CN112784516B - High-voltage direct-current transmission direct-current magnetic bias level calculation method based on unified loop construction - Google Patents
High-voltage direct-current transmission direct-current magnetic bias level calculation method based on unified loop construction Download PDFInfo
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Abstract
The invention discloses a high-voltage direct-current transmission direct-current magnetic bias level calculation method based on unified loop construction, which comprises the following steps of: 1) obtaining a soil model of a high-voltage direct-current transmission radiation area; 2) dividing the soil model into a plurality of hexahedral unit grids; 3) calculating the axial resistance value of each unit grid; 4) constructing a three-dimensional resistance network; 5) establishing a system matrix equation; 6) obtaining the surface potential distribution; 7) establishing an underground-overground unified loop model comprising a soil model and an alternating current line based on the surface potential distribution; 8) to obtain neutral point current I ij . The method can be widely applied to simulation calculation work of the direct current magnetic biasing level of the substation in the early stage of direct current transmission planning, and has good practical value and application prospect for evaluating whether the current magnitude of the neutral point of the substation meets safety regulations and preventing and controlling the direct current magnetic biasing effect in advance.
Description
Technical Field
The invention relates to the field of electric engineering direct current electric field calculation, in particular to a high-voltage direct current transmission direct current magnetic biasing horizontal simulation calculation method based on an underground-overground unified loop model construction technology.
Background
In recent years, the ultra-high voltage direct current transmission technology in China has been developed vigorously, and has become the country with the most direct current transmission projects built and operated in the world. With the standardized large-scale application of the +/-800 kV direct-current transmission project and the start construction of the +/-1100 kV direct-current project, China enters a new key period in the technical field of direct-current transmission. When the direct current transmission is in monopolar earth or bipolar unbalanced operation, partial direct current flows into an alternating current system through a transformer with a neutral point grounded near an earth electrode, and the problems of direct current magnetic biasing, vibration, noise, temperature rise, harmonic waves and the like of the transformer are caused. Under the operation mode of the single-pole ground return wire of the direct current system, when direct current flows into the ground through the grounding electrode, a constant direct current field can be formed in soil near the grounding electrode site, and components such as a transformer substation, an underground metal pipeline and the like with a nearby transformer neutral point grounded can provide a better conduction channel for the ground current than the ground soil, so that adverse effects are brought to equipment facilities and an above-ground alternating current system. At present, the research on the influence of the ground current of the direct current transmission project on the alternating current system can be divided into two stages: firstly, the distribution characteristics and the influence factors of an underground current field of a direct-current transmission project are mainly researched, and the surface potential distribution and the corresponding electrical parameters near an earth electrode are calculated; and secondly, establishing a direct current distribution calculation model comprising an integral overground alternating current power grid and an integral underground grounding grid, and solving the direct current in the transformer by utilizing the surface potential.
The neutral point current is an important index for reflecting the safe operation of electric power facilities in a high-voltage direct-current transmission radiation area. The current of the neutral point of the transformer is overlarge, so that the direct-current magnetic biasing effect is caused, and the safe and stable operation of power equipment such as the transformer and the like can be seriously influenced. Therefore, the simulation calculation of the current of the neutral point of the transformer is necessary work for evaluating the direct current magnetic biasing level of the alternating current power grid during direct current engineering planning and taking inhibition measures in advance, and the calculation method mainly comprises the steps of firstly establishing a direct current model of the overground alternating current power grid, then coupling the direct current model with the ground potential of the grounding point of the transformer substation, establishing an underground-overground field coupling model, forming an active loop, and finally calculating the direct current distribution of the overground alternating current power grid. Although the distribution characteristics of the underground current field and the complexity of the ground network can be fully considered in the process, the calculation process is too complicated and low in efficiency, and the underground-ground field circuit coupling model does not consider the influence of a transformer substation or an alternating current network when calculating the ground potential distribution, and is actually combined although the coupling is adopted. Some researches establish a three-dimensional model of a soil structure by using finite element analysis software and the like, and calculate the direct current distribution of the power grid by simplifying the connection between the underground transformer substations. The method considers the influence of a transformer substation or an alternating current network on the ground surface potential, but because the size of the ground power grid is greatly different from that of soil, a low-quality grid is inevitably generated when the grid is divided by a finite element, and the accuracy of the direct current distribution result of the power grid is difficult to guarantee.
Disclosure of Invention
The invention aims to provide a high-voltage direct-current transmission direct-current magnetic bias level simulation calculation method based on an underground-overground unified loop model construction technology, which comprises the following steps of:
1) and obtaining a soil model of the high-voltage direct-current transmission radiation area.
2) And dividing the soil model of the high-voltage direct-current transmission radiation area into a plurality of hexahedral unit grids. The center point of the cell grid is marked as the resistivity representative point of the corresponding grid. The resistivity of the center point of the cell grid characterizes the resistivity of the entire cell grid.
3) And calculating the axial resistance value of each unit grid.
The axial resistance values of the unit grids are respectively as follows:
in the formula, ρ i Is the resistivity of the ith cell. dx, dy and dz are the lengths of the cell grid in the x, y and z directions, respectively. Rx, Ry and Rz are the axial resistance values of the cell grid in the positive or negative directions of the x, y, z axes, respectively.
4) And connecting the central points of the grids of the adjacent units, and linearly combining the axial resistances of the adjacent units to construct a three-dimensional resistance network.
5) And establishing a node admittance matrix A of the three-dimensional resistance network. And establishing a system matrix equation based on the node admittance matrix and the source point information.
The step of establishing the node admittance matrix of the three-dimensional resistance network comprises the following steps:
5.1) adopting a node voltage method to construct a node voltage equation of all node potentials and currents entering and exiting the three-dimensional resistance network, namely:
in the formula (I), the compound is shown in the specification,
and I is a column vector comprising the magnitude and the position of the grounding current of the grounding electrode. In the column vector I, only the node where the grounding electrode is located has a numerical value, and other nodes are all 0. The dimension of matrix a is n × n. Column vector
And the dimensions of the column vector I are each n × 1. The admittance matrix a is set to a sparse matrix.
5.2) calculating admittance matrix A of all nodes based on the node voltage equation, namely:
in the formula, n is the number of all nodes. R ij Is the resistance between the ith node and the jth node. A. the ii Is the self-admittance of each node and is located on the diagonal of the nodal admittance matrix. A. the ij Is the mutual admittance between different nodes.
6) And solving a system matrix equation by using a stable double-conjugate gradient method to obtain the surface potential distribution.
7) And establishing an underground-overground unified loop model comprising a soil model and an alternating current line based on the surface potential distribution.
The underground-ground unified loop model comprises a three-dimensional resistance network representing a ground model and a ground alternating current circuit equivalent model connected with the three-dimensional resistance network.
8) Solving the underground-overground unified loop model by using a stable double-conjugate gradient method to obtain a neutral point current I ij 。
The method for solving the underground-overground unified loop model by using the stable double-conjugate gradient method comprises the following steps:
8.1) establishing node admittance matrix A of the underground-overground unified loop model total Namely:
A total ＝A soil +A line (4)
in the formula, A soil And (4) a node admittance matrix of the soil model. A. the line And (4) carrying out admittance matrix on nodes among transformer stations. Matrix A soil And matrix A line Are the same.
8.2) obtaining the equivalent resistance R of the ground line ij (ii) a Based on node admittance matrix A total And calculating the potential distribution of each node in the loop model by using a stable double-conjugate gradient method.
8.3) calculating the neutral Point Current I ij Namely:
I ij ＝(U i -U j )/R ij (5)
in the formula, i and j are the numbers of the substation nodes respectively. U shape i ，U j Respectively the potentials at the nodes of two substations, R ij Is the equivalent resistance of the ground line.
The technical effect of the invention is undoubted, the invention can more accurately and effectively carry out simulation calculation on the direct current magnetic biasing level of the grounding transformer in the transformer substation in the high-voltage direct current transmission radiation area, and the reasonable degree and the accuracy of the neutral point current calculation model can better accord with the actual situation. The method not only processes the soil model from a three-dimensional angle, but also considers the difference between the sizes of the soil structure and the ground line, so that the researched calculation model can better accord with the real coupling condition, and the direct current distribution result of the power grid, namely the neutral point current prediction, has practical value. The invention models the soil model from a three-dimensional angle, and the ground line is equivalent to the resistance, and the neutral point current is jointly solved on the soil three-dimensional resistance network, thereby realizing the mutual coupling of the underground model and the ground model. Meanwhile, the three-dimensional effect of the soil is considered, and the real reliability of the calculation model is realized on the three-dimensional layer.
The method can be widely applied to simulation calculation work of the direct current magnetic biasing level of the substation in the early stage of direct current transmission planning, and has good practical value and application prospect for evaluating whether the current magnitude of the neutral point of the substation meets safety regulations and preventing and controlling the direct current magnetic biasing effect in advance.
Drawings
FIG. 1 is a block flow diagram of the process of the present invention;
FIG. 2 is a soil model subdivision schematic diagram;
FIG. 3 is a schematic diagram of a three-dimensional resistor network;
FIG. 4 is a schematic diagram of the axial resistance of a cell grid;
FIG. 5 is a schematic view of a subsurface-above ground identical circuit model;
FIG. 6 is a diagram of BiCGSTAB method pseudo-codes;
FIG. 7(1) is a comparison graph of the earth surface potential distribution obtained by finite element method and unified model resolving the model 1 in the Table 1;
fig. 7(2) is a comparison graph of the surface potential distribution of the finite element method and the unified model solution table 1 model 2.
FIG. 7(3) is a comparison graph of the surface potential distributions of the finite element method and the unified model solution Table 1 model 3.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
referring to fig. 1 to 6, the high-voltage direct-current transmission direct-current magnetic bias level simulation calculation method based on the underground-overground unified loop model construction technology comprises the following steps:
1) and obtaining a soil model of the high-voltage direct-current transmission radiation area.
2) And dividing the soil model of the high-voltage direct-current transmission radiation area into a plurality of hexahedral unit grids. The center point of the cell grid is marked as the resistivity representative point of the corresponding grid. The resistivity of the center point of the cell grid characterizes the resistivity of the entire cell grid.
3) And calculating the axial resistance value of each unit grid.
The axial resistance values of the unit grids are respectively as follows:
in the formula, ρ i Is the resistivity of the ith cell. dx, dy and dz are the lengths of the cell grid in the x, y and z directions, respectively. Rx, Ry and Rz are the axial resistance values of the cell grid in the positive or negative directions of the x, y, z axes, respectively.
4) And connecting the central points of the adjacent unit grids, namely connecting the central points of all the unit grids along the three directions of x, y and z, wherein the connection sequence is not limited, and the axial resistances of the adjacent units are linearly combined, so that the three-dimensional resistance network is constructed.
5) And establishing a node admittance matrix A of the three-dimensional resistance network. And establishing a system matrix equation based on the node admittance matrix and the source point information.
The step of establishing the node admittance matrix of the three-dimensional resistance network comprises the following steps:
5.1) adopting a node voltage method to construct a node voltage equation of all node potentials and currents entering and exiting the three-dimensional resistance network, namely:
in the formula (I), the compound is shown in the specification,
for all nodesBit, I is a column vector containing the magnitude and location of the ground current to the ground electrode. In the column vector I, only the node where the grounding electrode is located has a numerical value, and other nodes are all 0. The dimension of the matrix a is n × n. Column vector
And the dimensions of the column vector I are each n × 1. The admittance matrix a is set to a sparse matrix.
5.2) calculating admittance matrix A of all nodes based on the node voltage equation, namely:
in the formula, n is the number of all nodes. R ij Is the resistance between the ith node and the jth node. A. the ii Is the self-admittance of each node and is located on the diagonal of the nodal admittance matrix. A. the ij Is the mutual admittance between different nodes.
6) And solving a system matrix equation by using a stable double-conjugate gradient method to obtain the surface potential distribution.
7) And establishing an underground-overground unified loop model comprising a soil model and an alternating current line based on the surface potential distribution.
The underground-ground unified loop model comprises a three-dimensional resistance network representing a ground model and a ground alternating current circuit equivalent model connected with the three-dimensional resistance network.
8) Solving the underground-overground unified loop model by using a stable double-conjugate gradient method to obtain a neutral point current I ij The method comprises the following steps:
8.1) establishing node admittance matrix A of the underground-overground unified loop model total Namely:
A total ＝A soil +A line (4)
in the formula, A soil And (4) a node admittance matrix of the soil model. A. the line And (4) carrying out admittance matrix on nodes among transformer stations. Matrix A soil And matrix A line Are the same.
8.2) obtaining the equivalent resistance R of the ground line ij . Based on node admittance matrix A total And calculating to obtain the potential distribution of each node in the traditional loop model by using a stable double-conjugate gradient method, namely obtaining the potential values of all the nodes.
8.3) calculating the neutral Point Current I ij Namely:
I ij ＝(U i -U j )/R ij (5)
in the formula, i and j are the numbers of the substation nodes respectively. U shape i ，U j Respectively the potentials at the nodes of two substations, R ij Is the equivalent resistance of the ground line.
Example 2:
referring to fig. 7, the high-voltage direct-current transmission direct-current magnetic bias level simulation calculation method based on the underground-overground unified loop model construction technology comprises the following steps:
1) discrete subdivision of soil model
The existing conditions of the two transformer substations are calculated, point current sources for simulating the high-voltage direct-current transmission grounding current and grounding current are all located 3m below the ground surface, and the positive and negative poles of the grounding electrode source point and the two transformer substations are all on the same straight line. An underground-overground unified model with the same structure is established by using a finite element method, the equivalent resistance of an overground power grid is simulated by using a long straight conductor, and two ends of the conductor are connected with nodes of a transformer substation in the soil model. The model of different soil scales is shown in table 1, wherein the soil resistivity of different models and the resistivity of the long straight conductor are kept unchanged, and are respectively 100 Ω · m and 1 Ω · m, and the line equivalent resistance is the equivalent resistance of the long straight conductor.
The method adopts the principle of equal-distance subdivision in the directions of x, y and z for the dispersion of the three soil models, namely the lengths of single grids of the three models are 1m, 10m and 100m respectively.
TABLE 1 calculation of model parameters
| Model (model) | Soil model scale | In/out ground current | Distance between transformer stations | Equivalent resistance of |
| 1 | 0.1km×0.1km×0.06km | 10A/-10A | 0.04km | 57.749Ω |
| 2 | 1km×1km×0.6km | 100A/-100A | 0.4km | 15.991Ω |
| 3 | 10km×10km×6km | 1000A/-1000A | 4km | 13.71Ω |
2) Establishment of three-dimensional resistor network
After the soil structure is dispersed into a plurality of hexahedral unit grids, the centers of all the units are respectively connected along the three directions of x, y and z, and the axial resistances of the adjacent units are linearly combined, so that the three-dimensional resistance network shown in the attached figure 2 can be formed.
When analyzed on a single grid, the resistive effect is equivalent to the axial resistance between the center of the cell and the six surfaces, as shown in FIG. 3. The resistance network node represents the center of all unit grids of the discrete earth electric structure, and the resistance between the nodes is the sum of the corresponding axial resistances of the adjacent units. The determination of the axial resistance value may be referenced to a calculation formula for the transmission line resistance. For model 1, the axial resistance value is:
3) establishment and post-processing of system matrix equation
After the resistance network of the soil structure is established, a node voltage method is adopted to establish a node voltage equation of all node potentials and currents entering and exiting the resistance network. Part of the system equations corresponding to model 1 in table 1 are given below.
A is a square matrix with dimensions of 600k x 600k,
and I are both arrays with dimensions 600k 1. It should be noted that the dimension of the node admittance matrix a is usually very large, and most areas in the matrix are 0, so in order to save the calculation memory and reduce the calculation time, it is necessary to set a as a sparse matrix for storage.
4) Solution of surface potential
In order to rapidly and accurately solve the equation node voltage equation, considering the sparsity and symmetry of the node admittance matrix A and the large dimensionality of the node admittance matrix A, a stable double conjugate gradient method (BiCGSTAB) is adopted to iteratively solve the equation, and then the node potential of the earth surface position is taken to obtain the earth surface potential distribution.
5) Construction of underground-overground unified loop model
The DC model of the ground AC power grid can be simplified into a pure resistance model through the actual position of the transformer substationThe equivalent nodes in the resistance network are connected with the resistance network to form an underground-overground unified loop model, as shown in figure 5. The node admittance matrix A between model 1 and the strain power station in Table 1 is given below line Comprises the following steps:
thus, when analyzing two substation nodes, the neutral point current is:
I ij ＝(U i -U j )/R ij (5)
in the formula, i and j are respectively the serial numbers of the nodes of the transformer substation, U i ，U j Respectively the potentials at the two substation nodes, R ij Is the equivalent resistance of the ground line.
The earth surface potential distribution obtained by the method and the three models calculated by the finite element method are respectively shown in the attached figure 7. The neutral point current values calculated by the three models are compared with the finite element method as shown in table 2.
TABLE 2 neutral point Current (A)
| Model (model) | Finite element method | Unified | Relative error | |
| 1 | 0.2488 | 0.2296 | 7.72％ | |
| 2 | 1.2384 | 1.2629 | 1.98％ | |
| 3 | 6.3799 | 6.9866 | 9.51％ |
The experimental effect is as follows:
1) as can be seen from fig. 7, the potential attenuation trends of the potential distribution curves of the finite element method and the uniform model method corresponding to each model are substantially the same, and the potential amplitudes at the two substation nodes are reduced to a certain degree relative to the adjacent nodes, and the reduced amplitudes are approximately the same. As can be seen from table 2, for the three models with different dimensions, the neutral point currents obtained by the two methods are not different greatly, and the relative error is less than 10%. Therefore, the unified model method can be considered to have certain feasibility and accuracy for calculating the system neutral point current.
2) In the underground-overground unified loop model, only the soil model is divided, the overground branches are equivalent to a single resistor, and the contribution of the resistor to the increase of the number of grids is 0, so that the difference between the overground transmission line scale and the soil scale is not required to be considered. For a wide-area direct current transmission model, the ground transmission line scale and the soil scale are quite different, and in simulation calculation, when a long direct conductor is processed by a finite element method, the number of grids of the whole model is greatly increased, and the calculation difficulty and time consumption are further increased. Therefore, the unified model method enables the ground branch to be equivalent to a single resistor, and has algorithm superiority compared with the finite element method.
Claims (4)
1. The method for calculating the DC magnetic bias level of the high-voltage DC power transmission constructed based on the unified loop is characterized by comprising the following steps of:
1) obtaining a soil model of a high-voltage direct-current transmission radiation area;
2) dividing a soil model of the high-voltage direct-current transmission radiation area into a plurality of hexahedral unit grids;
3) calculating the axial resistance value of each unit grid;
the axial resistance values of the unit grids are respectively as follows:
in the formula, ρ i Is the resistivity of the ith cell; dx, dy and dz are the lengths of the unit grid in the x, y and z directions respectively; rx, Ry and Rz are the axial resistance values of the cell grid in the positive or negative directions of the x, y, z axes, respectively;
4) connecting the central points of the adjacent unit grids, and linearly combining the axial resistances of the adjacent units to construct a three-dimensional resistance network;
5) establishing a node admittance matrix A of the three-dimensional resistance network; establishing a system matrix equation based on the node admittance matrix and the source point information; the source point information comprises the position and the current magnitude of a source point;
the step of establishing the node admittance matrix of the three-dimensional resistance network comprises the following steps:
5.1) adopting a node voltage method to construct a node voltage equation of all node potentials and currents entering and exiting the three-dimensional resistance network, namely:
in the formula (I), the compound is shown in the specification,
i is a column vector including the magnitude and the position of the grounding current of the grounding electrode; only the node where the grounding electrode is located in the column vector I has a numerical value, and other nodes are all 0; the dimension of the matrix A is n multiplied by n; potentials of all nodes
And the dimensions of the column vector I are n multiplied by 1;
5.2) calculating admittance matrix A of all nodes based on the node voltage equation, namely:
in the formula, n is the number of all nodes; r ij The resistance between the ith node and the jth node; a. the ii Is the self-admittance of each node and is positioned on the diagonal of the node admittance matrix; a. the ij Mutual admittance between different nodes;
6) solving a system matrix equation by using a stable double-conjugate gradient method to obtain surface potential distribution;
7) establishing an underground-overground unified loop model comprising a soil model and an alternating current line based on the surface potential distribution;
8) solving the underground-overground unified loop model by using a stable double-conjugate gradient method to obtain a neutral point current I ij The method comprises the following steps:
8.1) establishing node admittance matrix A of the underground-overground unified loop model total Namely:
A total ＝A soil +A line (4)
in the formula, A soil A node admittance matrix for the soil model; a. the line An admittance matrix of nodes among transformer stations; matrix A soil And matrix A line Are the same in dimension;
8.2) obtaining the equivalent resistance R of the ground line ij (ii) a Based on node admittance matrix A total Calculating to obtain the potential distribution of each node in the loop model by using a stable double-conjugate gradient method;
8.3) calculating the neutral Point Current I ij Namely:
I ij ＝(U i -U j )/R ij (5)
in which i, j are eachNumbering the transformer substation nodes; u shape i ，U j Respectively the potentials at the nodes of two substations, R ij Is the equivalent resistance of the ground line.
2. The method for calculating the DC bias level of the HVDC based on the unified loop architecture of claim 1, wherein: recording the central point of the unit grid as a resistivity representative point of the corresponding grid; the resistivity at the center point of the cell grid characterizes the resistivity of the entire cell grid.
3. The method for calculating the DC bias level of the HVDC based on the unified loop architecture of claim 1, wherein the admittance matrix A is set as a sparse matrix.
4. The HVDC DC bias level calculation method based on unified loop construction according to claim 1, wherein the underground-to-aboveground unified loop model comprises a three-dimensional resistance network representing a ground model and an aboveground AC line equivalent model connected to the three-dimensional resistance network.
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