Overhead ground wire loss assessment method based on improved finite element algorithm

Abstract

The invention discloses an overhead ground wire loss assessment method based on an improved finite element algorithm, belongs to the technical field of overhead ground wire loss assessment, and utilizes a mesh refinement technology to improve the approximation precision of a finite element analysis result; by using a double-variable dimension reduction method, approximate processing of a structural interval stiffness matrix is effectively simplified; the inverse matrix of the structural interval stiffness matrix is solved through Neumann series, an explicit expression of interval displacement response is obtained, and the calculation convergence speed is increased. According to the overhead ground wire loss assessment method based on the improved finite element algorithm, the problems of calculation efficiency, precision, complexity and boundary condition processing of an existing assessment method are solved, and balance of calculation precision and efficiency is achieved; the method is especially suitable for processing nonlinearity and uncertainty problems related to a plurality of interval parameters, and an efficient and accurate solution is provided for loss evaluation of the overhead ground wire.

Description

Technical Field

[0001] The invention relates to the technical field of overhead ground wire loss assessment, and in particular to an overhead ground wire loss assessment method based on an improved finite element algorithm. Background Art

[0002] With the increase in the length of power transmission lines and the increase in voltage levels, the problem of overhead ground wire loss has become increasingly prominent. As an important part of the transmission line, the overhead ground wire is exposed to the natural environment for a long time and is easily affected by factors such as climate change, mechanical stress, and electrochemical corrosion, which exacerbate the loss of the ground wire. In particular, with the continuous increase in electricity demand, the overhead ground wire bears an increasingly large power load, resulting in increasingly serious impact of ground wire loss in the operation of the power system. With the increase in voltage levels, the loss of the ground wire shows a sharp increase trend, which in turn causes an increase in the operating cost of the power system.

[0003] Since the spatial position of the overhead transmission line is asymmetric relative to the two ground wires, an induced voltage will be generated on the ground wire. When the ground wire conducts electricity with the earth, a circulating current will be generated, causing power loss in the overhead ground wire. The energy loss of the overhead ground wire will bring huge waste of electricity and economic losses, and as the voltage level increases, the loss of the ground wire will also increase sharply, leading to an increase in the operating cost of the power system. Therefore, it is crucial to evaluate the factors affecting the energy loss of the overhead ground wire and reduce the loss.

[0004] Overhead ground wires in power systems are usually used for lightning protection and to maintain safe operation of power equipment. However, as power demand increases, the load on transmission lines also increases, causing ground wire loss problems to become increasingly prominent. Especially in high-voltage, high-capacity transmission lines, due to the induction effect between the ground wire and the earth, the loss problem becomes more serious, resulting in considerable energy waste. In addition, with the efficiency of power equipment and the expansion of the power grid, how to accurately predict and control ground wire loss has become one of the urgent issues to be solved in modern power systems.

[0005] At present, the research on overhead ground wire loss mainly focuses on the electrical performance and electromagnetic effects of the ground wire. However, in actual applications, due to environmental changes and the complexity of transmission lines, there are far more factors affecting the loss than these. For example, the material, structure and installation method of the ground wire will affect the loss, and these factors are often ignored in traditional evaluation methods. With the development of power transmission technology, the operating environment of the power system has become more complex, and the limitations of traditional evaluation methods have become more obvious.

[0006] Traditional overhead ground wire loss assessment methods mainly rely on empirical formulas and simplified models, such as uniform electric field models or approximate current distribution models. However, these methods have certain limitations when dealing with complex electromagnetic field distribution and ground wire characteristics, resulting in large errors in the assessment results.

[0007] In addition, the traditional evaluation method has low computational efficiency and is difficult to meet the actual engineering needs. Therefore, in order to improve the accuracy and computational efficiency of overhead ground wire loss evaluation, it is necessary to study an overhead ground wire loss evaluation method based on an improved finite element algorithm. Summary of the invention

[0008] The purpose of the present invention is to provide an overhead ground wire loss evaluation method based on an improved finite element algorithm, which can solve the problems of existing evaluation methods in calculation efficiency, accuracy, complexity and boundary condition processing, and can achieve a balance between calculation accuracy and efficiency; it is particularly suitable for processing nonlinear and uncertainty problems involving multiple interval parameters, and provides an efficient and accurate solution for overhead ground wire loss evaluation.

[0009] To achieve the above object, the present invention provides an overhead ground wire loss evaluation method based on an improved finite element algorithm, comprising the following steps:

[0010] S1. Use Maxwell 3D software to build a simulation model of the electromagnetic field distribution around the ground wire of the double-circuit transmission line, and perform numerical simulation of the electric field intensity and magnetic field intensity at the height above the ground wire installation position;

[0011] S2. Scale the simulation model and construct finite element simulation models of different types of transmission towers in COMSOL;

[0012] S3, based on the electromagnetic field distribution data around the ground wire of the double-circuit transmission line obtained in S1 and the requirements of the mesh refinement technology, determine the area that needs to be refined in the early stage of simulation;

[0013] S4. Identify the key uncertainty parameters that affect the overhead ground wire loss, use the two-variable dimensionality reduction method to approximate the structural interval finite element equilibrium equation, and achieve the identification and dimensionality reduction of the key uncertainty parameters;

[0014] S5. Based on the derivation results of S4, the inverse matrix of the interval stiffness matrix of the structure is approximated using the Neumann series to obtain the explicit expression of the interval displacement response and the dynamic response of the overhead ground wire under different working conditions;

[0015] S6. Verify the effectiveness of the algorithm based on the error estimation formula, and determine whether the grid needs to be further refined based on the error estimation results.

[0016] Preferably, in S1, the electromagnetic field simulation is performed using Maxwell 3D toolbox.

[0017] Preferably, the simulation model of the electromagnetic field simulation is based on a 750kV umbrella-shaped double-circuit transmission tower.

[0018] Preferably, the model scaling ratio of S2 is 125:1, and a 50A three-phase alternating current is added in the conductor as excitation.

[0019] Preferably, in said S3, the refinement area in the initial stage of finite element simulation is determined as the area where the gradient and derivative of the electromagnetic field variables change dramatically, as well as the contact point between the ground wire and the ground, and the connection point between the ground wire and other structures.

[0020] Preferably, in S3, the unit subdivision method of the quadtree structure refers to dividing the unit that fails the error check into four, wherein the non-independent hanging nodes generated by local encryption should be specially constrained.

[0021] Preferably, in S4, the key uncertainty parameters of the overhead ground wire loss include the density, diameter, and temperature coefficient of the ground wire, and the calculation formula of the two-variable dimensionality reduction method is:

[0022]

[0023] Where n is the dimension of the random variable, 0≤i≤n and 0≤i 1 ≤i 2 ≤n, and represents the i-th 1 and i 2 random variables, is the interval stiffness matrix, is the two-variable interval stiffness matrix, is the univariate interval stiffness matrix, a C represents the mean of the random variable.

[0024] Preferably, in S5, if Satisfy the convergence condition ρ(K C δK)<1, the Neumann series is used to efficiently solve the stiffness matrix in the uncertain domain, and the calculation formula is:

[0025]

[0026] Among them, u I is the interval displacement response, K c is the interval stiffness matrix at the mean of the variable, is the node load vector, δK is the linear variation of the matrix, r is the order of the Neumann series expansion, I∈R n×n is the identity matrix.

[0027] Preferably, the S6 uses a relative error formula to evaluate the convergence of the finite element calculation. If the error does not meet the technical requirements, the process returns to S3 to refine the mesh in the area with large error, that is, to increase the mesh density.

[0028] Preferably, if the error meets the requirement, the finite element simulation calculation is terminated;

[0029] The relative error calculation formula is:

[0030]

[0031] Among them, ε rel With ε abs are the relative error and absolute error of the interval displacement response, respectively, and m is the response order.

[0032] Therefore, the present invention adopts the above-mentioned overhead ground wire loss evaluation method based on the improved finite element algorithm, which solves the problems of existing evaluation methods in calculation efficiency, accuracy, complexity and boundary condition processing, and achieves a balance between calculation accuracy and efficiency; it is particularly suitable for processing nonlinear and uncertainty problems involving multiple interval parameters, and provides an efficient and accurate solution for overhead ground wire loss evaluation.

[0033] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of an improved finite element algorithm of an embodiment of an overhead ground wire loss evaluation method based on an improved finite element algorithm of the present invention;

[0035] Figure 2 It is a structural diagram of a quadtree structural unit subdivision method of an overhead ground wire loss evaluation method embodiment based on an improved finite element algorithm of the present invention. DETAILED DESCRIPTION

[0036] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0037] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0038] Embodiment 1

[0039] The design concept of the present invention is: due to the problems of low computational efficiency, low precision, high requirements, and difficult boundary condition processing in the existing overhead ground wire loss assessment methods, the existing technology is often unable to cope with complex electromagnetic field distribution and multivariate uncertainty, resulting in poor accuracy and reliability of the assessment results.

[0040] Based on this, the present invention aims to solve these problems by improving the traditional finite element analysis method, improving the accuracy and efficiency of calculations, and reducing the consumption of computing resources.

[0041] Specifically, the present invention has made a series of innovative improvements based on the conventional finite element algorithm, and the general process is as follows:

[0042] First, mesh refinement technology is used to improve the approximate accuracy of finite element analysis results. Through finer mesh division, the electromagnetic field distribution and structural response of complex areas can be accurately captured, thereby reducing the error caused by coarse mesh.

[0043] Secondly, in order to solve the problem of calculating the complex structural interval stiffness matrix in the traditional finite element method, this paper proposes to use a dual variable dimensionality reduction method to approximate it. This method effectively reduces the dimensions that need to be processed during the calculation process through mathematical optimization and dimensionality reduction techniques, reduces the complexity of the solution, and maintains the high accuracy of the evaluation results.

[0044] Finally, the present invention introduces the Neumann series method to approximately solve the inverse matrix of the interval stiffness matrix of the structure, and obtains an explicit expression of the interval displacement response, thereby significantly improving the convergence speed. This method not only improves the calculation efficiency, but also makes the solution process more stable.

[0045] Therefore, the present invention effectively balances computational accuracy and efficiency, making it more suitable for nonlinear and uncertain problems with multiple interval parameters.

[0046] Based on the above design ideas, such as Figure 1 As shown, the present invention proposes an overhead ground wire loss evaluation method based on an improved finite element algorithm, comprising the following steps:

[0047] S1. Use Maxwell 3D software to build a simulation model of the electromagnetic field distribution around the ground wire of a double-circuit transmission line, and realize the numerical simulation of the electric field strength and magnetic field strength at a specific height above the ground wire installation position. The model takes the 750kV umbrella-shaped double-circuit transmission tower on the same tower as a reference, and takes into account the electromagnetic environment characteristics of this tower type in actual operation.

[0048] Maxwell 3D software can accurately simulate the distribution of electric and magnetic fields around the ground wire, and then predict the electromagnetic characteristics of the ground wire under different operating conditions. This process provides a reliable data basis for subsequent finite element simulation and ensures high accuracy and reliability of the evaluation results.

[0049] S2. Scale the above actual model according to a ratio of 125:1, add a 50A three-phase alternating current in the conductor as excitation, and build finite element simulation models of different types of transmission towers in COMSOL.

[0050] This scaling ensures the tractability of the simulation model in a computer environment and can effectively retain the key features of the electromagnetic field distribution. On this basis, the finite element simulation model of different types of transmission towers is constructed using COMSOL software to further optimize and simulate the influence of the transmission tower structure on the electromagnetic field and current distribution. Through the establishment of this multi-tower model, different types of transmission towers can be compared and analyzed to evaluate their influence on overhead ground wire losses.

[0051] S3. Based on the electromagnetic field distribution data around the ground wire of the double-circuit transmission line obtained in S1, and combined with the requirements of the mesh refinement technology, the area that needs to be refined in the early stage of the simulation is determined. The refined area is determined to be the area where the gradient or derivative of the electromagnetic field variable changes drastically, as well as the contact point between the ground wire and the ground, and the connection point between the ground wire and other structures. The unit subdivision method of the quadtree structure refers to dividing the unit that fails the error test into four, among which the non-independent suspension nodes generated by local encryption should be specially constrained. .

[0052] S4. Identify the key uncertainty parameters that affect the overhead ground wire loss. The key uncertainty parameters of the overhead ground wire loss mainly include the density, diameter, temperature coefficient, etc. of the ground wire.

[0053] The dual variable dimension reduction method is used to approximate the structural interval finite element equilibrium equation to achieve the identification and dimension reduction of key uncertainty parameters.

[0054] The calculation formula of the correlation coefficient of the bivariate dimensionality reduction method is:

[0055]

[0056] Where n is the dimension of the random variable, 0≤i≤n and 0≤i 1 ≤i 2 ≤n, and represents the i-th 1 and i 2 random variables, is the interval stiffness matrix, is the two-variable interval stiffness matrix, is the univariate interval stiffness matrix, a C represents the mean of the random variable.

[0057] S5. Based on the derivation results of S4, the inverse matrix of the interval stiffness matrix of the structure is approximated using the Neumann series to obtain an explicit expression of the interval displacement response and the dynamic response of the overhead ground wire under different working conditions.

[0058] like Satisfy the convergence condition ρ(K CδK)<1, the Neumann series can efficiently solve the stiffness matrix in the uncertainty domain, and the calculation formula of the correlation coefficient is:

[0059]

[0060] Among them, u I is the interval displacement response, K c is the interval stiffness matrix at the mean of the variable, is the node load vector, δK is the linear variation of the matrix, r is the order of the Neumann series expansion, I∈R n×n is the identity matrix.

[0061] S6. Verify the effectiveness of the algorithm based on the error estimation formula, use the relative error formula to evaluate the convergence of the finite element calculation, and determine whether the grid needs to be further refined based on the error estimation results.

[0062] The relative error calculation formula is:

[0063]

[0064] Among them, ε rel With ε abs are the relative error and absolute error of the interval displacement response, respectively, and m is the response order.

[0065] If the error in S6 does not meet the technical requirements, return to S3, further process the finite element mesh based on the quadtree unit subdivision method, and refine the mesh in the area with large errors, that is, increase the mesh density; if the error meets the requirements, end the finite element simulation calculation.

[0066] like Figure 2 As shown in the figure, the unit subdivision method of the quadtree structure refers to dividing the unit that fails the error check into four, among which the non-independent suspension nodes generated by local encryption should be specially constrained; through this quadtree unit subdivision method, while ensuring the overall calculation efficiency, it is possible to perform refined processing on key areas, greatly improving the accuracy of the simulation results and meeting the requirements of overhead ground wire loss assessment for high precision and high efficiency.

[0067] The present invention has the following advantages and positive effects:

[0068] 1. The present invention realizes high-precision and high-efficiency evaluation of overhead ground wire loss through a series of innovative technical steps.

[0069] First, the model built using Maxwell 3D software can accurately simulate the electromagnetic field distribution around the ground wire, providing a reliable data basis for subsequent finite element simulation. This precise simulation helps to more accurately predict the actual working state of the ground wire, thereby providing a more reliable basis for loss assessment.

[0070] Secondly, by constructing finite element simulation models of different types of transmission towers through COMSOL software, the present invention can adapt to the needs of different engineering scenarios and improve the applicability and versatility of the evaluation.

[0071] 2. The present invention adopts mesh refinement technology in the finite element simulation process, and the quadtree unit subdivision method optimizes the finite element mesh to ensure the accuracy of the simulation results.

[0072] At the same time, the structural interval finite element equilibrium equation is approximated by the two-variable dimensionality reduction method, which effectively identifies and reduces the dimension of key uncertainty parameters, which not only simplifies the calculation process but also improves the calculation efficiency.

[0073] In addition, the inverse matrix of the interval stiffness matrix of the structure is approximated by Neumann series, and an explicit expression of the interval displacement response is obtained, which makes the dynamic response analysis of the overhead ground wire under different working conditions more convenient and accurate.

[0074] Therefore, the present invention adopts the above-mentioned overhead ground wire loss evaluation method based on the improved finite element algorithm, which solves the problems of existing evaluation methods in calculation efficiency, accuracy, complexity and boundary condition processing, and achieves a balance between calculation accuracy and efficiency; it is particularly suitable for processing nonlinear and uncertainty problems involving multiple interval parameters, and provides an efficient and accurate solution for overhead ground wire loss evaluation.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. An overhead ground wire loss evaluation method based on an improved finite element algorithm, characterized in that: The following steps are involved: S1. Use Maxwell 3D software to build a simulation model of the electromagnetic field distribution around the ground wire of the double-circuit transmission line, and perform numerical simulation of the electric field intensity and magnetic field intensity at the height above the ground wire installation position; S2. Scale the simulation model and construct finite element simulation models of different types of transmission towers in COMSOL; S3, based on the electromagnetic field distribution data around the ground wire of the double-circuit transmission line obtained in S1 and the requirements of the mesh refinement technology, determine the area that needs to be refined in the early stage of simulation; S4. Identify the key uncertainty parameters that affect the overhead ground wire loss, use the two-variable dimensionality reduction method to approximate the structural interval finite element equilibrium equation, and achieve the identification and dimensionality reduction of the key uncertainty parameters; S5. Based on the derivation results of S4, the inverse matrix of the interval stiffness matrix of the structure is approximated using the Neumann series to obtain the explicit expression of the interval displacement response and the dynamic response of the overhead ground wire under different working conditions; S6. Verify the effectiveness of the algorithm based on the error estimation formula, and determine whether the grid needs to be further refined based on the error estimation results.

2. The method for evaluating overhead ground wire loss based on improved finite element algorithm according to claim 1, characterized in that: In S1, the electromagnetic field simulation was performed using the Maxwell 3D toolbox.

3. The overhead ground wire loss evaluation method based on improved finite element algorithm according to claim 2 is characterized in that: The simulation model of the electromagnetic field simulation is based on a 750kV umbrella-shaped double-circuit transmission tower.

4. The method for evaluating overhead ground wire loss based on improved finite element algorithm according to claim 1, characterized in that: The model scaling ratio of S2 is 125:1, and a 50A three-phase alternating current is added in the wires as excitation.

5. The overhead ground wire loss evaluation method based on improved finite element algorithm according to claim 1 is characterized in that: In S3, the refinement area in the initial stage of finite element simulation is determined as the gradient of the electromagnetic field variables, the area where the derivative changes dramatically, and the contact point between the ground wire and the ground, and the connection point between the ground wire and other structures.

6. The overhead ground wire loss evaluation method based on improved finite element algorithm according to claim 1 is characterized in that: In S3, the unit subdivision method of the quadtree structure refers to dividing the unit that fails the error check into four, wherein the non-independent hanging nodes generated by local encryption should be specially constrained.

7. The overhead ground wire loss evaluation method based on improved finite element algorithm according to claim 1 is characterized in that: In S4, the key uncertainty parameters of overhead ground wire loss include density, diameter, and temperature coefficient of the ground wire. The calculation formula of the two-variable dimensionality reduction method is: Where n is the dimension of the random variable, 0≤i≤n and 0≤i1≤i2≤n, and represents the i1th and i2th random variables of the two-dimensional response function, is the interval stiffness matrix, is the two-variable interval stiffness matrix, is the univariate interval stiffness matrix, a C represents the mean of the random variable.

8. The method for evaluating overhead ground wire loss based on improved finite element algorithm according to claim 1, characterized in that: In S5, if Satisfy the convergence condition ρ(K C δK)<1, the Neumann series is used to efficiently solve the stiffness matrix in the uncertain domain, and the calculation formula is: Among them, u I is the interval displacement response, K c is the interval stiffness matrix at the mean of the variable, is the node load vector, δK is the linear variation of the matrix, r is the order of the Neumann series expansion, I∈R n×n is the identity matrix.

9. The overhead ground wire loss evaluation method based on improved finite element algorithm according to claim 1 is characterized in that: The S6 uses a relative error formula to evaluate the convergence of the finite element calculation. If the error does not meet the technical requirements, the process returns to S3 to refine the mesh in the area with large errors, that is, to increase the mesh density.

10. The method for evaluating overhead ground wire loss based on improved finite element algorithm according to claim 9, characterized in that: If the error meets the requirements, the finite element simulation calculation is terminated; The relative error calculation formula is: Among them, ε rel With ε abs are the relative error and absolute error of the interval displacement response, respectively, and m is the response order.

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