Calculation method for transformer winding considering frequency-dependent loss, and related apparatus

Abstract

A calculation method for a transformer winding considering a frequency-dependent loss, comprising: according to simulation requirements, defining key parameters calculated by using a finite-difference time-domain (FDTD) algorithm; constructing an equivalent flat wire model in an FDTD grid; calculating frequency-dependent internal impedance per unit length of a flat wire; and on the basis of a vector fitting method and a time-domain convolution calculation method, substituting the frequency-dependent internal impedance into a time-domain equation of the FDTD algorithm for updating and iterative solving, so as to obtain an electromagnetic field calculation result. In the present invention, on the basis of the vector fitting method and time-domain convolution calculation, the impact of the frequency-dependent characteristics of an electromagnetic field distributed in a conductor on an electromagnetic transient process is accurately considered during the FDTD time-domain solving, so that the calculation accuracy and efficiency of conventional FDTD algorithms and even conventional cross-scale modeling techniques can be significantly improved, thereby carrying out the targeted electromagnetic transient analysis on the reliability, safety, and predictability of transformers, and achieving the early detection of potential faults and defects, or formulating targeted maintenance plans and repair schemes.

Description

Transformer winding calculation method considering frequency-dependent loss and related device

[0001] The present application claims priority to the Chinese patent application No. 202410670883.0, filed on May 28, 2024, and entitled "Transformer winding calculation method considering frequency-dependent loss and related device", the content of which is incorporated herein by reference in its entirety. TECHNICAL FIELD

[0002] The present application belongs to the technical field of electromagnetic transient analysis of power transformers, and specifically relates to a transformer winding calculation method considering frequency-dependent loss and related device. BACKGROUND

[0003] Power transformers play a crucial role in the operation of power systems and society. They not only achieve efficient transmission of electric energy in power systems, adapt to voltage demands in different regions through voltage transformation, but also play a key role in ensuring the stability and reliability of the power grid. The power transmission, current adjustment and isolation functions of transformers help optimize the performance of the power network and improve the efficiency of electric energy transmission. At the same time, the existence of transformers enables the power system to adapt to different load conditions and respond to changes in power demand, thereby promoting the normal operation of various fields of society. These characteristics not only directly affect the normal operation of the power system, but also have a profound impact on the normal operation of various fields of society, making power transformers one of the indispensable infrastructures of modern society.

[0004] Accurate calculation of transformer electromagnetic transient processes plays an important role in the design, operation and maintenance of power transformers. It provides engineers with a tool to gain a deep understanding of device behavior, helps optimize design and improve reliability, and provides strong support during operation and maintenance. Frequency-dependent loss is the eddy current loss caused by the change of current in the winding over time, which is more significant under high frequency and transient conditions. Considering the frequency-dependent loss of the winding is a necessary condition for accurate calculation of transformer electromagnetic transients.

[0005] Currently, time-domain electromagnetic transient simulation of power transformer winding structure flat conductors is mainly based on the finite difference time domain (FDTD) algorithm to analyze the dynamic electromagnetic process of electromagnetic wave conduction and reflection in the winding.

[0006] However, the recently proposed simulation technique based on FDTD parasitic capacitance conversion can simulate long straight lossless conductors with non-circular cross-sections, but cannot accurately calculate the frequency-dependent loss of the conductors. When the conductivity of the conductor is a finite value and the high frequency band proportion of the excitation signal is high, it will increase the error of electromagnetic transient calculation and affect the accuracy of simulation verification. SUMMARY

[0007] Therefore, the present application aims to provide a transformer winding calculation method and related device considering frequency-dependent loss for time-domain electromagnetic transient simulation of flat wire of power transformer winding structure, which is based on vector matching method and time-domain convolution calculation, accurately considers the influence of frequency-dependent characteristics of electromagnetic field distribution in the conductor on electromagnetic transient process in FDTD time-domain solution, can significantly improve the calculation accuracy and efficiency of traditional FDTD algorithm and even traditional cross-scale modeling technology, and solves the above-mentioned deficiencies of simulation technology based on FDTD parasitic capacitance conversion.

[0008] In order to solve the above technical problems, the technical scheme provided by the present application is as follows:

[0009] In the first aspect, the present application provides a transformer winding calculation method considering frequency-dependent loss, comprising the following steps:

[0010] Defining key parameters of finite time-domain difference algorithm (FDTD) calculation according to simulation requirements, the key parameters being related parameters for constructing and calculating FDTD model in simulation calculation;

[0011] Based on the defined key parameters, constructing an equivalent flat wire model in the FDTD grid;

[0012] Calculating the frequency-dependent internal impedance of the flat wire per unit length in the equivalent flat wire model;

[0013] Based on vector matching method and time-domain convolution calculation method, substituting the frequency-dependent internal impedance into the time-domain equation of the finite time-domain difference algorithm (FDTD) for updating and iterative solution to obtain electromagnetic field calculation results;

[0014] The vector matching method is used to fit and convert the calculated frequency-dependent internal impedance of the flat wire per unit length into a rational function, and the time-domain convolution calculation method is used to transform the rational function into a time-domain convolution form, so as to directly substitute into the time-domain equation of the FDTD algorithm, thereby considering the influence of frequency-dependent characteristics of electromagnetic field distribution in the conductor on electromagnetic transient process in FDTD time-domain solution.

[0015] Further, the arrangement mode of the flat wire model in the FDTD grid is as follows:

[0016] The flat wire model is arranged on an edge of one orthogonal direction in the FDTD grid, and coincides with the electric field vector of one orthogonal direction;

[0017] The grid size of the flat wire model in the axial direction is set as non-uniform grid, and the grid size in the radial direction is set as uniform grid.

[0018] Further, the vector matching method converts the calculated frequency-dependent internal impedance of the flat conductor per unit length into a rational function, as follows:

[0019] where Z int represents the internal impedance of the flat conductor per unit length, s represents the complex frequency domain, d is the DC component, h is the inductive component, c m is the residue, a m is the pole, and N is the order of the vector matching.

[0020] Further, the calculation expression of the frequency-dependent internal impedance of the flat conductor per unit length is as follows: Z int = Z total -jωL ext

[0021] where Z int represents the internal impedance of the flat conductor per unit length, Z total represents the total impedance of the flat conductor per unit length varying with frequency, ω is the angular frequency, L ext is the external inductance of the flat conductor per unit length,

[0022] ν represents the transmission speed of electromagnetic waves in the flat conductor, β CC is the self-capacitance coefficient of the flat conductor.

[0023] Further, the calculation process of the total impedance of the flat conductor per unit length varying with frequency is as follows:

[0024] The cross section of the flat conductor of the transformer is divided into a plurality of rectangular elements;

[0025] One of the rectangular elements is selected as an observation element, and another rectangular element is selected as a source element, to obtain the voltage drop ΔV of the observation element per unit length in the axial direction under the influence of the source element:

[0026] where E is the electric field intensity, A is the magnetic vector potential, σ is the electrical conductivity, μ is the magnetic permeability, J is the current density in a certain element, R is the distance between the source element and the observation element, (x, y) is the coordinate of a certain point in the source element, and (x0, y0) is the coordinate of a certain point in the observation element.

[0027] The observation element and the source element are extended to the entire cross section of the flat conductor, to obtain the voltage drop of the flat conductor per unit length in the axial direction:

[0028] where Δs i is the area of the i-th rectangular element, n is the number of discrete elements of the cross section of the flat conductor, L ij represents the mutual inductance of the source element j to the observation element i,

[0029] S j represents the integral path of the source unit;

[0030] The resistive component and the inductive component are extracted and combined to obtain:

[0031] In the formula, Z ii and Z ij respectively represent self-impedance and mutual impedance;

[0032] The impedance matrix on the right side of the above formula is inverted and moved to the left side of the formula to obtain:

[0033] In the formula, the item on the left side of the formula represents the current distribution in each discrete rectangular element of the flat wire, Y ii represents self-admittance, Y ij represents mutual admittance;

[0034] The same kind of items are combined to obtain:

[0035] In the formula, I total represents the total current of the cross section of the flat wire, Y sum represents total admittance;

[0036] The total admittance is taken as the reciprocal to obtain the total impedance of the flat wire per unit length varying with frequency

[0037] In the formula, Z total represents total impedance.

[0038] Further, the frequency-varying internal impedance is substituted into the time-domain equation of the finite time-domain difference algorithm FDTD for updating, which specifically includes:

[0039] The axial electric field at the flat wire model is updated, and the update equation is as follows:

[0040] In the formula, E l is the axial FDTD electric field vector coinciding with the flat wire model, I total represents the total current of the cross section of the flat wire, n represents the time step number, Z(t) represents the frequency-varying internal impedance in the time domain, K p =d+h / Δt, K q =-h / Δt, d is a direct current component, h is an inductive component, Δt represents a time step, is a convolution item, c m is a residue, a m represents a pole, I (n) represents the total current of the conductor at the n time, and N represents the order of vector matching;

[0041] The axial currents of each segment of the flat conductor are updated, and the updating equation is as follows:

[0042] In the formula, Δy and Δz are the minimum grid sizes of the FDTD grid in the Y and Z two orthogonal directions, H y , H z are the magnetic field vectors in the Y and Z two orthogonal directions, m is the electromagnetic field vector space position number based on the axial segmentation number of the flat conductor, j and k are the electromagnetic field vector space position numbers based on the FDTD grid along the Y and Z directions.

[0043] Further, the finite time domain difference algorithm FDTD is used for iterative solution, specifically including:

[0044] According to the steps of the updating calculation equation, the electric field and magnetic field vectors in the calculation region are repeatedly iteratively solved, and each iteration solution is equivalent to updating and estimating the electromagnetic field quantity in the calculation region to the next time step Δt in time, realizing step-by-step solution of the electromagnetic field quantity in time. When the calculation iteration meets the preset condition, the electromagnetic field calculation is terminated, and the calculation result is output.

[0045] Further, an equivalent flat conductor model is constructed in the FDTD grid, specifically including:

[0046] Based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the flat conductor surface and the virtual circular surface, the correction coefficient of the flat conductor model in the FDTD grid is calculated;

[0047] The material parameters of the corresponding position of the FDTD calculation region are corrected by using the correction coefficient to construct the equivalent flat conductor model;

[0048] The equivalent flat conductor model obtained based on the correction coefficient can meet the calculation requirements of the FDTD without reducing the FDTD grid size.

[0049] Further, the calculation expression of the correction coefficient is as follows:

[0050] In the formula, m represents the correction coefficient, C Mu represents the mutual capacitance value of the flat conductor, r0 represents the simulation radius of the lossless circular conductor, Δs is the radial FDTD grid size around the flat conductor model, and ε is the characteristic parameter of the attached dielectric material of the orthogonal grid around the flat conductor model.

[0051] Further, the key parameters specifically include:

[0052] The calculation region size, the grid size, the time step, the material parameter, the excitation, and the termination calculation condition.

[0053] In a second aspect, the present application further provides a transformer winding calculation device considering frequency-dependent loss, comprising:

[0054] A parameter defining module is configured to define key parameters of finite time domain difference (FDTD) calculation according to simulation requirements, wherein the key parameters are related parameters used for constructing and calculating the FDTD model in the simulation calculation.

[0055] A model constructing module is configured to construct an equivalent flat conductor model in the FDTD grid based on the defined key parameters.

[0056] A first calculation module is configured to calculate the frequency-dependent internal impedance of the flat conductor per unit length in the equivalent flat conductor model.

[0057] A second calculation module is configured to substitute the frequency-dependent internal impedance into the time domain equation of the finite time domain difference (FDTD) to update and iteratively solve, so as to obtain the electromagnetic field calculation result.

[0058] The vector matching method is used to fit and convert the calculated frequency-dependent internal impedance of the flat conductor per unit length into a rational function, and the time domain convolution calculation method is used to transform the rational function into a time domain convolution form, so as to directly substitute into the time domain equation of the FDTD algorithm, thereby considering the influence of the frequency-dependent characteristics of the electromagnetic field distribution in the conductor on the electromagnetic transient process in the FDTD time domain solution.

[0059] Correspondingly, the present application further provides a computer device, which comprises a processor and a memory:

[0060] The memory is configured to store a computer program and send instructions of the computer program to the processor.

[0061] The processor executes the instructions of the computer program to perform the transformer winding calculation method considering frequency-dependent loss according to the first aspect.

[0062] Correspondingly, the present application further provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program is executed by the processor to implement the transformer winding calculation method considering frequency-dependent loss according to the first aspect.

[0063] In summary, the application provides a transformer winding calculation method considering frequency-dependent loss, including defining key parameters of finite time domain difference algorithm (FDTD) calculation according to simulation requirements; constructing an equivalent flat wire model in the FDTD grid; calculating the frequency-dependent internal impedance per unit length of the flat wire; based on the vector matching method and the time domain convolution calculation method, the frequency-dependent internal impedance is substituted into the time domain equation of the finite time domain difference algorithm (FDTD) for updating and iterative solving to obtain the electromagnetic field calculation result; wherein the vector matching method is used to fit and convert the calculated frequency-dependent internal impedance per unit length of the flat wire into a rational function, and the time domain convolution calculation method is used to convert the rational function into a time domain convolution form, so as to directly substitute the frequency-dependent internal impedance into the time domain equation of the FDTD algorithm, thereby considering the influence of the frequency-dependent characteristics of the electromagnetic field distribution in the conductor on the electromagnetic transient process in the FDTD time domain solving. The application converts the frequency-dependent internal impedance per unit length of the flat wire into a rational function by the vector matching method, and then converts the rational function into a time domain convolution form by the time domain convolution calculation, so that the frequency-dependent internal impedance can be substituted into the time domain equation of the FDTD algorithm, the influence of the frequency-dependent characteristics of the electromagnetic field distribution in the conductor on the electromagnetic transient process is considered in the FDTD calculation of the transformer electromagnetic transient process, and the influence of the frequency-dependent characteristics of the electromagnetic field distribution in the conductor on the electromagnetic transient process is considered in the FDTD time domain solving. The method can significantly improve the calculation accuracy and efficiency of the traditional FDTD algorithm and even the traditional cross-scale modeling technology, thereby carrying out electromagnetic transient analysis of transformer reliability, safety, predictability, etc., discovering possible faults and defects early, or developing targeted maintenance plans and repair schemes, to reduce the transformer failure rate and maintenance cost, and improve the reliability and economy of the transformer operation. BRIEF DESCRIPTION OF DRAWINGS

[0064] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0065] Fig. 1 is a flowchart of a transformer winding calculation method considering frequency-dependent loss provided by an embodiment of the present application;

[0066] Fig. 2 is a schematic diagram of setting a flat wire model in a FDTD grid provided by an embodiment of the present application;

[0067] Fig. 3 is a schematic diagram of calculating a correction coefficient based on mutual capacity of the FDTD grid and the outer surface of the conductor provided by an embodiment of the present application;

[0068] Fig. 4 is a one-dimensional discrete schematic diagram of the flat wire surface and the virtual circular surface provided by an embodiment of the present application;

[0069] Fig. 5 is a schematic diagram of a flat wire cross section divided into several rectangular units according to an embodiment of the present application;

[0070] Fig. 6 is a flow chart of an implementation of an electromagnetic transient calculation model of a power transformer winding flat wire according to an embodiment of the present application;

[0071] Fig. 7 is a block diagram of a transformer winding calculation device considering frequency-dependent loss according to an embodiment of the present application;

[0072] Fig. 8 is a block diagram of a computer device according to an embodiment of the present application. DETAILED DESCRIPTION

[0073] In order to make the objectives, features and advantages of the present application more obvious and easy to understand, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the embodiments described below are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application.

[0074] The disadvantages of the prior art will be further introduced below.

[0075] 1) The traditional FDTD algorithm uses global grid discretization for each simulated object in the calculation region. For a flat wire with a small radial size (centimeter level) and a large axial size (kilometer level), the number of grids will increase sharply, resulting in long calculation time and large memory consumption;

[0076] 2) The thin wire model technology based on the hybrid algorithm can construct a long straight lossless conductor with a circular cross section in a large size FDTD grid, but cannot simulate the transformer winding structure with a non-circular cross section. Directly using the circular cross section model will produce significant calculation errors;

[0077] 3) The simulation technology based on FDTD parasitic capacitance conversion proposed recently can simulate a long straight lossless conductor with a non-circular cross section, but cannot accurately calculate the frequency-dependent loss of the conductor. When the conductivity of the conductor is a finite value and the high frequency band proportion of the excitation signal is high, the error of electromagnetic transient calculation will be increased, affecting the simulation and checking accuracy.

[0078] Therefore, the application provides a transformer winding electromagnetic transient calculation method considering frequency-variable loss, which firstly obtains a flat conductor correction coefficient considering the influence of a non-circular cross section by solving parasitic capacitance and flat conductor mutual capacitance, and completes equivalent modeling of a small-size flat conductor in a large-size FDTD grid, and secondly accurately considers the influence of frequency-variable characteristics of electromagnetic field distribution in a conductor on electromagnetic transient process in FDTD time domain solving based on derivation of unit conductor internal impedance, vector matching method and time domain convolution calculation.

[0079] Referring to FIG. 1, the embodiment provides a transformer winding calculation method considering frequency-variable loss, including the following steps.

[0080] S1: defining key parameters of finite time domain difference algorithm (FDTD) calculation according to simulation requirements, wherein the key parameters are related parameters used for constructing and calculating the FDTD model in simulation calculation;

[0081] S2: constructing an equivalent flat conductor model in the FDTD grid based on the defined key parameters;

[0082] S3: calculating frequency-variable internal impedance of unit length of the flat conductor in the equivalent flat conductor model;

[0083] S4: based on vector matching method and time domain convolution calculation method, replacing the frequency-variable internal impedance into time domain equations of the finite time domain difference algorithm (FDTD) for updating and iterative solving to obtain electromagnetic field calculation results.

[0084] The vector matching method is used for fitting and converting the calculated frequency-variable internal impedance of unit length of the flat conductor into a rational function, and the time domain convolution calculation method is used for converting the rational function into a time domain convolution form, so as to directly replace the time domain equations of the FDTD algorithm, thereby considering the influence of frequency-variable characteristics of electromagnetic field distribution in a conductor on electromagnetic transient process in FDTD time domain solving.

[0085] It should be noted that the internal impedance calculated in step S3 is a resistance parameter characteristic curve varying with frequency, which cannot be directly replaced into the time domain equations of the FDTD algorithm for solving. The vector matching method is a method for fitting frequency domain data into a rational function, which is used for fitting network functions of linear circuits into rational functions in the theory of electrical networks, and is particularly suitable for modeling involving frequency-variable effects. It expresses the network function in the form of poles and residues, and uses a set of test data to solve the to-be-determined parameters, including poles, residues, d and e.

[0086] Therefore, the vector matching method is used in the embodiment to fit and convert the complex resistance parameter characteristics into a set of rational functions, and then time domain convolution calculation is used to replace the FDTD time domain simulation calculation in the form of convolution.

[0087] The transformer winding calculation method considering frequency variation loss provided by the embodiment is based on vector matching method and time domain convolution calculation, accurately considers the influence of the frequency variation characteristics of electromagnetic field distribution in the conductor on electromagnetic transient process in FDTD time domain solution, can significantly improve the calculation accuracy and efficiency of traditional FDTD algorithm and even traditional cross-scale modeling technology, and thus can carry out electromagnetic transient analysis of transformer reliability, safety, predictability and the like, discover possible faults and defects early, or formulate targeted maintenance plan and repair scheme, so as to reduce the transformer failure rate and maintenance cost, and improve the operation reliability and economy of the transformer.

[0088] In a preferred embodiment of the application, the key parameters of FDTD calculation include: calculation region size, grid size, time step, material parameters, excitation, and termination calculation condition. The specific definitions of the parameters can be as follows:

[0089] 1) Calculation region size

[0090] The FDTD calculation region size is reasonably determined according to the actual model size of the simulation, and the region is generally extended by about 50% of space on the basis of containing all the simulated objects, so as to eliminate the influence of boundary effect, stray signal reflection and the like.

[0091] 2) Grid size

[0092] The grid discretization scheme is determined according to the topological structure of the model, and the grid size in the region of the simulated object containing fine structures needs to be appropriately encrypted, and the grid size in the region where the electromagnetic field changes slowly is increased, so as to consider the simulation accuracy and efficiency at the same time.

[0093] 3) Time step

[0094] The selection range of the time step of the FDTD algorithm is determined by the minimum FDTD discrete grid size, and needs to satisfy the Courant-Friedrich-Levy (CFL) criterion to prevent problems such as data divergence, oscillation, non-convergence and the like that may occur in time domain calculation, that is,

[0095] In the formula, Δx, Δy and Δz are the minimum grid sizes of the FDTD grid in the X, Y and Z three orthogonal directions, and c is the propagation speed of light in the corresponding medium. Generally, the maximum value in formula (1) is selected as the FDTD time step, so as to reduce the simulation times and improve the simulation efficiency.

[0096] 4) Material parameters

[0097] According to the spatial position of the simulated object, the conductivity, dielectric constant and magnetic permeability in the FDTD grid are set.

[0098] 5) Excitation

[0099] According to the actual demand, the load is arranged in the specified position in the form of spatial electromagnetic field or concentrated circuit parameter element.

[0100] 6) termination calculation condition

[0101] According to the transient process to be simulated, the total iteration step number is determined, or according to the calculation precision requirement, the calculation result convergence condition is set.

[0102] In a preferred embodiment of the present application, an arrangement scheme of the flat wire model is proposed, and the subsequent equivalent flat wire model is constructed based on the arrangement scheme.

[0103] The flat wire model should be arranged on the edge of a certain orthogonal direction in the FDTD grid, and the electric field vector of the direction is overlapped, as shown in FIG. 2. It should be noted that since the radial direction of the flat wire is not discretized by the FDTD grid, the radial electromagnetic field distribution cannot be directly solved by the FDTD algorithm iteration, so the radial material parameters of the flat wire in the FDTD space need to be corrected by the correction coefficient, so as to establish the equivalent flat wire model in the large-size FDTD grid, as shown in FIG. 3. The grid size in the axial direction of the model can be set as a non-uniform grid, but in the two directions of the radial direction of the model, a uniform grid needs to be set. For example, for the flat wire model in the Z direction, the grid size in the Z direction can be set as a non-uniform grid, while the grid size in the adjacent XY direction needs to be uniform and equal, that is, Δx=Δy=Δs.

[0104] Based on the arrangement scheme of the flat wire model proposed in the foregoing embodiment, in a preferred embodiment of the present application, a construction method of the equivalent flat wire model is further proposed. The method comprises:

[0105] Step 1: based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the flat wire surface and the virtual circular surface, the correction coefficient of the flat wire model in the FDTD grid is calculated;

[0106] Step 2: the material parameters of the corresponding position of the FDTD calculation region are corrected by using the correction coefficient, and the equivalent flat wire model is constructed;

[0107] Among them, the equivalent flat wire model obtained based on the correction coefficient can meet the calculation requirements of the FDTD without reducing the FDTD grid size.

[0108] Based on the construction method of the equivalent flat wire model proposed in the foregoing embodiment, in a preferred embodiment of the present application, a calculation method of the parasitic capacitance value is further proposed.

[0109] When the FDTD material parameters are not modified, a certain segment of the FDTD electric field vector is assigned a value of 0, thereby constructing a lossless circular conductor with a radius of r0, as shown in Fig. 3(c). Here, r0 is referred to as the intrinsic radius of the FDTD grid, and the capacitance between the surface of the lossless circular conductor and the virtual circular surface with a radius of Δs is referred to as the parasitic capacitance. The parasitic capacitance value can be calculated as follows:

[0110] In the formula, Δs is the radial FDTD grid size around the flat wire model, and ε is the characteristic parameter of the dielectric material around the orthogonal grid of the flat wire model. Through multiple numerical solutions of the lossless circular conductor, the relationship between the intrinsic radius (r0) and the radial grid size (Δs) is r0 = 0.2298Δs.

[0111] In a preferred embodiment of the present application, a method for calculating the mutual capacitance value of a flat wire is further provided.

[0112] As shown in Fig. 3(a), when the flat wire model is constructed, the conductor surface, the virtual circular surface (shown by a dashed line in the figure) with a radius of Δs, and the dielectric between the two surfaces can constitute a group of capacitors. Under the condition of a quasi-static electric field, the electric charges are nonlinearly distributed on the outer surface of the conductor, and this distribution law is not affected by the frequency and the conductivity of the conductor. Assuming that the total amount of electric charges per unit length in the axial direction of the flat wire is Q, and the total amount of electric charges per unit length in the axial direction of the virtual circular surface is -Q. To accurately analyze the electric charge distribution in the flat wire with a non-circular cross section, the boundary of the flat wire surface and the virtual circular surface in the cross section can be divided into N line segments of equal length, as shown in Fig. 4, and the electric charge amount and length of each line segment are q j and L j , respectively. Line segment j is the source line segment, and line segment i is selected as the observation line segment, with infinity as the reference point. The electric potential φ i on the observation line segment i can be expressed as:

[0113] In the formula, ε is the dielectric constant of the material between the two surfaces, N is the total number of discrete points of the flat wire surface and the virtual circular surface, q j is the electric charge density on the corresponding line segment, s j is the line integral path of the corresponding source line segment, and ρ i,j is the distance between the observation line segment and the source line segment, and its calculation formula is (x i ,y i ) is the coordinate of a point on the source line segment, and (x j ,y j ) is the coordinate of a point on the source line segment. P i,j represents the electric charge coefficient between the i observation line segment and the j source line segment.

[0114] The relationship between the potential of the axial unit length and the charge on the line segment can be expressed as

[0115] wherein P CC and P BB respectively represent the self-charge coefficient sub-matrix of the discrete line segments of the flat conductor surface and the virtual circular surface, P CB and P CB represent the mutual-charge coefficient sub-matrix between the discrete line segments of the flat conductor surface and the virtual circular surface, φ C and φ B are the discrete charge quantity sub-matrix of the flat conductor surface and the virtual circular surface. For the conductors, the unit length of the flat conductor and the virtual circular surface are equipotential bodies, i.e., the element values of the sub-matrix φ C and φ B are the same. Inverting the charge coefficient matrix to the right side of the equation and rearranging can obtain

[0116] wherein β CC and β BB respectively represent the self-capacitance coefficient of the flat conductor surface and the virtual circular surface, β CB and β BC represent the mutual-capacitance coefficient between the flat conductor surface and the virtual circular surface, φ C and φ B are the potential of the flat conductor surface and the virtual circular surface. Inverting the capacitance coefficient matrix to the left side of the equation can obtain

[0117] wherein P' CC and P' BB respectively represent the self-charge coefficient of the flat conductor surface and the virtual circular surface, P' CB and P' BC represent the mutual-charge coefficient between the flat conductor surface and the virtual circular surface. At this time, the capacitance between the two surfaces can be derived as

[0118] Using the calculation method of the parasitic capacitance value and the mutual capacitance value of the flat conductor proposed in the above embodiment, the FDTD parasitic capacitance and the mutual capacitance of the flat conductor are solved, the correction coefficient of the flat conductor considering the influence of the non-circular cross section is accurately obtained, and the transformer winding structure with the irregular cross section is accurately simulated.

[0119] In a preferred embodiment of the present application, a calculation expression of the correction coefficient is provided, as follows:

[0120] wherein m represents the correction coefficient, C Muwhere C represents the mutual capacitance value of the flat wire, r0 represents the analog radius of the lossless circular wire, Δs represents the radial FDTD grid size around the flat wire model, and ε represents the characteristic parameter of the dielectric material of the orthogonal grid around the flat wire model. It can be understood that the parameters in formula 8 can be determined according to the foregoing embodiments.

[0121] The correction coefficient can also be obtained from the annular inductance composed of the conductor surface, the virtual circular surface with a radius of Δs, and the magnetic permeability between the two surfaces, as shown in FIGS. 3(b) and (d). The solving idea is similar to that through the capacitance, and the solving result is the same, which will not be described herein again.

[0122] In a preferred embodiment of the present application, the material parameters of the FDTD calculation region corresponding position are corrected, and the equivalent flat wire model is constructed as follows:

[0123] Based on the correction coefficient obtained in the previous step, the material parameters attached to the electric field vectors and the magnetic field vectors around the flat wire model are modified, and the equivalent flat wire model is constructed. The material parameter correction method is as follows

[0124] 1) The dielectric constant corresponding to the four orthogonal electric field vectors perpendicular to the axial direction of the flat wire model is multiplied by the correction coefficient, to obtain the corrected dielectric constant ε', as shown in FIG. 3(c), and the original dielectric constant ε' is replaced. ε' = mε (9)

[0125] 2) The magnetic permeability corresponding to the four orthogonal magnetic field vectors around the axial direction of the flat wire model is divided by the correction coefficient, to obtain the corrected magnetic permeability μ', as shown in FIG. 3(d), and the original magnetic permeability μ' is replaced. μ' = μ / m (10)

[0126] By correcting the material parameters of the FDTD calculation region to construct the equivalent flat wire model, small-size modeling can be completed in a large-size grid, thereby increasing the FDTD grid size and the time step, reducing the FDTD grid quantity and the time step number, and significantly improving the calculation efficiency.

[0127] In a preferred embodiment of the present application, a calculation method of the frequency-dependent internal resistance per unit length of the flat wire is provided. Specifically as follows:

[0128] 1) Total resistance per unit length

[0129] The current in the operating transformer winding has a wide frequency characteristic, and the current frequency range usually covers tens to tens of megahertz. Due to the existence of the skin effect, the current distribution in the wire is different at different frequencies. When the frequency is low, the current distribution tends to be uniform, and when the frequency is high, the current distribution is concentrated at the cross-sectional boundary. Therefore, the current distribution in the cross section of the operating wire can be regarded as the superposition of the current distribution at multiple frequencies.

[0130] To analyze the current distribution of the cross section of the flat conductor accurately, the cross section of the flat conductor of the transformer can be divided into several rectangular units in a uniform or non-uniform form by using the idea of numerical analysis, as shown in Fig. 5. One of the rectangular units is selected as an observation unit, and another rectangular unit is selected as a source unit. Then, the voltage drop ΔV of the observation unit per unit length in the axial direction under the influence of the source unit can be expressed as

[0131] In the formula, E is the electric field intensity, A is the magnetic vector potential, ω is the angular frequency, σ is the electrical conductivity, μ is the magnetic conductivity, J is the current density in a unit, and R is the distance between the source unit and the observation unit, and the calculation formula is (x, y) is the coordinate of a point in the source unit, and (x0, y0) is the coordinate of a point in the observation unit.

[0132] It is assumed that the current density is uniformly distributed in each rectangular unit, and then the formula (11) can be rewritten as

[0133] In the formula, I i is the total current in the observation unit, I j is the total current in the source unit, Δs i and Δs j are the areas of the observation unit and the source unit respectively. The observation unit and the source unit are extended to the entire cross section of the flat conductor, and then the voltage drop per unit length in the axial direction of the flat conductor can be expressed as

[0134] In the formula, Δs i is the area of the i-th rectangular unit, n is the number of the discrete units of the cross section of the flat conductor, and L ij represents the mutual inductance of the source unit j to the observation unit i, and the calculation formula is

[0135] In the formula (13), the first term on the right side of the equal sign represents the resistive component, and the second term represents the inductive component. The resistive component and the inductive component are extracted and combined, and then the formula (13) can be derived as

[0136] In the formula, Z

[0137] The impedance matrix on the right side of the equal sign in the formula (15) is inverted, and is moved to the left side of the equal sign, and then the following formula can be obtained

[0138] In the above formula, the term on the left side of the equal sign represents the current distribution in each discrete rectangular unit of the flat conductor, and the total current I total of the cross section of the flat conductor is obtained by adding all the currents. Since the flat conductor is usually made of a good conductor such as copper, the voltage differences on the right side of the equal sign are equal, and thus the same terms can be combined, that is, all the rows and columns of the formula (16) are added, and then the following formula can be obtained

[0139] Taking the total admittance in formula (17) as the reciprocal, the total impedance Z of the unit length of the flat conductor varying with frequency can be obtained total

[0140] 2) Impedance per unit length

[0141] The total impedance per unit length of the flat conductor includes the resistive component, the internal inductive component and the external inductive component of the conductor. For the conductor model embedded in the FDTD calculation domain, the external inductive effect is obtained by the iterative calculation of the FDTD electromagnetic field vectors, so the total impedance cannot be directly substituted into the FDTD conductor model, and the internal impedance Z per unit length of the flat conductor needs to be obtained by subtracting the external inductive component in the total impedance. int Z int = Z total -jωL ext (19)

[0142] In the formula, L ext is the external inductance per unit length of the flat conductor, which can be calculated by the self-capacitance coefficient β CC in formula (5), that is,

[0143] In the formula, v represents the transmission speed of electromagnetic waves in the flat conductor, and the transmission speed is usually approximately equal to the speed of light.

[0144] In the embodiment, the frequency-dependent internal impedance per unit length of the conductor is derived in advance, the vector matching method and the time-domain convolution embedding technology are combined, and the frequency loss of the flat conductor can be accurately considered in the FDTD time-domain iterative solution.

[0145] In a preferred embodiment of the present application, a frequency-dependent internal impedance rational function conversion method based on the vector matching method is proposed.

[0146] The internal impedance obtained by formula (19) is a resistance parameter characteristic curve varying with frequency, which cannot be directly substituted into the time-domain equation of the FDTD algorithm for solving, and the vector matching method (Vector Fitting Technique, VFT) needs to be used to fit and convert the complex impedance parameter characteristic into a set of rational functions, and then substituted into the time-domain simulation calculation in the form of convolution.

[0147] The vector matching method was proposed by Bjorn Gustavsen in 1999, has the advantages of high stability, less iteration times and fast convergence, and has been widely used in the fields of microwave and antenna design, and the frequency response fitting technology is mature, which will not be described here. Through the vector matching method, the frequency characteristic curve of the internal impedance per unit length of the flat conductor can be fitted in the complex frequency domain as

[0148] where s represents the complex frequency domain, d is the direct current component, h is the inductive component, c m is the residue, a m is the pole, and N is the vector matching order. It is noted that as many frequency points as possible are selected uniformly within each frequency order of the original characteristic frequency curve to improve the accuracy of the curve fitting.

[0149] In a preferred embodiment of the present application, a method for substituting the frequency-dependent internal impedance into the time-domain equation of the finite time-domain difference algorithm (FDTD) for updating is provided, mainly including the updating of the axial electric field at the flat wire model and the axial electric current of each section of the flat wire model, and the FDTD electric field equation and magnetic field equation are combined to update the embodiment.

[0150] 1) Updating the FDTD magnetic field equation

[0151] The magnetic field vector of the whole domain is calculated by using the classical FDTD magnetic field vector updating equation for iterative calculation.

[0152] The specific equation is shown as follows

[0153] where μ' and σ m are the corrected magnetic permeability and permeability coefficient, and the permeability coefficient is generally set to 0. Among them, the magnetic permeability corresponding to the four orthogonal magnetic field vectors around the axial direction of the flat wire model has been replaced by the corrected magnetic permeability μ'.

[0154] 2) Updating the axial electric field at the flat wire model

[0155] Based on the first-order rational fraction of the frequency characteristic curve fitted by the vector matching method, i.e., formula (19), it can be more convenient to convert it into a time-domain convolution form by inverse Laplace transform. The updating equation of the axial FDTD electric field vector E l coinciding with the flat wire model can be replaced by the following equation

[0156] where K p =d+h / Δt, K q =-h / Δt, is the convolution term, c m is the residue, a m represents the pole, represents the total current of the conductor at time n, and N represents the vector matching order. In order to ensure the stability of the simulation, the time step can be appropriately reduced when the time-domain convolution calculation is combined. According to the current practical experience, the time step generally needs to be reduced to 0.8-0.9 times.

[0157] 3) Update FDTD magnetic field equation

[0158] The magnetic field vector of the whole domain is calculated by using the classical FDTD magnetic field vector update equation to iteratively calculate.

[0159] The specific equation is shown as follows

[0160] In the formula, μ' and σ m The corrected permeability and permeability coefficient are used, and the permeability coefficient is generally set to 0. The permeability corresponding to the four orthogonal magnetic field vectors around the axis of the flat wire model is replaced by the corrected permeability μ'.

[0161] 4) Update the axial current of each segment of the flat wire

[0162] Total current for calculating the axial electric field of the flat wire in the next period The total current flowing through the cross section of the flat conductor is calculated by the loop integral estimation of the magnetic field vector at n+1 / 2 in the FDTD calculation region, and for the wire model with the axial direction x and the lth segment The calculation equation is as follows

[0163] In a preferred embodiment of the present application, according to the flow of the update calculation equation proposed in the foregoing embodiment, the electric field and the magnetic field vector in the calculation region are iteratively solved, and each iteration is equivalent to updating and estimating the electromagnetic field quantity in the calculation region to the next time step Δt in time, so as to realize step-by-step solution of the electromagnetic field quantity in time. When the calculation iteration meets the preset condition, the electromagnetic field calculation is terminated, and the calculation result is output.

[0164] The calculation method of the electromagnetic transient effect of the transformer winding based on any one of the foregoing embodiments and combinations thereof is shown in the flowchart of FIG. 6, and specifically includes the following steps.

[0165] S1: Define the FDTD calculation key parameters according to the simulation requirements;

[0166] S2: Calculate the correction coefficient of the flat wire model in the FDTD grid;

[0167] S3: Correct the material parameters of the corresponding position of the FDTD calculation region, and construct the equivalent flat wire model;

[0168] S4: Update the FDTD electric field equation;

[0169] S5: Update the axial electric field of the flat wire model;

[0170] S6: Update the FDTD magnetic field equation;

[0171] S7: Update the axial current of each segment of the flat wire;

[0172] S8: determining whether a preset condition is reached, if not, jumping to step S5, if yes, ending the calculation.

[0173] Based on the same inventive concept, the embodiment of the present application further provides a transformer winding calculation device considering frequency variation loss for implementing the above-mentioned transformer winding calculation method considering frequency variation loss. The implementation scheme for solving problems provided by the device is similar to the implementation scheme recorded in the above-mentioned method, so the specific limitations in the following provided embodiment of the transformer winding calculation device considering frequency variation loss can be referred to the limitations of the transformer winding calculation method considering frequency variation loss in the above, which will not be repeated here.

[0174] Please refer to FIG. 7, the embodiment of the present application further provides a transformer winding calculation device considering frequency variation loss, comprising:

[0175] a parameter defining module, configured to define key parameters of finite time domain difference algorithm (FDTD) calculation according to simulation requirements, wherein the key parameters are related parameters used for constructing and calculating FDTD model in simulation calculation;

[0176] a model constructing module, configured to construct an equivalent flat wire model in FDTD grid based on the defined key parameters;

[0177] a first calculation module, configured to calculate frequency variation internal impedance of flat wire unit length in the equivalent flat wire model;

[0178] a second calculation module, configured to substitute the frequency variation internal impedance into time domain equation of the finite time domain difference algorithm (FDTD) for updating and iterative solving based on vector matching method and time domain convolution calculation method, to obtain electromagnetic field calculation result;

[0179] wherein the vector matching method is used for fitting and converting the calculated frequency variation internal impedance of flat wire unit length into a rational function, and the time domain convolution calculation method is used for transforming the rational function into time domain convolution form, so as to directly substitute into time domain equation of FDTD algorithm, thereby considering the influence of frequency variation characteristics of electromagnetic field distribution in the conductor on electromagnetic transient process into FDTD time domain solving.

[0180] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above functional units and modules is exemplified, and in actual application, the above functions can be completed by different functional units and modules according to needs, that is, the internal structure of the system is divided into different functional units or modules to complete all or part of the above described functions. Each functional unit or module in the embodiment can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or in the form of software functional unit. In addition, the specific names of each functional unit or module are only for the convenience of mutual distinction, and do not limit the protection scope of the present application. The specific working process of the unit or module in the system can refer to the corresponding process in the foregoing method embodiment, which will not be described here.

[0181] Referring to FIG. 8, the embodiment of the present application further provides a computer device 8, including a memory 802 and a processor 801 and a computer program 803 stored in the memory 802, when the computer program 803 is executed on the processor 801, the transformer winding calculation method considering frequency variation loss is realized as any one of the above methods.

[0182] The computer device 8 can be a desktop computer, a notebook computer, a palm computer, a cloud server and the like. The computer device 8 can include, but is not limited to, a processor 801 and a memory 802. Those skilled in the art can understand that FIG. 8 is only an example of the computer device 8, and does not constitute a limitation on the computer device 8, and can include more or fewer components than the illustrated components, or combine certain components, or different components, for example, can also include input / output devices, network access devices and the like.

[0183] The processor 801 can be a central processing unit (CPU), and the processor 801 can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor.

[0184] The memory 802 may, in some embodiments, be an internal storage unit of the computer device 8, such as a hard disk or a memory of the computer device 8. The memory 802 may, in other embodiments, also be an external storage device of the computer device 8, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, and the like, equipped on the computer device 8. Further, the memory 802 may also include both an internal storage unit and an external storage device of the computer device 8. The memory 802 is used to store an operating system, application programs, a boot loader, data, and other programs, such as program codes of the computer program, and the like. The memory 802 may also be used to temporarily store data that has been output or is to be output.

[0185] The embodiment of the present application further provides a computer readable storage medium, which stores a computer program. When the computer program is run by a processor, the transformer winding calculation method considering frequency variation loss is realized.

[0186] In the embodiment, the integrated unit, if realized in the form of a software function unit and sold or used as an independent product, can be stored in a computer readable storage medium. Based on such understanding, the present application can realize all or part of the processes of the above-mentioned embodiment methods by a computer program to instruct relevant hardware, and the computer program can be stored in a computer readable storage medium. The computer program can realize the steps of the above-mentioned various method embodiments when executed by a processor. The computer program includes computer program codes, which can be in the form of source code, object code, executable files or some intermediate forms, etc. The computer readable medium at least includes any entity or device capable of carrying the computer program code to a photographing device / terminal equipment, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal and a software distribution medium. For example, a U disk, a mobile hard disk, a magnetic disk or an optical disk, etc. In some jurisdictions, according to legislation and patent practice, the computer readable medium cannot be an electrical carrier signal and a telecommunication signal.

[0187] In the above embodiments, the description of each embodiment has its own focus, and the parts not described or recorded in detail in a certain embodiment can be referred to the relevant description of other embodiments.

[0188] Those skilled in the art can understand that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0189] In the embodiments disclosed in the present application, it should be understood that the disclosed apparatus / terminal device and method can be implemented in other ways. For example, the apparatus / terminal device embodiments described above are merely schematic, for example, the division of the modules or units is merely a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the displayed or discussed each other can be indirect coupling or communication connection through some interfaces, devices or units, and can be electrical, mechanical or other forms.

[0190] The above embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced by equivalents; and these modifications or replacements do not make the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for transformer winding calculation taking into account frequency- dependent losses, characterized in that, The method comprises the following steps: According to the simulation requirements, define the key parameters of the finite time domain difference algorithm FDTD calculation, which are the related parameters for constructing and calculating the FDTD model in the simulation calculation; Based on the defined key parameters, construct an equivalent flat wire model in the FDTD grid; Calculate the frequency-dependent internal impedance per unit length of the flat wire in the equivalent flat wire model; Based on the vector matching method and the time domain convolution calculation method, substitute the frequency-dependent internal impedance into the time domain equation of the finite time domain difference algorithm FDTD for updating and iterative solution to obtain the electromagnetic field calculation result; The vector matching method is used to fit and convert the calculated frequency-dependent internal impedance per unit length of the flat wire into a rational function, and the time domain convolution calculation method is used to transform the rational function into a time domain convolution form for direct substitution into the time domain equation of the FDTD algorithm.

2. The transformer winding calculation method considering frequency variation losses according to claim 1, characterized in that, The arrangement mode of the flat wire model in the FDTD grid is as follows: The flat wire model is arranged on the edge of one orthogonal direction in the FDTD grid, and the electric field vector of the one orthogonal direction is coincident with the flat wire model; The grid size of the axial direction of the flat wire model is set as a non-uniform grid, and the grid size of the radial direction is set as a uniform grid.

3. The method for transformer winding calculation considering frequency- dependent loss according to claim 1, characterized in that, The vector matching method converts the calculated frequency-dependent impedance fitting of the unit length of the flat wire into a rational function, specifically as follows: In the formula, Z int represents the internal impedance per unit length of flat conductor, s represents the complex frequency domain, d is the direct current component, h is the inductive component, c m is the residue, a m is the pole, and N is the vector matching order.

4. The method for transformer winding calculation considering frequency- dependent loss according to claim 1, characterized in that, The calculation expression of the frequency-variable internal impedance of the flat wire per unit length is specifically as follows: Z int = Z total -jωL ext where Z int is the internal impedance per unit length of the flat conductor, Z total represents the total impedance per unit length of the flat conductor as a function of frequency, ω is the angular frequency, L ext is the external inductance per unit length of the flat conductor, and ν represents the propagation speed of electromagnetic waves in the flat conductor, β CC is the self-capacitance coefficient of the flat conductor.

5. The method for transformer winding calculation considering frequency- dependent loss according to claim 4, characterized in that, The calculation process of the total impedance per unit length of the flat wire varying with frequency is as follows: Divide the cross section of the transformer flat wire into a plurality of rectangular elements; Selecting one of the rectangular cells as an observation cell and another rectangular cell as a source cell, a voltage drop AV of the observation cell per unit length in the axial direction under the influence of the source cell is obtained: In the formula, E is the electric field intensity, A is the magnetic vector potential, σ is the conductivity, μ is the magnetic permeability, J is the current density in a certain element, R is the distance between the source element and the observation element, (x, y) is the coordinates of a certain point in the source element, and (x0, y0) is the coordinates of a certain point in the observation element; Extending the observation unit and the source unit to the whole flat conductor cross section results in the voltage drop per axial unit length of the flat conductor: where Δs i is the area of the ith rectangular element, n is the number of discrete elements of the cross section of the flat conductor, L ij denotes the mutual inductance of the source element j on the observation element i, S j representing an integral path of the source unit; The resistive component and the inductive component are extracted and combined to obtain: In the formulae, Z ii and Z ij represent self-impedance and mutual impedance, respectively; The impedance matrix on the right side of the above equation is inverted and moved to the left side of the equation to obtain: wherein the left-hand side term represents the current distribution in each discrete rectangular element of the flat conductor, Y ii represents the self-impedance, Y ij represents the mutual-impedance; Merging the like items operation, we get: where I total represents the total current through the cross section of the flat conductor, Y sum represents the total admittance; Taking the total admittance inverse, the total impedance of the flat conductor per unit length is obtained as a function of frequency wherein Z total represents the total impedance.

6. The method for transformer winding calculation considering frequency- dependent loss according to claim 1, characterized in that, Substitute the frequency-dependent internal impedance into the time domain equation of the finite time domain difference algorithm FDTD for updating, which specifically includes: The axial electric field at the flat conductor model is updated using the following equation: where E l is the axial FDTD electric field vector coinciding with the thin wire model, I total denotes the total current through the thin wire cross section, n denotes the time step number, Z(t) denotes the frequency-dependent impedance in the time domain, K p = d + h / Δt, K q = -h / Δt, d is the DC component, h is the inductive component, Δt denotes the time step size, for the convolution term, c m for the record, a m denotes a pole, Indicates the total current of the conductor at time n, and N indicates the vector matching order; The axial currents of each segment of the flat conductor are updated, and the updating equation is as follows: where Δy, Δz are the minimum grid size of FDTD grid in Y, Z two orthogonal directions, H y , H z are the magnetic field vectors in Y, Z two orthogonal directions, m is the electromagnetic field vector space position number based on the axial segmentation number of the flat wire, j, k are the electromagnetic field vector space position numbers based on the FDTD grid numbering along Y, Z directions.

7. The method for transformer winding calculation considering frequency- dependent loss according to claim 6, characterized in that, Iterative solution is performed by using the finite time domain difference algorithm FDTD, which specifically includes: Repeat the iterative solution of the electric field and magnetic field vectors in the calculation region according to the steps of the updating calculation equation. Each iterative solution is equivalent to updating and estimating the electromagnetic field quantity in the calculation region to the next time step Δt, so as to realize the step-by-step solution of the electromagnetic field quantity in time. When the calculation iteration meets the preset condition, the electromagnetic field calculation is terminated, and the calculation result is output.

8. The method for transformer winding calculation considering frequency- dependent loss according to claim 1, characterized in that, Constructing an equivalent flat wire model in the FDTD grid specifically includes: Based on the principle that the corrected parasitic capacitance value is equal to the mutual capacitance value between the flat wire surface and the virtual circular surface, calculate the correction coefficient of the flat wire model in the FDTD grid; Use the correction coefficient to correct the material parameters of the corresponding position of the FDTD calculation region to construct the equivalent flat wire model.

9. The method for transformer winding calculation taking frequency variation loss into consideration according to claim 8, characterized in that, The calculation expression of the correction coefficient is as follows: wherein m represents the correction factor, C Mu wherein C represents the mutual capacitance value of the flat wire, r0 represents the analog radius of the lossless circular wire, Δs is the radial FDTD grid size around the flat wire model, and ε is the characteristic parameter of the dielectric material of the orthogonal grid around the flat wire model.

10. The method for transformer winding calculation considering frequency- dependent loss according to claim 1, characterized in that, The key parameters specifically include: Calculation region size, grid size, time step, material parameter, excitation, and termination calculation condition.

11. A transformer winding calculation device considering frequency- dependent losses, characterized by It comprises: A parameter definition module is configured to define the key parameters of the finite time domain difference algorithm FDTD calculation according to the simulation requirements, which are the related parameters for constructing and calculating the FDTD model in the simulation calculation; A model construction module is configured to construct an equivalent flat wire model in a FDTD grid based on the defined key parameters; A first calculation module is configured to calculate a frequency-dependent internal impedance per unit length of the flat wire in the equivalent flat wire model; A second calculation module is configured to substitute the frequency-dependent internal impedance into a time-domain equation of the finite time-domain difference algorithm (FDTD) for updating and iterative solving to obtain an electromagnetic field calculation result based on a vector matching method and a time-domain convolution calculation method. The vector matching method is configured to fit and convert the calculated frequency-dependent internal impedance per unit length of the flat wire into a rational function, and the time-domain convolution calculation method is configured to transform the rational function into a time-domain convolution form so as to be directly substituted into the time-domain equation of the FDTD algorithm.

12. A computer device, comprising: The device comprises a processor and a memory: The memory is configured to store a computer program and send instructions of the computer program to the processor; The processor executes the instructions of the computer program to perform the transformer winding calculation method considering frequency-dependent loss according to any one of claims 1-10.

13. A computer-readable storage medium, characterized in that, The computer program is stored on the computer readable storage medium and is executed by the processor to implement the transformer winding calculation method considering frequency-dependent loss according to any one of claims 1-10.

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