JP2022045167A - Electromagnetic field analyzer, electromagnetic field analysis method, and program - Google Patents

Abstract

To make it possible to perform electromagnetic field analysis in a short time in consideration of fine stepwise temporal change in magnetic flux density generated when switching a switching element of an inverter power source.SOLUTION: An electromagnetic field analyzer 100 derives a correction current I+ based on a difference φINV-φI between a flux linkage φINV at the time of inverter excitation and a flux linkage φI at the time of target excitation. The electromagnetic field analyzer 100 derives magnetic flux density in a stator core when the correction current I+ flows into a stator coil by executing linear electromagnetic field analysis based on a Maxwell equation.SELECTED DRAWING: Figure 1

Description

The present invention relates to an electromagnetic field analyzer, an electromagnetic field analysis method, and a program, and is particularly suitable for use in analyzing an electromagnetic field in a motor driven by an inverter power supply.

Variable speed drive motors used in electric vehicles (EVs (Electric Vehicles)) and hybrid electric vehicles (HEVs (Hybrid Electric Vehicles)) are often driven by an inverter power source. An inverter is a power supply circuit that repeatedly turns a DC voltage on and off by switching operations of a semiconductor element for an inverter to give a voltage close to a sine wave. In recent years, the drive frequency of a motor has been improved along with the improvement of the characteristics of a semiconductor element for an inverter, and the need for an iron loss analysis method that becomes remarkable in a high frequency region is increasing.

Therefore, in Non-Patent Document 1, the loss W _sin is derived by executing the sinusoidal current source nonlinear non-stationary finite element method analysis (Δt FEA), and the harmonic component of the PWM voltage waveform is input as a complex number approximation finite. It is described that the carrier loss W _carrier is derived by performing the element method analysis (jω FEA), and the sum of these losses W _sin and W _carrier is taken as the total loss.

Katsumi Yamazaki, Kyoichi Iida, "High-speed efficiency map calculation method considering inverter carriers in embedded magnet synchronous motors-Comparison with the case of using magnetic flux map-", Institute of Electrical Engineers of Japan, SA-19-86 / RM- 19-106, p. 77-82, September 13, 2019 Takayoshi Nakata, Norio Takahashi, "Limited Element Method of Electrical Engineering", 2nd Edition, Morikita Publishing Co., Ltd., April 1986 3D Electromagnetic Field Analysis Practical Technology Research Committee for Rotating Machines, "3D Electromagnetic Field Analysis Practical Technology for Rotating Machines", Institute of Electrical Engineers of Japan Technical Report, No. 1296, 2013

However, in the technique described in Non-Patent Document 1, since the iron loss due to the harmonic component of the PWM voltage waveform is calculated, only the iron loss due to the predetermined frequency component (frequency component that is an integral multiple of the modulated wave) is derived. Can't. Therefore, it is not possible to accurately consider the minute stepwise change in magnetic flux density (change in magnitude with the passage of time) that occurs when the semiconductor element for an inverter is switched. Therefore, in order to take into account the time-dependent changes in the magnetic flux density in small steps that occur when the switching element of the inverter power supply is switched, it is necessary to execute the nonlinear electromagnetic field analysis with high time resolution, which increases the calculation load.

The present invention has been made in view of the above problems, and it is possible to execute an electromagnetic field analysis in a short time in consideration of a time change of a fine stepwise magnetic flux density that occurs when switching of a switching element of an inverter power supply. The purpose is to be able to do.

The electromagnetic field analysis device of the present invention is an electromagnetic field analysis device that analyzes an electromagnetic field in a motor driven based on an inverter voltage output from an inverter power supply, and the inverter voltage is applied to the stator coil of the motor. In this case, the interlinking magnetic flux at the time of inverter excitation, which is the magnetic flux interlinking the stator coil, and the interlinkage magnetic flux at the time of target excitation, which is the magnetic flux interlinking the stator coil when the target exciting current flows through the stator coil. A linear electromagnetic field analysis based on Maxwell's equation is performed for the correction current derivation means for deriving the correction current based on the difference and the magnetic flux density in the stator core of the motor when the correction current flows through the stator coil. It has a linear electromagnetic field analysis means derived by the above, and the correction current is used when the switching element of the inverter power supply is switched with respect to the magnetic flux density in the stator core when the target exciting current flows through the stator coil. It is a current that needs to be passed through the stator coil in order to compensate for the time change of the generated magnetic flux density.

The electromagnetic field analysis method of the present invention is an electromagnetic field analysis method for analyzing an electromagnetic field in a motor driven based on an inverter voltage output from an inverter power supply, and the inverter voltage is applied to a stator coil of the motor. In this case, the magnetic flux interlinking with the stator coil, which is the magnetic flux interlinking with the stator coil, and the magnetic flux interlinking with the stator coil when the target exciting current flows through the stator coil, A linear electromagnetic field analysis based on Maxwell's equation is performed for the correction current derivation step for deriving the correction current based on the difference and the magnetic flux density in the stator core of the motor when the correction current flows through the stator coil. It has a linear electromagnetic field analysis step derived by the above, and the correction current is obtained when the switching element of the inverter power supply is switched with respect to the magnetic flux density in the stator core when the target exciting current flows through the stator coil. It is a current that needs to be passed through the stator coil in order to compensate for the time change of the generated magnetic flux density.

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

According to the present invention, it is possible to execute an electromagnetic field analysis in a short time in consideration of the time change of the magnetic flux density in a fine stepwise manner that occurs when the switching element of the inverter power supply is switched.

It is a figure which shows an example of the functional structure of an electromagnetic field analyzer. It is a figure which shows an example of the model of an IPM motor. It is a figure explaining an example of the operation of a PWM inverter. It is a figure which shows an example of the time-series waveform of the magnetic flux density. It is a figure which shows an example of the power supply circuit used at the time of a linear unsteady electromagnetic field analysis. It is a flowchart explaining an example of the electromagnetic field analysis method. It is a figure which shows the calculation example of the time series waveform of the magnetic flux density.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
It should be noted that the same comparison target such as length, position, size, spacing, etc. is not only the case where they are exactly the same, but also the ones which differ within the range not deviating from the gist of the invention (for example, the tolerance determined at the time of design). Those that differ within the range) are also included.
FIG. 1 is a diagram showing an example of a functional configuration of the electromagnetic field analyzer 100. The hardware of the electromagnetic field analysis device 100 is realized by using, for example, an information processing device including a CPU, ROM, RAM, HDD, and various hardware, or dedicated hardware.

The electromagnetic field analysis device 100 analyzes the electromagnetic field in the motor driven based on the inverter voltage output from the inverter power supply.
<< IPM (Interior Permanent Magnet) Motor >>
In this embodiment, the case where the motor is a three-phase IPM motor is illustrated. FIG. 2 is a diagram showing an example of a model of an IPM motor. Specifically, FIG. 2 is a diagram showing a region of 1/4 of the cross section perpendicular to the rotation axis of the IPM motor. The region of 1/4 of the cross section perpendicular to the rotation axis of the IPM motor is two virtual lines extending from the origin 0 in the radial direction of the IPM motor with the center of the rotation axis of the IPM motor as the origin 0. It is an area partitioned by two virtual lines having an angle of 90 °. In FIG. 2, these two virtual lines correspond to the x-axis and the y-axis. The IPM motor has a configuration that is symmetrical four times, and when the IPM motor is rotated by 90 °, it overlaps with the one before the rotation. Therefore, the result of the analysis of the electromagnetic field also has a four-fold symmetric relationship. Therefore, by analyzing the electromagnetic field in the region of 1/4 of the cross section perpendicular to the rotation axis of the IPM motor, the electromagnetic field in the remaining region of the IPM motor can be derived. In the following description, the radial direction of the IPM motor and the circumferential direction of the IPM motor are abbreviated as the radial direction and the circumferential direction, if necessary.

In FIG. 2, the IPM motor has a rotor 201 and a stator 202.
The rotor 201 has, for example, a plurality of electrical steel sheets and permanent magnets. A plurality of electrical steel sheets have the same shape. The plurality of electrical steel sheets are formed with holes for arranging permanent magnets and shafts (rotating shafts). Permanent magnets and shafts are placed in through holes formed when a plurality of electrical steel sheets are stacked.

The stator 202 has a stator core and a stator coil. The stator core has a yoke portion extending in the circumferential direction and a plurality of teeth portions magnetically coupled to the yoke portion. The tip surfaces of the plurality of teeth portions are arranged at positions facing the rotor 201. FIG. 2 illustrates an IPM motor that is an inner rotor type in which the rotor 201 is arranged inside the stator 202 and is a radial gap type in which the gap between the rotor 201 and the stator 202 is arranged in the radial direction of the IPM motor. do. Therefore, the plurality of teeth portions are arranged at equal intervals in the circumferential direction of the IPM motor so as to face the direction of the rotation axis of the IPM motor from the inner peripheral surface of the rotor 201. The stator core has, for example, a plurality of electrical steel sheets. A plurality of electrical steel sheets have the same shape. The planar shape of the plurality of electrical steel sheets is the same as the planar shape of the yoke portion and the plurality of teeth portions. By stacking a plurality of electrical steel sheets, a yoke portion and a plurality of teeth portions are formed. The regions 202a to 202g are regions having a lower magnetic permeability than the other regions of the stator core. The reason for doing this will be described later. The stator coil is arranged in a slot that is a region between two adjacent teeth portions in the circumferential direction and is wound around the teeth portions. In FIG. 2, a U-phase stator coil is placed in the slot indicated by U + and U-, a V-phase stator coil is placed in the slot indicated by V-, and a V-phase stator coil is arranged in the slot indicated by W +. The case where the W phase stator coil is arranged is illustrated.

Since the IPM motor itself is realized by a known technique, only an outline thereof will be described here, and a detailed description thereof will be omitted. Further, in the present embodiment, various known IPM motors can be applied, and the IPM motor applied in the present embodiment is not limited to that shown in FIG. Further, the motor applied in this embodiment is not limited to the IPM motor as long as it is a motor driven by an inverter power supply.

<< Inverter power supply >>
In this embodiment, a case where the inverter power supply, which is an exciting power supply, is a PWM (Pulse Width Modulation) inverter is illustrated. FIG. 3 is a diagram illustrating an example of operation of the PWM inverter.

In FIG. 3, the PWM inverter compares the size of the positive phase modulated wave 310 with the size of the carrier wave 320 at each time. Then, the PWM inverter outputs "1" when the size of the positive phase modulated wave 310 is larger than the size of the carrier wave 320, and outputs "0 (zero)" when it is not, at each time. , Generates a positive phase notch wave 340.

Further, the PWM inverter shifts the phase of the positive phase modulated wave 310 by 180 [°] to generate the negative phase modulated wave 330. By multiplying the positive phase modulated wave 310 by (-1), the phase of the positive phase modulated wave 310 can be shifted by 180 [°]. The PWM inverter compares the size of the negative phase modulated wave 330 thus generated and the size of the carrier wave 320 at each time. Then, the PWM inverter outputs "1" when the size of the negative phase modulated wave 330 is larger than the size of the carrier wave 320, and outputs "0 (zero)" when it is not, at each time. , Generates a negative phase notch wave 350.
In FIG. 3, the values of the modulated wave and the carrier wave are shown as relative values.

The PWM inverter outputs a voltage based on the positive DC voltage supplied to the PWM inverter during the period indicating "1" in the pulse wave obtained by subtracting the negative phase notch wave 350 from the positive phase notch wave 340. Further, the PWM inverter outputs a voltage based on the negative DC voltage supplied to the PWM inverter during the period indicating "-1" in the pulse wave obtained by subtracting the negative phase notch wave 350 from the positive phase notch wave 340. Further, the PWM inverter does not output a voltage based on the DC voltage supplied to the PWM inverter during the period indicating "0 (zero)" in the pulse wave obtained by subtracting the negative phase notch wave 350 from the positive phase notch wave 340. The pulse train (pulse wave) composed of the voltage thus obtained is output from the PWM inverter as the inverter voltage 360. In FIG. 3, the value of the inverter voltage 360 is shown as a relative value.

The PWM inverter generates and outputs such an inverter voltage 360 for each of the U phase, the V phase, and the W phase. A U-phase inverter voltage 360, a V-phase inverter voltage 360, and a W-phase inverter voltage 360 are applied to both ends of the U-phase stator coil, both ends of the V-phase stator coil, and both ends of the W-phase stator coil. To.

The parameters that determine the modulation operation in the PWM inverter as described above include the modulation factor m and the carrier frequency f _c . In the PWM inverter, the modulation factor m is represented by the value obtained by dividing the amplitude E ₀ of the positive phase modulated wave 310 and the negative phase modulated wave 330 by the amplitude E _c of the carrier wave 320 (m = E ₀ ÷ E _c ). In the carrier frequency, f _c is the frequency of the carrier wave 320.
As the PWM inverter, a PWM inverter driven by various known methods can be applied, and the PWM inverter is not limited to the one driven by the method shown in FIG.

<< Non-linear electromagnetic field analysis unit 101 >>
The non-linear electromagnetic field analysis unit 101 derives the magnetic flux density in the stator core when the target exciting current I _I flows through the stator coil by performing the non-linear electromagnetic field analysis based on Maxwell's equation. In this embodiment, a case where the time-series waveform of the target exciting current I _I is a sine wave is illustrated. However, the time-series waveform of the target exciting current I _I is not limited to the sine wave, and the target exciting current I _I of various time-series waveforms adopted as the time-series waveform of the target exciting current of the IPM motor can be adopted. .. The time-series waveform of the target exciting current I _I is information indicating the value of the target exciting current I _I at each time. This also applies to time-series waveforms of physical quantities other than the target exciting current I _I. The target exciting current I _I is the target exciting current when the inverter voltage 360 is generated in the PWM inverter, and the inverter voltage 360 is generated so that the exciting current flowing through the stator coil approaches the target exciting current I _I. ..

In the present embodiment, the nonlinear electromagnetic field analysis unit 101 performs electromagnetic field analysis using the nonlinear unsteady finite element method, so that the target exciting current I _I flows through the stator coil and the stator core is excited. The magnetic flux density B and the eddy current density J _e in each of the elements (mesh) set for the IPM motor model are derived.

There is a method using the A-φ method as a method of electromagnetic field analysis using the finite element method. In this case, the basic equation for performing the electromagnetic field analysis is given by the following equations (1) to (4) based on Maxwell's equations. In each equation, → indicates that it is a vector.

In equations (1) to (4), μ is the magnetic permeability, A is the vector potential, σ is the conductivity, J ₀ is the exciting current density, and J _e is the eddy current. It is a current density, and B is a magnetic flux density. After solving equations (1) and (2) simultaneously to derive the vector potential A and the scalar potential φ, the magnetic flux density B and the eddy current density J _e are used as elements from the equations (3) and (4). Derived for each of. In equation (1), in order to simplify the notation, the equation when the x component μ _x , y component μ _y , and z component μ _z of magnetic permeability are equal (when μ _x = μ _y = μ _z ) is used. show. In the non-linear electromagnetic field analysis, the relationship between the magnetic flux density B and the magnetic field strength H is a non-linear relationship, so that the magnetic permeability can take a different value depending on the magnetic flux density. Since the method for performing the nonlinear unsteady electromagnetic field analysis is a general method as described in Non-Patent Documents 1, 2, etc., detailed description thereof will be omitted.

The nonlinear electromagnetic field analysis unit 101 derives the magnetic flux density B and the eddy current density J _e in each element for each phase (that is, for each U phase, V phase, and W phase) at each time t of the time interval of the time step Δt1. do. The time step Δt1 is longer than the time step Δt2 in the linear electromagnetic field analysis executed by the linear electromagnetic field analysis unit 106 described later. For example, the time step Δt1 is preferably 3 times or more longer than the time step Δt2 in the linear electromagnetic field analysis described later, more preferably 5 times or more, and even more preferably 10 times or more. This is because the calculation time in the nonlinear electromagnetic field analysis can be shortened. However, the time step Δt1 in the nonlinear electromagnetic field analysis does not have to be longer than the time step Δt2 in the linear electromagnetic field analysis. For example, the time step Δt1 in the nonlinear electromagnetic field analysis and the time step Δt2 in the linear electromagnetic field analysis are the same. It may be.

<< Target Excitation Voltage Derivation Unit 102 >>
The target exciting voltage derivation unit 102 sets a target exciting voltage V _I , which is an exciting voltage corresponding to the target exciting current I _I , based on the magnetic flux density B of each element at each time t derived by the non-linear magnetic field analysis unit 101. Derived. The target excitation voltage _VI corresponds to a modulated wave (eg, positive phase modulated wave 310). In the present embodiment, the target exciting voltage V _I at each time t is derived based on the magnetic flux density B of each element at each time t derived by the nonlinear electromagnetic field analysis unit 101 and the circuit equation of the IPM motor. A specific example of the processing in the target excitation voltage derivation unit 102 will be described below.

First, the target exciting voltage derivation unit 102 includes the area of one element (mesh) in the cross section when one tooth portion is cut perpendicular to the radial direction at a predetermined position in the radial direction. It is executed for each phase to derive the product of the magnetic flux density B with the radial component of the magnetic flux density B at the time t in the element as the magnetic flux of the element at the time t. Then, the target exciting voltage derivation unit 102 derives the value obtained by integrating the magnetic fluxes of all the elements included in the cross section as the magnetic flux interlinking with the stator coil wound around the teeth portion at the time t. Run phase by phase. Further, the target exciting voltage derivation unit 102 integrates the magnetic flux interlinking with the stator coil wound around the teeth portion for all the teeth portions at the time t, and the interlinking magnetic flux φ at the target excitation time t. Derivation as _I is performed phase by phase. The target exciting voltage derivation unit 102 executes the derivation of the target excitation time-linking magnetic flux φ _I of each phase at the time t as described above at the time interval of the time step Δt1.

The target exciting voltage derivation unit 102 includes the target excitation magnetic flux φ _I of each phase at time t, the target exciting current I _I of each phase at time t, the DC resistance R of the stator coil of each phase, and each phase. Based on the number of turns N of the stator coil of the above, the target exciting voltage V _I of each phase at time t is derived by the circuit equation of the IPM motor. The circuit equation of the IPM motor used here is expressed by the following equation (5), for example.

The DC resistance R of the stator coil of each phase and the number of turns N of the stator coil of each phase are predetermined from the specifications of the IPM motor. For example, the target exciting voltage V _I of each phase at time t is derived by differentially approximating dφ _I / dt in the equation (5). The difference approximation may be a forward difference, a backward difference, or a central difference. The target excitation voltage V _I of each phase is also derived at the time interval of the time step Δt1.

The circuit equation of the IPM motor is an equation expressing the magnetic circuit of the IPM motor. In the equation (5), the voltage drop in the stator coil when an exciting current is passed through the stator coil, the time change of the magnetic flux interlinking the teeth portion around which the stator coil is wound, and the number of times the stator coil is wound. Represents that the product of is equal to. The circuit equation of the IPM motor is prepared for each phase.

Even if the target exciting voltage derivation unit 102 derives the target exciting voltage V _I of each phase at a certain time t each time the magnetic flux density B at a certain time t is derived by the non-linear magnetic field analysis unit 101, the non-linear electromagnetic field After the magnetic flux density B at each time t for one cycle is derived by the analysis unit 101, the target exciting voltage V _I of each phase at each time t for one cycle may be collectively derived.
In the present embodiment, as described above, the target exciting time interlinkage magnetic flux φ _I of each phase and the target exciting voltage V _I of each phase at each time t for one cycle are derived at the time interval of the time step Δt1. ..

When the time step Δt1 in the non-linear electromagnetic field analysis is longer than the time step Δt2 in the linear electromagnetic field analysis, the non-linear electromagnetic field analysis unit 101 uses the magnetic flux density of each element (mesh) at each time t of the time interval of the time step Δt1. By interpolating B and the eddy current density J _e , the magnetic flux density B and the eddy current density J _e of each element at each time determined by the time interval of the time step Δt2 are derived for each phase. Further, the nonlinear electromagnetic field analysis unit 101 derives the magnetic field strength H corresponding to the magnetic flux density B of each element at each time determined by the time interval of the time step Δt2.

Further, the target exciting voltage derivation unit 102 interpolates the target exciting time interlinkage magnetic flux φ _I of each phase at each time t of the time interval of the time step Δt1 to each time at each time determined by the time interval of the time step Δt2. Derivation of the interlinkage magnetic flux φ _I at the time of target excitation of the phase. Similarly, the target exciting voltage derivation unit 102 interpolates the target exciting voltage V _I of each phase at each time t of the time interval of the time step Δt1 so that the target exciting voltage deriving unit 102 of each phase at each time determined by the time interval of the time step Δt2. Derive the target excitation voltage V _I. If the target exciting current I _I of each phase is not determined at each time determined by the time interval of the time step Δt2, the target exciting current I _I of each phase at each time determined by the time interval of the time step Δt2 is also Derived.

After the magnetic flux density B at each time t for one cycle is derived by the nonlinear electromagnetic field analysis unit 101, the interlinkage magnetic flux φ _I and the target exciting voltage V _I of each phase at each time t for one cycle. When deriving collectively, the following may be used. That is, the nonlinear electromagnetic field analysis unit 101 derives the magnetic flux density B for one cycle as the magnetic flux density B of each element at each time determined by the time interval of the time step Δt2. The target excitation voltage derivation unit 102 performs the calculation of Eq. (5) using the magnetic flux density B of each element at each time determined by the time interval of the time step Δt2, and at each time determined by the time interval of the time step Δt2. Derivation of the interlinkage magnetic flux φ _I and the target exciting voltage V _I at the time of target excitation of each phase. In this case, the target exciting voltage derivation unit 102 does not need to derive the target exciting time interlinkage magnetic flux φ _I and the target exciting voltage V _I at the time interval of the time step Δt1.

<< Inverter voltage derivation unit 103 >>
The inverter voltage derivation unit 103 is a modulated wave (positive phase modulation) of each phase based on the target excitation voltage V _I of each phase at each time determined by the time interval of the time step Δt2, which is derived by the target excitation voltage derivation unit 102. The wave 310 and the negative phase modulated wave 330) are derived. Then, the inverter voltage derivation unit 103 of each phase at each time determined by the time interval of the time step Δt2 based on the result of comparing the modulated wave (positive phase modulated wave 310 and negative phase modulated wave 330) with the carrier wave 320. Inverter voltage V _INV is derived. The inverter voltage V _INV corresponds to the inverter voltage 360. An example of the method for deriving the inverter voltage V _INV is as described with reference to FIG. In this embodiment, the inverter voltage V _INV of each phase at each time determined by the time interval of the time step Δt2 is derived in this way.

<< Inverter excitation interlinkage magnetic flux derivation unit 104 >>
The inverter excitation time-linkage magnetic flux derivation unit 104 is based on the inverter voltage V _INV of each phase at each time determined by the time interval of the time step Δt2 and the circuit equation of the IPM motor, which are derived by the inverter voltage derivation unit 103. , Derives the interlinkage magnetic flux φ _INV when the inverter is excited. The interlinkage magnetic flux φ _INV during inverter excitation is a magnetic flux interlinking with the stator coil when the inverter voltage V _INV of each phase derived by the inverter voltage lead-out unit 103 is applied to the stator coil of each phase of the IPM motor. .. The circuit equation of the IPM motor used here is expressed by the following equation (6), for example.

As described above, the DC resistance R of the stator coil of each phase and the number of turns N of the stator coil of each phase are predetermined from the specifications of the IPM motor. Further, as described above, the circuit equation of the IPM motor is prepared for each phase. The interlinkage magnetic flux derivation unit 104 during excitation of the inverter includes the target exciting current I _I at each time for one cycle of a certain phase, the DC resistance R of the stator coil of the phase, and the number of turns N of the stator coil of the phase. Using the inverter voltage V _INV at each time for one cycle of the phase, the interlinkage magnetic flux φ _INV during excitation of the inverter at each time for one cycle in the phase is derived by Eq. (6). The inverter-excited interlinkage magnetic flux derivation unit 104 executes such derivation of the inverter-excitation interlinkage magnetic flux φ _INV for each phase. Here, the interlinkage magnetic flux φ _INV at the time of inverter excitation of each phase at each time is derived by executing the integration. At this time, the constant of integration is set so that the average value of the magnetic flux in one cycle becomes 0 (zero). In the present embodiment, as described above, the interlinkage magnetic flux φ _INV at the time of inverter excitation in each phase is derived at each time determined by the time interval of the time step Δt2.

By applying the inverter voltage V _INV to the stator coil, the exciting current flowing through the stator coil does not exactly match the target exciting current I _I and becomes a distorted waveform. However, the impedance of the motor is dominated by the inductance, and the contribution of the DC resistance to the impedance of the motor is small. Therefore, in the equation (6), the left side (= _{Ndφ INV} / dt) is sufficiently larger than the second term (= IIR) on the right side ( _{Ndφ INV} / dt >> IIR). Therefore, the shape of the waveform of the interlinkage magnetic flux φ _INV when the inverter is excited is almost determined by the shape of the waveform of the inverter voltage V _INV . Therefore, even if the target exciting current I _I is used in the equation (6), the interlinkage magnetic flux φ _INV at the time of inverter excitation in each phase can be derived with the accuracy required for practical use. From this point of view, the second term on the right side of the equation (6) may be omitted. Similarly, the second term on the right side of the equation (5) may be omitted.

<< Corrected current derivation unit 105 >>
The correction current derivation unit 105 is based on the following (7) based on the target exciting interlinkage magnetic flux φ _I , the inverter exciting interlinkage magnetic flux φ _INV , the number of turns N of the stator coil, and the magnetoresistance R _m of the stator core. ), The correction current I ₊ is derived. The correction current I ₊ is derived for each phase at each time determined by the time interval of the time step Δt2. In the following equation (7), the magnetoresistance R _m is expressed by the following equation (8).

In equation (8), ν _high is the reluctance coefficient. In this embodiment, in order to shorten the calculation time in the linear electromagnetic field analysis unit 106 described later, the magnetic permeability of a part of the element (mesh) on the path of the magnetic flux flowing through the stator core is used as the magnetic permeability of the stator core in the electromagnetic field analysis. The magnetic permeability should be sufficiently lower than the expected magnetic permeability. In the following description, an element having such a low magnetic permeability will be referred to as a low magnetic permeability element, if necessary. For example, the magnetic permeability of the low magnetic permeability element is preferably set to be equal to or lower than the magnetic permeability of vacuum, and more preferably to be 1/2 or less of the magnetic permeability of vacuum. The reluctance ν _high in the equation (8) is the reciprocal of the magnetic permeability set for the low magnetic permeability element. Further, in the equation (8), L is the length of the low magnetic permeability element in the traveling direction of the magnetic flux. Further, A is the cross-sectional area of the low magnetic permeability element in the direction perpendicular to the traveling direction of the magnetic flux.
In the present embodiment, as described above, the correction current I ₊ in each phase is derived at each time determined by the time interval of the time step Δt2.

Here, the correction current I ₊ will be described. FIG. 4 is a diagram showing an example of a time-series waveform of the magnetic flux density in the stator core. FIG. 4A is a diagram conceptually showing an example of a time-series waveform 410 of the magnetic flux density in the stator core when the target exciting current I _I flows through the stator coil. FIG. 4B is a diagram conceptually showing an example of a time-series waveform 420 of the magnetic flux density in the stator core when the inverter voltage V _INV is applied to the stator coil.

As shown in FIGS. 4A and 4B, in the time-series waveform 420 of the magnetic flux density in the stator core when the inverter voltage V _INV is applied to the stator coil, the target exciting current I _I flows in the stator coil. In this case, the time-series waveform 410 of the magnetic flux density in the stator core is superposed with a fine stepwise time change of the magnetic flux density (see the small uneven portion of the time-series waveform 420 of the magnetic flux density). Such a fine stepwise change in magnetic flux density with time is caused by the rise and fall of the inverter voltage V _INV at the time of switching the semiconductor element included in the PWM inverter. The correction current I ₊ is the current that needs to be passed through the stator coil in order to compensate for such a small stepwise change in the magnetic flux density with respect to the magnetic flux density in the stator core when the target exciting current I _I flows through the stator coil. Corresponds to. As described above, the correction current I ₊ is a current corresponding to a fine stepwise change in magnetic flux density. Therefore, it is necessary to derive it in fine time steps (that is, high time resolution). Therefore, in the present embodiment, the target exciting interlinkage magnetic flux φ _I and the inverter exciting interlinkage magnetic flux φ _INV used for deriving the correction current I ₊ are executed by the nonlinear electromagnetic field analysis unit 101. It is derived at the time interval of the time step Δt2 shorter than the time step Δt1 in the field analysis. From this point of view, the time step Δt2 is preferably 1.0 × 10 ^-5 seconds or less, and more preferably 5.0 × 10 ^-6 seconds or less.

<< Linear electromagnetic field analysis unit 106 >>
The linear electromagnetic field analysis unit 106 derives the magnetic flux density in the stator core when the correction current I ₊ flows through the stator coil by performing linear electromagnetic field analysis based on Maxwell's equation.
In the present embodiment, the linear electromagnetic field analysis unit 106 performs an electromagnetic field analysis using the linear unsteady finite element method, so that a correction current I ₊ flows through the stator coil and the stator core is excited. The magnetic flux density B and the eddy current density J _e for each of the elements set for the motor model are derived. In the present embodiment, for the sake of simplicity, the non-linear electromagnetic field analysis unit 101 executes the non-linear electromagnetic field analysis as the element set when the linear electromagnetic field analysis unit 106 executes the linear electromagnetic field analysis. Same as the element set at the time. However, the element set when the linear electromagnetic field analysis is executed by the linear electromagnetic field analysis unit 106 and the element set when the nonlinear electromagnetic field analysis is executed by the nonlinear electromagnetic field analysis unit 101 are different from each other. You may. In this case, for example, the magnetic flux density B and the eddy current density J _e in the other element are derived by interpolating or supplementing the magnetic flux density B and the eddy current density J _e in one element.

As shown in FIGS. 4A and 4B, the time-series waveform 410 of the magnetic flux density in the stator core when the target exciting current I _I flows through the stator coil and the inverter voltage V _INV are applied to the stator coil. In this case, the magnetic flux density in the stator core is not significantly different from the time-series waveform 420, and it is assumed that the distribution of the magnetic flux density in the stator coil is approximately the same in all cases. That is, the magnetic flux density does not change significantly with time in each element. Therefore, even if the linear electromagnetic field analysis is performed by approximating that the magnetic flux density in each element changes with time along the tangent of the magnetization curve, the magnetic flux density B and the eddy current density J _e satisfy the accuracy required for practical use. can do.

Therefore, in the present embodiment, the linear electromagnetic field analysis unit 106 is determined by the time step Δt2 based on the magnetic flux density B of each element at each time determined by the time step Δt2 derived by the nonlinear electromagnetic field analysis unit 101. The differential magnetic permeability (= dB / dBH) of each element at time is derived.
The linear electromagnetic field analysis unit 106 is derived from the nonlinear electromagnetic field analysis unit 101, and is determined by the time step Δt1 based on the magnetic flux density B and the magnetic field strength H of each element at each time determined by the time step Δt1. By deriving the differential magnetic permeability of each element in the above and interpolating the derived differential magnetic permeability, the differential magnetic permeability of each element at each time determined by the time step Δt2 may be derived. The linear electromagnetic field analysis unit 106 derives a coefficient matrix using the differential magnetic permeability derived as described above in the linear unsteady electromagnetic field analysis.

Further, the magnetic flux density derived by the linear electromagnetic field analysis unit 106 is only the portion where the magnetic flux density is finely changed over time as described with reference to FIG. That is, the time-series waveform of the magnetic flux density derived by the linear electromagnetic field analysis unit 106 has a target exciting current I _I from the time-series waveform 420 of the magnetic flux density in the stator core when the inverter voltage V _INV is applied to the stator coil. It corresponds to the time-series waveform of the magnetic flux density obtained by subtracting the time-series waveform 410 of the magnetic flux density in the stator core when flowing through the stator coil. Therefore, the magnitude of the magnetic flux density derived by the linear electromagnetic field analysis unit 106 is smaller than the magnitude of the actual magnetic flux density in the stator core. Therefore, as shown in FIG. 5, the stator coils 511, 512, and 513 of each phase (U phase, V phase, W phase) are not electrically connected to each other, and the stator coils 511, 512 of each phase, Even if the electromagnetic field analysis is performed assuming that the current sources 521, 522, and 523 are directly connected to each of the 513, the magnetic flux density B and the eddy current density J _e can satisfy the accuracy required for practical use. It is thought that it can be done.

Therefore, in the present embodiment, the linear electromagnetic field analysis unit 106 assumes that the correction current I ₊ of each phase flows from the mutually unconnected current sources 521, 522, 523 to the stator coils 511, 512, and 513, and is linear unsteady. Perform electromagnetic field analysis. In FIG. 5, the stator coils 511, 512, and 513 are not electrically connected, but are magnetically coupled by the stator core 530.

Further, as described above, a part of the elements on the path of the magnetic flux flowing through the stator core is a low magnetic permeability element. The low magnetic permeability element has a magnetic permeability sufficiently lower than the magnetic permeability assumed as the magnetic permeability of the stator core in the electromagnetic field analysis. For example, in FIG. 2, in FIG. 2, the center of each tooth portion in the radial direction so as to separate the region on the tip end side (rotating shaft side of the IPM motor) and the region on the proximal end side (yoke portion side) of the teeth portion of the stator core. Regions 202a to 202g along the circumferential direction, which are nearby regions, are defined as low magnetic permeability elements. The radial length of the regions 202a to 202g is, for example, 2% or more and 3% or less of the radial length of the teeth portion. By doing so, the reluctance in the stator core can be determined by the magnetic permeability in the regions 202a to 202g. Therefore, regardless of the magnetic flux density of the stator core, the magnetic resistance of the magnetic circuit of the IPM motor can be approximated to the magnetic resistance in the regions 202a to 202g. Therefore, the relationship between the exciting current and the magnetic flux can be linearly approximated without being affected by the spatial distribution of the differential magnetic permeability. Therefore, the calculation time in the linear electromagnetic field analysis unit 106 can be shortened. The magnitude of the magnetic flux density derived by the linear electromagnetic field analysis unit 106 is smaller than the magnitude of the actual magnetic flux density in the stator core, and the area of the low magnetic permeability element is sufficient for the area of the entire stator core. Therefore, it is considered that the magnetic flux density B and the eddy current density J _e can satisfy the accuracy required for practical use even if the electromagnetic field analysis is performed in this way.
When the areas 202a to 202g are the low magnetic permeability elements, in the equation (8), L is the radial length of the low magnetic permeability element, and A is perpendicular to the radial direction of the low magnetic permeability element. It is the cross-sectional area in the direction.

Other processes in the linear electromagnetic field analysis unit 106 can be realized by the same method as a general linear unsteady electromagnetic field analysis method. Since the method for performing the linear unsteady electromagnetic field analysis is a general method as described in Non-Patent Document 2 and the like, detailed description thereof will be omitted. As described above, at each time determined by the time interval of the time step Δt2, the magnetic flux density B and the eddy current density J _e of each element when the correction current I ₊ of each phase flows through the stator coil of each phase are in phase. Derived every time.

<< Loss Derivation Unit 107 >>
The loss derivation unit 107 derives the loss in the stator core based on the magnetic flux density in the stator core derived by the linear electromagnetic field analysis unit 106. In this embodiment, a case where a loss in the stator core is derived when a current obtained by combining the target exciting current I _I and the correction current I ₊ flows through the stator coil is illustrated.

Therefore, the loss derivation unit 107 is derived from the magnetic flux density B of each element at each time determined by the time interval of the time step Δt2 derived by the nonlinear electromagnetic field analysis unit 101, and the time derived by the linear electromagnetic field analysis unit 106. The magnetic flux density B of each element at each time determined by the time interval of step Δt2 is added for each element, each phase, and each time. As a result, at each time determined by the time interval of the time step Δt2, the magnetic flux density B of each element when the current obtained by combining the target exciting current I _I and the correction current I ₊ flows through the stator coil of each phase becomes phase by phase. Derived to. In the following description, the magnetic flux density B derived in this way is referred to as an overall magnetic flux density B, if necessary.

Further, the loss derivation unit 107 was derived by the eddy current density J _e of each element at each time determined by the time interval of the time step Δt2, which was derived by the nonlinear electromagnetic field analysis unit 101, and by the linear electromagnetic field analysis unit 106. , The eddy current density J _e of each element at each time determined by the time interval of the time step Δt2 is added for each element, each phase, and each time. As a result, at each time determined by the time interval of the time step Δt2, the eddy current density J _e of each element when the current obtained by combining the target exciting current I _I and the correction current I ₊ flows through the stator coil of each phase becomes Derived for each phase. In the following description, the eddy current density J _{e derived in this way is referred to as an overall eddy current density J e ,} if necessary.

The loss derivation unit 107 derives the hysteresis loss and the eddy current loss (classical eddy current loss) of the IPM motor (stator core) by using the total magnetic flux density B and the total eddy current density J _e in each element of the stator core.

For example, the loss derivation unit 107 derives the difference B _m between the maximum value and the minimum value in one cycle of the total magnetic flux density B of each element, and derives the hysteresis loss Wh of each element by the following equation (9). ..

In equation (9), f is the excitation frequency (the electrical frequency of the target excitation voltage _VI and the target excitation current I _I ), Kh is the hysteresis loss coefficient, and β is a constant (eg, 1.6 or 2). ). The hysteresis loss coefficient Kh is obtained in advance by, for example, the dual frequency method.
The loss derivation unit 107 derives the above-mentioned hysteresis loss Wh for all elements and all phases, and derives the sum of the hysteresis loss Wh in all the elements and all phases as the hysteresis loss of the IPM motor (stator core). do. The hysteresis loss can be derived by a known method, and may be derived by any method as long as it is derived by using the magnetic flux density of each element.

Further, the loss derivation unit 107 derives the eddy current loss We (classical eddy current loss) of each element from the total eddy current density J _e of each element by the following equation (10).

In equation (10), v is the size of the element, and T is the time corresponding to one electrical cycle of the target exciting voltage V _I and the target exciting current I _I. The size of the element is the area when performing a two-dimensional analysis and the size of the volume when performing a three-dimensional analysis.
The loss derivation unit 107 derives the above eddy current loss We for all elements and all phases, and sums the eddy current losses We for all elements and all phases to the eddy current of the IPM motor (stator core). Derived as a loss. The eddy current loss can be derived by a known method, and any method may be used as long as it is derived by using the eddy current density of each element.
Then, the loss derivation unit 107 derives the sum of the hysteresis loss and the eddy current loss of the IPM motor as the iron loss of the IPM motor.

<< Output unit 108 >>
The output unit 108 outputs information regarding the loss of the IPM motor (stator core) derived by the loss derivation unit 107. The information regarding the loss of the IPM motor includes, for example, information indicating at least one of the hysteresis loss of the IPM motor, the eddy current loss of the IPM motor, and the iron loss of the IPM motor. As the form of the output, for example, at least one of display on a computer display, transmission to an external device, and storage in an internal or external storage medium of the electromagnetic field analysis device 100 can be adopted.

<< Flowchart >>
Next, an example of the electromagnetic field analysis method by the electromagnetic field analysis device 100 will be described with reference to the flowchart of FIG.
First, in step S601, the nonlinear electromagnetic field analysis unit 101 executes electromagnetic field analysis using the nonlinear non-stationary finite element method, so that the target exciting current I _I of each phase flows through the stator coil of each phase and the stator core. The magnetic flux density B and the eddy current density J _e of each element when is excited are derived. Here, the nonlinear electromagnetic field analysis unit 101 has a magnetic flux density B in each element at each time t of a time interval of a time step Δt1 longer than the time step Δt2 in the linear unsteady electromagnetic field analysis executed in step S607 described later. And the eddy current density J _e shall be derived for each phase. The target exciting current I _I of each phase is set in the electromagnetic field analyzer 100 before the processing of step S601 is started.

Next, in step S602, the target exciting voltage derivation unit 102 is based on the magnetic flux density B of each element at each time t derived in step S601 and the circuit equation (Equation (5)) of the IPM motor. The interlinkage magnetic flux φ _I and the target exciting voltage V _I at the time of target excitation are derived. Here, the target exciting voltage derivation unit 102 derives the target exciting time interlinkage magnetic flux φ _I of each phase and the target exciting voltage V _I of each phase at each time t of the time interval of the time step Δt1.

Even if the values for one cycle of the electric cycle are derived in steps S601 and S602, the processes of steps S601 and S602 are repeated at each time t of the time interval of the time step Δt1 for one cycle. The value of may be derived.

Next, in step S603, the nonlinear electromagnetic field analysis unit 101 is determined by the time interval of the time step _Δt2 by interpolating the magnetic flux density B and the eddy current density Je of each element at each time t derived in step S601. The magnetic flux density B and the eddy current density J _e of each element at each time are derived for each phase. Further, when the target exciting current I _I of each phase at each time determined by the time interval of the time step Δt1 is set as the exciting condition in the non-stationary unsteady magnetic field analysis executed in step S601, the non-linear electromagnetic field analysis unit. 101 derives the target exciting current I _I of each phase at each time determined by the time interval of time step Δt2 by interpolating the target exciting current I _I of each phase at each time determined by the time interval of time step Δt1. .. Further, the target exciting voltage derivation unit 102 interpolates the target exciting time interlinkage magnetic flux φ _I of each phase at each time t derived in step S602, so that the target exciting voltage derivation unit 102 of each phase at each time determined by the time interval of the time step Δt2. Derivation of the interlinkage magnetic flux φ _I at the time of target excitation. Similarly, the target exciting voltage derivation unit 102 interpolates the target exciting voltage V _I of each phase at each time t derived in step S602, so that the target exciting voltage of each phase at each time determined by the time interval of the time step Δt2 is excited. Derivation of voltage V _I.

Next, in step S604, the inverter voltage derivation unit 103 derives a modulated wave (for example, a positive phase) based on the target exciting voltage _VI of each phase at each time determined by the time interval of the time step Δt2 derived in step S603. The modulated wave 310 and the negative phase modulated wave 330) are derived. Then, the inverter voltage derivation unit 103 of each phase at each time determined by the time interval of the time step Δt2 based on the result of comparing the modulated wave (positive phase modulated wave 310 and negative phase modulated wave 330) with the carrier wave 320. Inverter voltage V _INV is derived.

Next, in step S605, the interlinkage magnetic flux derivation unit 104 at the time of inverter excitation has the inverter voltage V _INV of each phase at each time determined by the time interval of the time step Δt2 derived in step S604, and the circuit equation of the IPM motor. Based on (Equation (6)), the interlinkage magnetic flux φ _INV at the time of inverter excitation of each phase at each time determined by the time interval of the time step Δt2 is derived.

Next, in step S606, the correction current derivation unit 105 is derived in step S605 and the target excitation time interlinkage magnetic flux φ _I of each phase at each time determined by the time interval of time step Δt2 derived in step S603. Further, based on the inverter excitation time interlinkage magnetic flux φ _INV of each phase at each time determined by the time interval of the time step Δt2, the number of turns N of the stator coil of each phase, and the magnetic resistance R _m of the stator core, (7). ), The correction current I ₊ of each phase at each time determined by the time interval of the time step Δt2 is derived. The number of turns N of the stator coil and the magnetic resistance R _m of the stator core are set in the electromagnetic field analyzer 100 before the processing of step S606 is started.

Next, in step S607, the linear electromagnetic field analysis unit 106 executes the electromagnetic field analysis using the linear unsteady finite element method, so that the stator coils of each phase are used at each time determined by the time interval of the time step Δt2. The magnetic flux density B and the eddy current density J _e of each element when the correction current I ₊ of each phase flows and the stator core is excited are derived for each phase.

In the present embodiment, the linear electromagnetic field analysis unit 106 is based on the result of the electromagnetic field analysis using the nonlinear unsteady finite element method in step S601 before executing the electromagnetic field analysis by the linear unsteady finite element method. The differential magnetic permeability of each element at each time determined by the time step Δt2 is derived. Then, in step S607, the linear electromagnetic field analysis unit 106 executes the electromagnetic field analysis by the linear unsteady finite element method using the differential magnetic permeability derived in this way.

Further, in the present embodiment, the linear electromagnetic field analysis unit 106 assumes that the correction current I ₊ of each phase flows from the current sources 521, 522, 523 to the stator coils 511, 512, 513, and is a linear unsteady finite element method. Perform electromagnetic field analysis by.
Further, in the present embodiment, the linear electromagnetic field analysis unit 106 sets the magnetic permeability of the element corresponding to the regions 202a to 202g to be sufficiently lower than the magnetic permeability of the element corresponding to the other region of the stator core, and is linear non-linear. Perform electromagnetic field analysis by the stationary finite element method.

Next, in step S608, the loss derivation unit 107 has the magnetic flux density B of each element at each time determined by the time interval of the time step Δt2 derived in step S603, and the time step Δt2 derived in step S607. The total magnetic flux density B of each element is derived for each phase based on the magnetic flux density B of each element at each time determined by the time interval. The magnetic flux density B of each element derived in step S603 is the magnetic flux density B of each element when the target exciting current I _I of each phase flows through the stator coil of each phase and the stator core is excited. The magnetic flux density B of each element derived in step S607 is the magnetic flux density B of each element when the correction current I ₊ of each phase flows through the stator coil of each phase and the stator core is excited. The total magnetic flux density B is the magnetic flux density B of each element at each time determined by the time interval of the time step Δt2 when the current obtained by combining the target exciting current I _I and the correction current I ₊ flows through the stator coils of each phase. be.

Further, the loss derivation unit 107 is derived from the eddy current density J _e of each element at each time determined by the time interval of the time step Δt2 derived in step S603 and the time interval of the time step Δt2 derived in step S607. Based on the eddy current density J _e of each element at each fixed time, the total eddy current density J _e of each element is derived for each phase. The eddy current density J _e of each element derived in step S603 is the target exciting current I _{I of each phase when the target exciting current I I of} each phase flows through the stator coil of each phase and the stator core is excited. .. The eddy current density J _e of each element derived in step S607 is the eddy current density J _e of each element when the correction current I ₊ of each phase flows through the stator coil of each phase and the stator core is excited. The total eddy current density J _e is the eddy current of each element at each time determined by the time interval of the time step Δt2 when the total current of the target exciting current I _I and the correction current I ₊ flows through the stator coil of each phase. The density J _e .

Next, in step S609, the loss derivation unit 107 of each element of the IPM motor (stator core) uses the total magnetic flux density B of each element and the total eddy current density J _e of each element derived in step S608. The hysteresis loss Wh and the eddy current loss We are derived. The loss derivation unit 107 derives the sum of the hysteresis loss Wh of each element of the IPM motor and each phase as the hysteresis loss of the IPM motor. Further, the loss derivation unit 107 derives the sum of the eddy current loss We of each element of the IPM motor and each phase as the eddy current loss of the IPM motor. Then, the loss derivation unit 107 derives the sum of the hysteresis loss and the eddy current loss of the IPM motor as the iron loss of the IPM motor.

Next, in step S610, the output unit 108 outputs the information regarding the loss of the IPM motor derived in step S609.
The process according to the flowchart of FIG. 6 ends when the process of step S610 is completed.

<< Calculation example >>
Next, a calculation example is shown. In this calculation example, the electromagnetic field analysis was performed using the D1 motor described in Non-Patent Document 3 as a model of the IPM motor. In this calculation example, the frequency of the modulated wave is 1 kHz, the amplitude of the target exciting current I _I is 20 A, the advance angle is 0 °, the carrier frequency is 20 kHz, and the DC voltage is 500 V. A field analysis was performed. The results are shown in Table 1.

In Table 1, the PWM analysis is one of the comparative examples, and the iron loss of the IPM motor when the inverter voltage V _INV is applied to the stator coils of each phase is measured by the electromagnetic field using the non-stationary unsteady finite element method. It is shown that it was derived by executing the analysis. In the PWM analysis, the magnetic flux density B and the eddy current density J _e were derived with high time resolution (each time determined by the time interval of the time step Δt2).

The invention example shows that the iron loss of the IPM motor was derived by the method described in this embodiment.
The current source analysis is one of the comparative examples, and the iron loss of the IPM motor when the target exciting current I _I flows through the stator coil of each phase is analyzed by the electromagnetic field analysis using the non-stationary unsteady finite element method. It shows that it was derived by doing. In the current source analysis, the magnetic flux density B and the eddy current density J _e were derived with low time resolution (each time determined by the time interval of the time step Δt1).

In Table 1, the iron loss and calculation time of the IPM motor derived by the methods of PWM analysis, invention example, and current source analysis are relative to each other when the iron loss and calculation time derived by PWM analysis are 100%. Value is shown.
FIG. 7 is a diagram showing a calculation example of a time-series waveform of the magnetic flux density. Note that FIG. 7 is a time-series waveform of the magnetic flux density in the same element. Further, in this calculation example, since the frequency of the modulated wave is 1 kHz, the electric angle (= θ) on the horizontal axis in FIG. 7 is θ (°) ÷ (360 (°) × 1 × 10 ³ (Hz)). By executing the calculation of, the time (seconds) with 0 as the reference time on the horizontal axis of FIG. 7 is converted.

In the PWM analysis, which is a comparative example, the iron loss of the IPM motor when the inverter voltage V _INV is applied to the stator coils of each phase is derived with high time resolution by the non-stationary unsteady electromagnetic field analysis. Therefore, the iron loss of the IPM motor can be derived with high accuracy, but the calculation time becomes long.

Further, in the current source analysis which is a comparative example, the fine stepwise time change of the magnetic flux density caused by the rise and fall of the inverter voltage V _INV at the time of switching the semiconductor element included in the PWM inverter is not taken into consideration. Therefore, unlike the time-series waveform of the magnetic flux density of the current source analysis shown in FIG. 7, a fine stepwise time change of the magnetic flux density is not expressed. As a result, in the current source analysis, as shown in Table 1, the iron loss of the IPM motor is significantly different from that derived by the PWM analysis.

On the other hand, in the time-series waveform of the magnetic flux density of the example of the invention shown in FIG. 7, a fine stepwise time change of the magnetic flux density is expressed, and the time-series waveform is close to the time-series waveform of the magnetic flux density of the PWM analysis. .. As a result, as shown in Table 1, in the example of the invention, the iron loss of the IPM motor can be made equivalent to that derived by the PWM analysis. Further, in the invention example, the calculation time can be significantly shortened as compared with the PWM analysis.

<< Summary >>
As described above, in the present embodiment, the electromagnetic field analyzer 100 calculates the correction current I ₊ based on the difference φ _INV − φ _I between the interlinkage magnetic flux φ _INV during excitation of the inverter and the interlinkage magnetic flux φ _I during excitation of the target. Derived. Then, the electromagnetic field analysis device 100 derives the magnetic flux density in the stator core when the correction current I ₊ flows through the stator coil by performing a linear electromagnetic field analysis based on Maxwell's equation. Therefore, it is necessary to flow the target exciting current I _I through the stator coil in order to compensate for the small stepwise change in the magnetic flux density that occurs during switching of the semiconductor element for the inverter with respect to the magnetic flux density in the stator core when the target exciting current I I flows through the stator coil. The current can be derived as the correction current I ₊ . Since the magnitude of the correction current I ₊ is small, the calculation accuracy does not decrease significantly even if the linear electromagnetic field analysis is performed. Therefore, it is possible to execute the electromagnetic field analysis in a short time in consideration of the time change of the magnetic flux density in a fine stepwise manner that occurs when the semiconductor element for the inverter is switched.

Further, in the present embodiment, the electromagnetic field analyzer 100 derives the interlinkage magnetic flux φ _INV at the time of inverter excitation based on the inverter voltage V _INV and the circuit equation (equation (5)) of the IPM motor. Therefore, it is possible to perform electromagnetic field analysis using various inverter-excited interlinkage magnetic fluxes φ _INV without measuring the inverter-excited interlinkage magnetic flux φ _INV .

Further, in the present embodiment, the electromagnetic field analysis device 100 derives the magnetic flux density in the stator core when the target exciting current I _I flows through the stator coil by performing a nonlinear electromagnetic field analysis based on Maxwell's equation. .. Then, the electromagnetic field analyzer 100 derives the target exciting voltage V _I based on the magnetic flux density in the stator core when the target exciting current I _I flows through the stator coil and the circuit equation of the IPM motor, and the target exciting voltage V The inverter voltage V _INV is derived based on _I. Therefore, it is possible to perform electromagnetic field analysis using various inverter voltages V _INV without measuring the inverter voltage V _INV actually output from the inverter power supply. Further, an inverter voltage _INV different from the inverter voltage V _INV actually output from the inverter power supply can be used, and the inverter voltage _INV required to obtain a motor having desired characteristics can be investigated. This can be useful, for example, in the development of an inverter power supply capable of outputting such an inverter voltage _INV .

Further, in the present embodiment, the electromagnetic field analysis device 100 makes the time resolution of the magnetic flux density derived in the linear electromagnetic field analysis higher than the time resolution of the magnetic flux density in the nonlinear electromagnetic field analysis. Then, the electromagnetic field analysis device 100 derives the magnetic flux density at each time corresponding to the time resolution of the magnetic flux density derived in the linear electromagnetic field analysis based on the magnetic flux density in the nonlinear electromagnetic field analysis. Further, the electromagnetic field analyzer 100 derives the target exciting voltage _VI , the inverter voltage V _INV , and the interlinkage magnetic flux φ _INV at each time corresponding to the time resolution of the magnetic flux density derived in the linear electromagnetic field analysis. .. In the example described in this embodiment, each time corresponding to the time resolution of the magnetic flux density derived in the linear electromagnetic field analysis is each time determined by the time interval of the time step Δt2. Therefore, in the linear electromagnetic field analysis, by increasing the time resolution, the magnetic flux density can be derived so as to follow the time change of the magnetic flux density in small steps generated at the time of switching of the semiconductor element for inverter. On the other hand, in non-stationary unsteady electromagnetic field analysis, the time series data of magnetic flux density changes relatively smoothly, so it is possible to shorten the calculation time while ensuring practical accuracy by lowering the time resolution. can.

Further, in the present embodiment, the electromagnetic field analyzer 100 maximizes the magnetic flux density in the stator core in a state where the magnetic permeability of a part of the region 202a to 202g through which the magnetic flux passes is lower than the magnetic permeability of the other region. Derived by performing a linear electromagnetic field analysis based on Well's equation. Then, the electromagnetic field analyzer 100 derives the correction current I ₊ by using the magnetic permeability of a part of the region 202a to 202g through which the magnetic flux passes. Therefore, the relationship between the exciting current and the magnetic flux can be linearly approximated without being affected by the spatial distribution of the differential magnetic permeability. Therefore, the calculation time in the linear electromagnetic field analysis unit 106 can be shortened. Since the reluctance is the reciprocal of the magnetic permeability, using the magnetic permeability is equivalent to using the magnetic resistance.

Further, in the present embodiment, in the electromagnetic field analysis device 100, the current sources 521, 522, 523 of the other phases and the unconnected current sources 521, 522, 523 are provided with respect to the stator coils 511, 512, and 513 of each phase. , Perform linear electromagnetic field analysis assuming that it is connected as a current source to output the correction current I ₊ . Therefore, the configuration of the power supply circuit in the linear electromagnetic field analysis can be simplified. Therefore, the calculation time in the linear electromagnetic field analysis unit 106 can be shortened.

Further, in the present embodiment, the electromagnetic field analysis device 100 derives various losses of the IPM motor based on the result of the linear electromagnetic field analysis. Therefore, the loss of the IPM motor can be derived in consideration of the time change of the magnetic flux density in a fine stepwise manner that occurs when the semiconductor element for the inverter is switched.

<< Modification example >>
In this embodiment, the case where the magnetic resistance R _m is derived by the equation (8) is illustrated. However, the method for deriving the magnetic resistance R _m is not limited to such a method. For example, the same electromagnetic field analysis as the electromagnetic field analysis using the linear unsteady finite element method executed by the linear electromagnetic field analysis unit 106 is executed in only one step, and the magnetic flux passing through the stator core is derived at one time. In this case, the exciting current does not have to be the correction current I ₊ , and may be a current of any value. Further, in this case, the magnetic permeability (= 1 / ν _high ) in the low magnetic permeability element is used as the magnetic permeability. Then, the magnetic resistance R _m is derived based on the magnetic flux derived in this way, the exciting current used when the magnetic flux is derived, and the number of turns of the stator coil.

In the present embodiment, the case where the regions 202a to 202 g along the circumferential direction, which are the regions near the center in the radial direction of each tooth portion, are used as the low magnetic permeability element is exemplified. However, the magnetic permeability of a part of the region through which the magnetic flux of the stator core passes is approximated so that the correction current I ₊ and the magnetic flux flowing through the stator core when the correction current I ₊ flows through the stator coil are approximately proportional to each other. As long as the magnetic permeability is lower than the magnetic permeability of the other regions of the stator core, the region to be the low magnetic permeability element is not limited to the regions 202a to 202g. For example, a region of the yoke portion near the center in the circumferential direction of each slot and along the radial direction may be a low magnetic permeability element.

In the present embodiment, the target exciting voltage V _I is derived based on the magnetic flux density in the stator core when the target exciting current I _I flows through the stator coil, and the inverter voltage V _IN V is derived based on the target exciting voltage V _I. Was exemplified. However, it is not necessary to derive the inverter voltage V _INV in this way. For example, the time-series waveform of the inverter voltage actually output from the PWM inverter is measured, data showing the time-series waveform of the measured inverter voltage is input to the electromagnetic field analyzer 100, and the data is used as the inverter voltage V _INV . You may. In this case, for example, the data of the modulated wave used in the PWM inverter is input to the electromagnetic field analyzer 100, and the data is used as the data of the target exciting voltage _VI . Further, when the modulated wave used in the PWM inverter is applied to the stator coil, the magnetic flux flowing through the stator coil is measured, the measured magnetic flux data is input to the electromagnetic field analyzer 100, and the data is input to the target excitation time chaining. Used as magnetic flux φ _I. Further, the differential magnetic permeability used in the linear electromagnetic field analysis is determined based on, for example, the magnetization characteristics (BH curve) of the electromagnetic steel sheet constituting the stator core.

In this embodiment, a case where the interlinkage magnetic flux φ _INV at the time of inverter excitation is derived based on the inverter voltage V _INV and the circuit equation of the IPM motor is illustrated. However, it is not necessary to derive the interlinkage magnetic flux φ _INV when the inverter is excited in this way. For example, the magnetic flux interlinking the stator coil when the inverter voltage is actually applied from the PWM inverter to the stator coil is measured, the measured magnetic flux data is input to the electromagnetic field analyzer 100, and the input data is input when the inverter is excited. It may be used as the interlinkage magnetic flux φ _INV .

In the present embodiment, as a loss in the stator core, a case where a loss in the stator core is derived when a current obtained by combining the target exciting current I _I and the correction current I ₊ flows through the stator coil is illustrated. Further, the case where the hysteresis loss, the eddy current loss, and the iron loss are derived as the loss in the stator core has been exemplified. However, it is not always necessary to do this. For example, it is not necessary to derive the iron loss. Further, only one of the hysteresis loss and the eddy current loss may be derived. Further, at least one of hysteresis loss, eddy current loss, and iron loss may be derived as the loss in the stator core when only the correction current I ₊ flows through the stator coil. Further, for example, when only the magnetic flux density is targeted for evaluation and the loss is not targeted for evaluation, it is not necessary to derive the loss in the stator core.

In this embodiment, the case where the inverter power supply is a PWM inverter is illustrated. However, the inverter power supply is not limited to the PWM inverter. For example, a PAM (pulse Amplitude Modulation) inverter may be used as an inverter power source.

The embodiment of the present invention described above can be realized by executing a program by a computer. Further, a computer-readable recording medium on 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 non-volatile memory card, a ROM, or the like can be used. Further, the embodiment of the present invention may be realized by a PLC (Programmable Logic Controller) or by dedicated hardware such as an ASIC (Application Specific Integrated Circuit).
In addition, the embodiments of the present invention described above are merely examples of embodiment of the present invention, and the technical scope of the present invention should not be construed in a limited manner by these. It is a thing. That is, the present invention can be implemented in various forms without departing from the technical idea or its main features.

100 Electromagnetic field analysis device 101 Non-linear electromagnetic field analysis unit 102 Target exciting voltage derivation unit 103 Inverter voltage derivation unit 104 Inverter excitation time chained magnetic flux derivation unit 105 Corrected current derivation unit 106 Linear electromagnetic field analysis unit 107 Loss derivation unit 108 Output unit 201 Rotor 202 Stator 202a-202g Low magnetic permeability region 310 Positive phase modulation wave 320 Carrier 330 Negative phase modulation wave 340 Positive phase notch wave 350 Negative phase notch wave 360 Inverter voltage 410 Time series of magnetic flux density when excited by target exciting current Waveform 420 Time-series waveform of magnetic flux density when excited by inverter voltage 511 to 513 Stator coil 521 to 523 Current source 530 Stator core

Claims (11)

It is an electromagnetic field analysis device that analyzes the electromagnetic field in a motor driven based on the inverter voltage output from the inverter power supply.
When the inverter voltage is applied to the stator coil of the motor, the magnetic flux interlinking the stator coil is the magnetic flux during the inverter excitation, and when the target exciting current flows through the stator coil, the stator coil is chained. A correction current derivation means that derives a correction current based on the difference between the crossing magnetic flux and the interlinkage magnetic flux at the time of target excitation.
It has a linear electromagnetic field analysis means for deriving the magnetic flux density in the stator core of the motor when the correction current flows through the stator coil by performing a linear electromagnetic field analysis based on Maxwell's equation.
The correction current flows through the stator coil in order to compensate for the time change of the magnetic flux density that occurs when the switching element of the inverter power supply is switched with respect to the magnetic flux density in the stator core when the target exciting current flows through the stator coil. Electromagnetic field analyzer, which is the required current. The electromagnetic field analysis device according to claim 1, further comprising an inverter excitation time-linkage magnetic flux deriving means for deriving the inverter excitation time-chain magnetic flux based on the inverter voltage and the motor circuit equation. A non-linear electromagnetic field analysis means for deriving the magnetic flux density in the stator core when the target exciting current flows through the stator coil by performing a non-linear electromagnetic field analysis based on Maxwell's equation.
A target exciting voltage deriving means for deriving a target exciting voltage, which is an exciting voltage corresponding to the target exciting current, based on the magnetic flux density derived by the nonlinear electromagnetic field analysis means and the circuit equation of the motor.
Further having an inverter voltage deriving means for deriving the inverter voltage based on the target exciting voltage derived by the target exciting voltage deriving means.
The inverter-excited interlinkage magnetic flux derivation means derives the inverter-excitation interlinkage magnetic flux based on the inverter voltage derived by the inverter voltage derivation means and the circuit equation of the motor.
The electromagnetic field analysis device according to claim 2, wherein the linear electromagnetic field analysis means executes the linear electromagnetic field analysis using the magnetization characteristics based on the magnetic flux density derived by the nonlinear electromagnetic field analysis means. The time resolution of the magnetic flux density derived by the linear electromagnetic field analysis means is higher than the time resolution of the magnetic flux density derived by the nonlinear electromagnetic field analysis means.
Based on the magnetic flux density derived by the nonlinear electromagnetic field analysis means, the magnetic flux density at each time corresponding to the time resolution of the magnetic flux density derived by the linear electromagnetic field analysis means is derived.
The target exciting voltage at each time corresponding to the time resolution of the magnetic flux density derived by the linear electromagnetic field analysis means is derived.
The inverter voltage at each time corresponding to the time resolution of the magnetic flux density derived by the linear electromagnetic field analysis means is derived.
The electromagnetic field analysis device according to claim 3, wherein the interlinkage magnetic flux at the time of excitation of the inverter is derived at each time corresponding to the time resolution of the magnetic flux density derived by the linear electromagnetic field analysis means. The linear electromagnetic field analysis means measures the magnetic flux density in the stator core in a state where the magnetic permeability in a part of the region through which the magnetic flux passes is lower than the magnetic permeability in the other region, based on Maxwell's equation. Derived by performing an analysis,
The electromagnetic field analysis device according to any one of claims 1 to 4, wherein the corrected current deriving means derives the corrected current by using the magnetic permeability of a part of the region through which the magnetic flux passes. In the linear electromagnetic field analysis means, a current source connected to the stator coil of another phase and an unconnected current source are connected to the stator coil of each phase as a current source to output the correction current. The electromagnetic field analysis apparatus according to any one of claims 1 to 5, which performs the linear electromagnetic field analysis as if it were. The electromagnetic field analysis apparatus according to any one of claims 1 to 6, further comprising a loss deriving means for deriving a loss in the stator core based on the magnetic flux density in the stator core derived by the linear electromagnetic field analysis means. .. The electromagnetic field analysis device according to claim 7, wherein the loss deriving means derives a loss in the stator core when a current obtained by combining the target exciting current and the correction current flows through the stator coil. The electromagnetic field analysis apparatus according to claim 7, wherein the loss is any one of a vortex current loss, a hysteresis loss, and a vortex current loss and a hysteresis loss. It is an electromagnetic field analysis method that analyzes the electromagnetic field in a motor driven based on the inverter voltage output from the inverter power supply.
When the inverter voltage is applied to the stator coil of the motor, the magnetic flux interlinking the stator coil is the magnetic flux during the inverter excitation, and when the target exciting current flows through the stator coil, the stator coil is chained. A correction current derivation process that derives a correction current based on the difference between the crossing magnetic flux and the interlinkage magnetic flux at the time of target excitation,
It has a linear electromagnetic field analysis step of deriving the magnetic flux density in the stator core of the motor when the correction current flows through the stator coil by performing a linear electromagnetic field analysis based on Maxwell's equation.
The correction current flows through the stator coil in order to compensate for the time change of the magnetic flux density that occurs when the switching element of the inverter power supply is switched with respect to the magnetic flux density in the stator core when the target exciting current flows through the stator coil. Electromagnetic field analysis method, which is the required current. A program for operating a computer as each means of the electromagnetic field analyzer according to any one of claims 1 to 9.

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