 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:
Wherein, S
_{j}for the equivalent crosssection 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 kth2, k1 and k section, and the conductor segment be connected on node j has kth, k+1 and k+2 section.Obtain kth2, k1 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 (k2)
^{}, (k1)
^{+}(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 (k2)
^{}, (k1)
^{+}(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:
In formula, L
_{k2}, L
_{k1}, L
_{k}the 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 kth2, k1 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
Wherein,
with
be respectively (k2)
^{}, (k1)
^{+}(k)
^{}current potential in section;
For whole grounding body, being write as matrix form is:
Internodal mutual resistance matrix is:
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 abovedescribed 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, selfinduction and frequency dependent characteristic is determined;
(5) mutual resistance and timevarying characteristics between the selfresistance 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:
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 × b}the incidence matrix between node and branch road, E
_{n × n}it 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:
In formula, Φ
_{n}each 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:
In formula,
for the incidence matrix between node and branch road, Φ
_{n}for 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:
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:
In formula, N
_{n × b}for 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 × b}for:
In formula, l
_{ij}for the length of the conductor segment that this node is connected, L
_{k}for the length of kth bar branch road, q is the branch road number associated with node i, L
_{p}for 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 selfimpedance Z of each conductor segment of each moment
^{c}conversion is determined; Described selfimpedance Z
^{c}determined by following formula:
In formula, σ
_{c}and μ
_{c}be respectively conductivity and the magnetic permeability of conductor material therefor, a is the equivalent redius of cylindrical conductor, I
_{0}and I
_{1}be respectively first kind zeroth order and the firstorder bessel function of correction;
The selfinduction L of described grounding body conductor is determined by following formula:
L＝L
^{e}+L
^{c}
In formula, L
^{e}for the outer selfinduction of cylindrical conductor section, L
^{c}for the selfinductance of conductor segment everywhere;
Described selfinductance L
^{c}by the selfimpedance Z of each conductor segment of each moment
^{c}conversion is determined; Described outer selfinduction L
^{e}determined by following formula:
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:
In formula, w is cosine wave frequency, is also the equivalent frequency of t lightning current; I
_{light}(tΔ t), I
_{light}(t) what I
_{light}(t+ Δ t) is respectively three thunder and lightning flow valuves in tΔ 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 selfresistance 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 selfresistance is over the ground:
When the horizontal buried depth of grounding body is in h soil, described selfresistance is over the ground:
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:
In formula, l
_{i}represent the path of integration of ith conductor segment, l
_{j}represent the path of integration of jth root conductor segment, l
_{i}' represent the path of integration of ith conductor segment mirror image in atmosphere, D
_{ij}represent the segment dl respectively on conductor segment i and conductor segment j two path of integration
_{i}and dl
_{j}between distance, D
_{i'j}represent 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
_{j}between 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 selfresistance and conductor segment when mutual resistance, need to determine according to described equivalent redius a; Because equivalent redius a is timevarying parameter, the mutual resistance over the ground between selfimpedance and conductor of conductor is also timevarying 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:
with
be respectively the conductor segment be connected in node i to have in kth2, k1 and k section (k2)
^{}, (k1)
^{+}(k)
^{}duan Yu (k)
^{+}mutual resistance between section; L
_{k2}, L
_{k1}, L
_{k}the length of the conductor segment be connected with node i;
with
the electric current that the conductor segment be connected in node i has kth2, k1 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:
Wherein,
with
be respectively (k2)
^{}, (k1)
^{+}(k)
^{}current potential in section;
For whole grounding body, each node potential Φ
_{n}matrix form be:
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 × 2b}for weight coefficient matrix, i.e. the relational matrix of node and new conductor segment;
Then internodal mutual resistance matrix, namely impulse earthed resistance is:
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 selfimpedance 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:
Wherein, S
_{j}for the equivalent crosssection of jth root conductor segment.
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CN110889225A (en) *  20191128  20200317  贵州电网有限责任公司  Method for calculating grounding resistance of artificial grounding body 
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