CN111753247B - Method for acquiring horizontal layered soil grounding parameters by using segmented sampling - Google Patents

Abstract

The invention discloses a method for acquiring horizontal stratified soil grounding parameters by means of segmented sampling, which is a method for computing the green function by means of segmented sampling according to integral kernel function extreme points of the green function in stratified soil. Through the analysis of the examples and the comparison of CDEGS calculation results, the effectiveness and the correctness of the work of the invention are verified. The research result shows that the calculation method provided by the invention has excellent calculation efficiency and adaptability, and can provide theoretical reference for ground parameter analysis and ground device design in layered soil.

Description

A Method of Obtaining Grounding Parameters of Horizontally Layered Soil Using Segmented Sampling

technical field

The invention belongs to the field of power systems, and in particular relates to a method for obtaining grounding parameters of horizontally layered soil by subsection sampling.

Background technique

The grounding device is the prerequisite for the safe and stable operation of the power system and power equipment. Accurate calculation of grounding parameters lays a theoretical foundation for the design, operation and maintenance of grounding devices. The grounding device is buried in the soil, and the stratification of the soil medium greatly increases the difficulty of calculating the grounding parameters. Therefore, the calculation of grounding parameters in horizontally stratified soil media has always been a focal issue in the field of electrical grounding.

At present, many researches at home and abroad are still mainly based on the complex image method under global sampling to improve the calculation method of grounding parameters, which has not fundamentally solved the calculation problem caused by global sampling. Global sampling usually cannot accurately invert the integral kernel function of the Green's function in complex stratified soil with many layers and large thickness, which may easily lead to inaccurate calculation results or no convergence at all. In addition, the number of complex mirror methods is twice the number of soil layers, and there is a disadvantage that the amount of calculation increases linearly with the number of soil layers. For example, taking a 10-layer soil as an example, the soil resistivity of the 10th layer of the soil is 100, 233, 42.9, 185.7, 11.1, 185.7, 900, 150, 42.9, 17.6, from the 1st layer to the 9th layer The soil thickness is 2m, 6m, 33m, 120m, 188m, 270m, 301m, 332m, 368m, and the integral kernel function cannot be fitted by the global sampling method at all.

Contents of the invention

The existing calculation methods of grounding parameters in layered soils are mainly based on the complex image method under global sampling. On the one hand, for a complex soil model with many layers and large thickness, global sampling may cause problems such as large errors in calculation results or non-convergence; is a problem that increases linearly with the number of soil layers. In view of this, the present invention proposes a method for obtaining grounding parameters in horizontally layered soil. By analyzing the segmental sampling calculation method of Green's function in horizontal layered soil, the grounding parameters calculation of the grounding device in layered soil is studied.

The technical scheme that the present invention adopts is as follows:

A method for obtaining grounding parameters of horizontal layered soils by subsection sampling, comprising the following steps:

Establish a horizontal layered soil calculation model under the cylindrical coordinate system, and divide the soil into n layers horizontally;

Construct the integral kernel function including soil layer structure parameters, further construct the second integral kernel function and perform segmental sampling according to the extreme points of the second integral kernel function, perform third-order fitting on different segments, and then pass the integral variable Replacement, according to the integral nature of the Bessel function and combined with the integration by parts method to solve the above integral, obtain the soil Green's function whose source point is in the first layer;

Divide the grounding device into several small sections, and define two types of nodes on the grounding device: the first type of node is the e-type conductor node, and it is considered that the external injection current passes through the e-type node, and the second type of node is the m-type grounding node. There is only leakage current on the

Using the node voltage method, establish the node voltage equation including e-type nodes and m-type nodes and the voltage equation only for m-type nodes;

According to the above two sets of node voltage equations, the potential of any node on the grounding grid is solved, and the leakage current I _mi of each m-type node is further obtained;

The leakage current I _mi of each section is regarded as a point source, combined with the soil Green's function of the first layer, and the superposition principle is used to obtain the grounding resistance and surface potential distribution of the grounding device.

The present invention also calculates the grounding parameters of typical grounding devices in three typical layered soils, and compares the calculation results of CDEGS to verify the effectiveness and accuracy of the work of the present invention.

The segmental sampling numerical calculation method of the grounding parameters in the horizontal layered soil proposed by the present invention performs segmental sampling according to the extremum point of the integral kernel function, avoiding the deficiency that the amount of calculation increases linearly with the number of soil layers in the traditional complex image method, It has higher computational efficiency. For example, when calculating the grounding resistance with monotonic soil resistivity, no matter how many soil layers there are, as long as the integral kernel function F(λ) does not have an extreme point, only a fixed number of sampling points are needed, and the calculation amount will not increase.

The global sampling method is not suitable for thicker soil layers. When the soil layer thickness is too thick, the sampling step size is too small, which will cause the calculation results to diverge. In addition, the actual soil stratification is complex and changeable, and the global sampling method cannot avoid missing the key features of the integral kernel function. After subsection sampling, the grounding parameters in any complex horizontal layered soil can be calculated more accurately, and it has stronger adaptability.

In the calculation of the grounding parameters, the grounding device is divided into several small sections and the m and e sections are defined. The e-type nodes are the two end nodes of each section. It is considered that the external injection current passes through the e-type nodes, and the m-type nodes are at the midpoint of each section, and there is only leakage current on this node, and it is not connected to external electrical equipment. , no external current injection. Such processing makes there be a slight potential difference between different nodes, which solves the problem that different nodes are not equipotential in practice.

The calculation method proposed by the invention lays a solid theoretical foundation for the design of the grounding device and the accurate calculation of the grounding parameters in the layered soil medium.

Description of drawings

Figure 1 is the Green's function in stratified soil;

Figure 2 is the distribution of F(λ);

Fig. 3 is the actual model of the rectangular frame grounding grid;

Fig. 4 is a rectangular box ground grid circuit model;

Figure 5 is the calculation model of the horizontal ground electrode;

Figure 6 is the calculation of the leakage current of the horizontal ground electrode.

Detailed ways

A non-limiting example is given below to further illustrate the method of the present invention.

The method of the present invention is concretely analyzed below:

(1) Establishment of Green's function in horizontally stratified soil

According to the basic electromagnetic field theory, a horizontally layered soil calculation model in the cylindrical coordinate system is established, as shown in Figure 1. Using the method of solving the spatial Poisson equation, the potential equation of any point in the i-th layer of soil:

In formula (1), δ is the point current source located in the first layer of soil in the soil medium, and _ρ1 is the resistivity of the first layer of soil where the point current source is located. is the potential of any point in the soil, and r and z are the coordinates in the r and z directions in the cylindrical coordinate system.

The layered soil boundary conditions are:

is the potential at the interface of the first layer of soil, /> is the potential of the i-th layer soil interface, h ₀ is the vertical distance from the source point to the surface, h _i is the vertical distance of the i-th layer soil lower interface below the surface, _ρi represents the resistivity of the i-th layer soil, i=1,2,3...n, n is the number of soil layers.

Using the method of separating variables in cylindrical coordinates, formula (1) can be written as the following general formula:

in is the potential of the source point in the first layer of soil, J ₀ (λr) is the Bessel function of the first kind, A _i (λ,X) and B _i (λ,X) are integral kernel functions, and X is the layered The resistivity and thickness of the soil, λ is the integral constant.

When the source point is located in the first layer of soil, formula (3) can be rewritten as:

Among them, G ₁ (r,z) is the Green's function whose source point is in the first layer of soil, h ₀ is the buried depth of the source point, and f(λ) is the integral kernel function including the soil layer structure parameters.

The expression of f(λ) is:

(2) Segmented sampling calculation of Green's function

Define a new integral kernel function (that is, the second integral kernel function) F(λ):

As the number of soil layers increases, F(λ) cannot obtain its analytical expression. In order to ensure that the approximate expression can well approximate the actual function F(λ), the distribution law of F(λ) needs to be studied, and z ₀ is the vertical distance between the field point and the point source.

Let the point source buried depth _h0 be 0.8m, _z0 be 0.006m (choose the calculation position of the potential on the surface of the round steel grounding conductor with a radius of 0.006m). Select horizontal 2-layer soil to horizontal 5-layer soil with monotonic soil resistivity, and calculate F(λ) of layered soil.

Among them, soil parameters of horizontal 5 layers ρ ₁ =50, ρ ₂ =100, ρ ₃ =150, ρ ₄ =200, ρ ₅ =250, h ₁ =2, h ₂ =1, h ₃ =1.5, h ₄ =1 , the horizontal 4-layer soil parameters are ρ ₁ , ρ ₂ , ρ ₃ , ρ ₄ and h ₁ , h ₂ , h ₃ , and so on for 2-layer soil and 3-layer soil. The parameters of complex horizontal 8-layer soil are ρ ₁ =100, ρ ₂ =550, ρ ₃ =250, ρ ₄ =190, ρ ₅ =30, ρ ₆ =900, ρ ₇ =350, ρ ₈ =50, h ₁ =2, h ₂ =10, h ₃ =30, h ₄ =130, h ₅ =50, h ₆ =350, h ₇ =450. The calculation results are shown in Figure 2.

Figure 2 shows that 1) when F(λ) is monotonous in soil resistivity, the distribution of F(λ) in any multi-layered soil is similar to that of horizontal 2 layers; 2) the distribution of F(λ) in complex layered soil may have multiple an extreme point.

According to the extreme points of F(λ), the F(λ) is sampled in sections, and then the third-order least square method is used to fit the F _i (λ) on the i-th segment, which can be obtained as follows:

a _k is the coefficient of each term in the fitted polynomial.

The Green's function in stratified soils translates to:

Where λ ₀ is 0, and λ _n is the value of λ when F(λ) is 0.01 or -0.01. When λ>λ _n , it can be considered that F(λ) is always equal to 0.

Let x=λr replace the integral variable, and according to the integral properties of the Bessel function combined with the integration by parts method, the above integral can be solved, so as to obtain the Green's function G(r) of the stratified soil whose source point is in the first layer.

(3) Numerical calculation of segmental sampling grounding parameters

Two types of nodes are defined. The first type of node is the e-type conductor node, which is the two end nodes of each segment, and the external injection current is considered to pass through the e-type node. The second type of node is the m-type ground (leakage current) node, which is the midpoint of each segment, and there is only leakage current on this node, no connection with external electrical equipment, and no external current injection.

Taking the rectangular frame grounding grid as an example, the number of segments is 4 segments, and the segment length is consistent with the actual rectangular frame side length. The four corners of the frame are e-type nodes for external current injection; Points flow out, and the midpoint of the segment should be 4 m-type nodes. The analysis model of the frame ground grid is shown in Figures 3 and 4.

Write out the node voltage equations for all e-type nodes and m-type nodes according to the column in Figure 4:

Among them, Y _j,i is the mutual admittance between node j and node i, Y _j,j is the self-admittance of node j, I _ei is the injected current on the e-type node ei, I _mi is the m-type node mi on leakage current. In the calculation process of the grounding grid, I _ei is usually the grounding current of the grounding electrical equipment, which can be obtained by measurement, but the leakage current I _mi of the grounding grid is an unknown quantity and cannot be obtained by measurement. In order to eliminate the leakage current variable, the following node voltage equation should be written only for m-type nodes:

R _j,i is the mutual resistance of m-type nodes, and R _j,j is the self-resistance of m-type nodes.

The simultaneous formula (10) (11) eliminates the leakage current I _mi , and obtains the matrix equations of all node voltages and injection current I _ei .

The above analysis is based on the electrical network model of simple nodes, and formulas (10) (11) can be extended to any node:

RI _m =U _m (13)

Among them, Y _ee and Y _mm are the self-guidance of e-type nodes and m-type nodes respectively, and Y _em and Y _me are equal, which are the mutual conductance of e-type nodes and m-type nodes. U _e is the node voltage of e-type nodes, U _m is the node voltage of m-type nodes, I _e is the injection current of e-type nodes, I _m is the leakage current of m-type nodes, R is the mutual resistance or self-resistance of m-type nodes resistance.

Simultaneous formula (12) (13) can get:

According to formula (14), the potential of any node on the grounding grid can be obtained, and further according to formula (11), the leakage current I _mi of each type m node can be obtained. The leakage current I _mi of each segment is regarded as a point source, and the grounding resistance and ground potential distribution of any grounding device can be obtained by using the superposition principle. The above calculation can realize the calculation of the grounding parameters of any grounding device with different potentials.

The present invention mainly aims at the low-frequency steady-state characteristics of the grounding device, ignoring the inductive part of the grounding device, and the admittance in formula (14) becomes conductance. The target node is connected to the adjacent nodes through the ground conductor, and the other nodes are connected through the soil medium. The conductance of the conductor is much greater than that of the soil medium, and the self-conductance of the node can be approximately considered as the conductance of the adjacent segmented metal conductor. The self-conductance and mutual conductance of the m-type nodes can be obtained as:

Among them, ρ is the resistivity of the metal conductor, S is the cross-sectional area of the conductor, l is the length of the segmented conductor, and is the conductivity of the conductor.

The self-conductance of the e-type node is:

Among them, N represents a total of N segments of conductors connected to the end node e, ρ _i is the resistivity of the i-th segment conductor connected to node e, S _i is the cross-sectional area of the i-th segment conductor, l _i is the i-th segment conductor's length.

The mutual conductance of the target node and non-adjacent nodes needs to be solved by the Green's function of the point source in the layered soil. The physical meaning of the point current source is the linear current density on the micro-segment, and it has been assumed that the current is uniformly distributed on each segment. The matching point is selected at the midpoint of each segment, and the mutual resistance generated by the source segment at the matching point is:

Among them, I _i is the leakage current of the i-th segment, and the unit is A, l _i is the length of the i-th segment, and ds is the curve integral of the micro-segment l _i of the source point. G is the Green's function of the layered soil, r _j is the position vector of the midpoint of the jth segment, and r _i is the position vector of the midpoint of the ith segment.

In order to further improve the calculation accuracy, the average potential generated by the source point segment at the matching point segment is usually used as the potential coefficient of the matching point, and its expression needs to be integrated and averaged once for the micro-segment where the matching point is located, as follows:

Where l _j is the length of the micro-segment where the matching point is located.

In this real-time example, the leakage current distribution and grounding resistance calculation of the horizontal ground electrode in three different horizontal layered soils is taken as an example. The parameters of different layered soils are shown in Table 1.

1. The diameter of the horizontal grounding pole is 12mm, so the radius r ₀ =0.006m=z ₀ , and the buried depth is 0.8m, so h ₀ =0.8m. The specific integral kernel function can be obtained by substituting h ₀ and z ₀ into formula (7). Sampling with a smaller step size to get all the extreme points corresponding to the kernel function. Then use the third-order least squares method to fit F _i (λ) on the i-th segment, and replace the integral variable, and then according to the integral properties of the Bessel function and the integration by parts method, the source point at Green's function G(r) for layer 1 stratified soil.

2. The length of the horizontal ground electrode is 10m, which is divided into 10 sections, that is, the number of the m-type nodes is from 1 to 10, and the 1A current is injected from the terminal of the No. 1 m-type node, as shown in Figure 5. The conductivity ρ of the ground electrode is 1e-7, the length of each section is l=1m, and the cross-sectional area S of the ground electrode can be calculated from the diameter of the conductor. From this, the self-conductance of m-type nodes can be calculated by formula (17). Since there is no e-node, the other conductance coefficients are all 0. Then, the potential of any node on the grounding grid can be obtained from formula (13), and the leakage current I _mi of each type m node can be obtained further according to formula (10).

3. According to the Green's function of the first layer of soil obtained above and the leakage current of each node, the grounding resistance value can be obtained by formula (17). And the calculation result is compared with the CDEGS software calculation result, as shown in accompanying drawing 6 and table 2, proves the accuracy of the method that the present invention proposes.

Table 1 Layered soil parameters

Table 2 Horizontal ground electrode ground resistance

Claims (3)

1. a method for obtaining horizontal layered soil grounding parameters with subsection sampling, it is characterized in that, may further comprise the steps: Establish a horizontal layered soil calculation model under the cylindrical coordinate system, and divide the soil into n layers horizontally; Construct the integral kernel function including soil layer structure parameters, further construct the second integral kernel function and perform segmental sampling according to the extreme points of the second integral kernel function, perform third-order fitting on different segments, and then pass the integral variable Replacement, according to the integral nature of the Bessel function and combined with the integration by parts method to solve the above integral, obtain the soil Green's function whose source point is in the first layer; The integral kernel function f(λ) The second integral kernel function F(λ), Where z ₀ is the vertical distance from the field point to the point source; The grounding device is divided into several small sections, and two types of nodes are defined on the grounding device: the first type of node is the e-type conductor node, and the external injection current is considered to pass through the e-type node, and the second type of node is the m-type grounding node. There is only leakage current on the Using the node voltage method, establish the node voltage equation including e-type nodes and m-type nodes and the voltage equation only for m-type nodes; The two sets of node voltage equations are: RI _m =U _m In the formula, Y _ee and Y _mm are the self-guidance of e-type nodes and m-type nodes respectively, Y _em and Y _me are equal, and are the mutual conductance of e-type nodes and m-type nodes, and U _e is the node of e-type nodes Voltage, U _m is the node voltage of m-type nodes, I _e is the injection current of e-type nodes, I _m is the leakage current of m-type nodes, and R is the mutual resistance or self-resistance of m-type nodes; The self-conductance and mutual conductance of m-type nodes are: Among them, ρ is the resistivity of the metal conductor, S is the cross-sectional area of the conductor, and l is the length of the segmented conductor; The self-conductance of the e-type node is: Among them, N represents that there are N segments of conductors connected to the end node e, ρ _i is the resistivity of the i-th segment conductor connected to node e, S _i is the cross-sectional area of the i-th segment conductor, l _i is the length of the i-th segment conductor ; According to the above two sets of node voltage equations, the potential of any node on the grounding grid is solved, and the leakage current I _mi of each m-type node is further obtained; The leakage current I _mi of each section is regarded as a point source, combined with the soil Green's function of the first layer, and the superposition principle is used to obtain the grounding resistance and surface potential distribution of the grounding device. 2. according to claim 1, a kind of method for acquiring horizontal layered soil grounding parameters with subsection sampling, is characterized in that: what described 3rd order fitting adopted is 3rd order least squares method. 3. according to claim 1, a kind of method for obtaining horizontal layered soil grounding parameters with subsection sampling, is characterized in that: described e class nodes are two end nodes of each subsection, and described m class nodes are at the midpoint of each segment.