JP6384208B2 - Electromagnetic field analysis apparatus, electromagnetic field analysis method, and program - Google Patents

Description

  The present invention relates to an electromagnetic field analysis device, an electromagnetic field analysis method, and a program, and is particularly suitable for use in deriving magnetic flux density and eddy current in a magnetic material.

Conventionally, an electromagnetic field in an electric device using a magnetic material such as a rotating electric machine or a transformer is calculated by numerical analysis, and the result is used for designing or improving the electric device.
When performing such numerical analysis, there is a method in which the magnetic characteristics of the magnetic material are used as initial magnetization characteristics. However, the magnetic characteristics of actual magnetic materials have magnetic hysteresis characteristics. For this reason, in order to analyze the electromagnetic field generated under complicated excitation conditions, it is necessary to perform numerical analysis in consideration of the magnetic hysteresis characteristics of the magnetic material. In particular, when the initial magnetization characteristic is used as the magnetic characteristic of the magnetic material, the accuracy of the calculated value of the current flowing through the coil of the electric device is reduced, and the copper loss of the electric device is estimated and the magnetic field in the iron core (core) is reduced. In some cases, estimation cannot be performed with high accuracy.

  Therefore, Non-Patent Documents 1 and 2 disclose a technique using a play hysteresis model as a technique for analyzing an electromagnetic field in consideration of the magnetic hysteresis of a magnetic material. In the play hysteresis model, a shape function is identified so as to match the measured data of the magnetic hysteresis characteristics, and the relationship between the magnetic flux density and the magnetic field is formulated using this shape function.

A. Akane, 1 other, “Examination of hysteresis analysis by finite element method using isotropic vector play model”, IEEJ stationary and rotating machine joint study material, SA-09-67, RM-09-73 , P. 71-p. 76, 2009 Junji Kitao, 6 others, “Study on application of play model to hysteresis magnetic field analysis”, Electrotechnical Institute of Static and Rotating Machine Joint Research Materials, SA-12-16, RM-12-16, p. 89-p. 94, 2012 Takayoshi Nakata, Norio Takahashi, "Finite Element Method of Electrical Engineering", 2nd edition, Morikita Publishing Co., Ltd., April 1986

However, in the methods described in Non-Patent Documents 1 and 2, measured data of DC magnetic hysteresis characteristics is used as measured data of magnetic hysteresis characteristics. The hysteresis characteristics of a magnetic material to which an AC magnetic field is applied are affected by three characteristics: a DC magnetic hysteresis characteristic, a hysteresis characteristic due to classical eddy currents, and a hysteresis characteristic due to abnormal eddy currents. Among these, the hysteresis characteristics due to classical eddy currents are considered in the process of numerically analyzing eddy currents by electromagnetic field analysis. Therefore, the methods described in Non-Patent Documents 1 and 2 are based on DC magnetic hysteresis characteristics and classical eddy currents. Hysteresis characteristics are considered, but hysteresis characteristics due to abnormal eddy currents are not considered. For this reason, it is not easy to derive the magnetic hysteresis characteristics with high accuracy. Therefore, it is not easy to derive the magnetic flux density and eddy current calculated by the analysis of the electromagnetic field with high accuracy, and this tendency becomes remarkable particularly when an AC magnetic field of several hundred Hz is applied.
Therefore, an object of the present invention is to perform an analysis of an electromagnetic field when an alternating magnetic field is applied with high accuracy.

The electromagnetic field analysis apparatus of the present invention includes a corrected DC magnetic hysteresis characteristic deriving means for deriving a corrected DC magnetic hysteresis characteristic obtained by correcting a DC magnetic hysteresis characteristic of a magnetic material, and a corrected DC magnetic hysteresis characteristic derived means. Model identification means for identifying a model in which the relationship between magnetic flux density and magnetic field in the magnetic material is formulated from data of magnetic hysteresis characteristics, excitation conditions that are conditions for exciting the magnetic material, and the model Using the model identified by the identification means, the magnetic flux density vector and eddy current vector generated in the magnetic material when the magnetic material is excited are calculated for each of a plurality of minute regions based on Maxwell's equations. Electromagnetic field analysis means for calculating, and the corrected DC magnetic hysteresis characteristic deriving means includes: Performing calculations based on formula (A), to derive the magnitude B of the magnetic flux density vector [i] size H _ha of the magnetic field vector after correction corresponding to [T] [i] [A / m], derived The corrected DC magnetic hysteresis characteristic is derived using the corrected magnetic field vector magnitude H _ha [i] corresponding to the magnetic flux density vector magnitude B [i].

The electromagnetic field analysis method of the present invention includes a corrected DC magnetic hysteresis characteristic deriving step in which a corrected DC magnetic hysteresis characteristic deriving means derives a corrected DC magnetic hysteresis characteristic obtained by correcting a DC magnetic hysteresis characteristic of a magnetic material; A model identification step for identifying a model in which the relationship between magnetic flux density and magnetic field in the magnetic material is formulated from the corrected DC magnetic hysteresis characteristic data derived by the hysteresis characteristic deriving step; A magnetic flux density vector generated in the magnetic material when the magnetic material is excited using an excitation condition that is a condition for exciting the magnetic material and a model identified by the model identification step; The eddy current vector is calculated for each small region based on Maxwell's equations. An electromagnetic field analysis step of calculating by the electromagnetic field analysis means, and the correction DC magnetic hysteresis characteristic derivation step performs a calculation based on the following equation (A) to calculate the magnitude B [i of the magnetic flux density vector: ] The corrected magnetic field vector magnitude H _ha [i] [A / m] corresponding to [T] is derived, and the corrected magnetic field vector magnitude corresponding to the derived magnetic flux density vector magnitude B [i] is derived. The corrected DC magnetic hysteresis characteristic is derived using the magnitude H _ha [i].

In the formula (A), i is a variable for specifying the time step, i−1 is a variable for specifying the time step immediately before the time step specified by the variable i, and H _h [i] is the magnetic field vector magnitude [A / m] corresponding to the magnetic flux density vector magnitude B [i] in the DC magnetic hysteresis characteristic data, and t [i] corresponds to the variable i. Κ is an abnormal eddy current loss coefficient [−], which is a coefficient multiplied by the classical eddy current loss when expressing the total eddy current loss of the magnetic material, and ρ is the magnetic step The specific resistivity [Ω · m] of the material, and h is the thickness [m] of the magnetic material.

  The program of the present invention causes a computer to function as each means of the electromagnetic field analyzer.

  According to the present invention, a model in which the relationship between the magnetic flux density and the magnetic field is formulated is identified using the corrected DC magnetic hysteresis characteristic in which the DC hysteresis data is corrected to DC hysteresis data reflecting the influence of abnormal eddy currents. The electromagnetic field analysis is performed using the identified model. Therefore, the magnetic flux density vector and the eddy current vector can be calculated in consideration of the abnormal eddy current. Thereby, the analysis of the electromagnetic field when an alternating magnetic field is applied can be performed with high accuracy.

It is a figure which shows an example of a functional structure of an electromagnetic field analyzer. It is a figure which shows an example of the shape of a ring-shaped sample. It is a figure which shows the 1st example of a magnetic hysteresis characteristic. It is a figure which shows the 2nd example of a magnetic hysteresis characteristic. It is a flowchart explaining an example of a process of an electromagnetic field analyzer. It is a figure which shows an example of the model of an IPM motor. It is a figure which shows the 1st example of the magnetic hysteresis characteristic in an Example. It is a figure which shows the 2nd example of the magnetic hysteresis characteristic in an Example.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a diagram illustrating an example of a functional configuration of the electromagnetic field analysis apparatus 100. In the present embodiment, a case where an electromagnetic field in an electric device including an iron core (core) in which electromagnetic steel plates are laminated is analyzed will be described as an example. Hereinafter, when referred to as an electromagnetic steel sheet, it refers to the electromagnetic steel sheet itself that is the object of the electromagnetic field analysis or the same type of electromagnetic steel sheet as the electromagnetic steel sheet that is the object of the electromagnetic field analysis. However, the analysis target of the electromagnetic field is not limited to the electromagnetic steel sheet as long as it is a magnetic material (for example, a ferromagnetic material).
The hardware of the electromagnetic field analysis device 100 can be realized by using, for example, an information processing device including a CPU, ROM, RAM, HDD, and various interfaces, and dedicated hardware.

(DC hysteresis data input unit 101)
The DC hysteresis data input unit 101 inputs data of DC magnetic hysteresis characteristics of an electrical steel sheet that is an object of electromagnetic field analysis. The DC magnetic hysteresis characteristic refers to a magnetic hysteresis characteristic based on a magnetic flux density and a magnetic field that change slowly with time. In the present embodiment, such a magnetic hysteresis characteristic, and a magnetic hysteresis characteristic of a portion corresponding to the major loop is a DC magnetic hysteresis characteristic.

  When the DC magnetic hysteresis characteristic data can be directly measured, the DC hysteresis data input unit 101 inputs the measurement data of the DC magnetic hysteresis characteristic. For example, as described in Non-Patent Document 2, DC magnetic hysteresis characteristic data may be measured from hysteresis characteristic measurement data at a plurality of frequencies for the same maximum magnetic flux density. In this case, the DC hysteresis data input unit 101 inputs estimation data of DC magnetic hysteresis characteristics.

The DC hysteresis data input unit 101 inputs the above-described DC magnetic hysteresis characteristic data for each of a plurality of peak values of magnetic flux density. The peak value of the magnetic flux density can be appropriately determined according to, for example, the excitation conditions when analyzing the electromagnetic field.
The input form of the data of the DC magnetic hysteresis characteristic is not particularly limited. For example, in a form based on an operation by an operator on the user interface of the electromagnetic field analysis apparatus 100 or a form in which data transmitted from an external apparatus is input, data is stored from a portable storage medium electrically connected to the electromagnetic field analysis apparatus 100. It may be in the form of reading. This also applies to input forms in the magnetic flux density condition input unit 102, the abnormal eddy current loss coefficient deriving unit 103, the magnetic material condition input unit 104, and the electromagnetic field analysis condition input unit 107 described below.
The DC hysteresis data input unit 101 can be realized by using, for example, a CPU, a ROM, a RAM, an HDD, and an interface corresponding to a data input form.

(Magnetic flux density condition input unit 102)
The magnetic flux density condition input unit 102 inputs a magnetic flux density condition. The magnetic flux density condition is information including a peak value, a frequency, and a waveform of the magnetic flux density (an outline of a change in the magnitude of the magnetic flux density vector over time). The frequency of the magnetic flux density can be determined, for example, according to the excitation conditions when analyzing the electromagnetic field. Note that the peak value of the magnetic flux density can be obtained from the DC hysteresis characteristic data input by the DC hysteresis data input unit 101, and therefore it is not necessarily input by the magnetic flux density condition input unit 102.
The magnetic flux density condition input unit 102 can be realized by using, for example, a CPU, a ROM, a RAM, an HDD, and an interface corresponding to a data input form.

(Abnormal eddy current loss coefficient deriving unit 103)
The abnormal eddy current loss coefficient deriving unit 103 derives the abnormal eddy current loss coefficient κ [−]. The abnormal eddy current loss coefficient κ is expressed by the following equation (1), for example.

In the formula (1), D is the specific gravity [kg / m ³ ] of the magnetic steel sheet, h is the (one) plate thickness [m] of the magnetic steel sheet, and σ is the conductivity [S / m] of the magnetic steel sheet. , K _e is an eddy current loss Steinmetz coefficient [W / kg / T ² · sec ² ], which is expressed by the following equation (2).
W _e = K _e · f ² · | B | ² (2)
(2) In the equation, W _e is the eddy current loss [W / kg], f is the frequency [Hz], | B | is the magnitude of the magnetic flux density vector B [T].

Eddy current loss Steinmetz coefficient K _e, for example, can be obtained as follows.
First, B-W data about a magnetic material is derived at each of a plurality of frequencies by using, for example, measured values of magnetic measurement by an Epstein measurement method or a single plate test measurement method defined by a standard. The BW data is data of a curve indicating the relationship between the magnitude of the magnetic flux density vector B and the magnitude of the iron loss W.
Next, the magnitude of the iron loss W corresponding to the magnetic flux density vector B having the same magnitude is extracted from the B-W data, and the magnitude of the extracted iron loss W is set to the frequency f to which the B-W data belongs. The value of the iron loss per unit frequency W / f, which is a value divided by ## EQU3 ## is derived.

Thereby, W / f-f data indicating the relationship between the magnitude W / f of the iron loss per unit frequency and the frequency f is obtained for each magnitude of the magnetic flux density vector B.
Next, from the W / f-f data, “iron per unit frequency” corresponding to the lowest frequency f (for example, 50 [Hz]) and a higher fundamental frequency f (for example, 100 [Hz]). The intercept of the straight line passing through the value of the loss magnitude W / f (the iron loss magnitude W / f per unit frequency when the value of the frequency f is 0 (zero)) per unit frequency at DC Derived as the iron loss magnitude W _h0 .

Then, per unit frequency at a direct current of iron loss in size W _h0, by multiplying the lowest frequency f in W / f-f data (e.g. 50 [Hz]), the plate-like sample at the frequency f The hysteresis loss W _hf is derived.
Next, the lowest frequency f (for example, 50 [Hz]) in the W / f-f data is substituted as the frequency f into the following equation (3), and the hysteresis loss W _h is derived as described above. The hysteresis loss W _hf is substituted, and the magnitude of the magnetic flux density vector B to which the “W / f−f data” used to derive the hysteresis loss W _hf belongs is substituted as the magnitude B of the magnetic flux density vector. As a result, the hysteresis loss Steinmetz coefficient K _h when the magnitude of a certain magnetic flux density vector B is obtained.
W _h = K _h · f · B ^1.6 (3)

Next, the hysteresis loss W _h is derived for each piece of W / f−f data derived as described above. Thereby, the hysteresis loss Steinmetz coefficient K _h when the magnitude of the magnetic flux density vector B has various values is obtained. Note that “1.6” in the expression (3) can be replaced with β which is a value in the range of 1 to 2.

Then, the iron loss magnitude of W hysteresis loss Steinmetz coefficient K _h corresponds to the size of belonging magnetic flux density vector B, and extracted from the B-W data described above. As described above, since the BW data exists for each frequency f, the magnitude of the iron loss W is extracted for a plurality of frequencies f.
Next, a corresponding hysteresis loss Steinmetz coefficient K _h, of the magnetic flux density vector B in which the hysteresis loss Steinmetz coefficient K _h belongs and size, and the size of the iron loss W were extracted as described above, of the iron loss W The frequency f corresponding to the magnitude is substituted into the above-described equations (2) and (3) and the following equation (4).
W = W _e + W _h (4)
Thus, the size of a magnetic flux density vector B, the eddy current loss Steinmetz coefficient K _e when a certain frequency f is obtained.

Deriving the eddy current loss Steinmetz coefficient K _e as described above is performed for each of the hysteresis loss Steinmetz coefficient K _h. Thereby, the eddy current loss Steinmetz coefficient K _e when the magnitude of the magnetic flux density vector B and the frequency f are various values is obtained.
As described above, the DC hysteresis data input unit 101 inputs data of DC magnetic hysteresis characteristics for each of a plurality of peak values of magnetic flux density. Further, the magnetic flux density condition input unit 102 inputs the frequency of the magnetic flux density vector.
Abnormal eddy current loss coefficient deriving unit 103 inputs the eddy current loss Steinmetz coefficient K _e corresponding to these peak value and frequency.
In this manner, by entering the eddy current loss Steinmetz coefficient K _e corresponding to the peak value and frequency, it is possible to derive the abnormal eddy current loss coefficient κ preferred. However, in a simplified manner, it may be input eddy current loss Steinmetz coefficient K _e does not depend on the peak value and frequency.

The abnormal eddy current loss coefficient deriving unit 103 inputs the specific gravity D of the electromagnetic steel sheet, the thickness h of the electromagnetic steel sheet, and the electrical conductivity σ of the electromagnetic steel sheet.
Then, the abnormal eddy current loss coefficient deriving unit 103 calculates the equation (1) to derive the abnormal eddy current loss coefficient κ.
The abnormal eddy current loss coefficient deriving unit 103 can be realized by using, for example, a CPU, a ROM, a RAM, an HDD, and an interface corresponding to a data input form. Here, the abnormal eddy current loss coefficient κ is derived in the electromagnetic field analyzer 100. However, an abnormal eddy current loss coefficient κ derived separately by an external device or the like may be input.

(Magnetic material condition input unit 104)
The magnetic material condition input unit 104 inputs magnetic material conditions. The magnetic material condition is information including the thickness h [m] of the magnetic steel sheet and the specific resistivity ρ [Ω · m] of the magnetic steel sheet.
The magnetic material condition input unit 104 can be realized by using, for example, a CPU, a ROM, a RAM, an HDD, and an interface corresponding to a data input form. When the abnormal eddy current loss coefficient deriving unit 103 inputs the thickness h of the electromagnetic steel sheet and the electrical conductivity σ of the electromagnetic steel sheet, these can be used as magnetic material conditions. That is, the magnetic material condition input unit 104 can be omitted.

(Correction DC magnetic hysteresis characteristic deriving unit 105)
The corrected DC magnetic hysteresis characteristic deriving unit 105 includes the magnetic flux density condition (frequency of the magnetic flux density vector) input by the magnetic flux density condition input unit 102 and the abnormal eddy current loss coefficient κ derived by the abnormal eddy current loss coefficient deriving unit 103. And DC magnetic hysteresis characteristic data input by the DC hysteresis data input unit 101 based on the magnetic material conditions (the thickness h of the magnetic steel sheet and the specific resistivity ρ) input by the magnetic material condition input unit 104 Data of corrected DC magnetic hysteresis characteristics, which is data obtained by correcting the magnitude [A / m] of the magnetic field vector, is derived. The corrected DC magnetic hysteresis characteristic data is DC hysteresis data reflecting the influence of the abnormal eddy current.
In the present embodiment, it is assumed that the magnitude of the magnetic flux density vector changes in a sine wave under the excitation condition when analyzing the electromagnetic field. In the present embodiment, the corrected DC magnetic hysteresis characteristic deriving unit 105 calculates corrected DC magnetic hysteresis characteristic data by calculating the following equation (5).

In equation (5), i is a variable for specifying a time step, and is a variable that increases by 1 up to a positive integer I with 0 as an initial value (i = 0, 1, 2,... • Takes the value of I). t [i] indicates a time step corresponding to the variable i, and t [i−1] indicates a time step corresponding to the variable i−1 immediately before the variable i. I is a value corresponding to one cycle determined by the magnetic flux density condition (frequency of the magnetic flux density vector) input by the magnetic flux density condition input unit 102.
B [i] is the magnitude of the magnetic flux density vector that is time-varying with the sine wave of the peak value and the frequency input by the magnetic flux density condition input unit 102, and the magnitude of the magnetic flux density vector at time step t [i] It is. B [i-1] is the magnitude of the magnetic flux density vector that changes with time according to the peak value and the frequency sine wave input by the magnetic flux density condition input unit 102, and the magnetic flux density at the time step t [i-1]. The magnitude of the vector. H _h [i] is the magnitude of the magnetic field vector corresponding to the magnitude B [i] of the magnetic flux density vector in the DC magnetic hysteresis characteristics. κ is an abnormal eddy current loss coefficient at the frequency indicated by the peak value and the excitation condition.

By performing the calculation of equation (5) at each time step t [i] in one cycle of the magnetic flux density vector, the corrected magnetic field vector magnitude H _ha [i] for the same magnetic flux density peak value. And a plurality of sets of magnetic flux density vector magnitudes B [i]. The corrected DC magnetic hysteresis characteristic deriving unit 105 uses a plurality of sets of data strings of the corrected magnetic field vector magnitude H _ha [i] and the magnetic flux density vector magnitude B [i] as corrected DC at the peak value. Derived as data of magnetic hysteresis characteristics.

  As described above, the DC hysteresis data input unit 101 inputs data of DC magnetic hysteresis characteristics for each of a plurality of peak values of magnetic flux density. The corrected DC magnetic hysteresis characteristic deriving unit 105 derives the corrected DC magnetic hysteresis characteristic data as described above for each of the plurality of peak values.

Here, how the equation (5) is derived will be described.
Table by the sum of the iron loss W is a hysteresis loss W _h, represented by the sum of the eddy current loss W _e, eddy current loss W _e is the abnormal eddy current loss W _ea, the classical eddy current loss W _e0 Therefore, the following equation (6) is obtained.
W = W _h + W _e = W _h + W _ea + W _e0 (6)
When the magnetic flux density vector B is uniform in the thickness direction of the electrical steel sheet, the classical eddy current loss _We0 is expressed by the following (7).

The actually measured eddy current loss W _e (total eddy current loss) is expressed by the following equation (8) using the abnormal eddy current loss coefficient κ and the classical eddy current loss W _e0 .
W _e = κ · W _e0 (8)
Therefore, from the equations (6) to (8), the abnormal eddy current loss W _ea is expressed by the following equation (9).

Since the magnetic energy P _m is expressed by the following equation (10), the magnitude H of the magnetic field vector is expressed by the following equation (11).

Substituting the hysteresis loss W _h and the abnormal eddy current loss W _ea into the magnetic energy P _m in the equation (11), a direct current is obtained with respect to a given magnetic flux density vector B as shown in the following equation (12). the size H _ha of the magnetic field vector of the contribution of hysteresis loss and abnormal eddy current loss is obtained.

The first term on the right side of the equation (12) is equal to the magnitude H _h of the magnetic field vector of the DC magnetic hysteresis characteristic. Also, formula (9) is substituted into the second term on the right side of formula (12). As a result, the following expression (13) is obtained.

Then, the time t in the equation (13) is represented by the discrete time steps t [i] (t [0], t [1],..., T [I]) as described above (5). The formula is obtained.
The corrected DC magnetic hysteresis characteristic deriving unit 105 can be realized by using, for example, a CPU, ROM, RAM, and HDD.

(Model identification unit 106)
The model identification unit 106 is a model in which the relationship between the magnetic flux density and the magnetic field is formulated based on the corrected DC magnetic hysteresis characteristic data for each peak value of the magnetic flux density calculated by the corrected DC magnetic hysteresis characteristic deriving unit 105. Is identified.

In the present embodiment, a play hysteresis model described in Non-Patent Documents 1 and 2 is used as such a model. More specifically, an isotropic vector play hysteresis model described in Non-Patent Document 1 is used. Since the technique for performing electromagnetic field analysis using the isotropic vector play hysteresis model is described in Non-Patent Document 1 and the like, only the outline thereof will be described here, and detailed description thereof will be omitted.
In the isotropic vector play hysteresis model, the magnetic field vector H [A / m] is expressed by, for example, the following equations (14) and (15).

In the expressions (14) and (15), → represents a vector (this is the same in other expressions).
In the equation (15), p _ζ (| B |) is the value [T] of prehysterone with respect to the magnetic flux density vector B [T]. p _ζ ⁰ is the value of prehysterone p _{ζ at} the previous time. max (| B−p _ζ ⁰ | / ζ, 1) indicates that the larger value of | B−p _ζ ⁰ | / ζ and 1 is adopted. ζ is a parameter [T] that gives the width of prehysterone. p _ζ / | p _ζ | is a unit vector of prehysterone p _ζ . As described in Non-Patent Document 1, if the direction is set to one direction in the equations (14) and (15), a scalar play hysteresis model is obtained. Therefore, the equations (14) and (15) Can also be applied to the scalar play hysteresis model.

When the magnetic flux density vector B ^{0 at} the previous time changes to the magnetic flux density vector B at the current time, the radius ζ with the point at the tip of the prehysteron value p _ζ ⁰ at the previous time as the center If there is a time density vector B at the current time in the circle, the circle does not move. On the other hand, when the magnetic flux density vector B ⁰ at the previous time changes to the magnetic flux density vector B at the current time, the time density vector B at the current time becomes the value p _{ζ of} prehysterone at the previous time. ^When located outside the circle of radius ζ centered on the point at the tip of ⁰ , the center of the circle starts from the point at the tip of the prehysteron value p _ζ ⁰ at the previous time, and the magnetic flux density at the current time Move in the direction of the point at the tip of vector B.
In the isotropic vector play hysteresis model shown in Non-Patent Document 1, the magnetic field vector H is expressed as in equation (14) using prehysterone p _ζ having such properties.
In the equation (14), f (ζ, p _ζ (B)) is a shape function [A / (m · T)]. This shape function is expressed by a function of prehysterone width ζ and prehysterone p _ζ (B). Identifying the play hysteresis model is synonymous with identifying this shape function.

The model identification unit 106, for example, sets the corrected DC magnetic hysteresis characteristic data for each peak value of the magnetic flux density (a set of the corrected magnetic field vector magnitude H _ha [i] and the magnetic flux density vector magnitude B [i]. ) To extract a plurality of data determined according to the magnetic hysteresis characteristics (minor loop, etc.) to be created. Then, the model identification unit 106 uses the extracted data to perform calculations based on the equations (14) and (15), thereby deriving the distribution of prehysterone p _ζ (B) and deriving the derived play hysteresis. The shape function f (ζ, p _ζ (B)) is identified by the distribution of Ron p _ζ (B).

By identifying the shape function f (ζ, p _ζ (B)) as described above, the magnetic hysteresis characteristic is more complicated than the magnetic hysteresis characteristic obtained from the corrected DC magnetic hysteresis characteristic data. It is possible to derive the magnetic hysteresis characteristics necessary for the analysis. The magnetic hysteresis characteristics include, for example, a DC magnetic hysteresis characteristic including a minor loop, an AC magnetic hysteresis characteristic including a major loop on which harmonics are superimposed, an AC magnetic hysteresis characteristic including a minor loop, a vector magnetic hysteresis characteristic, and the like. included.
The model identification unit 106 can be realized by using, for example, a CPU, ROM, RAM, and HDD.

(Electromagnetic field analysis condition input unit 107)
The electromagnetic field analysis condition input unit 107 inputs an electromagnetic field analysis condition. The electromagnetic field analysis condition is information necessary for calculation by an electromagnetic field analysis unit 108 described later. In this embodiment, an electromagnetic field is analyzed using a finite element method. Therefore, the electromagnetic field analysis conditions include, for example, a minute region (mesh) division condition (coordinate information of the division position), a shape of the iron core (core), a condition when exciting the iron core (core) (excitation condition), and various It is an initial value.
The electromagnetic field analysis condition input unit 107 can be realized by using, for example, a CPU, a ROM, a RAM, an HDD, and an interface corresponding to a data input form.

(Electromagnetic field analysis unit 108)
The electromagnetic field analysis unit 108 calculates the magnetic flux density vector B and the eddy current vector J _e in each minute region (mesh) based on the electromagnetic field analysis conditions input by the electromagnetic field analysis condition input unit 107. In the present embodiment, the magnetic flux density vector B and the eddy current vector J _e in each minute region are calculated using the finite element method based on Maxwell's equations. A technique for analyzing an electromagnetic field by the finite element method is a general technique as described in detail in Non-Patent Document 3 and the like. Incidentally, if it is possible to calculate the magnetic flux density vector B and the eddy current vector J _e in each minute area, it may be used a method other than the finite element method (differential method).

The basic equations for calculating the magnetic flux density vector B and the eddy current vector J _e are generally given by the following equations (16) to (19).

In the equations (16) to (19), μ is a magnetic permeability [H / m], A is a vector potential [T · m], σ is a conductivity [S / m], J ₀ is the excitation current density [A / m ² ], and φ is the scalar potential [V].
After solving the equations (16) and (17) simultaneously to obtain the vector potential A and the scalar potential φ, the magnetic flux density vector B and the eddy current vector J _e are obtained from the equations (18) and (19). Calculated.
There is a Newton-Raphson method as a solution using the vector potential A and the scalar potential φ as unknown variables when analyzing the electromagnetic field in a magnetic material (magnetic steel sheet in this embodiment) having a non-linear permeability μ. . Also in this embodiment, the Newton-Raphson method is used. As described in Non-Patent Document 1, when the Newton-Raphson method is used, a magnetic field vector H and a differential magnetic resistivity ∂H / ∂B are required during the iteration.

The magnetic field vector H is calculated by the equations (14) and (15).
Further, when the differential permeability ∂H / ∂B is expressed as in the following equation (20), from the equations (14) and (15), the differential permeability ∂H / ∂B is expressed by the following equation (21). And (22).

  The electromagnetic field analysis unit 108 can be realized by using, for example, a CPU, ROM, RAM, and HDD.

(Intra-region hysteresis loss calculation unit 109)
The minute area hysteresis loss calculation unit 109 calculates the magnetic field in the minute region from the magnetic flux density vector B analyzed by the electromagnetic field analysis unit 108 for a certain minute region and the waveform in one cycle of the magnetic field vector H corresponding to the magnetic flux density vector B. The hysteresis characteristics are derived. Then, the hysteresis loss calculating unit 109 in the minute region calculates the following equation (23), and calculates the area of the derived magnetic hysteresis characteristic as the hysteresis loss w _ha in the minute region.

  The in-microregion hysteresis loss calculation unit 109 performs the above calculation for all the microregions.

In the present embodiment, the shape function f (ζ, p _ζ (B)) is identified by using the corrected DC magnetic hysteresis characteristic data. Therefore, the corrected DC magnetic hysteresis characteristic is also reflected in the magnetic flux density vector B calculated by the electromagnetic field analysis unit 108. As described above, the corrected DC magnetic hysteresis characteristic is a DC magnetic hysteresis characteristic that reflects the influence of an abnormal eddy current. Therefore, the hysteresis loss w _ha in each minute region calculated by the minute region hysteresis loss calculation unit 109 is a hysteresis loss reflecting the influence of the abnormal eddy current.
The in-region hysteresis loss calculation unit 109 can be realized by using, for example, a CPU, ROM, RAM, and HDD.

(Small region eddy current loss calculation unit 110)
Based on the eddy current vector J _e analyzed by the electromagnetic field analysis unit 108 for a certain micro area, the volume of the micro area, and the electrical conductivity σ of the electrical steel sheet, The classical eddy current loss _we0 in the minute region is derived by calculating the equation (24).

In the equation (24), T is the period of the eddy current vector J _e .
The small area eddy current loss calculation unit 110 performs the above calculation for all the small areas.
In the present embodiment, the shape function f (ζ, p _ζ (B)) is identified by using the corrected DC magnetic hysteresis characteristic data. Therefore, the corrected DC magnetic hysteresis characteristic is reflected in the numerical calculation of the eddy current vector J _e calculated by the electromagnetic field analysis unit 108. The calculation of the eddy current vector J _e is the magnetic permeability of the magnetic hysteresis characteristic main influence is calculated by the minute region eddy current loss calculation unit 110, a classical eddy current loss w _e0 in each micro area This is a classic eddy current loss that reflects the effect of changes in permeability due to abnormal eddy currents.
The minute area eddy current loss calculation unit 110 can be realized by using, for example, a CPU, a ROM, a RAM, and an HDD.

(Total Iron Loss Department 111)
The iron loss summation unit 111 performs the calculation shown in the following equation (25) to derive the sum of the hysteresis loss w _ha and the classic eddy current loss _{we0 in} the same minute region as the iron loss w of the minute region. Then, the following equation (26) is calculated to derive the total iron loss w of all the minute regions as the iron loss W of the entire iron core (core) that is the object of electromagnetic field analysis.
w = w _ha + w _e0 (25)
W = Σw (26)
The iron loss summation unit 111 can be realized by using, for example, a CPU, ROM, RAM, and HDD.

(Iron loss output unit 112)
The iron loss output unit 112 outputs the iron loss W of the entire iron core (core) calculated by the iron loss summation unit 111. The output form of the iron loss W of the entire iron core (core) is not particularly limited. For example, it may be stored in a storage medium inside the electromagnetic field analysis device 100 or a portable storage medium connected to the electromagnetic field analysis device 100, displayed on a computer display, or transmitted to an external device.
The iron loss output unit 112 can be realized by using, for example, a CPU, a ROM, a RAM, an HDD, and an interface corresponding to a data output form.

(Calculation example)
FIG. 2 is a diagram showing an example of the shape of a ring-shaped sample to be analyzed in this calculation example.
As shown in FIG. 2, the ring-shaped sample 200 is configured by stacking a plurality of ring-shaped non-oriented electrical steel sheets. A plurality of ring-shaped non-oriented electrical steel sheets are formed by punching and stacking non-oriented electrical steel sheets having the same type and thickness so as to have the same shape. As shown in FIG. 2, the ring-shaped sample 200 has an outer diameter of 45 [mm], an inner diameter of 33 [mm], and a height of 7 [mm].

In the case when electric current is run in accordance with the excitation condition the ring-shaped sample 200, the magnetic flux density vector B in the ring sample 200, the magnetic field vector H, and the eddy current vector J _e, using the correction dc magnetic hysteresis properties, dc magnetic hysteresis properties The analysis was performed in each of the cases of using. As excitation conditions, the frequency is 50 [Hz], the peak value of the magnetic flux density is 1 [T], the waveform of the magnetic flux density is a sine wave, the frequency is 400 [Hz], and the peak value of the magnetic flux density is 1 [T]. T] and two conditions were adopted in which the magnetic flux density waveform was a sine wave. The other methods and conditions used in each analysis are the same in each analysis.
Further, the magnetic flux density vector B, the magnetic field vector H, and the eddy current vector J _e were measured when the ring-shaped sample 200 was excited according to these excitation conditions.

  3 and 4 are diagrams showing magnetic hysteresis characteristics based on the magnetic flux density vector B and the magnetic field vector H obtained as described above. Here, FIGS. 3A and 4A show a case where the corrected DC magnetic hysteresis characteristic is used as in the electromagnetic field analysis apparatus 100 of the present embodiment, and FIGS. 3B and 4B. ) Shows the case of using the DC magnetic hysteresis characteristic as in Non-Patent Documents 1 and 2. 3 shows a case where the frequency is 50 [Hz], the peak value of the magnetic flux density is 1 [T], and the waveform of the magnetic flux density vector B is a sine wave. In FIG. 4, the frequency is 400 [Hz], The case where the peak value of the magnetic flux density is 1 [T] and the waveform of the magnetic flux density is a sine wave is shown. In FIGS. 3 and 4, the solid line indicates the calculated value, and the broken line indicates the actual measurement value. 3 and 4, the magnitude of the magnetic flux density vector B and the magnitude of the magnetic field vector H are both shown as relative values.

Table 1 shows the results of calculation of the iron loss obtained from the results shown in FIG. 3 and FIG.
The eddy current loss shown in FIGS. 3A and 4A in Table 1 is a classic eddy current loss as described in the section of the eddy current loss calculation unit 110 in the micro region. On the other hand, the eddy current loss shown in FIGS. 3B and 4B is the sum of classical eddy current loss and abnormal eddy current loss. The abnormal eddy current loss is a value obtained by multiplying the classical eddy current loss _weo obtained by the calculation of the equation (24) by the abnormal eddy current loss coefficient κ shown in the equation (1).

  As can be seen by comparing FIG. 3A and FIG. 3B, and FIG. 4A and FIG. 4B, it is better to use the corrected DC magnetic hysteresis characteristic at any frequency. A calculated value (magnetic hysteresis characteristic) closer to the actually measured value can be obtained than using the characteristic. As can be seen from a comparison between FIG. 3 and FIG. 4, when the DC magnetic hysteresis characteristic is used, the calculated value greatly deviates from the actually measured value when the frequency is increased. On the other hand, when the corrected DC magnetic hysteresis characteristic is used, the calculated value is close to the actually measured value even if the frequency is increased. Also in Table 1, when the frequency is high, if the DC magnetic hysteresis characteristic is used, the error of the calculated value with respect to the measured value of the iron loss W becomes large. On the other hand, if the corrected DC magnetic hysteresis characteristic is used, The error of the calculated value with respect to the actually measured value of the loss W remains small (see the columns in FIGS. 4A and 4B in Table 1). Therefore, it is preferable to use the corrected DC magnetic hysteresis characteristic particularly when the frequency is high.

(Operation flowchart)
Next, an example of processing of the electromagnetic field analysis apparatus 100 will be described with reference to the flowchart of FIG. The flowchart in FIG. 5 is realized, for example, when the CPU executes a program stored in the ROM.
First, in step S501, the DC hysteresis data input unit 101 inputs data of DC magnetic hysteresis characteristics of an electromagnetic steel sheet to be analyzed for an electromagnetic field.
Next, in step S502, the magnetic flux density condition input unit 102 inputs a magnetic flux density condition (the peak value, frequency, and waveform of the magnetic flux density).

Next, in step S503, the abnormal eddy current loss coefficient deriving unit 103 inputs the eddy current loss Steinmetz coefficient K _e , the specific gravity D of the electrical steel sheet, the thickness h of the electrical steel sheet, and the electrical conductivity σ of the electrical steel sheet, The calculation of equation (1) is performed to derive the abnormal eddy current loss coefficient κ.
Next, in step S504, the magnetic material condition input unit 104 inputs magnetic material conditions (the thickness h of the electromagnetic steel sheet and the specific resistivity ρ of the electromagnetic steel sheet).

Next, in step S505, the corrected DC magnetic hysteresis characteristic deriving unit 105 calculates the data of the corrected DC magnetic hysteresis characteristic by calculating equation (5).
Next, in step S506, the model identification unit 106 identifies the play hysteresis model by identifying the shape function f (ζ, p _ζ (B)) using the corrected DC magnetic hysteresis characteristic data.

Next, in step S507, the electromagnetic field analysis condition input unit 107 performs electromagnetic field analysis conditions (a method for setting a minute region (mesh), a shape of the iron core (core), conditions for exciting the iron core (core) (excitation conditions), And various initial values).
Next, in step S508, the electromagnetic field analysis unit 108, the finite element method and using the Newton Raphson method, to calculate the magnetic flux density vector B and the eddy current vector J _e in each minute area of the core (core).

Next, in step S509, the hysteresis loss calculation unit 109 in the minute region calculates the equation (23) to derive the hysteresis loss w _ha in each minute region.
Next, in step S510, the eddy current loss calculation unit 110 in the minute region calculates the equation (24) to derive the classical eddy current loss _we0 in each minute region.
Next, in step S511, the iron loss summation unit 111 calculates the equations (25) and (26) to derive the iron loss W of the entire iron core.
Next, in step S512, the iron loss output unit 112 outputs the iron loss W of the entire iron core (core).

(Example)
Next, examples will be described.
FIG. 6 is a diagram illustrating an example of an IPM (Interior Permanent Magnet Motor) motor model to be analyzed in the present embodiment. More specifically, FIG. 6 shows two lines extending from the origin 0 in the radial direction with the center of the rotation axis of the IPM motor as the origin 0 and having an angle of 90 [°]. It is a figure which shows the surface of a direction perpendicular | vertical to the rotating shaft of an IPM motor when a motor is turned off.

  In FIG. 6, the IPM motor has a rotor 601 and a stator 602. In this embodiment, the electromagnetic field in the stator core included in the stator 602 is analyzed. The stator core is formed by, for example, laminating a plurality of electromagnetic steel plates. 6 shown in FIG. 6 is the origin and coincides with the center of the rotation axis of the IPM motor. x and y indicate the x-axis and the y-axis, respectively. R indicates the radial direction of the IPM motor, and θ indicates the circumferential direction of the IPM motor. The analysis was performed by setting the radius of the rotor 601 to 110 [mm], the outer diameter of the stator 602 to 224.4 [mm], and the rotational speed of the IPM motor to 6000 [rpm] (= frequency: 200 [Hz]).

The case where the corrected DC magnetic hysteresis characteristic was used was taken as this example, and the case where the DC hysteresis characteristic was used was taken as a comparative example. As described above, in this embodiment, the classic eddy current loss is calculated as the eddy current loss. In contrast, in the comparative example, classical eddy current loss and abnormal eddy current loss are individually calculated as eddy current loss. The abnormal eddy current loss in the comparative example is a value obtained by multiplying the classical eddy current loss _weo obtained by the calculation of the equation (24) by the abnormal eddy current loss coefficient κ shown in the equation (1). The other methods and conditions of the present example and the comparative example are the same. In each of the examples and comparative examples, the iron loss of the entire stator core and the torque of the IPM motor were calculated. The results are shown in Table 2 together with actual measurement values.

  Torque F was calculated by the following equation (27) (assuming Maxwell stress).

(27) In the formula, n _x, n _y, respectively, x-axis is the unit vector in the y-axis direction, mu ₀ is the permeability of vacuum. ∫dΓ indicates a line integral along a closed curve surrounding an object (the rotor 601 in this embodiment) for which an electromagnetic force is to be obtained. Also, B is the magnitude of the magnetic flux density vector, B _x, B _y, respectively, x-axis component of the magnetic flux density vector, the y-axis component.

7 and 8 show magnetic hysteresis characteristics in the radial direction R and the circumferential direction θ at the positions 611 to 616 shown in FIG. Specifically, FIG. 7A, FIG. 7B, FIG. 7C, FIG. 8A, FIG. 8B, and FIG. 8C show positions 611, 612, 613, 614, 615, and 616 are magnetic hysteresis characteristics in the radial direction R and the circumferential direction θ. The magnetic hysteresis characteristics shown in FIGS. 7 and 8 are all obtained from the magnetic flux density vector B and the magnetic field vector H analyzed by the method of this embodiment.
As shown in Table 2, the calculated value of the torque F is closer to the actually measured value in the method of the present embodiment than in the method of the comparative example. As shown in the equation (27), the torque F is determined by the magnetic flux density vector B. Therefore, obtaining the calculated value of the torque F accurately means that the magnetic flux density vector B is accurately calculated. Therefore, when the corrected DC magnetic hysteresis characteristic is used as in this embodiment, the vector potential A (the magnetic flux density vector B and the eddy current vector J _e ) can be calculated more accurately than when the DC hysteresis characteristic is used. .

As described above, in the present embodiment, as described, the abnormal eddy current loss coefficient κ with representing the eddy current loss W _e the value obtained by multiplying the classical eddy current loss W _e0, classical eddy current loss W from eddy current loss W _{e The} abnormal eddy current loss W _ea is expressed by a value obtained by subtracting _e0 . A value obtained by adding the magnitude of the magnetic field vector based on the abnormal eddy current loss W _ea to the magnitude of the magnetic field vector H _h in the DC magnetic hysteresis characteristic is defined as a corrected magnetic field vector magnitude H _ha . The magnitude H _ha of the corrected magnetic field vector corresponding to the magnetic flux density vector in which the peak value, the frequency, and the waveform are designated is derived at each time step, and the relationship between them is created as a corrected DC magnetic hysteresis characteristic. Then, using this corrected DC magnetic hysteresis characteristic, a play hysteresis model is identified (constructed) and used for analysis of the electromagnetic field. Therefore, the magnetic flux density vector B and the eddy current vector J _e can be calculated in consideration of the abnormal eddy current. Therefore, using the DC magnetic hysteresis characteristics, the play hysteresis model is identified (constructed), and compared with the case where the play hysteresis model is used for the analysis of the electromagnetic field, the electromagnetic field when the AC magnetic field is applied (the magnetic flux density vector B and the eddy current vector J _e ) Can be calculated with high accuracy. Thereby, for example, an electromagnetic field can be analyzed with high accuracy when an AC magnetic field (in particular, a high-frequency AC magnetic field of several hundred Hz or higher) is applied. Therefore, for example, it is driven (inverter driven) by a voltage having a fundamental frequency of several hundred Hz, which is a frequency band of a motor having a high rotational speed, such as a drive motor for a hybrid electric vehicle (HEV) or an electric vehicle (EV). (In some cases) The electromagnetic field of the motor is analyzed with high accuracy, and thereby iron loss, torque, and copper loss can be estimated with high accuracy. In addition, since the loss can be decomposed into a hysteresis loss and an eddy current loss and can be estimated with high accuracy, it can be used for clarifying the cause of the iron loss and studying an improvement measure.

  In the present embodiment, the case where the play hysteresis model (isotropic vector play hysteresis model) is identified as a model in which the relationship between the magnetic flux density and the magnetic field is formulated from the data of the magnetic hysteresis characteristics has been described as an example. However, such a model is not limited to the play hysteresis model. For example, as described in Non-Patent Documents 1 and 2, a Preisach model or the like may be used.

  Further, in the present embodiment, the case where a plurality of electromagnetic steel plates configured to be stacked on each other is an analysis target has been described as an example. However, the object of analysis is not limited to this. For example, one electromagnetic steel plate may be the object of analysis. For example, in a magnetic shield, one electromagnetic steel sheet may be the object of analysis.

The embodiment of the present invention described above can be realized by a computer executing a program. Further, a computer-readable recording medium in which the program is recorded and a computer program product such as the program can also be applied as an embodiment of the present invention. As the recording medium, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

  DESCRIPTION OF SYMBOLS 100: Electromagnetic field analyzer 101: DC magnetic hysteresis characteristic input part 102: Magnetic flux density condition input part 103: Abnormal eddy current loss coefficient deriving part 104: Magnetic material condition input part 105: Correction direct current magnetic hysteresis characteristic deriving part 106: Model identification section 107: Electromagnetic field analysis condition input section 108: Electromagnetic field analysis section 109: Hysteresis loss calculation section in minute area 110: Hysteresis loss calculation section in minute area 111: Iron loss summation section 112 Iron loss output section

Claims (6)

A corrected DC magnetic hysteresis characteristic deriving means for deriving a corrected DC magnetic hysteresis characteristic in which the DC magnetic hysteresis characteristic of the magnetic material is corrected;
Model identification means for identifying a model in which the relationship between the magnetic flux density and the magnetic field in the magnetic material is formulated from the corrected DC magnetic hysteresis characteristic data derived by the corrected DC magnetic hysteresis characteristic deriving means;
A magnetic flux density vector and a vortex generated in the magnetic material when the magnetic material is excited using an excitation condition which is a condition for exciting the magnetic material and a model identified by the model identification unit. An electromagnetic field analysis means for calculating a current vector for each of a plurality of minute regions based on Maxwell's equations,
The corrected DC magnetic hysteresis characteristic deriving means performs calculation based on the following equation (A), and corrects the magnitude H _ha [of the corrected magnetic field vector corresponding to the magnitude B [i] [T] of the magnetic flux density vector. i] [A / m] is derived, and the corrected DC magnetic hysteresis characteristic is calculated using the corrected magnetic field vector magnitude H _ha [i] corresponding to the derived magnetic flux density vector magnitude B [i]. An electromagnetic field analyzer characterized by deriving.
In the formula (A), i is a variable for specifying the time step, i−1 is a variable for specifying the time step immediately before the time step specified by the variable i, and H _h [i] is the magnetic field vector magnitude [A / m] corresponding to the magnetic flux density vector magnitude B [i] in the DC magnetic hysteresis characteristic data, and t [i] corresponds to the variable i. Κ is an abnormal eddy current loss coefficient [−], which is a coefficient multiplied by the classical eddy current loss when expressing the total eddy current loss of the magnetic material, and ρ is the magnetic step The specific resistivity [Ω · m] of the material, and h is the thickness [m] of the magnetic material.

The electromagnetic field analysis apparatus according to claim 1, wherein the model is a play hysteresis model in which a relationship between a magnetic flux density and a magnetic field is formulated using the following equation (B).

DC magnetic hysteresis characteristic input means for inputting a plurality of DC magnetic hysteresis characteristic data having different peak values of magnetic flux density;
Magnetic flux density condition input means for inputting magnetic flux density conditions including the frequency and waveform of the magnetic flux density;
An abnormal eddy current loss coefficient input means for inputting the abnormal eddy current loss coefficient κ,
Magnetic material condition input means for inputting a magnetic material condition for inputting a magnetic material condition including a thickness h of the magnetic material and a specific resistivity ρ of the magnetic material;
The corrected DC magnetic hysteresis characteristic deriving means derives the corrected magnetic field vector magnitude H _ha [i] corresponding to the magnitude B [i] at each time step of the magnetic flux density determined by the magnetic flux density condition. The electromagnetic field analysis apparatus according to claim 1, wherein the electromagnetic field analysis device is performed for each of the magnetic flux densities of the peak values. The electromagnetic field analysis apparatus according to claim 3, wherein the abnormal eddy current loss coefficient input means calculates the following equation (C) to derive the abnormal eddy current loss coefficient κ.
(C) In the equation, D is the a specific gravity of magnetic material [kg / m ^3], σ is the a conductivity of the magnetic material [S / m], K _e is the total vortex of the magnetic material The eddy current loss Steinmetz coefficient [−], which is a coefficient multiplied by the product of the square of the frequency and the square of the magnitude of the magnetic flux density vector when expressing the current loss.

A corrected DC magnetic hysteresis characteristic derivation step performed by the corrected DC magnetic hysteresis characteristic deriving means to derive a corrected DC magnetic hysteresis characteristic obtained by correcting the DC magnetic hysteresis characteristic of the magnetic material;
The model identification means identifies the model in which the relationship between the magnetic flux density and the magnetic field in the magnetic material is formulated from the data of the corrected DC magnetic hysteresis characteristic derived in the corrected DC magnetic hysteresis characteristic deriving step. A model identification process;
A magnetic flux density vector and a vortex generated in the magnetic material when the magnetic material is excited using an excitation condition which is a condition for exciting the magnetic material and a model identified by the model identification step. An electromagnetic field analysis step of performing, by an electromagnetic field analysis means, calculating a current vector for each of a plurality of minute regions based on Maxwell's equations,
In the correction DC magnetic hysteresis characteristic deriving step, a calculation based on the following equation (A) is performed, and the corrected magnetic field vector size H _ha [T] corresponding to the magnetic flux density vector size B [i] [T] is calculated. i] [A / m] is derived, and the corrected DC magnetic hysteresis characteristic is calculated using the corrected magnetic field vector magnitude H _ha [i] corresponding to the derived magnetic flux density vector magnitude B [i]. An electromagnetic field analysis method characterized by deriving.
In the formula (A), i is a variable for specifying the time step, i−1 is a variable for specifying the time step immediately before the time step specified by the variable i, and H _h [i] is the magnetic field vector magnitude [A / m] corresponding to the magnetic flux density vector magnitude B [i] in the DC magnetic hysteresis characteristic data, and t [i] corresponds to the variable i. Κ is an abnormal eddy current loss coefficient [−], which is a coefficient multiplied by the classical eddy current loss when expressing the total eddy current loss of the magnetic material, and ρ is the magnetic step The specific resistivity [Ω · m] of the material, and h is the thickness [m] of the magnetic material.

  A program for causing a computer to function as the electromagnetic field analysis apparatus according to claim 1.

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