Methods, apparatus, non-volatile storage media and electronic equipment for determining ground electric field

Abstract

This invention discloses a method, apparatus, non-volatile storage medium, and electronic device for determining the ground electric field. Relating to the field of electrical engineering, the method includes: in solving the electric field of a ground region passing through a spatial region where a DC conductor crosses an AC conductor, a tetrahedral mesh derived from a three-dimensional finite element mesh is used to solve the Poisson equation using the finite element method based on a preprocessed generalized minimum residual algorithm; and a current continuity equation is solved using the dual mesh of the tetrahedral mesh using the finite volume method based on a preprocessed generalized minimum residual algorithm, thereby obtaining the mixed electric field of the DC conductor crossing the AC conductor in the ground region. This application solves the technical problem of the difficulty in quickly determining the electric field formed in a ground region when a DC conductor crosses an AC conductor.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering technology, and more specifically, to a method, apparatus, non-volatile storage medium, and electronic device for determining a ground electric field. Background Technology

[0002] In the crossing area where high-voltage direct current (HVDC) conductors cross AC conductors, the corona discharge of the HVDC transmission conductors exceeding the corona induction field strength is affected to varying degrees, forming a mixed electric field on the ground where AC and DC interact. This mixed field is much more complex than the nominal electric field without considering the space charge generated by the discharge. The ground electric field in the crossing area is significantly enhanced, necessitating further understanding of the ground electric field distribution characteristics when HVDC conductors cross AC conductors. This understanding will provide a reference for power grid construction in practical engineering and environmental assessments of crossing areas. Existing methods for modeling and calculating the three-dimensional mixed electric field when DC conductors cross AC conductors are inefficient and exhibit poor convergence under certain operating parameters, failing to meet the calculation requirements of the three-dimensional mixed electric field under different operating modes and crossing angles. Therefore, there is an urgent need to research an efficient solution method for the mixed electric field of DC conductors crossing AC conductors.

[0003] There is currently no effective solution to the above problems. Summary of the Invention

[0004] This invention provides a method, apparatus, non-volatile storage medium, and electronic device for determining the ground electric field, to at least solve the technical problem of the difficulty in quickly determining the electric field formed in the ground area when a DC conductor crosses an AC conductor.

[0005] To achieve the above objectives, according to one aspect of the present invention, an electric field determination method is provided, comprising: performing three-dimensional finite element meshing on a target spatial region to obtain a tetrahedral mesh of the target spatial region, and generating a dual mesh of the tetrahedral mesh, wherein the target spatial region includes a DC conductor and an AC conductor, and the DC conductor crosses the AC conductor, and the target spatial region includes a ground region; calculating the nominal surface electric field of the DC conductor using the finite element method based on the tetrahedral mesh; and, given an initial value of the surface charge density of the DC conductor in the target spatial region, calculating the nominal surface electric field of the DC conductor based on the charge density... The system first sets the initial value of the surface charge density of the DC conductor to an external loop for surface charge density correction; then it enters an internal loop for surface field strength correction of the DC conductor, generating the time step and initial time of the internal loop, and repeatedly executing the following steps: Based on the initial value of the surface charge density of the DC conductor and the tetrahedral mesh, the Poisson equation is solved using the finite element method based on the preprocessed generalized minimum residual method to obtain the potential of each node in the target spatial region; based on the dual mesh of the tetrahedral mesh and the potential of each node in the target spatial region, the current continuity equation is solved using the finite volume method based on the preprocessed generalized minimum residual method to obtain the potential of the target spatial region. The charge density of each node within the domain is determined. The surface electric field strength of the DC conductor is determined in two consecutive loops within the inner loop. If the results are different, the latest loop result is used to assign an initial value to the surface charge density, and the inner loop is repeated. If the results are the same, the inner loop is exited to obtain the surface electric field strength of the DC conductor. If the surface electric field strength of the DC conductor does not satisfy the Kaptzov condition, the outer loop for surface charge density correction is re-entered, and the inner loop for surface charge density correction is re-entered. If the surface electric field strength of the DC conductor satisfies the Kaptzov condition, the outer loop is exited and the target value of the surface charge density of the DC conductor is output. The target value of the surface charge density of the DC conductor is determined based on the loop result of the inner loop. Based on the target value of the surface charge density of the DC conductor, the combined electric field generated by the DC conductor in the ground region when the AC conductor is grounded is determined. When the AC conductor in the target space region is pressurized, the combined electric field when the AC conductor is grounded is used as the initial value for calculating the mixed electric field, and the mixed electric field in the ground region when the AC conductor is pressurized is calculated.

[0006] Optionally, the step of solving the Poisson equation using the finite element method based on the preprocessed generalized minimum residual method according to the initial value of the surface charge density of the DC conductor and the tetrahedral mesh to obtain the potential of each node in the target spatial region includes: determining the equivalent functional used for the boundary electric field of the target spatial region as follows: Among them, E n Let Ω be the normal component of the boundary field strength, Γ1 be the first type of boundary, and Γ2 be the second type of boundary. The solution domain is discretized using the finite element method, and is divided into m elements and n nodes. Among these, m1 elements are coplanar with the first type of nodes, and m2 elements are coplanar with the second type of nodes. The potential of the unknown nodes within the solution domain is... The known node potential number is Potential function The approximate solution is: Where, N j Let be the shape function of the j-th node; substituting the approximate solution of the potential function into the equivalent functional of the boundary electric field, we obtain: Simplified, we get: Among them, s ij p i f i They are respectively:

[0007]

[0008]

[0009]

[0010] in, and Let i and j be the shape functions of nodes i and j on element e, respectively. The linear equations for the approximate solution of the potential function of the above equations are written in block matrix form: Among them, S 11 S 21 S 22 Here, S represents the stiffness coefficient matrix after partitioning, Φ is the column vector of unknown node potentials within the field, U is the column vector of known potentials at the first type of boundary nodes, P1 and P2 are known column vectors on the right side, F2 is a known column vector on the right side, F1 is an unknown column vector on the right side, and contains the normal vector of the electric field intensity to be determined on the first type of boundary; Φ is solved using the finite element potential Poisson equation: S 11 Φ = P1 + F2 - S2T1U, where F1 is solved using the boundary electric field equation: F1 = S 21 Φ+S 22 U-P2, by interpolating the electric field on the first type of boundary node, we can obtain: The above equation can be expressed in matrix form as: KE n =-F1, where K is the stiffness matrix of the first-kind boundary electric field distribution, E n Here are the column vectors of the electric field normal components at the boundary nodes; the coefficients of the stiffness matrix are calculated using the following formula: The boundary electric field equation can be obtained as: KE n =-(S21 Φ+S 22 U-P2), using the preprocessed generalized minimum residual method to solve for the normal component E of the electric field at the boundary nodes. n By finding the potential Φ of unknown nodes within the field, the potential of each node in the target space region can be obtained.

[0011] Optionally, the preprocessed generalized minimum residual method is used to solve for the normal component E of the electric field at the boundary nodes. n The unknown node potential Φ within the field includes: determining the finite element solution potential equation and boundary electric field constraint equation based on the initial value of the surface charge density of the DC conductor and the tetrahedral mesh, wherein the finite element solution potential equation includes the stiffness matrix S. 11 The boundary electric field constraint equation includes a stiffness matrix K; the potential Poisson equation to be solved and the boundary electric field equation are expressed in the following form: AX = b, where A is an n×n square matrix, which can be the stiffness matrix S. 11 Alternatively, the stiffness matrix K, where X is an n×1 dimensional column vector, can be the unknown nodal potential Φ or the normal component of the boundary nodal electric field E within the solution domain corresponding to the target spatial region. n b is an n-dimensional column vector, determined according to the boundary electric field constraint equation or the finite element solution potential equation; the preprocessed generalized minimum residual algorithm is used to solve AX = b to obtain the normal component E of the boundary node electric field. n Or the unknown node potential Φ within the solution domain corresponding to the target spatial region.

[0012] Optionally, the preprocessing generalized minimum residual algorithm is used to solve AX = b to obtain the normal component E of the electric field at the boundary nodes. n Or the unknown node potential Φ in the solution domain corresponding to the target spatial region, including: input matrices A and b, and unknown quantity X to be solved; performing row and column balancing preprocessing on matrix A, multiplying each row of A by a factor s, so that the target norms of all rows of A have similar lengths, where s is defined as: Define the row balance matrix of matrix A as: After performing row balancing on AX = b, the equivalent equation for AX = b is: D -1 AX=D -1 After performing row and column balancing on matrix A and equation AX = b, the equivalent equation is: RPACY = RPb, where matrix R is the permutation matrix, matrix P is the row balancing matrix, and matrix C is the column balancing matrix. The equivalent equation for the unknown X is: BY = d, where matrix B = RPAC, d = RPb, and the unknown X = CY. The generalized minimum residual algorithm is used to solve BY = d, the convergence condition ε is determined, and the initial solution Y0 is selected. The residual r is calculated. iThe initial residual vector r0 is defined as: BY0 = d - r0, where r0 is the initial residual vector; the m-dimensional Krylov subspace generated by r0 is determined as: K m (B,r0)=span{r0,Br0,B 2 r0,…,B m -1 r0};A set of orthonormal bases V is obtained through Gram-Schmidt orthogonalization. m ={v1,v2,···,v m From the Arnoldi process, we can obtain: Among them, H m =V m T BV m Let H be the upper Hessenberg matrix. m+1 For H m The augmented matrix, h m+1,m e m T For the augmented matrix H m+1 The last line, e m Let r represent the m-th column of the identity matrix I; iteratively generating an approximate solution in the Krylov subspace, the L2 norm of the residual vector of the approximate solution in the (i-1)-th iteration is expressed as: ||r i ||2=||d-BY i-1 ||2=||β i-1 e1-H m+1,i-1 z i-1 || 2,βi-1 =||r i-1 ||2, where z i-1 The following equation is minimized to obtain: z i-1 =argmin z ||β i-1 e1-H m+1,i-1 z i-1 ||2, after i iterations, an approximate solution Y is formed. i Satisfy: Y i =Y i-1 +V m,i-1 z i-1 Determine the approximate solution Y i Whether the convergence condition is met is determined by the following equation: ||r i-1 -BV m,i-1 z i-1 ||<ε, if Y i If the convergence condition is met, the solution to the unknown variable X is X = CY. i Exit the iteration process if Y iIf the convergence condition is not met, continue the iterative process described above, which uses the generalized minimum residual algorithm to solve BY = d, until Y... i Continue until the convergence condition is met.

[0013] Optionally, the step of solving the current continuity equation using the finite volume method based on the preprocessed generalized minimum residual method, according to the dual mesh of the tetrahedral mesh and the potential of each node in the target spatial region, to obtain the charge density of each node in the target spatial region, includes: determining the discretized current continuity equation as follows based on the dual network:

[0014] in, These represent the positive and negative charge densities of the i-th control volume at the n-th time step; Δt is the time step; V i N represents the volume of the i-th control volume; i L represents the number of faces controlling the i-th volume; i,k Let be the area of ​​the k-th face of the i-th control volume; These represent the positive and negative charge densities corresponding to the k-th surface of the i-th control volume at the n-th time step, respectively. The charge density corresponding to the windward control volume is used in the calculation. E i,k Let n be the electric field intensity at the k-th face of the i-th control volume, calculated using the electric field intensity of the tetrahedral element containing that face; i,k Let be the unit vector on the k-th surface of the i-th control volume pointing from the inside of the control volume to the outside of the control volume; based on the potential of each node in the target space region, the discretized current continuity equation is solved using the preprocessing generalized minimum residual algorithm to obtain the charge density of each node in the target space region.

[0015] Optionally, the method further includes: if the surface electric field strength of the DC conductor does not satisfy the Kaptzov condition, performing the external loop based on the following equation to correct the surface charge density of the DC conductor: Where v is the external cycle number corrected for charge density, and Q v-2 Q v-1 E represents the charge density on the surface of the DC conductor described in steps v-2 and v-1, respectively. v2 E v-1 E represents the electric field intensity on the surface of the DC conductor described in steps v-2 and v-1, respectively. on The corona field strength on the surface of the conductor.

[0016] To achieve the above objectives, according to another aspect of the present invention, a ground electric field determination device is also provided, comprising: a meshing module for performing three-dimensional finite element meshing on a target spatial region to obtain a tetrahedral mesh of the target spatial region, and generating a dual mesh of the tetrahedral mesh, wherein the target spatial region includes a DC conductor and an AC conductor, and the DC conductor crosses the AC conductor, and the target spatial region includes a ground region; a first calculation module for calculating the nominal surface electric field of the DC conductor using the finite element method based on the tetrahedral mesh; and an external circulation module for providing an initial surface charge density of the DC conductor in the target spatial region. The initial value is used to enter the external loop for surface charge density correction of the DC conductor based on the initial charge density value. The internal loop module is used to enter the internal loop for surface field strength correction of the DC conductor, generate the time step and initial time of the internal loop, and repeatedly execute the following steps: Based on the initial value of surface charge density of the DC conductor and the tetrahedral mesh, solve the Poisson equation using the finite element method based on the preprocessed generalized minimum residual method to obtain the potential of each node in the target space region; Based on the dual mesh of the tetrahedral mesh and the potential of each node in the target space region, solve the current continuity equation using the finite volume method based on the preprocessed generalized minimum residual method to obtain the potential of the target space region. The charge density of each node within the region; determining whether the surface field strength of the DC conductor is the same in two adjacent loop results within the inner loop; if the results are different, assigning the surface charge density correction value using the latest loop result of the inner loop, repeating the inner loop; if the results are the same, exiting the inner loop to obtain the surface field strength of the DC conductor; an output module, used to re-enter the outer loop for surface charge density correction of the DC conductor and re-enter the inner loop for surface field strength correction of the DC conductor if the surface field strength of the DC conductor does not satisfy the Kaptzov condition; the output module is also used to... If the surface electric field strength of the DC conductor satisfies the Kaptzov condition, the outer loop is exited and the target value of the surface charge density of the DC conductor is output, wherein the target value of the surface charge density of the DC conductor is determined based on the loop result of the inner loop; a determination module is used to determine the composite electric field generated by the DC conductor in the ground region when the AC conductor is grounded, based on the target value of the surface charge density of the DC conductor; a second calculation module is used to calculate the mixed electric field in the ground region when the AC conductor is pressurized, based on the composite electric field when the AC conductor is grounded as the initial value for calculating the mixed electric field.

[0017] According to another aspect of the present invention, a non-volatile storage medium is also provided, the non-volatile storage medium including a stored program, wherein, when the program is executed, the device where the non-volatile storage medium is located is controlled to perform any of the above-described electric field determination methods.

[0018] According to another aspect of the present invention, an electronic device is also provided, the electronic device including a memory and a processor, the memory being used to store a program, and the processor being used to run the program stored in the memory, wherein the program, when running, executes any of the above-described electric field determination methods.

[0019] In this embodiment of the invention, the Poisson equation and current continuity equation in the target spatial region are solved by using the preprocessing generalized minimum residual method. This achieves the goal of solving the electric field distribution in the ground region of a spatial region where a DC conductor crosses an AC conductor, thereby improving the speed of solving the electric field formed in the ground region when a DC conductor crosses an AC conductor. This solves the technical problem of the difficulty in quickly determining the electric field formed in the ground region when a DC conductor crosses an AC conductor. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0021] Figure 1 A hardware block diagram of a computer terminal for implementing a method for determining the ground electric field is shown.

[0022] Figure 2 This is a flowchart illustrating the method for determining the ground electric field according to an embodiment of the present invention;

[0023] Figure 3 This is a schematic diagram of a scenario where a DC conductor crosses an AC conductor, according to an optional embodiment of the present invention.

[0024] Figure 4 This is a schematic diagram of a tetrahedral mesh and a dual mesh provided according to an optional embodiment of the present invention;

[0025] Figure 5 This is a flowchart of a ground hybrid electric field solution method provided by an optional embodiment of the present invention;

[0026] Figure 6 This is a flowchart of the preprocessing generalized minimum residual algorithm provided by an optional embodiment of the present invention;

[0027] Figure 7 This is a structural block diagram of a ground electric field determination device provided according to an embodiment of the present invention. Detailed Implementation

[0028] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0029] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0030] According to an embodiment of the present invention, a method embodiment for determining an electric field is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0031] The method embodiment provided in Embodiment 1 of this application can be executed on a mobile terminal, computer terminal, or similar computing device. Figure 1 A hardware block diagram of a computer terminal for implementing a method for determining the ground electric field is shown. Figure 1 As shown, the computer terminal 10 may include one or more processors (shown as 102a, 102b, ..., 102n in the figure) (the processor may include, but is not limited to, a microprocessor MCU or a programmable logic device FPGA, etc.) and a memory 104 for storing data. In addition, it may also include: a display, an input / output interface (I / O interface), a universal serial bus (USB) port (which may be included as one of the ports of a BUS bus), a network interface, a power supply, and / or a camera. Those skilled in the art will understand that... Figure 1 The structure shown is for illustrative purposes only and does not limit the structure of the aforementioned electronic device. For example, computer terminal 10 may also include... Figure 1 The more or fewer components shown, or having the same Figure 1 The different configurations shown.

[0032] It should be noted that the aforementioned one or more processors and / or other data processing circuits are generally referred to herein as "data processing circuits". These data processing circuits may be implemented wholly or partially as software, hardware, firmware, or any other combination thereof. Furthermore, the data processing circuits may be a single, independent processing module, or may be wholly or partially integrated into any other element in the computer terminal 10. As involved in the embodiments of this application, the data processing circuits serve as processor control (e.g., selection of a variable resistor termination path connected to an interface).

[0033] The memory 104 can be used to store software programs and modules of application software, such as the program instructions / data storage device corresponding to the electric field determination method in this embodiment of the invention. The processor executes various functional applications and data processing by running the software programs and modules stored in the memory 104, thereby implementing the electric field determination method of the aforementioned application. The memory 104 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory 104 may further include memory remotely located relative to the processor, and these remote memories can be connected to the computer terminal 10 via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0034] The display may be, for example, a touchscreen liquid crystal display (LCD) that allows the user to interact with the user interface of the computer terminal 10.

[0035] The present invention will now be described in conjunction with preferred implementation steps. Figure 2 This is a flowchart illustrating the method for determining the ground electric field according to an embodiment of the present invention, as shown below. Figure 2 As shown, the method includes the following steps:

[0036] Step S201: Perform three-dimensional finite element meshing on the target space region to obtain a tetrahedral mesh of the target space region and a dual mesh that generates the tetrahedral mesh. The target space region has DC conductors crossing AC conductors and includes the ground region.

[0037] Step S202: Calculate the nominal electric field on the surface of the DC conductor using the finite element method based on the tetrahedral mesh.

[0038] Step S203: Provide an initial value for the surface charge density of the DC conductor within the target space region; based on the initial value of the charge density, enter the external loop for surface charge density correction of the DC conductor.

[0039] Step S204: Enter the inner loop for surface field strength correction of the DC conductor, generate the time step and initial time of the inner loop, and repeatedly execute the following steps S205 to S207:

[0040] Step S205: Based on the initial value of the surface charge density of the DC conductor and the tetrahedral mesh, the Poisson equation is solved using the finite element method based on the preprocessed generalized minimum residual method to obtain the potential of each node in the target spatial region.

[0041] Step S206: Based on the potential of each node in the dual grid and the target space region, the current continuity equation is solved using the finite volume method based on the preprocessed generalized minimum residual method to obtain the charge density of each node in the target space region.

[0042] Step S207: Determine whether the surface electric field strength of the DC conductor is the same in two adjacent loop results in the inner loop. If the results of two adjacent loops are different, use the latest loop result of the inner loop to assign a surface charge density correction value. Repeat the inner loop according to the correction value. If the results of two adjacent loops are the same, exit the inner loop to obtain the surface electric field strength of the DC conductor.

[0043] Step S208: If the surface field strength of the DC conductor does not meet the Kaptzov condition, re-enter the external loop for surface charge density correction of the DC conductor, and re-enter the internal loop for surface field strength correction of the DC conductor; if the surface field strength of the DC conductor meets the Kaptzov condition, exit the external loop and output the target value of surface charge density of the DC conductor, wherein the target value of surface charge density of the DC conductor is determined according to the loop result of the internal loop.

[0044] Step S209: Based on the target value of the surface charge density of the DC conductor, determine the combined electric field generated by the DC conductor in the ground area when the AC conductor is grounded; when the AC conductor in the target space area is pressurized, calculate the mixed electric field in the ground area when the AC conductor is pressurized, using the combined electric field when the AC conductor is grounded as the initial value for calculating the mixed electric field.

[0045] It should be noted that the above embodiments and optional embodiments provide a method for determining the electric field of the ground region in a spatial region where a DC conductor crosses an AC conductor. Figure 3 This is a schematic diagram of a scenario where a DC conductor crosses an AC conductor, as provided in an optional embodiment of the present invention. Figure 3As shown, the spatial region where a DC conductor crosses an AC conductor can be meshed using finite element methods and used as the study area. For example, Figure 3 In the corresponding embodiment, the study area is a cylinder formed by the intersection of DC positive conductor 17 and DC negative conductor 18, AC phase A conductor 21, AC phase B conductor 22, and AC phase C conductor 23. The midpoint of the line segment where DC positive conductor 17, DC negative conductor 18, and AC phase B conductor 21 intersect is set as the origin 19 of the cylinder's ground surface. The radius of the cylinder's ground surface is three times the distance between the intersection point 20 and the origin 19, and the height of the cylinder is five times the height of DC positive conductor 17 and DC negative conductor 18 above the ground surface.

[0046] In the above optional embodiments, the study area is divided into a three-dimensional finite element mesh to form a tetrahedral mesh. Then, the nodal potentials and electric fields in the study area are solved using the preprocessed generalized minimum residual method, and then the combined electric field of the ground area when the AC conductor is grounded is calculated. Furthermore, the combined electric field when the AC conductor is grounded can be used as the initial value for calculating the mixed electric field. The electric field generated when the AC conductor is pressurized, i.e., the mixed electric field, can be calculated to obtain the required calculation results.

[0047] Through the above steps, the Poisson equation and current continuity equation in the target spatial region are solved by using the preprocessing generalized minimum residual method. This achieves the goal of solving the electric field distribution in the ground region of a spatial region where a DC conductor crosses an AC conductor. This improves the speed of solving the mixed electric field formed in the ground region when a DC conductor crosses an AC conductor, and solves the technical problem of the difficulty in quickly determining the electric field formed in the ground region when a DC conductor crosses an AC conductor.

[0048] It should be noted that the above embodiments use the finite element method and the finite volume method to solve the potential Poisson equation and the current continuity equation, respectively. Figure 4 This is a schematic diagram of a tetrahedral mesh and its dual mesh provided by an optional embodiment of the present invention. The solution to the Poisson equation is performed on the tetrahedral mesh, while the solution to the current continuity equation is performed on the dual mesh of the tetrahedral mesh. Figure 4 (a) and Figure 4 As shown in (b), the solid lines in the figure represent tetrahedral meshes used for finite element method solutions, while the dashed lines represent dual meshes used for finite volume method solutions.

[0049] The principle of forming the dual mesh of a tetrahedral mesh is as follows: First, connect the centroids B1 to B4 of each face of the tetrahedron to the centroid O of the tetrahedron; then, connect the centroid of each face to the midpoints of the three edges on that face. For example... Figure 4As shown in (a), the tetrahedron is divided into four parts, each corresponding to a node of the tetrahedron. All parts surrounding each node are combined to form the control volume of the finite volume method. If the w-th node is not on the boundary and is surrounded by W... h Enclosed by several units, the control volume corresponding to node w will then be 3W. h One face; if node j is on the boundary and is simultaneously affected by W h Enclosed by several units, the control volume corresponding to node j will then be 3W. h +W F One side, W F Let $\frac{ ... Figure 4 (b) Taking node P1 as an example, face P1P2P3 is on the boundary, and P1M3B2M2 is a face of P1 with a control volume.

[0050] As an optional embodiment, based on the initial surface charge density and tetrahedral mesh, the finite element solution potential equation and boundary electric field constraint equation are determined, including:

[0051] The Poisson equation is:

[0052]

[0053] in, Let ρ be the potential, ρ be the space charge density, ε0 ​​be the vacuum permittivity, and the subscripts "+" and "-" represent the positive and negative terminals, respectively. The relationship between the electric field strength E and the electric field strength E is as follows:

[0054]

[0055] The boundary conditions for the potential Poisson equation are:

[0056]

[0057] in, and These three values ​​represent the potentials of the conductor surface, the ground, and the boundary of the target spatial region at a sufficiently distant location, satisfying the first type of boundary condition; U L U is the operating voltage of the conductor; nom Let be the boundary potential of the target space region, neglecting the influence of space charge. For solving the Poisson equation, the equivalent functional used for the boundary electric field is:

[0058]

[0059] In the formula, E n Let Ω be the normal component of the boundary field strength, Ω be the solution domain, г1 be the boundary of the first kind, and г2 be the boundary of the second kind.

[0060] Finite element method discretization is applied to the solution domain, which is divided into m elements and n nodes. Among these, m1 elements are coplanar with the first type of nodes, and m2 elements are coplanar with the second type of nodes. The potential of the unknown nodes in the solution domain is... ... The known node potential number is ... Potential function The approximate solution is:

[0061]

[0062] In the formula, N j Let be the shape function of the j-th node.

[0063] Substituting the approximate solution of the potential function into the equivalent functional of the boundary electric field, we obtain:

[0064]

[0065] The above equation can be simplified to:

[0066]

[0067] In the formula, s ij p i f i They are respectively:

[0068]

[0069]

[0070]

[0071] In the formula, and These are the shape functions of nodes i and j on unit e, respectively.

[0072] The system of linear equations for the approximate solution of the potential function is written in block matrix form:

[0073]

[0074] In the formula, S 11 S 21 S 22 These are the stiffness coefficient matrices after partitioning, Φ is the column vector of unknown node potentials in the field, U is the column vector of known potentials of the first type of boundary nodes, P1 and P2 are the known column vectors on the right side, F2 is the known column vector on the right side, F1 is the unknown column vector on the right side, and contains the normal vector of the electric field intensity to be determined on the first type of boundary.

[0075] Φ satisfies the finite element method for solving the potential equation:

[0076]

[0077] F1 satisfies the boundary electric field constraint equations:

[0078]

[0079] Interpolating the electric field on the first type of boundary node yields:

[0080]

[0081] The above equation can be expressed in matrix form as follows:

[0082] KE n =-F1

[0083] In the formula, K is the stiffness matrix of the first-kind boundary electric field distribution, and E n is the column vector of the electric field normal components at the boundary nodes.

[0084] The coefficients of the stiffness matrix are calculated using the following formula:

[0085]

[0086] The boundary electric field constraint equations can be obtained as follows:

[0087] KE n =-(S 21 Φ+S 22 U-P2)

[0088] The above equations and the finite element method for solving the potential equations are used to solve for the normal component E of the electric field at the boundary nodes. n When dealing with unknown nodal potentials Φ within the field, it is necessary to separately adjust the stiffness matrices K and S. 11 The calculations are performed, but the stiffness matrix is ​​a large-scale sparse matrix with the number of rows and columns equal to the number of nodes. Direct solutions are too time-consuming. This invention proposes a preprocessed generalized minimum residual algorithm for solving this problem. As an optional embodiment, the finite element method based on the preprocessed generalized minimum residual method is used to solve the Poisson equation and obtain the potential of each node in the target spatial region. This can include the following steps: Based on the initial value of the surface charge density and the tetrahedral mesh, the finite element solution potential equation and the boundary electric field constraint equation are determined. The finite element solution potential equation includes the stiffness matrix S... 11 The boundary electric field constraint equations include the stiffness matrix K; the potential Poisson equation and the boundary electric field equations to be solved are expressed in the following form: AX = b, where A is an n×n square matrix, which can be the stiffness matrix S. 11Alternatively, the stiffness matrix K, where X is an n×1 dimensional column vector, can represent the unknown nodal potential Φ or the normal component of the boundary nodal electric field E within the solution domain corresponding to the target spatial region. n b is an n-dimensional column vector, determined by the boundary electric field constraint equations or the finite element method for solving the potential equations. The preprocessed generalized minimum residual algorithm is used to solve AX = b, yielding the normal component E of the boundary node electric field. n Or the unknown node potential Φ within the solution domain corresponding to the target space region.

[0089] As an optional implementation, the preprocessed generalized minimum residual algorithm is used to solve AX = b, and the normal component E of the electric field at the boundary nodes is obtained. n Or, to determine the unknown node potential Φ within the solution domain corresponding to the target spatial region, the following steps are included: Input matrices A and b, and the unknown quantity X to be solved; perform row and column balancing preprocessing on matrix A, multiplying each row of A by a factor s, so that the target norms of all rows of A have similar lengths, where s is defined as: s = max 1≤j≤n |a ij |,i=1,2,…,n, define the row balance matrix of matrix A as: After performing row balancing on AX = b, the equivalent equation for AX = b is: D -1 AX=D -1 After performing row and column balancing on matrix A and equation AX = b, the equivalent equation is: RPACY = RPb, where matrix R is the permutation matrix, matrix P is the row balancing matrix, and matrix C is the column balancing matrix. The equivalent equation for the unknown X is: BY = d, where matrix B = RPAC, d = RPb, and the unknown X = CY. The generalized minimum residual algorithm is used to solve BY = d, the convergence condition ε is determined, and the initial solution Y0 is selected. The residual r is calculated. i The initial residual vector r0 is defined as: BY0 = d - r0, where r0 is the initial residual vector; the m-dimensional Krylov subspace generated by r0 is determined as: K m (B,r0)=span{r0,Br0,B 2 r0,…,B m-1 r0};A set of orthonormal bases V is obtained through Gram-Schmidt orthogonalization. m ={v1,v2,···,v m From the Arnoldi process, we can obtain: Among them, H m =V m T BV m Let H be the upper Hessenberg matrix. m+1 For H m The augmented matrix, h m+1,m em T For the augmented matrix H m+1 The last line, e m Let r represent the m-th column of the identity matrix I; iteratively generating an approximate solution in the Krylov subspace, the L2 norm of the residual vector of the approximate solution in the (i-1)-th iteration is expressed as: ||r i ||2=||d-BY i-1 ||2=||β i-1 e1-H m+1,i-1 z i-1 ||2,β i-1 =||r i-1 ||2, where z i-1 The following equation is obtained by minimizing it: An approximate solution Y is formed after i iterations. i Satisfy: Y i =Y i-1 +V m,i-1 z i-1 Determine the approximate solution Y i Whether the convergence condition is met is determined by the following equation: ||r i-1 -BV m,i-1 z i-1 ||<ε, if Y i If the convergence condition is met, the solution to the unknown variable X is X = CY. i Exit the iteration process if Y i If the convergence condition is not met, continue the iterative process described above, which uses the generalized minimum residual algorithm to solve BY = d, until Y... i Continue until the convergence condition is met.

[0090] As an optional embodiment, based on the dual mesh and the potential of each node in the target spatial region, the current continuity equation is solved using the finite volume method based on the preprocessed generalized minimum residual method to obtain the charge density of each node in the target spatial region, including:

[0091] The equation for the continuity of current is:

[0092]

[0093] Where k is the ion mobility; W is the wind speed; R is the ion recombination rate; e is the charge of a single electron; and the subscripts "+" and "-" represent the positive and negative electrodes, respectively.

[0094] The boundary conditions for the current continuity equation are:

[0095]

[0096] In the formula, E nom,AC and E nomE represents the electric field intensity on the surface of the DC conductor when the AC conductor is present and when the AC conductor is absent, respectively. nom q is calculated by grounding the AC conductor; 0,AC q0 and q0 are the charge densities on the surface of the DC conductor when the AC conductor is present and when the AC conductor is absent, respectively. q0 is obtained by the two-dimensional finite element finite volume method.

[0097] Based on the dual network, the discretized current continuity equation is determined as follows:

[0098] in, These represent the positive and negative charge densities of the i-th control volume at the n-th time step; Δt is the time step; V i N represents the volume of the i-th control volume; i L represents the number of faces controlling the i-th volume; i,k Let be the area of ​​the k-th face of the i-th control volume; These represent the positive and negative charge densities corresponding to the k-th surface of the i-th control volume at the n-th time step, respectively. The charge density corresponding to the windward control volume is used in the calculation. E i,k Let n be the electric field intensity at the k-th face of the i-th control volume, calculated using the electric field intensity of the tetrahedral element containing that face; i,k Let be the unit vector on the k-th surface of the i-th control volume, pointing from the inside of the control volume to the outside of the control volume; based on the potential of each node in the target space region, the discretized current continuity equation is solved using the preprocessing generalized minimum residual algorithm to obtain the charge density of each node in the target space region.

[0099] As an optional embodiment, the above method further includes: when the surface electric field strength of the DC conductor does not satisfy the Kaptzov condition, performing an external loop based on the following equation to correct the surface charge density of the DC conductor: Where v is the external cycle number corrected for charge density, and Q v-2 Q v-1 E represents the charge density on the surface of the DC conductor in steps v-2 and v-1, respectively. v-2 E v-1 E represents the electric field intensity on the surface of the DC conductor in steps v-2 and v-1, respectively. on Let V be the initiation electric field strength on the conductor surface; when v = 1 and v = 2, the surface charge densities Q1 and Q2 are given and cannot be equal. When v > 2, the surface charge density of the conductor is corrected using the secant method based on the electric field and charge density obtained in the previous two steps.

[0100] Figure 5 This is a flowchart of a ground hybrid electric field solution method provided by an optional embodiment of the present invention, as shown below. Figure 5As shown, the process may include the following steps:

[0101] Step 1: Begin calculating the mixed electric field formed when a DC conductor crosses an AC conductor.

[0102] Step 2: Select the area where the DC and AC conductors cross. Figure 3 The study area is defined as the area where DC and AC conductors cross. This study area is a cylinder formed by the crossing of DC positive conductor 17 and DC negative conductor 18, AC phase A conductor 21, AC phase B conductor 22, and AC phase C conductor 23. The midpoint of the line segment where DC positive conductor 17, DC negative conductor 18, and AC phase B conductor 21 intersect is set as the origin 19 of the cylinder's ground surface. The radius of the cylinder's ground surface is three times the distance between the intersection point 20 and the origin 19, and the height of the cylinder is five times the height of DC positive conductor 17 and DC negative conductor 18 above the ground.

[0103] Step 3: Perform three-dimensional finite element meshing on the study area to form a tetrahedral mesh.

[0104] Step 4: Generate the dual mesh of the tetrahedral mesh based on the tetrahedral mesh generated by the 3D finite element method.

[0105] Step 5: Calculate the nominal electric field on the surface of the conductor using the finite element method.

[0106] Step 6: Given the initial value of the surface charge density of the conductor, enter the outer loop for conductor surface charge density correction. The conductor surface charge density correction equation is:

[0107]

[0108] In the formula, v is the external cycle number corrected for charge density, and Q is... v-2 Q v-1 E represents the charge density on the surface of the wire in steps v-2 and v-1, respectively. v2 E v-1 E represents the electric field intensity on the surface of the conductor in steps v-2 and v-1, respectively. on The corona field strength on the surface of the conductor.

[0109] In the above equations, the surface charge densities Q1 and Q2 of the conductor are given when v = 1 and v = 2, and they cannot be equal. When v > 2, the surface charge density of the conductor is corrected using the secant method based on the electric field and charge density of the conductor obtained in the first two steps.

[0110] Step 7: Enter the inner loop for correcting the electric field strength on the conductor surface, and set the initial value of the electric field on the conductor surface, the time step of the inner loop, and the initial time.

[0111] Step 8: Using the tetrahedral mesh generated by the three-dimensional finite element mesh, the finite element method based on the preprocessed generalized minimum residual algorithm is used to solve the Poisson equation and calculate the potential of each node in space.

[0112] For solving the Poisson equation, the equivalent functional used for the boundary electric field is:

[0113]

[0114] In the formula, ε is the vacuum permittivity. E is the electric potential, ρ is the space charge density, and E is the electric potential. n Let denoted as the normal component of the boundary field strength, Ω be the solution domain, г1 be the boundary of the first kind, and г2 be the boundary of the second kind.

[0115] Finite element discretization is applied to the solution domain, which is divided into m elements and n nodes. Among these, m1 elements are coplanar with the first type of nodes, and m2 elements are coplanar with the second type of nodes. The potential of the unknown nodes in the solution domain is... ... The known node potential number is ... Potential function The approximate solution is:

[0116]

[0117] In the formula, N j Let be the shape function of the j-th node.

[0118] Substituting the approximate solution of the potential function into the equivalent functional of the boundary electric field, we obtain:

[0119]

[0120] The above equation can be simplified to:

[0121]

[0122] In the formula, s ij p i f i They are respectively:

[0123]

[0124]

[0125]

[0126] In the formula, and These are the shape functions of nodes i and j on unit e, respectively.

[0127] The linear equations for the approximate solution of the potential function of the above equations are written in block matrix form:

[0128]

[0129] In the formula, S 11 S 21 S 22 These are the stiffness coefficient matrices after partitioning, Φ is the column vector of unknown node potentials in the field, U is the column vector of known potentials of the first type of boundary nodes, P1 and P2 are the known column vectors on the right side, F2 is the known column vector on the right side, F1 is the unknown column vector on the right side, and contains the normal vector of the electric field intensity to be determined on the first type of boundary.

[0130] Φ is solved using the finite element method to solve the potential equation:

[0131]

[0132] F1 is solved using the boundary electric field constraint equations:

[0133] F1 = S 21 Φ+S 22 U-P2

[0134] Interpolating the electric field on the first type of boundary node yields:

[0135]

[0136] The above equation can be expressed in matrix form as follows:

[0137] KE n =-F1

[0138] In the formula, K is the stiffness matrix of the first-kind boundary electric field distribution, and E n is the column vector of the electric field normal components at the boundary nodes.

[0139] The coefficients of the stiffness matrix are calculated using the following formula:

[0140]

[0141] The boundary electric field constraint equations can be obtained as follows:

[0142] KE n =-(S 21 Φ+S 22 U-P2)

[0143] The above equations and the finite element method for solving the potential equations are used to solve for the normal component E of the electric field at the boundary nodes. n When dealing with unknown nodal potentials Φ within the field, it is necessary to separately adjust the stiffness matrices K and S. 11The calculation is performed, but the stiffness matrix is ​​a large-scale sparse matrix with the number of rows and columns equal to the number of nodes. The direct solution method is too time-consuming. This invention proposes a preprocessing generalized minimum residual algorithm to solve the problem.

[0144] The large-scale coefficient matrix solved by the preprocessing generalized minimum residual algorithm proposed in this invention can be rewritten as follows:

[0145] AX = b

[0146] In the formula, A is an n×n square matrix, which can be the stiffness matrix K in the boundary electric field solution equation and the stiffness matrix S in the potential equation. 11 X is an n×1 dimensional column vector, which can be the normal component E of the electric field at the boundary nodes. n Let Φ be the potential of unknown nodes within the field, and b be an n-dimensional column vector, representing the right-hand side of the boundary electric field constraint equation and the right-hand side of the potential equation.

[0147] Since the elements in the stiffness matrix have significantly different magnitudes, the convergence of the generalized minimum residual algorithm is poor when applied directly. Therefore, matrix A needs to be preprocessed by balancing rows and columns.

[0148] The preprocessing process of the generalized minimum residual algorithm is as follows: Figure 6 As shown.

[0149] Step G1: Input matrices A and b, and the unknown variable X to be determined.

[0150] Step G2: Perform row and column balancing preprocessing on matrix A. To reduce the condition number of matrix A, multiply each row of A by an appropriate number s, such that the norms of all rows of A have similar lengths. s is defined as:

[0151]

[0152] Define the row balance matrix of matrix A as:

[0153]

[0154] After performing row balancing on the above equation AX=b, the equivalent equation is:

[0155] D -1 AX=D -1 b

[0156] Step G3: To reduce the condition number of matrix A, matrix A is simultaneously subjected to row and column balancing. After row and column balancing, the equation AX = b becomes the equivalent equation:

[0157] RPACY = RPb

[0158] In the formula, matrix R is the permutation matrix, matrix P is the row balancing matrix, and matrix C is the column balancing matrix.

[0159] The equivalent equation for the unknown variable X is:

[0160] BY = d

[0161] In the formula, matrix B = RPAC, d = RPb, and the unknown quantity to be determined is X = CY.

[0162] Step G4: Solve BY = d using the generalized minimum residual algorithm, input the convergence condition ε, and select the initial solution Y0.

[0163] Step G5: Calculate the residual r i The initial residual vector r0 is defined as follows:

[0164] BY0 = d - r0

[0165] In the formula, r0 is the initial residual vector.

[0166] Step G6: The m-dimensional Krylov subspace generated by r0:

[0167] K m (B,r0)=span{r0,Br0,B 2 r0,…,B m-1 r0}

[0168] Step G7: A set of orthonormal bases V can be obtained through Gram-Schmidt orthogonalization. m ={v1,v2,…,v m From the Arnoldi process, we can obtain:

[0169]

[0170] In the formula, H m =V m T BV m Let H be the upper Hessenberg matrix (a square matrix A, where a(i,j)=0 when i>j+1), H m+1 For H m The augmented matrix, h m+1,m e m T For the augmented matrix H m+1 The last line, e m This represents the m-th column of the identity matrix I.

[0171] Step G8: Iterate in the Krylov subspace to generate an approximate solution. The L2 norm of the residual vector of the approximate solution in the (i-1)th iteration can be expressed as:

[0172] ||r i||2=||d-BY i-1 ||2=||β i-1 e1-H m+1,i-1 z i-1 ||2,β i-1 =||r i-1 ||2

[0173] In the formula, z i-1 The following equation is obtained by minimizing it:

[0174]

[0175] An approximate solution Y is formed after i iterations. i satisfy:

[0176] Y i =Y i-1 +V m,i-1 z i-1

[0177] Step G9: Determine the approximate solution Y i To determine whether the convergence condition is met, use the following equation:

[0178] ||r i-1 -BV m,i-1 z i-1 ||<ε

[0179] If Y i The convergence condition is met, and the solution to be found is X = CY. i If the iteration process ends, exit; otherwise, continue iterating from G5 to G9 until Y is reached. i Continue until the convergence condition is met.

[0180] Step G10: Calculation complete, exit the preprocessing generalized minimum residual algorithm.

[0181] Step 9: Using the dual mesh of the tetrahedral mesh, the finite volume method based on the preprocessed generalized minimum residual algorithm is used to solve the current continuity equation and calculate the charge density of each node in space.

[0182] Solving the current continuity equation using the finite volume method requires discretizing the equation using a tetrahedral dual network.

[0183]

[0184] In the formula, These represent the positive and negative charge densities of the i-th control volume at the n-th time step; Δt is the time step; V i N represents the volume of the i-th control volume; i L represents the number of faces controlling the i-th volume; i,kLet be the area of ​​the k-th face of the i-th control volume; These represent the positive and negative charge densities corresponding to the k-th surface of the i-th control volume at the n-th time step, respectively. The charge density corresponding to the windward control volume is used in the calculation. E i,k Let n be the electric field intensity at the k-th face of the i-th control volume, calculated using the electric field intensity of the tetrahedral element containing that face; i,k Let be the unit vector of the k-th face of the i-th control volume, pointing from the inside of the control volume to the outside of the control volume.

[0185] To improve the efficiency of charge density calculation, the above equation is also applied... Figure 3 The preprocessing generalized minimum residual algorithm shown is used for iterative solution.

[0186] Step 10: Check whether the surface field strength of the conductor changes between the two time cycles. If the surface field strength of the conductor does not change, stop the inner loop of the conductor surface field strength correction and output the steady-state result of the conductor surface field strength. Otherwise, enter the inner loop of the conductor surface field strength correction.

[0187] Step 11: Check whether the steady-state result of the electric field strength on the conductor surface satisfies the Kaptzov condition. If it does, exit the outer loop of the conductor surface charge density correction and output the DC conductor surface charge density. In this step, the Kaptzov condition means that after the conductor surface corona occurs, the electric field strength on the conductor surface remains unchanged.

[0188] Step 12: The steady-state result of the conductor surface electric field does not satisfy the Kaptzov condition, so the outer loop of conductor surface charge density correction is entered, and the inner loop of conductor surface electric field correction is performed again to achieve a new steady-state result of conductor surface electric field and output DC conductor surface charge density.

[0189] Step 13: Calculate the combined electric field when the AC conductor is grounded based on the surface charge density of the DC conductor;

[0190] Step 14: Using the combined electric field when the AC conductor is grounded as the initial value for calculating the mixed electric field, calculate the mixed electric field when the AC conductor is energized;

[0191] Step 15: Ground mixed electric field when output DC conductor crosses AC conductor;

[0192] Step 16: Calculation complete.

[0193] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0194] Through the above description of the embodiments, those skilled in the art can clearly understand that the ground electric field determination method according to the above embodiments can be implemented by means of software plus necessary general-purpose hardware platform. Of course, it can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0195] According to an embodiment of the present invention, a ground electric field determination device for implementing the above-described electric field determination method is also provided. Figure 7 This is a structural block diagram of a ground electric field determination device provided according to an embodiment of the present invention, such as... Figure 7 As shown, the ground electric field determination device includes: a segmentation module 71, a calculation module 72, an outer circulation module 73, an inner circulation module 74, an output module 75, a determination module 76, and a second calculation module 77. The ground electric field determination device will be described below.

[0196] The meshing module 71 is used to perform three-dimensional finite element meshing on the target space region to obtain a tetrahedral mesh of the target space region and a dual mesh that generates the tetrahedral mesh. The target space region includes DC conductors and AC conductors, with the DC conductors crossing the AC conductors, and the target space region includes the ground region.

[0197] The first calculation module 72 is used to calculate the nominal electric field on the surface of a DC conductor using the finite element method based on a tetrahedral mesh.

[0198] The outer circulation module 73 is used to provide an initial value of the surface charge density of the DC conductor in the target space region, and to enter the surface charge density correction outer circulation of the DC conductor based on the initial value of the charge density.

[0199] The inner loop module 74 is used to enter the inner loop of surface field strength correction of DC conductor, generate the time step and initial time of the inner loop, and execute the following steps in a loop: according to the initial value of surface charge density of DC conductor and tetrahedral mesh, the finite element method based on preprocessing generalized minimum residual method is used to solve the Poisson equation to obtain the potential of each node in the target space region.

[0200] This method is used to solve the current continuity equation using the finite volume method based on the preprocessed generalized minimum residual method, based on the potential of each node in the dual grid and the target space region, to obtain the charge density of each node in the target space region.

[0201] This is used to determine whether the surface electric field strength of the DC conductor is the same in two adjacent loop results in the inner loop. If the results of two adjacent loops are different, the latest loop result of the inner loop is used to assign a surface charge density correction value. The inner loop is repeated according to the correction value. If the results of two adjacent loops are the same, the inner loop is exited to obtain the surface electric field strength of the DC conductor.

[0202] The output module 75 is used to re-enter the external loop for surface charge density correction of the DC conductor when the surface electric field strength of the DC conductor does not meet the Kaptzov condition, and then re-enter the internal loop for surface electric field strength correction of the DC conductor. The output module is also used to exit the external loop and output the target value of surface charge density of the DC conductor when the surface electric field strength of the DC conductor meets the Kaptzov condition. The target value of surface charge density of the DC conductor is determined based on the loop result of the internal loop.

[0203] The determination module 76 is used to determine the combined electric field generated by the DC conductor in the ground area when the AC conductor is grounded, based on the target value of the surface charge density of the DC conductor;

[0204] The second calculation module 77 is used to calculate the mixed electric field in the ground area when the AC conductor is pressurized, based on the composite electric field when the AC conductor is grounded as the initial value for calculating the mixed electric field, under the condition that the AC conductor is pressurized in the target space area.

[0205] It should be noted that the above-mentioned segmentation module 71, calculation module 72, outer loop module 73, inner loop module 74, output module 75, determination module 76, and second calculation module 77 correspond to steps S201 to S209 in the embodiments. Multiple modules and their corresponding steps implement the same instances and application scenarios, but are not limited to the content disclosed in the above embodiments. It should also be noted that the above modules, as part of the device, can run on the computer terminal 10 provided in the embodiments.

[0206] Embodiments of the present invention may provide an electronic device, optionally located in at least one of a plurality of network devices in a computer network. The electronic device includes a memory and a processor.

[0207] The memory can be used to store software programs and modules, such as the program instructions / modules corresponding to the ground electric field determination method and apparatus in this embodiment of the invention. The processor executes various functional applications and data processing by running the software programs and modules stored in the memory, thereby realizing the aforementioned ground electric field determination method. The memory may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some instances, the memory may further include memory remotely located relative to the processor, and these remote memories can be connected to a computer terminal via a network. Examples of such networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

[0208] The processor can access information and application programs stored in memory via a transmission device to execute the following steps: Perform three-dimensional finite element mesh generation on the target space region to obtain a tetrahedral mesh of the target space region and a dual mesh for generating the tetrahedral mesh. The target space region includes DC and AC conductors, with the DC conductors crossing the AC conductors, and includes a ground region. Based on the tetrahedral mesh, calculate the nominal electric field of the DC conductor surface using the finite element method. Given an initial value for the surface charge density of the DC conductor within the target space region, enter an external loop for surface charge density correction of the DC conductor. Enter an internal loop for surface field strength correction of the DC conductor, generating the time step and initial time of the internal loop, and iteratively execute the following steps: Based on the initial value of the surface charge density of the DC conductor and the tetrahedral mesh, solve the Poisson equation using the finite element method based on the preprocessed generalized minimum residual method to obtain the potential of each node within the target space region. Based on the dual mesh and the potential of each node within the target space region, solve the current continuity equation using the finite volume method based on the preprocessed generalized minimum residual method to obtain the potential of each node within the target space region. The system calculates the charge density at a point; it checks if the surface electric field strength of the DC conductor is the same in two consecutive loops within the inner loop. If the results are different, it uses the latest loop result from the inner loop as the initial value for the surface charge density and repeats the inner loop. If the results are the same, it exits the inner loop and obtains the surface electric field strength of the DC conductor. If the surface electric field strength of the DC conductor does not satisfy the Kaptzov condition, it re-enters the outer loop for surface charge density correction and then re-enters the inner loop for surface electric field strength correction. If the surface electric field strength of the DC conductor satisfies the Kaptzov condition, it exits the outer loop and outputs the target value for the surface charge density of the DC conductor, which is determined based on the loop result of the inner loop. Based on the target value for the surface charge density of the DC conductor, it determines the combined electric field generated by the DC conductor in the ground region when the AC conductor is grounded. When the AC conductor is pressurized in the target space region, it uses the combined electric field when the AC conductor is grounded as the initial value for calculating the mixed electric field and calculates the mixed electric field in the ground region when the AC conductor is pressurized.

[0209] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing the hardware related to the terminal device. The program can be stored in a non-volatile storage medium, which may include: flash drive, read-only memory (ROM), random access memory (RAM), magnetic disk or optical disk, etc.

[0210] Embodiments of the present invention also provide a non-volatile storage medium. Optionally, in this embodiment, the aforementioned non-volatile storage medium can be used to store the program code executed by the ground electric field determination method provided in the above embodiments.

[0211] Optionally, in this embodiment, the non-volatile storage medium may be located in any computer terminal in a group of computer terminals in a computer network, or in any mobile terminal in a group of mobile terminals.

[0212] Optionally, in this embodiment, the non-volatile storage medium is configured to store program code for performing the following steps: performing three-dimensional finite element meshing on the target space region to obtain a tetrahedral mesh of the target space region, and a dual mesh for generating the tetrahedral mesh, wherein the target space region includes DC and AC conductors with the DC conductors crossing the AC conductors, and the target space region includes a ground region; calculating the nominal electric field of the DC conductor surface using the finite element method based on the tetrahedral mesh; given an initial value of the surface charge density of the DC conductor in the target space region, entering an external loop for surface charge density correction of the DC conductor based on the initial value of the charge density; entering an internal loop for surface field strength correction of the DC conductor, generating the time step and initial time of the internal loop, and repeatedly executing the following steps: solving the Poisson equation using the finite element method based on the preprocessed generalized minimum residual method based on the initial value of the surface charge density of the DC conductor and the tetrahedral mesh, obtaining the potential of each node in the target space region; solving the current continuity equation using the finite volume method based on the preprocessed generalized minimum residual method based on the dual mesh and the potential of each node in the target space region, obtaining the current continuity equation in the target space region. The charge density of each node is determined. The surface electric field strength of the DC conductor is compared between two consecutive loops within the inner loop. If the results differ, the latest loop result is used as the initial value for the surface charge density, and the inner loop is repeated. If the results are identical, the inner loop is exited, and the surface electric field strength of the DC conductor is obtained. If the surface electric field strength does not satisfy the Kaptzov condition, the outer loop for surface charge density correction is re-entered, followed by the inner loop for surface charge density correction. If the surface electric field strength satisfies the Kaptzov condition, the outer loop is exited, and the target value for the surface charge density of the DC conductor is output. This target value is determined based on the loop result of the inner loop. Based on the target value, the combined electric field generated by the DC conductor in the ground region when the AC conductor is grounded is determined. When the AC conductor is pressurized in the target space region, the combined electric field when the AC conductor is grounded is used as the initial value for calculating the mixed electric field. The mixed electric field in the ground region when the AC conductor is pressurized is then calculated.

[0213] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0214] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0215] In the several embodiments provided in this application, it should be understood that the provided technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between units or modules may be electrical or other forms.

[0216] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0217] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0218] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a non-volatile storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0219] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining a ground electric field, characterized in that, include: The target space region is meshed using three-dimensional finite element methods to obtain a tetrahedral mesh of the target space region and a dual mesh that generates the tetrahedral mesh. The target space region includes a DC conductor and an AC conductor, with the DC conductor crossing the AC conductor. The target space region also includes a ground region. The nominal electric field on the surface of the DC conductor is calculated using the finite element method based on the tetrahedral mesh. Given an initial value of the surface charge density of the DC conductor within the target space region, an external loop for surface charge density correction of the DC conductor is entered based on the initial value of the charge density. Enter the surface field strength correction inner loop of the DC conductor, generate the time step and initial time of the inner loop, and repeatedly execute the following steps: Based on the initial value of the surface charge density of the DC conductor and the tetrahedral mesh, the Poisson equation is solved using the finite element method based on the preprocessed generalized minimum residual method to obtain the potential of each node in the target spatial region. Based on the dual mesh of the tetrahedral mesh and the potential of each node in the target spatial region, the current continuity equation is solved using the finite volume method based on the preprocessed generalized minimum residual method to obtain the charge density of each node in the target spatial region. Determine whether the surface electric field strength of the DC conductor is the same in two consecutive loop results in the inner loop. If the results of two consecutive loops are different, use the latest loop result of the inner loop to assign a surface charge density correction value. Repeat the inner loop according to the correction value. If the results of two consecutive loops are the same, exit the inner loop to obtain the surface electric field strength of the DC conductor. If the surface field strength of the DC conductor does not meet the Kaptzov condition, the external loop for correcting the surface charge density of the DC conductor is re-entered, and the internal loop for correcting the surface field strength of the DC conductor is re-entered. If the surface field strength of the DC conductor meets the Kaptzov condition, the external loop is exited and the target value of the surface charge density of the DC conductor is output. The target value of the surface charge density of the DC conductor is determined based on the loop result of the internal loop. Based on the target value of the surface charge density of the DC conductor, determine the combined electric field generated by the DC conductor in the ground region when the AC conductor is grounded; When the AC conductor in the target space region is pressurized, the mixed electric field in the ground region when the AC conductor is pressurized is calculated using the combined electric field when the AC conductor is grounded as the initial value for calculating the mixed electric field.

2. The method according to claim 1, characterized in that, The process involves solving the Poisson equation using the finite element method based on the preprocessed generalized minimum residual method, based on the initial surface charge density of the DC conductor and the tetrahedral mesh, to obtain the potential of each node within the target spatial region, including: The Poisson equation is: in, Here, ρ is the electric potential, ε0 is the space charge density, and "+" and "-" represent the positive and negative terminals, respectively. The relationship between the electric field strength E and the electric field strength E is as follows: The boundary conditions for the potential Poisson equation are: in, and These three values ​​represent the potentials of the conductor surface, the ground, and the boundary of the target spatial region at a sufficiently distant location, satisfying the first type of boundary condition; U L U is the operating voltage of the conductor; nom This refers to the boundary potential of the target space region when the influence of space charge is neglected. The equivalent functional used to determine the boundary electric field of the target spatial region is: Among them, E n Let Ω be the normal component of the boundary field strength, Ω be the solution domain, i.e., the target space region, г1 be the first type of boundary, and г2 be the second type of boundary; The solution domain is discretized using the finite element method. Assume the solution domain is divided into m elements and n nodes, where m1 elements are coplanar with the first type of nodes, and m2 elements are coplanar with the second type of nodes. The potential of the unknown nodes in the solution domain is... The known node potential number is Potential function The approximate solution is: Where, N j Let j be the shape function of the j-th node; Substituting the approximate solution of the potential function into the equivalent functional of the boundary electric field, we obtain: Simplified, we get: Among them, s ij p i f i They are respectively: in, and Let be the shape functions of nodes i and j on element e, respectively. The system of linear equations for the approximate solution of the potential function is written in block matrix form: Among them, S 11 S 21 S 22 These are the stiffness coefficient matrices after partitioning, Φ is the column vector of unknown node potentials in the field, U is the column vector of known potentials of the first type of boundary nodes, P1 and P2 are the known column vectors on the right side, F2 is the known column vector on the right side, F1 is the unknown column vector on the right side, and contains the normal vector of the electric field intensity to be determined on the first type of boundary. Φ satisfies the finite element method for solving the potential equation: F1 satisfies the boundary electric field constraint equations: F1=S 21 Φ+S 22 U-P2, Interpolating the electric field on the first type of boundary node yields: The above equation can be expressed in matrix form as follows: KE n =-F1, Where K is the stiffness matrix of the first-kind boundary electric field distribution, E n For the column vector of the electric field normal components at the boundary nodes; The coefficients of the stiffness matrix are calculated using the following formula: The boundary electric field constraint equations are obtained as follows: IS n J-(S 21 Φ+S 22 U-P2), The normal component E of the electric field at the boundary nodes is solved using the preprocessed generalized minimum residual method. n By finding the potential Φ of unknown nodes within the field, the potential of each node in the target space region can be obtained.

3. The method according to claim 2, characterized in that, The normal component E of the electric field at the boundary nodes is solved by using the preprocessing generalized minimum residual method. n and the unknown node potential Φ within the field, including: Based on the initial surface charge density of the DC conductor and the tetrahedral mesh, the finite element method (FEM) potential equation and boundary electric field constraint equation are determined. The FEM potential equation includes the stiffness matrix S. 11 The boundary electric field constraint equations include the stiffness matrix K; The finite element solution potential equation and the boundary electric field constraint equation to be solved are expressed in the following form: AX = b, where A is an n×n square matrix, and represents the stiffness matrix S. 11 Alternatively, the stiffness matrix K; X is an n×1 dimensional column vector, representing the unknown nodal potential Φ or the normal component of the boundary nodal electric field E within the solution domain corresponding to the target spatial region. n b is an n-dimensional column vector, and b is determined according to the boundary electric field constraint equation or the finite element solution potential equation. The preprocessed generalized minimum residual algorithm is used to solve AX = b, and the normal component E of the electric field at the boundary node is obtained. n Or the unknown node potential Φ within the solution domain corresponding to the target spatial region.

4. The method according to claim 3, characterized in that, The preprocessing generalized minimum residual algorithm is used to solve AX = b, and the normal component E of the electric field at the boundary nodes is obtained. n Or the unknown node potential Φ within the solution domain corresponding to the target spatial region, including: Input matrices A and b, and unknowns X to be determined; Perform row and column balancing preprocessing on matrix A by multiplying each row of A by an s, so that the target norms of all rows of A have similar lengths. s is defined as: Define the row balance matrix of matrix A as: After performing row balancing on AX = b, the equivalent equation for AX = b is: D -1 AX=D -1 b, After performing row and column balancing on matrix A, and on the equation AX = b, the equivalent equation is: RPACY = RPb, Where matrix R is the permutation matrix, matrix P is the row balancing matrix, matrix C is the column balancing matrix, and the equivalent equation for the unknown X is: BY = d, Wherein, matrix B = RPAC, d = RPb, and unknown quantity X = CY; The generalized minimum residual algorithm is used to solve BY = d, the convergence condition ε is determined, and the initial solution Y0 is selected; Calculate the residual r i The initial residual vector r0 is defined as: BY0 = d - r0, Where r0 is the initial residual vector; The m-dimensional Krylov subspace generated by r0 is determined as follows: K m (B,r0)=span{r0,Br0,B 2 r0,…,B m-1 r0}; A set of orthonormal bases V is obtained through Gram-Schmidt orthogonalization. m ={v1,v2,…,v m From the Arnoldi process, we can obtain: Among them, H m =V m T BV m Let H be the upper Hessenberg matrix. m+1 For H m The augmented matrix, h m+1,m e m T For the augmented matrix H m+1 The last line, e m Represents the m-th column of the identity matrix I; The approximate solution is obtained by iterating in the Krylov subspace. The L2 norm of the residual vector of the approximate solution in the (i-1)th iteration is expressed as: ||r i ||2=||d-BY i-1 ||2=||β i-1 e1-H m+1,i-1 With i-1 ||2,β i-1 =||r i-1 ||2, Among them, z i-1 The following equation is obtained by minimizing it: An approximate solution Y is formed after i iterations. i satisfy: Y i =Y i-1 +V m,i-1 z i-1 ; Determine the approximate solution Y i To determine whether the convergence condition is met, use the following equation: ||r i-1 -BV m,i-1 z i-1 ||<ε, If Y i If the convergence condition is met, the solution to the unknown variable X is X = CY. i Exit the iteration process if Y i If the convergence condition is not met, continue the iterative process described above, which uses the generalized minimum residual algorithm to solve BY = d, until Y... i Continue until the convergence condition is met.

5. The method according to claim 1, characterized in that, The process involves solving the current continuity equation using the finite volume method based on the preprocessed generalized minimum residual method, based on the dual mesh of the tetrahedral mesh and the potential of each node within the target spatial region, to obtain the charge density of each node within the target spatial region. This includes: The equation for the continuity of current is: Where k is the ion mobility; W is the wind speed; R is the ion recombination rate; e is the charge of a single electron; and the subscripts "+" and "-" represent the positive and negative electrodes, respectively. The boundary conditions for the current continuity equation are: In the formula, E nom,AC and E nom E represents the electric field intensity on the surface of the DC conductor when the AC conductor is present and when the AC conductor is absent, respectively. nom q is calculated by grounding the AC conductor; 0,AC q0 and q0 are the charge densities on the surface of the DC conductor when the AC conductor is present and when the AC conductor is absent, respectively. q0 is obtained by the two-dimensional finite element finite volume method. Based on the dual network, the discretized current continuity equation is determined as follows: in, These represent the positive and negative charge densities of the i-th control volume at the n-th time step; Δt is the time step; V i N represents the volume of the i-th control volume; i L represents the number of faces controlling the i-th volume; i,k Let k be the area of ​​the k-th face of the i-th control volume; These represent the positive and negative charge densities corresponding to the k-th surface of the i-th control volume at the n-th time step, respectively. The charge density corresponding to the windward control volume is used in the calculation. E i,k Let n be the electric field strength at the k-th face of the i-th control volume, where the electric field strength of the tetrahedral element containing the k-th face is used in the calculation; i,k Let be the unit vector on the k-th face of the i-th control volume, pointing from the inside of the control volume to the outside of the control volume; Based on the potential of each node in the target spatial region, the discretized current continuity equation is solved using the preprocessing generalized minimum residual algorithm to obtain the charge density of each node in the target spatial region.

6. The method according to claim 1, characterized in that, The method further includes: when the surface electric field strength of the DC conductor does not satisfy the Kaptzov condition, performing the external loop based on the following equation to correct the surface charge density of the DC conductor: Where v is the external cycle number corrected for charge density, and Q v-2 Q v-1 E represents the charge density on the surface of the DC conductor described in steps v-2 and v-1, respectively. v-2 E v-1 E represents the electric field intensity on the surface of the DC conductor described in steps v-2 and v-1, respectively. on The corona field strength on the surface of the conductor.

7. A device for determining a ground electric field, characterized in that, include: The meshing module is used to perform three-dimensional finite element meshing on the target space region to obtain a tetrahedral mesh of the target space region and a dual mesh for generating the tetrahedral mesh. The target space region includes a DC conductor and an AC conductor, and the DC conductor crosses the AC conductor. The target space region also includes a ground region. The first calculation module is used to calculate the nominal electric field on the surface of the DC conductor using the finite element method based on the tetrahedral mesh. An external circulation module is used to provide an initial value of the surface charge density of the DC conductor within the target space region, and to enter an external circulation for surface charge density correction of the DC conductor based on the initial value of the charge density. The inner loop module is used to enter the surface field strength correction inner loop of the DC conductor, generate the time step and initial time of the inner loop, and repeatedly execute the following steps: Based on the initial value of the surface charge density of the DC conductor and the tetrahedral mesh, the Poisson equation is solved using the finite element method based on the preprocessed generalized minimum residual method to obtain the potential of each node in the target spatial region. Based on the dual mesh of the tetrahedral mesh and the potential of each node in the target spatial region, the current continuity equation is solved using the finite volume method based on the preprocessed generalized minimum residual method to obtain the charge density of each node in the target spatial region. Determine whether the surface electric field strength of the DC conductor is the same in two consecutive loop results in the inner loop. If the results of two consecutive loops are different, use the latest loop result of the inner loop to assign a surface charge density correction value. Repeat the inner loop according to the correction value. If the results of two consecutive loops are the same, exit the inner loop to obtain the surface electric field strength of the DC conductor. The output module is configured to re-enter the external loop for surface charge density correction of the DC conductor and re-enter the internal loop for surface charge density correction of the DC conductor when the surface electric field strength of the DC conductor does not meet the Kaptzov condition. The output module is also configured to exit the external loop and output the target value of surface charge density of the DC conductor when the surface electric field strength of the DC conductor meets the Kaptzov condition. The target value of surface charge density of the DC conductor is determined based on the loop result of the internal loop. The determination module is used to determine the combined electric field generated by the DC conductor in the ground area when the AC conductor is grounded, based on the target value of the surface charge density of the DC conductor; The second calculation module is used to calculate the mixed electric field in the ground area when the AC conductor is pressurized, based on the composite electric field when the AC conductor is grounded as the initial value for calculating the mixed electric field.

8. A non-volatile storage medium, characterized in that, The non-volatile storage medium includes a stored program, wherein, when the program is executed, it controls the device containing the non-volatile storage medium to perform the ground electric field determination method according to any one of claims 1 to 6.

9. An electronic device, characterized in that, It includes one or more processors and a memory, the memory being used to store one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the ground electric field determination method according to any one of claims 1 to 6.

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