CN118586243A - Calculation method and system for electromagnetic transient effect of transformer winding - Google Patents

Abstract

The invention provides a method and a system for calculating electromagnetic transient effects of a transformer winding, wherein key parameters of FDTD calculation are defined according to simulation requirements; calculating a correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the surface of the flat wire and the virtual circular surface; correcting material parameters at corresponding positions of the FDTD calculation region by using the correction coefficients, and constructing an equivalent flat wire model; based on an equivalent flat wire model, adopting a finite time domain difference algorithm FDTD to carry out iterative solution to obtain an electromagnetic field calculation result; the equivalent flat wire model obtained based on the correction coefficient can meet the calculation requirement without reducing the FDTD grid size. According to the invention, the equivalent flat wire model is constructed by correcting the FDTD calculation region material parameters, so that small-size modeling can be completed in a large-size grid, the grid size and time step length are further increased, the grid number and time step number are reduced, and the calculation efficiency is remarkably improved.

Description

Calculation method and system for electromagnetic transient effect of transformer winding

Technical Field

The invention belongs to the technical field of electromagnetic transient analysis of power transformers, and particularly relates to a method and a system for calculating electromagnetic transient effects of transformer windings.

Background

Power transformers play a vital role in the power grid. Its main functions include voltage raising and lowering, power transfer, blocking and isolating, regulating current, raising power factor and adapting to load variation. Through voltage rise and fall, the transformer enables electric energy to be efficiently transmitted in the power grid, and the power grids with different voltage grades are isolated, so that the power grid can meet voltage requirements of different areas, and stability and reliability of the power grid are improved. In the aspect of power transmission, the transformer adjusts current, reduces transmission line loss and improves power grid efficiency. It adjusts the phase relation between current and voltage, helps to improve the power factor, reduces the invalid power loss. In addition, the power transformer can flexibly cope with load change, and the adaptability of the power grid is improved. In general, the power transformer optimizes the operation of the power grid through various functions, ensures the efficient transmission of electric energy, and improves the stability and reliability of the power grid.

Electromagnetic transient analysis of power transformers is crucial to ensure stable operation in the grid. This analysis involves the response and behavior of the transformer in transient voltage, current disturbances, and other sudden electromagnetic events. Firstly, through the evaluation of overvoltage protection, the transformer is ensured to be capable of effectively coping with sudden events such as lightning stroke, switching operation and the like possibly occurring in a power grid, so that the stable operation of equipment is ensured. Secondly, electromagnetic transient analysis is helpful for optimizing an insulation system, and stability and safety of the system are improved. In terms of the surge currents that may occur in the event of an emergency, this analysis helps to evaluate the response of the transformer, prevent damage, and ensure proper operation of the protection device. In addition, through analyzing the loss, the performance of the transformer in a very instantaneous working state can be better known, and the loss is reduced through optimizing the design.

At present, a time domain electromagnetic transient simulation is carried out on a flat wire of a winding structure of a power transformer, and a dynamic electromagnetic process of electromagnetic wave conduction and reflection in the winding is analyzed, which is mainly realized based on a finite time domain difference algorithm (FINITE DIFFERENCE TIME domain, FDTD). The conventional FDTD algorithm adopts global grid dispersion for each object to be simulated in a calculation area, and for the object with small radial dimension (centimeter level) and large axial dimension (kilometer level) of a flat wire, the grid number can be increased sharply, so that the calculation time is long and the memory consumption is large. The thin wire model technology (thin wire model) proposed in recent years can construct long straight conductors with circular cross sections in large-sized FDTD grids, but cannot simulate transformer winding structures with non-circular cross sections.

Disclosure of Invention

In view of the above, the present invention aims to provide a method and a system for calculating electromagnetic transient effects of a transformer winding for performing time domain electromagnetic transient simulation on a flat wire of a power transformer winding structure, wherein the method completes equivalent modeling of a small-size flat wire in a large-size FDTD grid, and significantly improves the calculation accuracy and efficiency of a traditional FDTD algorithm, so as to solve the above-mentioned disadvantages of the traditional FDTD algorithm and thin wire model technology.

In order to solve the technical problems, the technical scheme provided by the invention is as follows:

In a first aspect, the present invention provides a method for calculating an electromagnetic transient effect of a transformer winding, including the steps of:

According to the electromagnetic transient simulation requirement of the transformer winding, defining key parameters calculated by a finite time domain difference algorithm FDTD, wherein the key parameters are related parameters used for constructing and calculating an FDTD model in simulation calculation;

calculating a correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface;

correcting material parameters at corresponding positions of the FDTD calculation region by using the correction coefficients, and constructing an equivalent flat wire model;

based on an equivalent flat wire model, adopting a finite time domain difference algorithm FDTD to carry out iterative solution to obtain an electromagnetic field calculation result;

The correction coefficient is a correction parameter used for considering the influence of a non-circular cross section when an equivalent flat wire model is constructed in a large-size FDTD grid.

Further, the arrangement mode of the flat wire model in the FDTD grid is specifically as follows:

The flat wire model is arranged on an edge in an orthogonal direction in the FDTD grid and is overlapped with an electric field vector in the orthogonal direction;

The axial grid size of the flat wire model is set by adopting non-uniform grids, and the radial grid size is set by adopting uniform grids.

Further, the parasitic capacitance is in the radial FDTD grid size on the surface of the lossless circular conductorThe non-destructive round wire is used for assigning a segment of FDTD electric field vector to 0 to form a virtual circle surface with radius, and the constructed simulation radius isThe calculation expression of the parasitic capacitance value of the lossless circular conductor is as follows:

in the method, in the process of the invention, The value of the parasitic capacitance is represented,The characteristic parameters of the auxiliary dielectric materials of the orthogonal grid around the flat wire model.

Further, assume that the total amount of charges in the axial unit length of the flat wire isThe total charge amount of the virtual circular surface in the axial unit length is-The calculation flow of the mutual capacitance value of the flat wire is specifically as follows:

Dividing the boundary of the surface of the flat wire and the virtual circular surface on the cross section into N line segments with one-dimensional equal length, wherein the charge quantity and the length of each line segment are respectively as follows 、；

Selecting a line segment i as an observation line segment by taking the line segment j as a source line segment and taking infinity as a reference point to obtain potential on the observation line segment iThe method comprises the following steps:

Wherein N is the total discrete number of the surface of the flat wire and the virtual circular surface, For a line integration path corresponding to a source line segment,To observe the distance between a line segment and a source line segment,A differential term representing a source line segment,Representing the charge coefficient between the i observation line segment and the j source line segment;

extending the observation line segment and the source line segment to the boundary between the whole flat wire surface and the virtual circular surface, the relation between the electric potential of the axial unit length and the electric charge on the line segment is as follows:

in the method, in the process of the invention, AndRespectively representing the self-charge coefficient submatrices of the discrete line segments of the surface and the virtual circular surface of the flat wire,AndRepresenting the mutual charge coefficient submatrix between the surface of the flat wire and the virtual circular surface discrete wire segment,、The charge quantum matrix is a discrete charge quantum matrix of a flat wire surface and a virtual circular surface;

inverting the charge coefficient matrix to the right side of the equal sign, and obtaining the charge coefficient matrix through arrangement:

in the method, in the process of the invention, AndRespectively represent the self-capacitance coefficients of the surfaces and the virtual circular surfaces of the flat wires,AndRepresenting the mutual capacitance coefficient between the surface of the flat wire and the virtual circular surface,、Is the electric potential of the surface of the flat wire and the virtual round surface;

Inverting the capacitance coefficient matrix to the left side of the equal sign to obtain:

in the method, in the process of the invention, AndRespectively represent the self-charge coefficients of the surface and the virtual circular surface of the flat wire,AndRepresenting the mutual charge coefficient between the surface of the flat wire and the virtual circular surface;

the capacitance between the two surfaces, i.e. the mutual capacitance value of the flat wire, is calculated as follows:

in the method, in the process of the invention, Representing the mutual capacitance value between the surface of the flat wire and the virtual circular surface.

Further, the calculation expression of the correction coefficient is as follows:

in the method, in the process of the invention, The correction coefficient is represented by a number of coefficients,Representing the mutual capacitance value between the surface of the flat wire and the virtual circular surface,Representing the simulated radius of a non-destructive round wire,For radial FDTD mesh dimensions around the flat wire pattern,The characteristic parameters of the auxiliary dielectric materials of the orthogonal grid around the flat wire model.

Further, the material parameters include dielectric constant and magnetic permeability, and the material parameters at the corresponding positions of the FDTD calculation region are corrected by using the correction coefficients, specifically including:

Multiplying the dielectric constants corresponding to the four orthogonal electric field vectors perpendicular to the axial direction of the flat wire model by the correction coefficients to obtain corrected dielectric constants epsilon ', wherein the corrected dielectric constants epsilon' are as follows:

in the method, in the process of the invention, In order to correct the dielectric constant before correction,Representing the correction coefficient;

Dividing magnetic permeability corresponding to four orthogonal magnetic field vectors surrounding the axial direction of the flat wire model by a correction coefficient to obtain corrected magnetic permeability mu ', wherein the magnetic permeability mu' is as follows:

in the method, in the process of the invention, To be permeability before correction.

Further, the iterative solution by adopting the finite time domain difference algorithm FDTD comprises updating a calculation equation, and the method comprises the following steps:

updating an FDTD electric field equation, wherein the updating equation is as follows:

in the method, in the process of the invention, 、、For the electric field vectors in three orthogonal directions, i, j and k are electric field vector position numbers based on FDTD grid numbers, n represents time step numbers, sigma and epsilon' respectively represent equivalent conductivities and corrected dielectric constants in corresponding spaces,Representing the time step, deltax, deltay, deltaz are the corresponding grid dimensions of the FDTD grid in X, Y, Z orthogonal directions,、、Magnetic field vectors in three orthogonal directions;

Updating the axial electric field at the flat wire model, wherein the updating equation is as follows:

in the method, in the process of the invention, Representing an axial FDTD electric field vector coincident with the flat wire model;

updating the FDTD magnetic field equation, the update equation being as follows:

Wherein μ' and To correct for permeability and magnetic permeability.

Further, the finite time domain difference algorithm FDTD is adopted for iterative solution, and the method specifically comprises the following steps:

And repeatedly and iteratively solving the electric field vector and the magnetic field vector in the calculation area according to the step of updating the calculation equation, terminating the electromagnetic field calculation when the calculation iteration meets the preset condition, and outputting a calculation result.

Further, the key parameters specifically include:

the calculation of the area size, the mesh size, the time step, the material parameters, the excitation, and the termination of the calculation conditions.

In a second aspect, the present invention provides a computing system for electromagnetic transient effects of a transformer winding, comprising:

the parameter definition unit is used for defining key parameters of FDTD calculation of a finite time domain difference algorithm according to electromagnetic transient simulation requirements of the transformer winding, wherein the key parameters are related parameters used for constructing and calculating an FDTD model in simulation calculation;

The correction coefficient calculation unit is used for calculating the correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface;

the equivalent model construction unit is used for correcting the material parameters at the corresponding positions of the FDTD calculation area by using the correction coefficients to construct an equivalent flat wire model;

the electromagnetic solving unit is used for carrying out iterative solving by adopting a finite time domain difference algorithm FDTD based on the equivalent flat conductor model to obtain an electromagnetic field calculation result;

The correction coefficient is a correction parameter used for considering the influence of a non-circular cross section when an equivalent flat wire model is constructed in a large-size FDTD grid.

In summary, the invention provides a method and a system for calculating electromagnetic transient effects of a transformer winding, which comprise defining key parameters calculated by a finite time domain difference algorithm FDTD according to simulation requirements; calculating a correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface; correcting material parameters at corresponding positions of the FDTD calculation region by using the correction coefficients, and constructing an equivalent flat wire model; based on an equivalent flat wire model, adopting a finite time domain difference algorithm FDTD to carry out iterative solution to obtain an electromagnetic field calculation result; the equivalent flat wire model obtained based on the correction coefficient can meet the calculation requirement of FDTD without reducing the grid size of FDTD. According to the invention, the equivalent flat wire model is constructed by correcting the FDTD calculation region material parameters, so that small-size modeling can be completed in a large-size grid, the FDTD grid size and time step length are further increased, the FDTD grid number and time step number are reduced, and the calculation efficiency is remarkably improved.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

Fig. 1 is a flowchart of a method for calculating an electromagnetic transient effect of a transformer winding according to an embodiment of the present invention;

fig. 2 is a schematic diagram of a flat wire model in an FDTD mesh according to an embodiment of the present invention;

Fig. 3 is a schematic diagram of calculating correction coefficients based on the mutual capacity of the FDTD mesh and the outer surface of the conductor according to the embodiment of the present invention;

FIG. 4 is a one-dimensional discrete diagram of a flat wire surface and a virtual circular surface according to an embodiment of the present invention;

fig. 5 is a flowchart of an embodiment of a calculation model for electromagnetic transient state of a flat wire of a winding of a power transformer according to an embodiment of the present invention.

Detailed Description

In order to make the objects, features and advantages of the present invention more obvious and understandable, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is apparent that the embodiments described below are only some embodiments of the present invention, not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Referring to fig. 1, the present embodiment provides a method for calculating an electromagnetic transient effect of a transformer winding, including the following steps:

S1: according to the electromagnetic transient simulation demand of the transformer winding, defining key parameters calculated by a finite time domain difference algorithm FDTD, wherein the key parameters are related parameters used for constructing and calculating an FDTD model in simulation calculation.

It should be noted that, according to the simulation requirement, the calculation parameters of the FDTD algorithm are set, including but not limited to space and time steps, boundary conditions, etc., so as to lay a foundation for the subsequent calculation.

S2: and calculating the correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface.

It should be noted that, based on the physical principle and the mathematical model, a correction coefficient is determined, and this coefficient makes the actual parasitic capacitance effect of the flat wire match with the simplified model (assumed virtual circular mutual capacitance), which is the key for constructing the equivalent model.

S3: and correcting the material parameters at the corresponding positions of the FDTD calculation region by using the correction coefficients, and constructing an equivalent flat wire model.

It should be noted that, the material parameters in the FDTD calculation area are adjusted by using the correction coefficients to form an equivalent model capable of accurately describing the electromagnetic characteristics of the flat wire, and the model can meet the accuracy requirement of FDTD calculation without an excessively fine grid.

S4: and (3) based on an equivalent flat wire model, adopting a finite time domain difference algorithm FDTD to carry out iterative solution to obtain an electromagnetic field calculation result.

It should be noted that: based on the established equivalent model, performing iterative calculation of the electromagnetic field by using an FDTD algorithm, and finally obtaining the accurate field distribution of the transformer winding under the electromagnetic transient effect.

The correction coefficient is a correction parameter used for considering the influence of a non-circular cross section when the equivalent flat wire model is constructed in a large-size FDTD grid.

It should be noted that, the finite time domain difference algorithm (FINITE DIFFERENCE TIME domain, FDTD) is to disperse the computation space and time into a finite number of difference units. Wherein the space unit is provided with three electric field vectors in orthogonal directions and three magnetic field vectors in orthogonal directions, and the three electric field vectors are used for dispersing the internal structure of the object to be simulated. The time unit (also called time step) is used for dispersing the time variation curve of the electromagnetic field quantity, so that the electromagnetic transient problem can be solved by means of the thought of static state. After the electromagnetic field quantity is discretized by the FDTD space-time unit, an iterative equation of the electromagnetic field quantity can be directly deduced by a Max Wei Weifen equation, the derivative in the equation is expressed by differential approximation, so that a continuous problem is converted into a discrete problem, and a second-order precision numerical solution of the system is obtained through iterative solution. The algorithm can not limit the application range of the algorithm due to the new mathematical model hypothesis, so the algorithm can theoretically solve any electromagnetic transient case for a simulation object with any structure.

However, as mentioned above, the conventional FDTD algorithm adopts global grid dispersion for each object to be simulated in the calculation area, and for such objects with small radial dimension (in cm order) and large axial dimension (in km order) of the flat wire, the number of grids increases sharply, resulting in long calculation time and large memory consumption. The thin wire model technology (thin wire model) proposed in recent years can construct long straight conductors with circular cross sections in large-sized FDTD grids, but cannot simulate transformer winding structures with non-circular cross sections.

In this embodiment, based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface, the flat wire correction coefficient considering the influence of the non-circular cross section is accurately obtained, and the equivalent flat wire model constructed by using the correction coefficient to correct the material parameters can meet the iteration solving requirement of the FDTD algorithm without FDTD grid dispersion.

The embodiment provides a calculation method for electromagnetic transient effects of transformer windings, which is characterized in that an equivalent flat wire model is constructed by correcting FDTD calculation region material parameters, so that small-size modeling can be completed in a large-size grid, the size and time step of the FDTD grid are further increased, the number and time step of the FDTD grid are reduced, and the calculation efficiency is remarkably improved.

In a preferred embodiment, the key parameters of the FDTD calculation include: the calculation of the area size, the mesh size, the time step, the material parameters, the excitation, and the termination of the calculation conditions. The specific definition of each parameter can be as follows:

1) Calculating region size

The size of the FDTD calculation area is reasonably determined according to the actual model size to be simulated, and the area extends outwards by about 50% of the space on the basis of containing all the objects to be simulated, so that the influences of boundary effect, stray signal refraction and reflection and the like are eliminated.

2) Mesh size

According to the topological structure of the model, a grid discrete scheme is determined, the grid size needs to be properly encrypted in the area of the object to be simulated containing the fine structure, and the grid size is increased in the area of the area with slower electromagnetic field change, so that the simulation precision and efficiency are considered at the same time.

3) Time step

The selection range of the FDTD algorithm time step is determined by the minimum FDTD discrete grid size, and the Kranit (Courant-Friedrich-Levy, CFL) criterion is required to be met to prevent the problems of data divergence, oscillation, non-convergence and the like possibly occurring in time domain calculation, namely

Where Δx, Δy, Δz are the minimum grid dimensions of the FDTD grid in the X, Y, Z orthogonal directions, and c is the propagation speed of light in the corresponding medium. In general, the maximum value in the formula (1) is selected for the FDTD time step, so as to reduce the simulation times and improve the simulation efficiency.

4) Material parameters

The electrical conductivity, dielectric constant and magnetic permeability of the response are set in the FDTD grid according to the spatial position of the object being simulated.

5) Excitation

And setting the load at a designated position according to actual requirements in the form of a space electromagnetic field or a concentrated circuit parameter element.

6) Terminating the computing condition

And determining the total iteration step number according to the transient process to be simulated, or setting the convergence condition of the calculation result according to the calculation precision requirement.

In a preferred embodiment, an arrangement of the flat wire model is proposed, on the basis of which a subsequent equivalent flat wire model construction is performed.

The flat wire pattern should be arranged on a certain orthogonal direction of the edges in the FDTD mesh, coinciding with the electric field vector in that direction, as shown in fig. 2. It should be noted that, since the radial direction of the flat wire is not scattered by the FDTD grid, the radial electromagnetic field distribution of the flat wire cannot be directly and iteratively solved by the FDTD algorithm, so that the radial material parameters of the flat wire in the FDTD space need to be corrected by the correction coefficient, thereby establishing an equivalent flat wire model in the large-size FDTD grid, as shown in fig. 3. The axial grid size of the model can be set by adopting non-uniform grids, but the uniform grids are required to be set in two radial directions of the model. For example, for a flat wire model in the Z direction, the grid size in the Z direction can be set unevenly, and the adjacent grids in the XY direction need to be uniform and equal, namely。

Based on the flat wire model layout scheme provided in the foregoing embodiment, in a preferred embodiment of the present invention, a calculation method of the parasitic capacitance value is further provided.

When the FDTD material parameters are not corrected, a certain segment of FDTD electric field vector is assigned to be 0, and then a lossless circular wire with the simulated radius r0 can be constructed, as shown in fig. 3 (c). Wherein, The capacitance between virtual circular surfaces with deltas as the radius is called parasitic capacitance, which is called the endogenous radius of the FDTD grid and is used for damaging the surfaces of the circular wires. The parasitic capacitance value can be calculated as follows:

Where Δs is the radial FDTD mesh size around the flat wire model and ε is the satellite dielectric material characteristic parameter of the orthogonal mesh around the flat wire model. The endophytic radius is known by solving the numerical value of the nondestructive round wire for a plurality of times ) The relation with the radial grid size (deltas) is。

In a preferred embodiment of the present invention, a method for calculating the mutual capacitance of the flat wires is further provided.

As shown in fig. 3 (a), when the flat wire model is constructed, the conductor surface, the virtual circular surface (shown by the dotted line) with Δs as the radius, and the dielectric between the two surfaces can form a set of capacitors. Under the condition of quasi-static electric field, the electric charges are distributed on the outer surface of the conductor in a nonlinear manner, and the distribution rule is not influenced by frequency and the conductivity of the conductor. Assuming that the total charge amount of the axial unit length of the flat wire isThe total charge amount of the axial unit length of the virtual circular surface is. To accurately analyze the charge distribution in a flat wire with a non-circular cross section, the surface of the flat wire and the virtual circular surface can be divided into N line segments with the same length at the boundary of the cross section, as shown in FIG. 4, the charge quantity and the length of each line segment are respectively、. The line segment j is a source line segment, the line segment i is selected as an observation line segment, and the potential on the observation line segment i is taken as a reference point at infinityCan be expressed as:

in the method, in the process of the invention, The dielectric constant of the material between the two surfaces, N is the total discrete number of the flat wire surface and the virtual circular surface,For the charge density on the corresponding line segment,For a line integration path corresponding to a source line segment,For observing the distance between the line segment and the source line segment, the calculation formula is，To observe the coordinates of a point on a line segment,For a point coordinate on the source line segment,Representing the charge coefficient between the i observation line segment and the j source line segment.

Extending the observation line segment and the source line segment to the boundary between the whole flat wire surface and the virtual circular surface, the relation between the potential of the axial unit length and the electric charge on the line segment can be expressed as

In the method, in the process of the invention,AndRespectively representing the self-charge coefficient submatrices of the discrete line segments of the surface and the virtual circular surface of the flat wire,AndRepresenting the mutual charge coefficient submatrix between the surface of the flat wire and the virtual circular surface discrete wire segment,、Is a discrete charge quantum matrix of a flat wire surface and a virtual circular surface. For conductors, the flat wires and the virtual circular surface of a unit length are equipotential bodies, namely submatrices on the right side of the equation、The respective element values are the same. Inverting the charge coefficient matrix to the right side of the equal sign, and obtaining the charge coefficient matrix after finishing

In the method, in the process of the invention,AndRespectively represent the self-capacitance coefficients of the surfaces and the virtual circular surfaces of the flat wires,AndRepresenting the mutual capacitance coefficient between the surface of the flat wire and the virtual circular surface,、Is the electric potential of the surface of the flat wire and the virtual circular surface. Inverting the above capacitance coefficient matrix to the left side of the equal sign to obtain

In the method, in the process of the invention,AndRespectively represent the self-charge coefficients of the surface and the virtual circular surface of the flat wire,AndRepresenting the mutual charge coefficient between the surface of the flat wire and the virtual circular surface. At this time, the capacitance between the two surfaces can be deduced as

In a preferred embodiment of the present invention, a calculation expression of the correction coefficient is provided as follows:

in the method, in the process of the invention, The correction coefficient is represented by a number of coefficients,The mutual capacitance value of the flat wire is represented,Representing the simulated radius of a non-destructive round wire,For radial FDTD mesh dimensions around the flat wire pattern,The characteristic parameters of the auxiliary dielectric materials of the orthogonal grid around the flat wire model. It will be appreciated that the parameters in equation 8 may be determined in accordance with the foregoing embodiments.

The correction coefficient can also be obtained by a toroidal inductance formed by the conductor surface, a virtual circular surface with deltas as a radius and magnetic permeability between the two surfaces, as shown in fig. 3 (b) and (d), the solving concept is similar to that of the solution by capacitance, and the solving result is the same and is not repeated here.

In a preferred embodiment of the present invention, material parameters at corresponding positions of the FDTD calculation region are corrected, and the equivalent flat wire model is constructed as follows:

Based on the correction coefficient obtained in the previous step, the material parameters attached to the electric field vector and the magnetic field vector around the flat wire model can be modified to construct an equivalent flat wire model. The material parameter correction method is as follows

1) Multiplying the dielectric constants corresponding to the four orthogonal electric field vectors perpendicular to the axial direction of the flat wire model by the correction coefficients to obtain a corrected dielectric constant epsilon', as shown in fig. 3 (c), and replacing the original dielectric constant at the corresponding position

2) Dividing the magnetic permeability corresponding to the four orthogonal magnetic field vectors surrounding the axial direction of the flat wire model by a correction coefficient to obtain corrected magnetic permeability mu', and replacing the original magnetic permeability of the corresponding position as shown in fig. 3 (d)

In a preferred embodiment of the present invention, the iterative solution using the finite time domain difference algorithm FDTD includes updating the calculation equation, specifically as follows:

1) Updating FDTD electric field equation

The iterative process involves the electric field vector value of the previous time step and four magnetic field vectors surrounding the electric field vector, and the specific update equation is shown below

In the method, in the process of the invention,、、The electric field vectors in three orthogonal directions, i, j and k are electric field vector position numbers based on FDTD grid numbers, n represents the number of time steps, sigma,Respectively representing the equivalent conductivity and the modified dielectric constant in the corresponding space.

2) Updating axial electric field at flat wire model

The flat wire of the transformer winding is commonly made of copper or aluminum, so that the loss is small, and the flat wire can be regarded as a nondestructive wire in calculation. For a lossless conductor, the conductivity is infinite, and the electric field values of the inside and the surface of the conductor are 0, so that the axial FDTD electric field vector overlapped with the flat wire model needs to be assigned to be 0 to simulate the lossless wire, namely

3) Updating FDTD magnetic field equation

And calculating the magnetic field vector of the whole domain by adopting a classical FDTD magnetic field vector update equation for iterative calculation. The specific equation is expressed as follows

In the middle of、To correct the permeability and the magnetic permeability, the magnetic permeability is generally set to 0. Wherein, the magnetic permeability corresponding to four orthogonal magnetic field vectors surrounding the axial direction of the flat wire model is replaced by the corrected magnetic permeability。

In a preferred embodiment of the present invention, according to the procedure of updating the calculation equation set forth in the foregoing embodiment, the iterative solution of the electric field and the magnetic field vector in the calculation region is repeated, and each iteration solution is performed once, which is equivalent to updating and estimating the electromagnetic field vector in the calculation region to the next time step Δt in time, so as to implement the step-wise solution of the electromagnetic field vector in time. And when the calculation iteration meets the preset condition, terminating the electromagnetic field calculation, and outputting a calculation result.

The preset conditions include two types: one is iteration number, namely stopping electromagnetic field calculation when the electromagnetic field update number reaches the preset iteration number; the other is a convergence condition, and when the space electromagnetic field is in steady-state distribution, or forms periodic variation, and the waveform deviation of two adjacent periods accords with the convergence condition.

The flow chart of the calculation method for the electromagnetic transient effect of the transformer winding based on any one of the embodiments and the combination thereof is shown in fig. 5.

Compared with the prior art, the method for calculating the electromagnetic transient effect of the transformer winding has the following advantages:

1) By correcting FDTD calculation region material parameters to construct an equivalent flat wire model, small-size modeling can be completed in a large-size grid, so that the size and time step of the FDTD grid are increased, the number and time step of the FDTD grid are reduced, and the calculation efficiency is remarkably improved;

2) By solving the FDTD parasitic capacitance and the mutual capacitance of the flat wires, the correction coefficient of the flat wires considering the influence of the non-circular cross section can be accurately obtained, and then the transformer winding structure with the irregular cross section can be accurately simulated.

Based on the same inventive concept, the embodiment of the application also provides a transformer winding electromagnetic transient effect calculation system for realizing the above-mentioned transformer winding electromagnetic transient effect calculation method. The implementation of the solution provided by the device is similar to the implementation described in the above method, so the specific limitation in the embodiment of the computing system of the electromagnetic transient effect of one or more transformer windings provided below may be referred to the limitation of the computing method of the electromagnetic transient effect of the transformer windings hereinabove, and will not be repeated herein.

The present embodiment provides a calculation system for electromagnetic transient effect of transformer winding, including:

the parameter definition unit is used for defining key parameters of FDTD calculation of a finite time domain difference algorithm according to electromagnetic transient simulation requirements of the transformer winding, wherein the key parameters are related parameters used for constructing and calculating an FDTD model in simulation calculation;

The correction coefficient calculation unit is used for calculating the correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface;

the equivalent model construction unit is used for correcting the material parameters at the corresponding positions of the FDTD calculation area by using the correction coefficients to construct an equivalent flat wire model;

the electromagnetic solving unit is used for carrying out iterative solving by adopting a finite time domain difference algorithm FDTD based on the equivalent flat conductor model to obtain an electromagnetic field calculation result;

The correction coefficient is a correction parameter used for considering the influence of a non-circular cross section when an equivalent flat wire model is constructed in a large-size FDTD grid.

The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. The method for calculating the electromagnetic transient effect of the transformer winding is characterized by comprising the following steps of:

Defining key parameters of FDTD calculation by a finite time domain difference algorithm according to electromagnetic transient simulation requirements of a transformer winding, wherein the key parameters are related parameters used for constructing and calculating an FDTD model in simulation calculation;

calculating a correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface;

Correcting material parameters at corresponding positions of the FDTD calculation region by using the correction coefficients, and constructing an equivalent flat wire model;

based on the equivalent flat conductor model, adopting a finite time domain difference algorithm FDTD to carry out iterative solution to obtain an electromagnetic field calculation result;

the correction coefficient is a correction parameter used for considering the influence of a non-circular cross section when the equivalent flat wire model is constructed in a large-size FDTD grid.

2. The method for calculating electromagnetic transient effects of transformer windings according to claim 1, wherein the arrangement of the flat wire model in the FDTD mesh is as follows:

The flat wire model is arranged on an edge in one orthogonal direction in the FDTD grid and is overlapped with the electric field vector in the one orthogonal direction;

The axial grid size of the flat wire model is set by adopting non-uniform grids, and the radial grid size is set by adopting uniform grids.

3. The method of claim 2, wherein the parasitic capacitance is in the form of a radial FDTD mesh size on the surface of the lossless circular conductorThe non-destructive round wire is formed by assigning a segment of FDTD electric field vector to 0 to form a virtual inter-round surface capacitance with radius, and the constructed simulation radius isThe calculation expression of the parasitic capacitance value is as follows:

in the method, in the process of the invention, Representing the value of the parasitic capacitance in question,The characteristic parameters of the auxiliary dielectric materials of the orthogonal grid around the flat wire model.

4. A method of calculating electromagnetic transient effects of a transformer winding as recited in claim 3 wherein the total amount of charge per unit length of the flat wire is assumed to beThe total charge amount of the virtual circular surface in the axial unit length is-The calculation flow of the mutual capacitance value of the flat wire is specifically as follows:

Dividing the boundary of the surface of the flat wire and the virtual circular surface on the cross section into N line segments with one-dimensional equal length, wherein the charge quantity and the length of each line segment are respectively as follows 、；

Selecting a line segment i as an observation line segment by taking the line segment j as a source line segment and taking infinity as a reference point to obtain potential on the observation line segment iThe method comprises the following steps:

Wherein N is the total discrete number of the surface of the flat wire and the virtual circular surface, For a line integration path corresponding to a source line segment,To observe the distance between a line segment and a source line segment,A differential term representing a source line segment,Representing the charge coefficient between the i observation line segment and the j source line segment;

extending the observation line segment and the source line segment to the boundary between the whole flat wire surface and the virtual circular surface, the relation between the electric potential of the axial unit length and the electric charge on the line segment is as follows:

in the method, in the process of the invention, AndRespectively representing the self-charge coefficient submatrices of the discrete line segments of the surface and the virtual circular surface of the flat wire,AndRepresenting the mutual charge coefficient submatrix between the surface of the flat wire and the virtual circular surface discrete wire segment,、The charge quantum matrix is a discrete charge quantum matrix of a flat wire surface and a virtual circular surface;

inverting the charge coefficient matrix to the right side of the equal sign, and obtaining the charge coefficient matrix through arrangement:

in the method, in the process of the invention, AndRespectively represent the self-capacitance coefficients of the surfaces and the virtual circular surfaces of the flat wires,AndRepresenting the mutual capacitance coefficient between the surface of the flat wire and the virtual circular surface,、Is the electric potential of the surface of the flat wire and the virtual round surface;

Inverting the capacitance coefficient matrix to the left side of the equal sign to obtain:

in the method, in the process of the invention, AndRespectively represent the self-charge coefficients of the surface and the virtual circular surface of the flat wire,AndRepresenting the mutual charge coefficient between the surface of the flat wire and the virtual circular surface;

the capacitance between the two surfaces, namely the mutual capacitance value of the flat wire, is calculated as follows:

in the method, in the process of the invention, And representing the mutual capacitance value between the surface of the flat wire and the virtual circular surface.

5. The method for calculating electromagnetic transient effects of a transformer winding according to claim 1, wherein the calculation expression of the correction coefficient is as follows:

in the method, in the process of the invention, The correction coefficient is represented by a value representing the correction coefficient,Representing the mutual capacitance value between the surface of the flat wire and the virtual circular surface,Representing the simulated radius of a non-destructive round wire,For radial FDTD mesh dimensions around the flat wire pattern,The characteristic parameters of the auxiliary dielectric materials of the orthogonal grid around the flat wire model.

6. The method for calculating electromagnetic transient effects of a transformer winding according to claim 1, wherein the material parameters include permittivity and permeability, and the correction coefficients are used to correct the material parameters at the corresponding positions of the FDTD calculation region, specifically comprising:

Multiplying the dielectric constants corresponding to the four orthogonal electric field vectors perpendicular to the axial direction of the flat wire model by the correction coefficients to obtain corrected dielectric constants epsilon ', wherein the corrected dielectric constants epsilon' are as follows:

in the method, in the process of the invention, In order to correct the dielectric constant before correction,Representing the correction coefficient;

Dividing magnetic permeability corresponding to four orthogonal magnetic field vectors surrounding the axial direction of the flat wire model by a correction coefficient to obtain corrected magnetic permeability mu ', wherein the magnetic permeability mu' is as follows:

in the method, in the process of the invention, To be permeability before correction.

7. The method of claim 1, wherein iteratively solving using a finite time domain difference algorithm FDTD comprises updating a calculation equation, comprising:

updating an FDTD electric field equation, wherein the updating equation is as follows:

in the method, in the process of the invention, 、、For the electric field vectors in three orthogonal directions, i, j and k are electric field vector position numbers based on FDTD grid numbers, n represents time step numbers, sigma and epsilon' respectively represent equivalent conductivities and corrected dielectric constants in corresponding spaces,Representing the time step, deltax, deltay, deltaz are the corresponding grid dimensions of the FDTD grid in X, Y, Z orthogonal directions,、、Magnetic field vectors in three orthogonal directions;

Updating the axial electric field at the flat wire model, wherein the updating equation is as follows:

in the method, in the process of the invention, Representing an axial FDTD electric field vector coincident with the flat wire model;

updating the FDTD magnetic field equation, the update equation being as follows:

Wherein μ' and To correct for permeability and magnetic permeability.

8. The method for calculating the electromagnetic transient effect of the transformer winding according to claim 7, wherein the iterative solution is performed by adopting a finite time domain difference algorithm FDTD, and specifically comprises:

And repeatedly and iteratively solving the electric field vector and the magnetic field vector in the calculation area according to the step of updating the calculation equation, terminating the electromagnetic field calculation when the calculation iteration meets the preset condition, and outputting a calculation result.

9. The method for calculating electromagnetic transient effects of a transformer winding according to claim 1, wherein the key parameters specifically comprise:

the calculation of the area size, the mesh size, the time step, the material parameters, the excitation, and the termination of the calculation conditions.

10. A computing system for electromagnetic transient effects of a transformer winding, comprising:

The parameter definition unit is used for defining key parameters of FDTD calculation of a finite time domain difference algorithm according to electromagnetic transient simulation requirements of the transformer winding, wherein the key parameters are related parameters used for constructing and calculating an FDTD model in simulation calculation;

The correction coefficient calculation unit is used for calculating the correction coefficient of the flat wire model in the FDTD grid based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the surface of the flat wire and the virtual circular surface;

The equivalent model construction unit is used for correcting the material parameters at the corresponding positions of the FDTD calculation area by using the correction coefficients to construct an equivalent flat wire model;

the electromagnetic solving unit is used for carrying out iterative solving by adopting a finite time domain difference algorithm FDTD based on the equivalent flat conductor model to obtain an electromagnetic field calculation result;

the correction coefficient is a correction parameter used for considering the influence of a non-circular cross section when the equivalent flat wire model is constructed in a large-size FDTD grid.