JP7246633B2 - Electromagnetic field simulator and electromagnetic field analysis method - Google Patents

Description

Article 30, Paragraph 2 of the Patent Law applies Published in the Institute of Electrical Engineers of Japan materials (published by The Institute of Electrical Engineers of Japan on August 21, 2018), pp. 69-74.

Article 30, Paragraph 2 of the Patent Act applies August 21, 2018 The Institute of Electrical Engineers of Japan Research Meeting Stationary Rotating Machine Joint Research Meeting was held at Sinfonia Technology Hibiki Hall Ise (1-13-15 Iwabuchi, Ise City, Mie Prefecture). Published in.

The present invention relates to an electromagnetic field simulator and an electromagnetic field analysis method, and more particularly to an electromagnetic field simulator and an electromagnetic field analysis method for analyzing frequency characteristics of magnetic elements.

The magnetic element has a core made of a magnetic material and a coil that supplies an exciting current to the core, and the excited core moves along a magnetization curve. Electromagnetic field analysis using a computer is widely used in research and development and design work in the design of magnetic elements. However, with the increasing current of booster circuits and other devices in recent years, the structure has become more complicated, such as by providing a magnetic gap in the magnetic path to alleviate the magnetic saturation of the core. is occurring. In addition, when considering the change in magnetic characteristics due to the influence of frequency in a magnetic element that operates with a complex current waveform that includes multiple frequencies, such as a current waveform in which ripples are superimposed on a sine wave of commercial frequency, Magnetic properties measured at arbitrary frequencies are required.

For example, International Publication No. 2010/038799 (Patent Document 1) describes an analysis method of calculating relative magnetic permeability that changes with an increase in current in consideration of a minor loop in order to analyze DC superimposition characteristics. It is However, in the analysis method of Patent Document 1, it is necessary to measure a large number of minor loop groups according to the ripple width in addition to the initial magnetization characteristics, so there is a concern that the measurement data will become enormous.

As another known analysis method, a technique called a play model, which uses a loop group of magnetization characteristics measured for each constant magnetic flux density, has been proposed. However, the method of calculating the change in inductance value due to multiple frequencies or changes in frequency has not been put into practical use. Therefore, it is necessary to measure a huge amount of data.

Alternatively, Non-Patent Document 1 proposes a magnetic characteristic modeling method using a Cauer circuit for the purpose of applying to dust cores. A dust core is a soft magnetic material produced by covering minute magnetic particles of about several tens of μm with an insulating film and compressing them. It has the advantage of being easy to process.

Based on the so-called homogenization, which assumes that the shape and size of individual magnetic particles are the same and that the particles are insulated from each other when performing a magnetic field analysis that takes into account the eddy current of the dust core. An analysis is proposed. However, the magnetic particles of the actual dust core are not uniform in shape and size, and it is not uncommon for the particles to contact each other unevenly because part of the insulation is destroyed by the pressure during molding. , there are local eddy currents flowing inside the particle and global eddy currents flowing across the particle. For these reasons, modeling of magnetic properties over a wide frequency range by simple homogenization methods is limited.

On the other hand, Non-Patent Document 1 expresses the DC hysteresis characteristic with a play model, and considers the frequency dependence due to eddy currents with a standard Cauer circuit (Cauer-I type circuit), so that in a wide frequency range It is possible to reproduce the measurement results with high accuracy.

WO2010/038799

Naoya Watanabe, Yasuto Takahashi, Koji Fujiwara, Kayo Sakai, Eiichiro Shimazu, "Fundamental Study on Magnetic Characteristic Modeling of Powder Magnetic Core Using Cauer Circuit", The Institute of Electrical Engineers of Japan Stationary Machines and Rotating Machines Joint Study Group, SA-17 -65, RM-17-96, pp.73-78 (2017)

However, in the magnetic property modeling according to Non-Patent Document 1, a standard Cauer circuit that considers the frequency dependence due to eddy currents is incorporated into the finite element method, so that a coupled analysis between the Cauer circuit and the finite element method is performed. In addition to the unknown variables defined by the normal finite element method, unknown variables corresponding to the Cauer circuit increase in the dust core element, so there is concern that the calculation cost will increase greatly.

The present invention has been made to solve such problems, and an object of the present invention is to reduce the calculation cost of an electromagnetic field simulator and an electromagnetic field analysis method by coupled analysis of the Cauer circuit and the finite element method. is to reduce

In one aspect of the present invention, an electromagnetic field simulator for an analysis model including magnetic elements, in which a Cauer circuit arranged corresponding to each element of the analysis model divided by the finite element method is coupled. For the first simultaneous linear equations containing the first variable corresponding to the finite element method and the second variable corresponding to the Cauer circuit obtained by Have the means.

According to another aspect of the present invention, there is provided an electromagnetic field analysis method for an analysis model including magnetic elements, in which Cauer circuits arranged corresponding to each element of the analysis model divided by the finite element method are connected. For the first simultaneous linear equations related to the first variable corresponding to the finite element method and the second variable corresponding to the Cauer circuit, obtained by forming Provide steps for asking.

According to the present invention, it is possible to reduce the calculation cost of the electromagnetic field simulator and the electromagnetic field analysis method based on the coupled analysis of the Cauer circuit and the finite element method.

4 is a chart showing a list of specifications of dust cores that were subjected to magnetic property measurement. 4 is a graph showing measurement results of a hysteresis loop of a dust core at a frequency of 50 (Hz). 4 is a graph showing the measurement results of the hysteresis loop of the dust core when the frequency is changed under constant maximum magnetic flux density. FIG. 4 is a graph showing measurement results of frequency characteristics of inductance of an inductor formed by winding a coil around the dust core described in FIGS. 1 to 3; FIG. 1 is a circuit diagram of a Cauer-I type circuit (standard Cauer circuit) used in electromagnetic field analysis according to the present embodiment; FIG. 1 is a conceptual diagram illustrating a first example of an analysis target and an analysis model of an electromagnetic field simulator according to the present embodiment; FIG. 4 is a flowchart for explaining computation processing of electromagnetic field analysis by the electromagnetic field simulator according to the present embodiment; 1 is a block diagram illustrating an example of a hardware configuration for realizing an electromagnetic field simulator according to an embodiment; FIG. 7 is a graph comparing the measurement result of the hysteresis loop and the simulation result according to the present embodiment; 7 is a graph comparing measurement results of inductance frequency characteristics with simulation results according to the present embodiment. 4 is a chart comparing the time required for electromagnetic field analysis according to the present embodiment with electromagnetic field analysis of other methods; FIG. 10 is a chart comparing convergence calculation results per time step in electromagnetic field analysis according to the present embodiment with electromagnetic field analysis of other methods; FIG. FIG. 7 is a conceptual diagram illustrating a second example of an analysis target and an analysis model of the electromagnetic field simulator according to the present embodiment; FIG. 5 is a chart comparing the time required for electromagnetic field analysis according to the present embodiment in AC reactor simulation results with electromagnetic field analysis of other methods; FIG. FIG. 10 is a chart comparing convergence calculation results per time step in the electromagnetic field analysis according to the present embodiment in AC reactor simulation results with electromagnetic field analyzes of other methods; FIG. 7 is a graph showing simulation results of inductance frequency characteristics according to the present embodiment.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the following description, the same reference numerals are given to the same or corresponding parts in the drawings, and the description thereof will not be repeated in principle.

(Measurement of magnetic properties of dust core)
As described above, the present embodiment is directed to electromagnetic field analysis capable of simulating the magnetic properties of a core formed by compressing a dust core (hereinafter also referred to as a dust core). Therefore, first, the magnetic properties of the dust core to be simulated were measured.

FIG. 1 is a chart showing a list of specifications of dust cores targeted for magnetic property measurement.
As shown in FIG. 1, it has an inner diameter of 12.6 (mm), an outer diameter of 20.26 (mm), a height of 6.44 (mm), and a density of 7.35 (g/cm ³ ). Magnetic properties were measured for an annular dust core.

In the dust core, the individual particles are insulated and the influence of eddy current is very small, so the hysteresis loop measured at a frequency of 50 (Hz) can be treated as a DC hysteresis characteristic. As for the hysteresis loop, the symmetrical hysteresis loop was measured from 0.01 (T) to 0.4 (T) at maximum magnetic flux densities in increments of 0.01 (T). The convergence conditions when measuring the magnetic properties are that the form factor of the induced electromotive force waveform with respect to the form factor of the sine wave is within 0.05 (%), the error with respect to the target value of the maximum magnetic flux density is within 0.05 (%), and The distortion rate of the induced electromotive force waveform was set within 2.0 (%).

FIG. 2 shows the measurement results of the hysteresis loop of the dust core shown in FIG. 1 at a frequency of 50 (Hz). In FIG. 2, among the above measurement points, the maximum magnetic flux density is 0.1 (T), 0.2 (T), 0.3 (T), and 0.4 (T) Hysteresis loops 101-104 are shown. If a play model is identified from these symmetrical hysteresis loops, it can be used to express the DC hysteresis characteristics of the dust core.

Next to the DC hysteresis characteristics, the hysteresis loop was measured by changing the frequency in order to clarify the influence of the eddy current on the magnetic characteristics of the dust core.

FIG. 3 shows the measurement results of the hysteresis loop when changing the frequency of the dust core shown in FIG. Here, the hysteresis loop was measured with a maximum magnetic flux density of about 50 (mT), and the measurement frequency was set in the range from 1 (kHz) to 1 (MHz) in consideration of heat generation.

FIG. 3 shows hysteresis loops 111 to 116 at measurement frequencies of 1 (kHz), 50 (kHz), 200 (kHz), 500 (kHz), 800 (kHz) and 1 (MHz).

From the measurement results in FIG. 3, it can be confirmed that as the measurement frequency increases, the loss increases due to the influence of the eddy current, that is, the hysteresis loop expands. Furthermore, it can be seen that the maximum magnetic flux density Bm and the magnetic permeability μ derived from the magnetic field strength Hb at Bm decrease with increasing frequency.

Next, regarding the frequency characteristics of the inductance of the inductor configured by winding a conducting wire (coil) around the powder magnetic core described in FIGS. 1 to 3, the measurement results using an LCR meter are shown in FIG. shown in

FIG. 4 shows the result of measuring the inductance by setting the number of turns of the coil to 14 and varying the frequency f from 1 (kHz) to 8 (MHz). The vertical axis of FIG. 4 is the normalized inductance (L/Ldc) by dividing the measured inductance value L at each frequency by the measured inductance value Ldc at the frequency f=1 (kHz).

From FIG. 4, it can be read that the inductance value decreases in the high frequency region from around f=100 (kHz). This is due to the fact that the magnetic permeability μ decreases as the frequency increases, as shown in FIG.

(Equivalent circuit model of magnetic properties)
Next, an equivalent circuit model used in the electromagnetic field analysis according to this embodiment will be described.

FIG. 5 is a circuit diagram showing the configuration of a Cauer-I type circuit (hereinafter also simply referred to as a Cauer circuit) used in the electromagnetic field analysis according to this embodiment.

As shown in FIG. 5, the Cauer circuit is a ladder-type circuit (ladder circuit) configured by repeating parallel and series connections of resistor elements and inductors. FIG. 5 shows a Cauer circuit composed of resistive elements R ₀ -R _n and inductors L ₀ -L _n . DC hysteresis characteristics can be expressed by the first inductor L ₀ , and frequency characteristics due to eddy currents can be expressed by inductors L ₁ to L _n after L ₀ . As shown in FIG. 5, the voltage across the terminals of the Cauer circuit indicates the time change dB/dt of the magnetic flux density, and the current indicates the magnetic field H. FIG.

Here, the DC hysteresis characteristic corresponding to inductor _L0 can be calculated by a play model. Further, the circuit element values (resistance or inductance) of the inductors L _{1 to} Ln and resistor elements R ₀ to Rn after the inductor L 0 are obtained by an optimization method using a genetic algorithm, for example, as shown in FIG. The measurement result of the hysteresis characteristic can be determined to be a reproducible value.

Next, application of the Cauer circuit shown in FIG. 5 to the finite element method will be described.
In the Cauer circuit shown in FIG. 5, the magnetic flux density B (vector) corresponding to the node voltage is decomposed into three-dimensional rectangular coordinates, and is defined by the following formula (1). In each of the equations below, vectors are written in bold.

In equation (1), the subscript i represents the number of stages of the Cauer circuit. Also, the following equations (2) and (3) are obtained from the relationship of each node in the Cauer circuit.

In equations (2) and (3), Hdc (vector) corresponding to the main magnetic flux can be obtained by applying a magnetization curve or play model. Furthermore, applying the Galerkin method to the finite element equation of the static magnetic field, the residual G _i (vector) is given by the following equation (4).

N _k (vector) in equation (4) is the edge element basis function. By substituting the formula (2) for H ₀ in the formula (4), the following formula (5) can be obtained.

Similarly, the residual Gci (vector) corresponding to each stage (i) of the Cauer circuit is given by the following equation (6).

In equation (6), B ₀ (vector) is the magnetic flux density corresponding to the main magnetic flux and is obtained by rotating the magnetic vector potential A defined in the finite element method. Applying the Newton-Raphson method to equations (5) and (6) yields the linearized equation shown in equation (7) below.

The block matrix in Equation (7) is given by Equations (8)-(11) below.

Note that e _α is a unit vector in the α direction (α=x, y, z), and in the block matrix of equation (7), the components other than those of equations (9) to (11) are 0. Here, the formula (7) is simply expressed as the following formula (12).

In equation (12), X _F and X _C are unknown variables corresponding to the finite element method and Cauer circuit, respectively. That is, the variable X _F corresponds to one embodiment of the 'first variable', the variable X _C corresponds to one embodiment of the 'second variable', and equation (12) corresponds to the 'first system of linear corresponds to "equation". By using the Schur's complement, equation (12) can be transformed into equation (13) below by eliminating the unknown variable X _C corresponding to the Cauer circuit.

Normally, it is not easy from the point of view of computational cost to explicitly obtain the matrix (K _FF −K _FC ·K _CC ⁻¹ ·K _CF ) in equation (13). However, in the magnetic characteristic model according to the present embodiment, the coefficient matrix corresponding to the Cauer circuit in K _CC is the same in each element except for the volume contribution, so the inverse matrix K _CC ^-1 can be easily can be calculated.

Since K _FC and K _CF are also sparse matrices that are nonzero only within the elements of the dust core, the derivation of Equation (13), which is a contraction of Equation (12), can be achieved at low cost. Equation (13) corresponds to an example of the "second simultaneous linear equations".

In addition, since the influence of the Cauer circuit calculated by the matrix (K _FC · K _CC ^-1 · K _CF ) appears only in the elements of the powder magnetic core, the matrix (K _FF −K _FC · K _CC ^-1 · K _CF ) and the non-zero element positions in K _FF are unchanged. Therefore, the reduced equations are easy to implement, and the computational cost of matrix-vector multiplication and preprocessing is reduced to that of matrix-vector multiplication and preprocessing for the matrix-K _FF- only equations, which is equivalent to normal hysteresis magnetic field analysis. Computational cost is almost the same. After deriving the unknown variable X _F corresponding to the finite element method by solving the reduced formula (13), the unknown variable X _C corresponding to the Cauer circuit can be derived by formula (14). That is, the calculation for solving equation (13) corresponds to the "first calculation". Also, in equation (14), the variable X _C is derived by substituting the variable X _F derived from equation (13) into equation (12). That is, the computation for solving equation (14) corresponds to the "second computation".

From the derived _XF and _XC , the residuals _GF and _GC , which are the terms on the right side of Equation (13), are calculated at the next time step. You can repeat until you get it. In equations (13) and (14), the matrix K _FF changes at each time step, while the matrices K _FC , K _CF , and K _CC are understood from equations (9) to (11). is a constant as Therefore, these K _FC , K _CF , and K _CC need only be calculated once at the start of the transient analysis, thus reducing the calculation cost.

As described above, by combining the frequency-dependent magnetic property modeling by the Cauer circuit and the method of solving the simultaneous linear equations shown in Equation (13), high-precision magnetic field analysis in a wide frequency range can be achieved at the same level as the conventional method. It can be implemented at computational cost.

(analysis example)
FIG. 6 is a conceptual diagram explaining a first example of an analysis target and an analysis model of the electromagnetic field simulator according to the present embodiment.

Referring to FIG. 6, ring core 300 is formed, for example, by compressing a dust core. In the present embodiment, a ring core inductor formed by winding a conductor (coil) (not shown) around the ring core 300 is analyzed.

The analysis model 200 is obtained by using the entire 1/400 model obtained by cutting out the upper half of the 1/200 region in the circumferential direction from the ring core inductor due to symmetry as the analysis region. In the example of FIG. 6 , the analysis area 310 of the ring core 300 is meshed into multiple elements 311 , and the analysis area 410 of the coil 400 wound around the ring core 300 is divided into the multiple elements 411 . Analysis region 410 corresponds to a partial region of coil 400 wound corresponding to analysis region 310 . In the simulation illustrated below, the total number of meshed elements is 1400, of which the number of divisions (that is, the number of elements 311) in the analysis area 310 of the ring core 300 is 55. A coupled analysis between the finite element method and the Cauer circuit shown is equivalent to placing a Cauer circuit (FIG. 5) in each element.

In the simulation, the BiCGstab method was used as the linear iterative method, and the Newton-Raphson method with linear search was used as the nonlinear iterative method. In the Newton-Raphson method, convergence was determined when the amount of correction |ΔB| of the magnitude of the magnetic flux density became 10 ⁻⁴ (T) or less in all elements, and the convergence determination value in the BiCGstab method was 10 ⁻⁴ . Furthermore, the frequencies f were 1 (kHz), 200 (kHz), 500 (kHz) and 1 (MHz), and the measured current waveforms obtained when measuring the magnetization characteristics (Figs. 2 and 3) were applied to each element. is given as an input for In addition, using a play model as a DC magnetization characteristic, the simple TP-EEC method was used to repeatedly calculate the voltage waveform calculated from the interlinkage magnetic flux until it reached a steady state.

Among the simulations, the calculation processing of the electromagnetic field analysis by the Cauer circuit described above is executed according to the flowchart shown in FIG.

Referring to FIG. 7, when the simulation is started, in step (hereinafter simply referred to as “S”) 110, as an input for each element, the actual measurement obtained when measuring the magnetization characteristics at the frequency to be simulated A current waveform (or voltage waveform) is provided. Further, through S120, matrices K _FC , K _CF , and K _CC which are constants as described above are calculated. Through S130, the matrix K _FF at the first time step is calculated.

Subsequently, in S140, the unknown variable _XF corresponding to the finite element method is derived according to the above equation (13) using the matrices _KFC , _KCF , _KCC and _KFF . At S150, using the unknown variable _XF obtained at S140, the unknown variable _Xc corresponding to the finite element method is derived according to the above equation (14). That is, the "first calculation" is executed in S140, and the "second calculation" is executed in S150.

At S160, the time step is advanced, and at S170, the variable _XF at the current time step (t) and the variable _Xc at the next time step (t+Δt) are converted to , G _F and G _c are calculated. In S180, a convergence determination is performed to determine whether the above convergence condition is satisfied by the calculated value at the current time step (t) and the calculated value at the next time step (t+Δt).

When the convergence condition is satisfied (when YES is determined in S180), the last calculated value is output as a stationary solution through S200. When the convergence condition is not satisfied (NO determination in S180), the matrix K _FF that changes at each time step is updated in S190 as described above, and then the process returns to S140, thereby resuming the time step. Arithmetic processing that is progressed sequentially can be repeatedly executed.

By executing the arithmetic processing shown in FIG. 7 under the hardware configuration shown in FIG. 8, it is possible to realize the electromagnetic field simulator according to the present embodiment.

Referring to FIG. 8, simulator 600 according to the present embodiment is configured by a computer or the like, and includes a CPU (Central Processing Unit) 610, memory 620, input device 630, output device 640, and external equipment. and a connection port 650 of . The CPU 610, the memory 620, the input device 630, the output device 640, and the connection port 650 are communicatively connected by an internal bus or the like, and can input/output data to/from each other.

The input device 630 is configured by a keyboard, mouse, etc., and receives commands, data, etc. input from the user. The output device 640 is composed of a liquid crystal display or the like, and outputs information visually recognized by the user. The connection port 650 is a connector for an external device and a peripheral device typified by a USB (Universal Serial Bus), and can input/output data to/from the external device and the peripheral device.

A program for executing the arithmetic processing shown in FIG. 7 is stored in advance in the memory 620, and the arithmetic processing according to the program is executed by the CPU 610, thereby executing the electromagnetic field analysis according to the present embodiment. .

(Simulation result 1)
Next, simulation results of a ring core inductor configured by winding a conductive wire (coil) around the powder magnetic core described with reference to FIGS.

FIG. 9 shows a graph comparing the measurement results and simulation results of the hysteresis loop.

In FIG. 9, the measurement results of the hysteresis loop shown in FIG. , the hysteresis loop obtained by simulation is indicated by a dotted line.

From the comparison of the dotted line and the solid line in FIG. 9, it can be seen that the electromagnetic field analysis according to this embodiment can accurately express the hysteresis characteristics that change depending on the frequency in a wide frequency range from low frequencies to high frequencies. understood.

FIG. 10 shows a graph comparing inductance measurement results and simulation results.

In FIG. 10, the measurement result of the inductance frequency characteristic shown in FIG. 4 is indicated by a characteristic line 151. In FIG. The vertical axis in FIG. 10 is normalized inductance (L/Ldc) similar to FIG.

Furthermore, a characteristic line 152 based on the inductance value obtained as a simulation result by the electromagnetic field analysis according to this embodiment is shown. In the simulation, the number of turns of the coil and the applied current were set to values similar to the inductance values in FIG. 4 using an LCR meter.

For comparison, a characteristic line 153 based on an inductance value obtained as a simulation result by a normal magnetic field analysis that does not consider eddy currents, that is, an analysis that does not introduce a Cauer circuit, considering only DC hysteresis, is further It is shown. In such an analysis, since the frequency dependence of magnetization characteristics is not modeled, the inductance is a constant value with respect to frequency changes.

On the other hand, in the present embodiment, since magnetic characteristic modeling is performed based on the Cauer circuit, it is understood that the frequency characteristic of the inductance can be estimated with high accuracy from low frequencies to high frequencies. It should be noted that the characteristic line 152 exhibits a tendency different from the measured value (characteristic line 151), in that the decrease in inductance becomes gentle in the frequency band exceeding 2 (MHz). This is probably because, as described above, only measured values up to 1 (MHz) are used in the optimization calculation of the Cauer circuit using the measurement results of FIG.

Furthermore, in order to confirm the effect of contraction of the simultaneous linear equations by using the equations (13) and (14) instead of the equation (12), the calculation time required for the simulation was compared. Specifically, with the analysis model 200 shown in FIG. Ordinary electromagnetic field analysis (case A) without consideration, electromagnetic field analysis (case B) in which a Cauer circuit is introduced but simultaneous linear equations are not contracted as in this embodiment, and in this embodiment An electromagnetic field analysis (Case C) was performed with contraction of the simultaneous linear equations.

FIG. 11 shows a chart for comparing the required calculation times in Cases A to C. In FIG.
Referring to FIG. 11, in case A, as described above, the time required for calculation is constant even if the frequency changes because the frequency dependence of the magnetization characteristics is not modeled. The calculation time required for Case A and Case C is shown as a ratio to the calculation time required for Case A.

In Case B, where reduction is not performed, the calculation time increases as the frequency increases. Computation time is reduced over Case B throughout the frequency range from 1 (kHz) to 1 (MHz).

FIG. 12 shows a chart for comparing the convergence calculation results per time step in Cases A to C. In FIG. Specifically, the average number of iterations until the convergence condition is satisfied per time step in the Neutraffson method (NR method), and the average number of iterations until the convergence condition is satisfied per time step in the BiCGstab method and the average Computation times are compared.

From FIG. 12, it is understood that there is almost no change in the number of iterations between cases A to C in the Neutraffson method, which is a nonlinear iterative method. On the other hand, in the BiCGstab method, which is a linear iterative method, the average number of iterations in case C (this embodiment) is significantly reduced, and as a result, the reduction in calculation time described with reference to FIG. 11 is achieved. is understood.

As described above, according to the electromagnetic field analysis according to the present embodiment, the frequency dependence of the magnetic characteristics can be calculated at the same calculation cost as the magnetic field analysis (Case A in FIGS. 11 and 12) in which only hysteresis is considered. It can be reproduced with high accuracy. In particular, in the high-frequency region where the influence of the Cauer circuit is relatively large, the effect of reducing the calculation cost by contracting the simultaneous linear equations is large.

(Simulation result 2)
Next, AC reactor simulation results based on electromagnetic field analysis according to the present embodiment will be described.

FIG. 13 is a conceptual diagram illustrating a second example of an analysis target and an analysis model of the electromagnetic field simulator according to the present embodiment.

Referring to FIG. 13, the AC reactor has a core 500, which is an assembly of eight rectangular parallelepiped blocks 501 and four cylindrical blocks 502, and a conductor (coil) (not shown) wound around the cylindrical portion. The analysis target is an AC reactor configured by Each rectangular parallelepiped block 501 and each columnar block 502 are formed, for example, by compressing a dust core, similarly to the ring core 300 of FIG. The density of each rectangular parallelepiped block 501 and each cylindrical block 502 is comparable to that of the ring core.

An analysis model 210 is obtained by setting a 1/8 model of the entire AC reactor as an analysis region due to symmetry.

In the example of FIG. 13 , the analysis area 510 of the core 500 is meshed into a plurality of elements 511 , and the analysis area 410 of the coil 400 wound around the cylindrical portion of the core 500 is divided into the plurality of elements 411 . Analysis region 410 corresponds to a partial region of coil 400 wound corresponding to analysis region 510 . Also, a gap element 450 was set on the joint surface between the blocks to simulate a minute gap corresponding to the adhesive. In the simulation illustrated below, the total number of meshed elements is 19780, of which the number of divisions (that is, the number of elements 511) in the analysis region 510 of the core 500 is 5360.

A simulation similar to that for the ring core inductor described above was performed on the analysis model shown in FIG. 13 by the electromagnetic field analysis according to the present embodiment. That is, with the analysis model shown in FIG. 13 as a common analysis object, at each of frequencies f = 1 (kHz), 200 (kHz), 500 (kHz) and 1 (MHz), cases A to A simulation for case C was performed.

FIG. 14 shows a chart comparing the time required for the electromagnetic field analysis according to the present embodiment, similar to FIG. 11, with the electromagnetic field analysis of other methods. In FIG. 14, similarly to FIG. 11, the reference value (1.0) is used for the frequency-independent calculation time in case A, and the case B in which the Cauer circuit is simulated without reduction, and the case with reduction The time required for calculation at each frequency by C (this embodiment) is expressed as a ratio to the reference time.

Similarly, FIG. 15 shows a chart for comparing the convergence calculation results per time step in the electromagnetic field analysis according to the present embodiment similar to FIG. 12 with the electromagnetic field analysis of other methods. In FIG. 15, similarly to FIG. 12, the average number of iterations until the convergence condition is satisfied per time step in the Neutraffson method, and the average number of iterations per time step until the convergence condition is satisfied in the BiCGstab method and the average computation time are compared between Cases A-C.

Also in FIG. 14, in Case B, the average number of iterations and the calculation time increase as the frequency increases, but in Case C, it can be understood that the increase in the average number of iterations and the calculation time is suppressed.

In the analysis model (ring core inductor) of FIG. 6, the number of elements of the dust core with respect to the total number of elements is about 4% (55/1400), whereas in the analysis model (AC reactor) of FIG. The number of elements of the dust core is 27% (5360/19780) of the number, and the proportion of the elements of the dust core is large. Therefore, in FIGS. 14 and 15, compared to FIGS. 11 and 12, the increase in the average number of iterations and the calculation time with respect to the increase in frequency in case B is remarkable.

On the other hand, the increase in the average number of iterations and the computation time with respect to the increase in frequency in case C is almost the same in FIGS. 14 and 15 as in FIGS. Therefore, it is understood that the larger the ratio of the number of elements of the dust core to the total number of elements in the analysis model, the higher the effect of reducing the calculation cost by the electromagnetic field analysis according to the present embodiment.

Further, FIG. 16 shows inductance values obtained as a simulation result of the electromagnetic field analysis according to the present embodiment for the analysis model (AC reactor) shown in FIG.

Also in FIG. 16, the inductance value L obtained as a simulation result at each frequency is a normalized value (L/Ldc ) are shown on the vertical axis.

As for the frequency characteristics of FIG. 16, as with the frequency characteristics of the ring core shown in FIG. 10, a decrease in inductance can be seen from frequencies exceeding 100 (kHz), but the decrease in inductance is gradual due to the effect of the gap between blocks. , and it is understood that qualitatively valid frequency characteristics are obtained from the simulation.

The electromagnetic field analysis according to this embodiment can be applied to cores of any shape by appropriately creating a mesh in the finite element method. Further, as described above, the electromagnetic field analysis according to the present embodiment can enjoy a great effect when the analysis target is a compression-molded core, but the analysis target material is arbitrary. That is, the electromagnetic field analysis according to the present embodiment is also applied to cores formed by injection molding using other magnetic materials, or cores in which thin-film magnetic materials or plate-shaped magnetic materials are laminated. It is possible to

Although the embodiment of the present invention has been described as above, it is also possible to modify the above-described embodiment in various ways. Also, the scope of the present invention is not limited to the above-described embodiments. The scope of the present invention is indicated by the scope of claims, and is intended to include all changes within the meaning and scope of equivalence to the scope of claims.

101 to 104, 111 to 116 hysteresis loop, 151 to 153 characteristic line (inductance frequency characteristic), 200, 210 analysis model, 300 ring core, 310, 410, 510 analysis area, 311, 411, 511 element, 400 coil, 450 gap Elements, 500 cores, 501 cuboid blocks, 502 cylinder blocks, 600 simulators, 620 memories, 630 input devices, 640 output devices, 650 connection ports.

Claims (3)

An electromagnetic field simulator for an analysis model including a magnetic element,
A first variable corresponding to the finite element method obtained by coupling Cauer circuits arranged corresponding to each element of the analysis model divided by the finite element method, and the Cauer circuit corresponding to the means for obtaining a stationary solution by repeated calculation at each time step for the first simultaneous linear equations including the second variable ,
The means for obtaining the steady-state solution includes:
At each said time step, deriving said first variable at that time step from a second system of linear equations not including said second variable, previously obtained by contracting said first system of linear equations. means for performing a first operation of
and means for executing a second operation for deriving the second variable from the first simultaneous linear equations into which the first variable derived by the first operation is substituted. 2. The electromagnetic field simulator according to claim 1, wherein the inductance of the first-stage inductance element of the Cauer circuit among the plurality of resistance elements and inductance elements forming said Cauer circuit is calculated according to a play model. An electromagnetic field analysis method for an analysis model including a magnetic element,
A first variable corresponding to the finite element method obtained by coupling Cauer circuits arranged corresponding to each element of the analysis model divided by the finite element method, and the Cauer circuit corresponding to the A step for obtaining a stationary solution by repeated calculation at each time step for the first simultaneous linear equations related to the second variable ,
The step for obtaining the stationary solution includes:
At each said time step, deriving said first variable at that time step from a second system of linear equations not including said second variable, previously obtained by contracting said first system of linear equations. performing a first operation to
and performing a second operation of deriving the second variable from the first simultaneous linear equations into which the first variable derived by the first operation is substituted. .

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