JP2000268061A - Method and device for analyzing electromagnetic field - Google Patents

Abstract

PROBLEM TO BE SOLVED: To highly accurately calculate an electromagnetic field in a short time while decreasing the number of unknown variables by avoiding an adverse influence caused by the oblateness of a finite element in electromagnetic field analysis based on a finite element method. SOLUTION: Concerning a method for calculating an eddy current to be generated in a non-magnetic conductor thinner than the depth of penetration while using a computer, this electromagnetic field analyzing method is provided with a process for calculating the electromagnetic field of an analytic object area, in which the characteristics of the non-magnetic conductor is assumed as air, through the finite element method using a magnetic vector potential. This analyzing method is also provided with a process for calculating the eddy current to be generated in the non-magnetic conductor through the finite element method using the current vector potential and a magnetic scalar potential for the electromagnetic field defining only the non-magnetic conductor and the periphery thereof as the analytic object area while defining a magnetic flux density distribution perpendicularly crossing a non-magnetic conductor part found by this calculation as initial conditions.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electromagnetic field analysis method and apparatus useful for designing electronic and electrical equipment utilizing electromagnetic phenomena such as transformers, reactors and motors, and an apparatus therefor. To improve the calculation accuracy and shorten the calculation time when the calculation is performed.

[0002]

2. Description of the Related Art A series of equations (Equation 1) to (Equation 3) or a series of equations (Equation 3) to (Equation 7) are used as basic equations used in the electromagnetic field analysis of the present invention.

RotH = Jo (Equation 1) B = rotA (Equation 2) B = μH (Equation 3) Je = σE (Equation 4) rotE = − (∂B / ∂t) (Equation 5) E = (1 / σ) rotT (Equation 6) H = T-gradΩ (Equation 7)

[0004] In these formulas, bold italic characters or symbols represent vectors having three-directional components of space (the same applies hereinafter, but are not shown in italics in the text of the specification). A is a magnetic vector potential, Jo is a forced current density vector (A / m ² ), and σ is conductivity (S / m ² ).
m) and μ are magnetic permeability (H / m), T is current vector potential, and Ω is magnetic scalar potential.

In order to actually solve these equations, a technique such as the finite element method is used. Hereinafter, a method of solving a series of equations (Equations 1) to (Equation 3) using the finite element method is referred to as a finite element method (hereinafter, A
Mod). On the other hand, using the finite element method,
A method of solving a series of equations (Equation 7) is called a finite element method (hereinafter, T-Ω method) using a current vector potential and a magnetic scalar potential.

The basic concept of the finite element method will be described below.

The finite element method is a method in which an analysis target area is spatially divided into a plurality of sub-areas having relatively simple shapes called "finite elements", and an unknown variable to be obtained is calculated on each element by a relatively simple function. For example, it is approximated by a linear function. Specifically, on each element, the potential to be obtained is developed by an approximation function, and the potential is obtained using the variational principle such that the energy in the analysis target is minimized.

As the above-mentioned approximation function, an approximation method using a function that imposes an unknown variable on a node of each finite element is called node element approximation. Galerk, a method equivalent to the variational principle, uses the nodal element approximation function to discretize the fundamental equation of the electromagnetic field.
This is performed using the in method. For the Galerkin method, for example,
"Matrix finite element method" (published by Baifukan in 1984)
It is described in.

An equation discretized for each finite element is created, and these equations are added together for all finite elements, and physical properties data, time data, boundary condition data, and forcing given to a conductor included in the analysis target area as initial conditions for analysis. By substituting a current density vector or the like, a simultaneous linear equation to be solved can be obtained. This equation is solved using, for example, a Gaussian elimination method, which is one of the direct methods, or an incomplete Cholesky conjugate gradient method, which is one of the iterative methods, to finally calculate a potential to be obtained. The Gaussian elimination method, the incomplete Cholesky conjugate gradient method, and the like are described in "Murata, Oguni, Karaki: Supercomputer; 1985".

The analysis accuracy and calculation time of the finite element method are as follows.
It depends greatly on the size of the finite element, the number of finite elements, and the oblateness of the finite element. In particular, when there is a non-magnetic conductor thinner than the skin thickness (hereinafter referred to as a thin conductor) in the analysis target area, in order to obtain a highly accurate solution, the inside of the thin conductor is divided by many finite elements. Computer memory and calculation time due to the increase in unknown variables. Also,
When the incomplete Cholesky conjugate gradient method is used,
A converged solution may not be obtained. Further, when the shape of the thin plate conductor is complicated, it is difficult to create the coordinate data of the finite element and the node numbers constituting the finite element.

The skin thickness δ (m) is a quantity determined by the following equation, for example, “Umoto: Electromagnetics; 1985
Year ".

Δ = SQR (1 / π × f × σ × μo) (Equation 8)

Here, f: frequency (Hz), σ: conductivity (S / m), μo: vacuum magnetic permeability (= 4π × 10 ⁷ ).

As a means for solving such a problem, "A. KAMEARI: Applied Electromagnetic in Mate"
rial: p225, 1989 ”etc. describes electromagnetic field analysis using edge element approximation. The approximate function used in edge element approximation is the literature“ Fujiwara: 3D magnetic field analysis using edge element; 2nd electromagnetic field Proceedings of Seminar on Numerical Analysis, 199
As described in 1 ”, since the magnetic field belongs to a function space in which the gauge transformation is satisfied, in the case of the method A using the magnetic vector potential, a part of the magnetic vector potential is converted into an unknown variable by graph theory. Can be excluded from

In the case of the T-Ω method, it is possible to take a gauge that makes the magnetic scalar potential Ω of (Equation 7) zero. Therefore, Ω = 0. Using such a side element approximation, when performing an electromagnetic field analysis when there is a thin plate conductor or a coil conductor in the analysis target area, it is possible to reduce unknown variables as compared with the case of using the nodal element approximation. , Computer memory and calculation time can be saved.

Also, "T.Nakata, N.Takahashi, K.Fujiw
ara and Y.Shiraki: 3-D MagneticField Analysis Usi
ng Special Element; IEEE Trans Magnetics, MAG-26,
5,2379 (1990) ”, a method of approximating a three-dimensional non-magnetic conductor or coil conductor with a two-dimensional finite element reduces unknown variables,
It is possible to easily create the node numbers constituting the finite element.

[0017]

[Problems to be solved by the invention] However, A.KAME
In the edge element approximation used in ARI and Fujiwara's literature, unknown variables can be reduced, but the inside of a thin conductor or coil conductor must be divided by many finite elements. Therefore, it is not possible to solve the disadvantageous effects on the calculation accuracy and the calculation time due to the flatness of the finite element, and the operator configures the input data, for example, the coordinate data of the finite element and the finite element. The creation of node numbers cannot be facilitated.

Also, if a method of approximating a three-dimensional thin plate conductor used in T. Nakata's document with a two-dimensional finite element is used, the problem in the above-mentioned KAMEARI and Hanno's documents can be solved. Although the problem can be solved, the properties of the system of linear equations to be finally solved are deteriorated, and the convergence of the incomplete Cholesky conjugate gradient method may take time or may not converge in some cases.

An object of the present invention is to reduce the oblateness of a finite element, reduce unknown variables to be solved, and calculate an electromagnetic field with high accuracy in a short time.

[0020]

According to a first electromagnetic field analysis method of the present invention, in a method of calculating an eddy current generated in a thin plate conductor thinner than a skin thickness by using a computer, the thin plate conductor is assumed to be a space. Calculating the electromagnetic field of the analysis target region by the finite element method using the magnetic vector potential, and the magnetic flux density distribution perpendicular to the thin plate conductor portion obtained by the calculation as an initial condition, the thin plate conductor and its vicinity The method includes a step of calculating an eddy current generated in the thin plate conductor by a finite element method using an electromagnetic field having only the analysis target region as a current vector potential and a magnetic scalar potential.

According to a second electromagnetic field analysis method of the present invention, in a method of calculating a total current generated in a coil conductor which is thinner than a skin thickness by using a computer, a uniform applied current is input to the coil conductor, and the coil conductor is connected to a space. Assuming that the electromagnetic field in the analysis target area assumed by the finite element method using a magnetic vector potential and a magnetic flux density distribution perpendicular to the coil conductor obtained by the calculation as an initial condition,
The step of calculating the eddy current generated in the coil conductor by the finite element method using the current vector potential and the magnetic scalar potential in the electromagnetic field with only the coil conductor and its vicinity as the analysis target area, and the distribution of the applied current flowing through the coil conductor The method includes a step of calculating by the finite element method, and a step of calculating the total current generated in the coil conductor by adding the applied current and the eddy current calculated in the above-described steps in a vector manner.

In a third electromagnetic field analysis method according to the present invention, the analysis target area calculated by the finite element method using a magnetic vector potential in the first or second electromagnetic field analysis method is a three-dimensional area.

According to a fourth electromagnetic field analysis method of the present invention, the analysis target region calculated by the finite element method using a magnetic vector potential in the first or second electromagnetic field analysis method is a rotationally symmetric region.

According to a fifth electromagnetic field analysis method of the present invention, in the first or second electromagnetic field analysis method, an analysis target area calculated by a finite element method using a magnetic vector potential is a two-dimensional area.

According to a sixth electromagnetic field analysis method of the present invention, in the first or second electromagnetic field analysis method, of the three components in the X, Y, and Z directions of the current vector potential, the three components are perpendicular to the surface of the coil conductor or the thin plate conductor. Only the components that are unknown are used as unknown variables.

The electromagnetic field analyzing apparatus according to the present invention includes computer means for executing any one of the first to sixth electromagnetic field analyzing methods.

[0027]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiment 1 FIG. 1 is a block diagram showing the configuration of computer means for executing an electromagnetic field analysis method according to the present invention. In FIG. 1, reference numeral 1 denotes an input device including a keyboard, a mouse, a scanner, and the like. Reference numeral 2 denotes a CPU, which controls each component connected to the bus 7 according to a program, by creating finite element data to be described later and performing an electromagnetic field analysis by a finite element method. 3
Is a display device such as a CRT.
Used to check input information and calculation status of electromagnetic field analysis. Reference numeral 4 denotes a program memory, which is a memory for storing a control program operating on the CPU 2. Reference numeral 5 denotes a data memory for storing data generated in various processes. Reference numeral 6 denotes an external storage device for storing data of the created finite element model, potential obtained by electromagnetic field analysis, and the like. Further, data or a processing program to be subjected to element division may be read from the external storage device 6. Reference numeral 7 denotes a bus for transferring an address signal indicating a component to be controlled by the CPU 2, a control signal for controlling each component, and data exchanged between components.

Next, the operation of the first embodiment will be described with reference to FIGS.
This will be described with reference to FIG. Here, a method of obtaining an eddy current generated in a nonmagnetic conductor thinner than the skin thickness will be described. FIG. 2 is a flowchart showing a processing procedure of the present method. Here, the thin plate conductor 8 as shown in FIG.
A method of analyzing the electromagnetic field in the analysis target area including the coil and the coil 9 will be described.

<Step S1> Coordinate data of nodes of a small area group obtained by dividing the analysis target area into a number of small areas so that the area is divided into a coil part and other parts and node number data constituting a finite element Then, various physical property data in the analysis target area, boundary condition data of the analysis target area, and current density data to be given as initial conditions to the conductor portion are created. Here, in the model used for the analysis by the method A, the analysis is performed by treating the thin plate conductor as equivalent to air without considering the physical properties of the thin plate conductor. Therefore, it is not necessary to divide the region of the thin plate conductor portion. The analysis target region was divided into elements as shown in FIG. 4 as a quarter region due to the symmetry of the model. If the boundary of the non-magnetic conductor is made to coincide with the node as shown in FIG. 4, it is convenient to obtain the magnetic flux density distribution interlinking the thin-plate conductor in step 3.

<Step S2> The magnetic vector potential at the nodes constituting each finite element is calculated by the A method. Since FIG. 4 has a three-dimensional shape, three-dimensional analysis is performed. However, when the model can be approximated by rotational symmetry or two-dimensional shape, analysis may be performed in each region. Also,
The method A may use either node element approximation that defines a magnetic vector potential, which is an unknown variable, as a node, or edge element approximation that defines an edge. When the edge element approximation is used, the magnetic vector potential is obtained by the sides constituting each finite element.

<Step S3> Using the above (Equation 2),
From the magnetic vector potential, the magnetic flux density distribution perpendicular to the thin plate conductor assumed to be air is calculated. The magnetic flux density distribution can be easily obtained with high precision if the thin-plate conductor portion assumed to be air in step S1 is matched with the node, but even if it is not matched, the magnetic flux density is approximated from the finite element close to the thin-plate conductor portion. The density distribution may be obtained.

<Step S4> The coordinate data of the nodes of the group of small regions obtained by dividing the thin-plate conductor region and its periphery into a number of small regions, the node number data constituting the finite element, and the physical data of the thin-plate conductor are created. FIG. 5 is a division view in which the vicinity including the thin plate conductor region is element-divided into small region groups. It is sufficient to form one layer above and below the thin conductor in the z direction of the air around the thin conductor. It is not necessary to create air regions in the x, y directions of the thin conductor.

<Step S5> From the magnetic flux density B obtained in step S3, a magnetic scalar potential Ω is obtained by the following equation. For example, the magnetic scalar potential Ω1 at node 1 in FIG. 5 is the z-direction component B10 of the magnetic flux density at node 10 shown in FIG.
From the following equation.

Ω1 = − (B10 × L) / μo (Equation 9)

Similarly, the magnetic scalar potential on the surface of the thin plate conductor is obtained up to Ωn, and the value of the magnetic scalar potential Ω on the upper surface of the thin plate conductor is determined. Further, as shown in FIG. 5, the value of the magnetic scalar potential Ω on the lower surface of the thin plate conductor is set to zero.

<Step S6> The current vector potential T and the magnetic scalar potential Ω of the nodes constituting each finite element are calculated by the T-Ω method. In addition, T-Ω
The method may use either node element approximation that defines the current vector potential T, which is an unknown variable, as a node, or edge element approximation that defines an edge. In the case where the edge element approximation is used, the current vector potential T is obtained from the side constituting each finite element.

In the low-voltage coil, since the magnetic flux exists only in the x direction, an eddy current is generated only in the yz direction. Therefore, even if only the x-direction component of the current vector potential T is set as an unknown variable, the analysis accuracy does not change and the unknown variables can be reduced, so that the calculation time can be reduced.

<Step S7> The eddy current density of each finite element can be obtained by substituting the current vector potential obtained at the nodes constituting each finite element into (Equation 4) and (Equation 6).

Here, in the analysis by the method A, the nonmagnetic conductor is regarded as air, and the interaction between the magnetic field and the eddy current is ignored. However, when the thickness of the nonmagnetic conductor is smaller than the skin thickness, the nonmagnetic The change in the magnetic field in the conductor is small. This fact means that the interaction between the magnetic field and the eddy current is small, and the reduction in calculation accuracy due to the neglect of the interaction is small. In the present invention, using this fact, modeling of the calculation target portion where the flatness of the finite element becomes a problem in the analysis stage by the A method is avoided.

As described above, according to this embodiment, even if the non-magnetic conductor has a thin sheet shape, it is possible to avoid the adverse effect of the flatness of the finite element, and the number of unknown variables is small. In addition, the electromagnetic field can be calculated with high accuracy in a short time. In addition, stable convergence of the calculation is guaranteed.

Embodiment 2 A method for analyzing a current distribution near a current outlet of a low-voltage coil for a transformer as shown in FIG. 6 will be described. It is assumed that the low-voltage coil is formed by winding a sheet-shaped coil wide in the z direction in the circumferential direction.

Since the currents at the current insertion port and the current extraction port have little effect on the magnetic flux linked to the coil, the method of step 1 in FIG. 2 is applied to a cylindrical coil excluding the current insertion port and the current extraction port. In the same manner as above, the input data of the method A is created.

Excluding the current inlet and the current outlet, the coil is completely cylindrical, and the applied current flowing through the coil is completely uniform. Therefore, in the low-voltage coil and the high-voltage coil, the current density in the steady state and the number of turns in the opposite directions and equal in magnitude are uniformly input to the low-voltage coil region and the high-voltage coil region. The analysis region is rotationally symmetric about the z-axis, and FIG. 7 shows a sectional view of the element used for the analysis in the Z-axis direction. Although the model of the present embodiment is not rotationally symmetric, the current distribution does not change even if the outer portion (return yoke) of the iron core 12 is replaced with a cylinder having the same cross-sectional area. Do.

In step 2, the magnetic vector potential A of each node constituting each finite element is calculated using the A method for the analysis region of FIG. In the method A, either a node element approximation that defines the magnetic vector potential A, which is an unknown variable, as a node, or a side element approximation that defines an edge may be used. When the edge element approximation is used, the magnetic vector potential A is obtained from the side constituting each finite element.

In step 3, as in the first embodiment, the magnetic flux density perpendicular to the low-voltage coil (radial component of the magnetic flux density linked to the low-voltage coil) is calculated from the magnetic vector potential A. At this time, the magnetic flux density perpendicular to the current outlet is also calculated.

In step 4, coordinate data of nodes of a small area group obtained by dividing the periphery of the coil conductor area near the current outlet into a large number of small areas, node number data constituting a finite element, and physical property data of a thin plate conductor are created. . FIG. 8 is a division diagram in which the vicinity including the coil conductor region is divided into small region groups. The length of the low-voltage coil in the y direction is 1 of the sheet coil.
It may be about the length of a winding.

In step 5, as in the first embodiment, a magnetic scalar potential Ω is determined from the magnetic flux density B determined in step S3. However, in steps 1 to 3, the calculation is performed with the model being rotationally symmetric, so that the magnetic flux density does not change in the y-direction in the division diagram shown in FIG.
Therefore, it is assumed that the magnetic scalar potential Ω does not change in the y direction. That is, the magnetic scalar potential has, for example, a relationship of Ω1 = Ω2 = ‥‥‥ = Ω11.

In step 6, as in the first embodiment, T
The current vector potential T and the magnetic scalar potential Ω of the nodes constituting each finite element are calculated by the −Ω method. Note that the T-Ω method may use either node element approximation that defines the current vector potential T, which is an unknown variable, as a node, or edge element approximation that defines an edge. In the case where the edge element approximation is used, the current vector potential T is obtained from the side constituting each finite element.

In FIG. 8, since the magnetic flux exists only in the x direction, an eddy current is generated only in the yz direction. Therefore, even if only the x-direction component of the current vector potential T is set as an unknown variable, the analysis accuracy does not change and the unknown variables can be reduced, so that the calculation time can be reduced.

In step 7, the eddy current density of each finite element is obtained as in the first embodiment.

In the low-voltage coil, the total applied current at the current outlet is known, but the distribution of the applied current density near the current outlet is unknown.

In step 8, under the element division diagram as shown in FIG. 9 and the boundary condition of φ, the following equation is subjected to a two-dimensional analysis using the finite element method to obtain an applied current density distribution.

Div (σ · gradφ) = 0 (Equation 10)

The applied current in the section A is calculated, and the ratio of the applied current to the steady current flowing through the low-voltage coil is defined as α. The applied current density flowing through the low-voltage coil is obtained by multiplying the applied current density obtained by each finite element in FIG. 9 by α.

In step 9, the eddy current obtained in step 7 and the applied current obtained in step 8 are vector-wise added to obtain a total current. FIG. 10 shows the total current density distribution obtained. The length of the arrow indicates the magnitude of the current density. It can be seen that the total current density is increased by the eddy current in the upper and lower portions of the low-voltage coil, and that the current is flowing toward the current outlet.

As described above, according to this embodiment, even if the nonmagnetic conductor has a thin sheet shape, it is possible to avoid the disadvantageous effect of the flatness of the finite element, and the number of unknown variables is small. In addition, the electromagnetic field can be calculated with high accuracy in a short time. In addition, stable convergence of the calculation is guaranteed.

[0057]

According to the present invention, in a method of calculating an eddy current generated in a non-magnetic conductor thinner than a skin thickness by using a computer for a calculation object having no current applied to the thin non-magnetic conductor, Calculating the electromagnetic field of the analysis target area by assuming that the physical properties of the magnetic conductor are air by a finite element method using a magnetic vector potential, and calculating the magnetic flux density distribution perpendicular to the nonmagnetic conductor portion obtained by the calculation. As an initial condition, a step of calculating an eddy current generated in the non-magnetic conductor by a finite element method using a current vector potential and a magnetic scalar potential with an electromagnetic field having only the non-magnetic conductor and its periphery as an analysis target region, Also, for a calculation target including a coil in which a current is applied to a thin non-magnetic conductor, a non-magnetic coil thinner than the skin thickness was calculated using a computer. In the method of calculating the total current generated in the body, a uniform applied current is input to the coil conductor, and the electromagnetic field in the analysis target area is calculated by the finite element method using the magnetic vector potential, assuming that the physical properties of the coil conductor are air. And a magnetic flux density distribution perpendicular to the coil conductor obtained by the above calculation as an initial condition, and using the current vector potential and the magnetic scalar potential to generate an electromagnetic field using only the coil conductor and its surroundings as an analysis target region. A step of calculating the eddy current generated in the coil conductor by the element method, a step of calculating the distribution of the applied current flowing through the coil conductor by the finite element method, and adding the applied current and the eddy current calculated in the step in a vector manner. And the step of calculating the total current generated in the coil conductor. In the electromagnetic field analysis to be handled, it is possible to avoid the adverse effects due to flattening of the finite elements can be calculated in a short time an electromagnetic field with high accuracy.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a first embodiment of the present invention.

FIG. 2 is an operation flowchart showing an operation sequence according to the first embodiment of the present invention.

FIG. 3 is an explanatory diagram of a target object used in the first embodiment of the present invention.

FIG. 4 is a schematic diagram in which an analysis target area used in the first embodiment of the present invention is divided into small areas.

FIG. 5 is an explanatory diagram showing boundary conditions of a magnetic scalar potential according to the first embodiment of the present invention.

FIG. 6 is an explanatory diagram of a target object used in Embodiment 2 of the present invention.

FIG. 7 is a schematic diagram in which an analysis target area used in Embodiment 2 of the present invention is divided into small areas.

FIG. 8 is an explanatory diagram showing boundary conditions of a magnetic scalar potential according to the second embodiment of the present invention.

FIG. 9 is an explanatory diagram showing a boundary condition of an electric scalar potential according to the second embodiment of the present invention.

FIG. 10 is a calculation result showing a total current density distribution obtained according to the second embodiment of the present invention.

[Explanation of symbols]

1 input unit, 2 CPU, 3 output unit, 4 program memory, 5 data memory, 6 external storage device, 8 thin conductor, 9 coil, 10, 11, 16 air, 12
Iron core, 13 low voltage coil, 14 high voltage coil, 15 coil conductor.

Claims (7)

[Claims] 1. A method for calculating an eddy current generated in a non-magnetic conductor thinner than a skin thickness using a computer,
Calculating the electromagnetic field of the analysis target region assuming that the physical properties of the nonmagnetic conductor are air by a finite element method using a magnetic vector potential; and a magnetic flux density distribution perpendicular to the nonmagnetic conductor portion obtained by the calculation. Calculating the eddy current generated in the non-magnetic conductor by the finite element method using the current vector potential and the magnetic scalar potential with respect to the electromagnetic field having only the non-magnetic conductor and its vicinity as the analysis target region as an initial condition. Electromagnetic field analysis method. 2. A method for calculating a total current generated in a non-magnetic coil conductor thinner than a skin thickness using a computer, wherein a uniform applied current is input to the coil conductor, and the physical properties of the coil conductor are assumed to be air. Calculating the electromagnetic field in the analysis target region by the finite element method using the magnetic vector potential, and the magnetic flux density distribution perpendicular to the coil conductor obtained by the calculation as an initial condition, and only the coil conductor and its vicinity are used. Calculating the eddy current generated in the coil conductor by the finite element method using the current vector potential and the magnetic scalar potential using the electromagnetic field with the analysis target area, and calculating the applied current distribution flowing through the coil conductor by the finite element method Step, and adding the applied current and the eddy current calculated in the step in a vector manner to calculate the total current generated in the coil conductor. Electromagnetic field analysis method comprising a step of calculating. 3. The electromagnetic field analysis method according to claim 1, wherein the analysis target area calculated by the finite element method using the magnetic vector potential is a three-dimensional area. 4. The electromagnetic field analysis method according to claim 1, wherein the analysis target region calculated by the finite element method using a magnetic vector potential is a rotationally symmetric region. 5. The electromagnetic field analysis method according to claim 1, wherein the analysis target area calculated by the finite element method using a magnetic vector potential is a two-dimensional area. 6. X, Y, Z of current vector potential
The electromagnetic field analysis method according to any one of claims 1 to 5, wherein, of the three unknown components in the direction, only a component perpendicular to the surface of the coil conductor or the thin plate conductor is set as the unknown variable. 7. An electromagnetic field analysis apparatus comprising computer means for executing the electromagnetic field analysis method according to claim 1.