JP7198334B2 - Power supply voltage waveform calculation method, circuit coupled magnetic field analysis method, program, and recording medium recording the program - Google Patents

Description

The present invention relates to a power supply voltage waveform calculation method, a circuit coupled magnetic field analysis method, a program for executing these methods, and a recording medium recording the program.

Conventionally, there are magnets and coil currents as magnetic field generating sources for driving electromagnetic devices such as motors. In order to cause an electromagnetic device to perform a predetermined operation, it is desirable to apply a coil current waveform as designed. Normally, in a circuit coupled magnetic field analysis that combines an electromagnetic device and a power supply circuit that drives it, the power supply voltage waveform is input, and the amount related to the magnetic vector potential that describes the magnetic field and the coil current are the unknown variables. executed.

In this case, the amplitude and phase of the power supply voltage waveform are adjusted to obtain a desired coil current waveform. However, this requires several rounds of trial and error. Moreover, since the coil current waveform is unknown even for one calculation, it takes a long calculation time to obtain a steady coil current waveform. Usually, 100 to several 100 steps of transient analysis are required to arrive at a steady-state solution, so three-dimensional analysis may require several days of calculation time.

In order to assist this, the coil induced voltage waveform is obtained from the backward difference of the average magnetic vector potential from the magnetic field analysis in which the desired coil current waveform is input, and the coil line voltage waveform is calculated from the winding resistance and the coil current. There is (see Non-Patent Document 1).

Norio Takahashi, Finite Element Method for Magnetic Engineering, Asakura Shoten (2013) pp. 251-253

However, in the conventional method described in Non-Patent Document 1, the calculation of the coil line-to-line voltage waveform is limited to the input of the desired coil current waveform, and the power supply voltage waveform is not calculated.
In addition, as a method of hastening the convergence to a stationary field, the TP-EEC (Time Periodic-Explicit Error Correction) method or the simplified TP-EEC method are known. Since a transient analysis with a certain amount of time steps is required to obtain

The object of the present invention is to solve the first problem (the problem that it is necessary to perform circuit coupled magnetic field analysis by inputting a power supply voltage waveform several times by trial and error so as to obtain a desired coil current waveform). The object of the present invention is to provide a method for calculating a power supply voltage waveform. In order to solve the second problem (it takes a certain amount of time to obtain a stationary solution of the coil current waveform after the final determination of the power supply voltage waveform), a circuit coupled magnetic field analysis method, a program and a program related to both the above methods, To provide a recording medium recording a program.

In order to solve the above problems, for example, the configurations described in the claims are adopted.
The present invention includes a plurality of means for solving the above problems. To give one example, the power supply voltage waveform calculation method of the present invention comprises the following steps (a) to (d).
(a) causing a computer to read input data consisting of discretized data for numerically solving differential equations and control data including coil current waveform data for controlling the analysis process;
(b) using the input data to perform a transient magnetic field analysis with a computer using the coil current waveform data as a forced current;
(c) A step of calculating a power supply voltage waveform from the coil induced voltage waveform obtained in the transient magnetic field analysis step and the coil current waveform data used as input data using a circuit equation in the power supply circuit.

In addition to the above steps (a) to (c), the circuit coupling magnetic field analysis method of the present invention includes the following (d) to (f).
(d) computing a fundamental sinusoidal voltage component from the power supply voltage waveform;
(e) inputting the power supply voltage fundamental sinusoidal voltage component as a power supply voltage waveform into a calculator;
(f) A step of performing a circuit coupling magnetic field analysis with a computer using the initial value of the coil current waveform input as control data as the initial value of the coil current, which is an unknown quantity.

According to the power supply voltage waveform calculation method of the present invention, it is possible to directly calculate the power supply voltage waveform for realizing a desired coil current waveform. In addition, since steps (a) to (d) described above are always performed in the motor design process, when the power supply voltage waveform is determined, substantially only steps (e) to (g) described above are performed. A final coil current waveform can be obtained. Therefore, according to the circuit coupled magnetic field analysis method of the present invention, there is an effect that the analysis time for the circuit coupled magnetic field analysis can be shortened. As a result, it is possible to reduce the time and cost of design development for designing and developing electrical equipment such as motors.
Problems, configurations, and effects other than those described above will be clarified by the following description of exemplary embodiments.

4 is a flow chart for explaining the first embodiment of the present invention; 9 is a flow chart for explaining a second embodiment of the present invention; 9 is a flow chart for explaining a third embodiment of the present invention; 1 is a schematic block diagram of an apparatus for implementing the present invention; FIG. FIG. 14 is a flow chart for explaining a fourth embodiment of the present invention; FIG. FIG. 11 is a flow chart for explaining a fifth embodiment of the present invention; FIG. FIG. 4 is a diagram showing the relationship between the coils of the synchronous motor and the power supply, which are the objects of analysis in the first to fifth embodiments of the present invention; FIG. 4 is a waveform diagram showing a procedure for stabilizing a coil current waveform from a power supply waveform in a conventional method; FIG. 4 is a waveform diagram showing a procedure for obtaining a coil current waveform stabilized with a small number of corrections from circuit coupled magnetic field analysis using the method of the present invention; FIG. 11 is a waveform diagram showing the difference between a coil current waveform obtained from circuit coupled magnetic field analysis with one correction and a coil current waveform without correction in the fifth embodiment.

First, before describing Embodiments 1 to 5 of the present invention shown in FIGS. 1 to 3 and FIGS. , with reference to FIGS.

<Explanation of conventional circuit coupling magnetic field analysis method>
FIG. 7 shows a magnetic field analysis area 100 including the machine motor, a motor coil 101, and a power supply circuit 200 connected to the motor coil 101. FIG.

As shown in FIG. 7, the motor coils 101 (U, V, W) in the magnetic field analysis area 100 including the synchronous motor are connected to the three-phase AC power supply 200 (UV, VW, WU) through the resistance R and the inductance L, respectively. It is connected to the.
The first purpose is to quickly obtain a power supply voltage waveform for realizing a coil current waveform that is appropriate for design in the motor coil 101 .

The waveform of the coil current flowing through the motor coil 101 is determined from the viewpoint of optimizing the operating characteristics of the motor. . Therefore, in the conventional method, the user temporarily sets the power supply voltage waveform of the three-phase AC and obtains the steady coil current waveform at a high speed. used the method.

FIG. 8 is a diagram for explaining a conventional method for obtaining a coil current waveform using this three-phase AC TP-EEC method. As shown in FIG. 8A, this conventional technique is based on the voltage waveform of a three-phase AC power supply. FIG. 8B shows the coil current waveform when the voltage waveform of the three-phase AC power supply shown in FIG. 8A is applied to the power supply 200 and no correction is made by the three-phase AC simple TP-EEC method.
On the other hand, in FIG. 8C, in the transient magnetic field analysis of the circuit coupling based on the voltage waveform of the three-phase AC power supply, three times at a time interval equivalent to an electrical angle of 60° by the three-phase AC simple TP-EEC method It shows the coil current waveform after correction.

In FIG. 8B, the coil current waveform of the motor coil 101 has not reached a steady state even after 25 ms because correction by the three-phase AC simple TP-EEC method is not performed. However, as shown in FIG. 8C, when correction is performed three times by the three-phase AC simplified TP-EEC method, the coil current waveform reaches a substantially steady state after 5 ms. There are three places where the coil current waveform in FIG. 8C changes discontinuously within 5 ms. Yes.

<Description of circuit coupling magnetic field analysis method of the present invention>
Next, with reference to FIG. 9, a technique for obtaining a stationary coil current waveform at high speed using the circuit coupled magnetic field analysis technique of the present invention will be described. As shown in FIG. 9A, the present invention differs from the conventional method in that it starts from a three-phase coil current basic sinusoidal waveform determined by design specifications. As will be described later, when the power supply voltage waveform is used as a reference, the coil current waveform becomes a slightly distorted waveform from this basic sinusoidal waveform. The technique of the present invention directly determines the source voltage waveform as shown in FIG. 9B from the original coil current waveform. As can be seen from FIG. 9B, at this time, the power supply voltage waveform is not a clean sine wave, and contains harmonic components due to the nonlinear magnetic properties of the magnetic material that constitutes the motor.

Next, the harmonic components are removed from the power supply voltage waveform of FIG. 9B to extract the fundamental sinusoidal voltage component. The results are shown in FIG. 9C.
Finally, circuit coupled magnetic field analysis is performed using the fundamental sinusoidal voltage component of the power supply voltage waveform shown in FIG. 9C. Since the power supply voltage waveforms shown in FIGS. 9B and 9C are close to each other, the coil current waveform obtained by this circuit coupled magnetic field analysis is close to the original coil current waveform shown in FIG. 9A. Therefore, in this circuit coupled magnetic field analysis, by using the initial value of the original coil current waveform shown in FIG. 9A as the initial value of the coil current of the motor coil 101, the steady waveform can form a waveform close to If you want to obtain a steady -state field with higher accuracy , you can further correct the initial field as shown in FIG . A steady coil current waveform is obtained from several steps (from the second step in FIG. 9D).

Compared to the conventional method shown in FIG. 8, the circuit coupled magnetic field analysis according to the present invention shown in FIG. 9 shows that the coil current is in a steady state instantaneously. That is, compared with the conventional method of FIG. 8, the method of the present invention significantly reduces the number of time steps for transient analysis until the steady state is reached.

<Explanation of circuit coupling magnetic field analysis based on circuit equation>
The outline of the principle of the circuit coupling magnetic field analysis method of the present invention has been described above, but the present invention is characterized in that the initial value of the coil current waveform is first inputted to perform a normal magnetic field analysis. A circuit system consists of a plurality of basic loops according to circuit theory. For example, in the example of FIG. 7, the following three basic loops are formed.
(a) Basic loop of motor coil U→resistor R→inductance L→power supply WU→inductance L→resistor R→motor coil W;
(b) A basic loop of motor coil U→resistor R→inductance L→power source UV→inductance L→resistor R→motor coil V;
(c) Basic loop of motor coil V→resistor R→inductance L→power source VW→inductance L→resistor R→motor coil W;

Therefore, the current flowing through the circuit is formed from a plurality of basic loop currents I _k ^ioop (k = 1 to n, where n = 3 here), and the power supply voltage can also be expressed by a plurality of basic loop voltages V _k ^loop . can. The basic loop voltage V _k ^loop is obtained by the following equation using the basic loop current I _k ^loop .

Here, the first term on the right side of equation (1) is a plurality of coil induced voltage terms in the basic loop k, and the second term is a voltage drop due to a plurality of resistances in the basic loop k. The third term is the amount of voltage drop due to multiple inductances in the basic loop k. In the case of circuit coupled magnetic field analysis of a three-phase AC synchronous motor as shown in FIG. 7, k is 1-3.

Also, a _j in equation (1) is an unknown variable related to the magnetic vector potential assigned to side j of the finite element region. R _k and L _k in equation (2) are the k-th resistance and inductance on the circuit, and T _ik is the current I _i flowing through the i-th circuit element and the k-th basic loop current I _k ^loop . matrix, where the matrix elements have values of '+1', '-1', or '0'.

Also, N _j in Equation (3) is a side element vector basis function for side j in the finite element domain, and n _p is a unit vector representing the current direction of the p-th coil. A current I _i flowing through the i-th circuit element can be expressed by Equation (4).

The basic loop voltage V _k ^loop is the power supply voltage itself if there is only one power supply in the basic loop k, and if there are a plurality of power supplies, it becomes the total amount considering the direction.
With the circuit configuration shown in FIG. 7, one power supply in the power supply 200 (WU, VW, UV) corresponds to the power supply of each basic loop, so the power supply voltage is calculated directly from the basic loop voltage. be.

However, in the Y-connection of the three-phase AC power supply system, if there is no neutral point connection line, two power supplies exist on the basic loop. However, in this case, if the total voltage of the three-phase AC power supply can be regarded as zero, the voltage of each power supply can be calculated from the basic loop voltage using this conditional expression.

Note that the equation (1) is an equation using the basic loop current on the circuit, but the coupled magnetic field analysis of the present invention is not limited to this equation, and the potential at each point on the circuit is used. It is also possible to use a circuit equation with The point of the present invention is to solve the circuit equation and calculate the power supply voltage waveform from the coil current waveform, and the type of circuit equation to be used is not limited.

Further, the amplitude and initial phase of the fundamental waveform component are extracted from the power supply voltage waveform obtained by the above formula, and normal magnetic field analysis is performed using these as the main components of the input voltage waveform for circuit coupled magnetic field analysis. At this time, the initial value of the coil current waveform described above is used as the initial value of the magnetic field analysis.

As described with reference to FIG. 9, in this case, the obtained coil current waveform becomes a waveform close to the original coil current waveform. Therefore, since the circuit coupled magnetic field analysis starts from the initial value of the coil current waveform that is close to the steady-state solution, the convergence to the steady-state solution becomes faster, and the analysis time required to reach the steady-state solution can be greatly shortened. Become.

Furthermore, after performing transient analysis for at least two time steps, one correction by the three-phase AC ETF method may be performed. Here, the time step means one increment in the time axis division in the transient analysis.

Further, the program relating to the power supply voltage waveform calculation method and the program relating to circuit coupled magnetic field analysis according to the present invention are characterized by coding the series of processes described above.

Embodiments of the present invention will be described in detail below with reference to FIGS. 1 to 6. FIG.
<Description of First Embodiment>
FIG. 1 is a flow chart for explaining the analysis process of the first embodiment of the present invention.
As shown in FIG. 1, first, it consists of discretized data 11 (mesh data) for numerically solving differential equations and control data 12 (including coil current waveform data) for controlling the analysis process. The input data file 10 is read into the computer (steps S13 and S14).

Here, the discretized data 11 (mesh data) is data obtained by decomposing a structure (here, the synchronous motor 100 in the magnetic field analysis area of FIG. 7) into a plurality of finite elements (mesh). In general, equations in an analytical space cannot be solved continuously, so a method called the finite element method (FEM) is used to solve the equations by dividing them into meshes. In other words, the finite element method is a method of performing numerical analysis by dividing the analysis space, and the finer the mesh, the higher the precision of the analysis. Control data 12 is input data relating to analysis conditions. This control data includes initial value data of the coil current waveform.

These input data are supplied to the analysis execution module 20 . The analysis executing module 20 uses these input data to execute a transient magnetic field analysis with the coil current waveform as a forced current (step S21).

Next, by substituting the value of the unknown variable a _j obtained at each time step into the equation (1), a process of obtaining all basic loop voltage waveforms is executed (step S22). Then, the power supply voltage waveform is calculated from the obtained basic loop voltage waveform (step S23). After that, the obtained power supply voltage waveform is stored in the storage device 3 (see FIG. 4) (step S31), and this power supply voltage waveform is displayed on the display device 2 (see FIG. 4) (step S32).

According to the first embodiment described above, the power supply voltage waveform can be directly calculated from the initial value of the coil current waveform input as control data, and the power supply voltage waveform can be displayed on the display device 2. can directly grasp the power supply voltage waveform.

<Description of Second Embodiment>
A second embodiment of the present invention will now be described with reference to FIG. In FIG. 2, the processing up to step S23, which is the process of calculating the power supply voltage waveform, is the same as in the first embodiment, so the description is omitted.

In the second embodiment, the basic sinusoidal voltage component is calculated from the power supply voltage waveform obtained in step S23 (step S24). The fundamental sinusoidal voltage component can be easily calculated by removing harmonics from the power supply voltage waveform obtained in step S23. The power supply voltage waveform obtained in step S23 and the fundamental sinusoidal voltage component obtained in step S24 are stored in the storage device 3 (step S31) and displayed on the display device 2 (step S32).

According to the second embodiment of the present invention, the basic sine wave voltage component is calculated from the power supply voltage waveform calculated from the initially input coil current waveform, and the basic sine wave voltage component is displayed on the display device 2 together with the power supply voltage waveform. Therefore, the user can directly grasp both the power supply voltage waveform and the fundamental sine wave voltage component.

<Description of Third Embodiment>
A third exemplary embodiment of the present invention will now be described with reference to the analysis process of FIG. This third embodiment is the same as the first or second embodiment up to step S23 for calculating the power supply voltage waveform, so the description thereof will be omitted.

In the third embodiment, a pulse width modulation (PWM) voltage waveform is calculated from the power supply voltage waveform obtained in step S23 (step S25). Then, the power supply voltage waveform and PWM voltage waveform obtained in steps S23 and S25 are stored in the storage device 3 (step S31), and the power supply voltage waveform and PWM voltage waveform are displayed on the display device 2 (step S32).

In the third embodiment, instead of the basic sine wave voltage waveform of the power supply voltage waveform, the PWM voltage waveform is used for the subsequent analysis. can be made. By using a PWM voltage waveform, switching control can be performed by repeatedly turning on and off, so although some noise is generated, it is easier to control the motor rotation speed than with a basic sine wave voltage drive with a fixed frequency. There is an advantage.

FIG. 4 shows an example of an analysis system that implements the first to third embodiments of the present invention.
As shown in FIG. 4, the analysis system of the first to third embodiments of the present invention comprises a computer 1, a display device 2, a storage device 3, and an input device 4. FIG.

In FIG. 4, the storage device 3 is shown outside the computer 1 for clarity, but it may be installed inside the computer 1 as well. The computer 1 stores a program based on at least one of the analysis processes of the first to third embodiments described above.

The input device 4 is, for example, a keyboard or a mouse, and input data including mesh data of the magnetic field analysis region and control data required for other operations are input from the input device 4 . When the input data is input, the computer 1 reads the input data and performs arithmetic processing related to the mesh data according to the stored program. Then, the processing result is displayed on the display device 2, or the processing result is stored in the storage device 3 as a data file. It should be noted that not all of the obtained processing results, but some of them may be displayed or stored.

<Description of Fourth Embodiment>
A fourth example embodiment of the present invention will now be described with reference to the analysis process shown in FIG. As shown in FIG. 5, the process up to step S24 for calculating the basic sine wave voltage component from the power supply voltage waveform is the same as in the second embodiment, so the description thereof will be omitted.

The basic sinusoidal voltage component of the power supply voltage waveform obtained in step S24 is input to the calculator 1 (FIG. 4) as a power supply voltage waveform (step S41). Calculator 1 executes the circuit coupling magnetic field analysis using the initial value of the coil current waveform input as control data as the initial value of the coil current (unknown variable) to be obtained (step S42).
Then, the motor characteristic data such as the coil current waveform and the torque waveform obtained in step S42 are stored in the storage device 3 (step S31). The motor characteristic data such as the coil current waveform and torque waveform are displayed on the display device 2 (step S32).

Here, since the fundamental sinusoidal voltage component of the power supply voltage waveform obtained in step S24 generally has a waveform close to the power supply voltage waveform, the coil current waveform obtained by circuit coupled magnetic field analysis is also used in step S14. It has a waveform close to the initial value of the coil current input to the control data 12 to be supplied.

For this reason, according to the fourth embodiment of the present invention, in step S42, the coil current, which is an unknown variable, can be started from an approximate initial value of the coil current to perform the circuit coupled magnetic field analysis. A quasi-stationary solution can be obtained much faster than the conventional method.

<Description of Fifth Embodiment>
Next, a fifth embodiment of the present invention will be described with reference to FIG.
The fifth embodiment is the same as the fourth embodiment up to the process 41 for inputting the basic sinusoidal voltage component of the power supply voltage waveform as the power supply voltage waveform, so the explanation thereof will be omitted.

As described above, in step S42, the initial value of the coil current waveform included in the control data is set to the initial value of the coil current, which is the unknown variable to be obtained, and the circuit coupling magnetic field analysis is executed. In step S42, normal circuit coupled magnetic field analysis is performed in time step 1 and time step 2. FIG. At the end of time step 2 in this circuit coupled magnetic field analysis, the three-phase component (typically three-phase coil interlinkage magnetic flux) whose time differential term is involved in the analysis is corrected by the three-phase AC ETF method described later. (step S43).

FIG. 10 is a diagram showing analysis results of the fifth embodiment. FIG. 10A is an example in which correction is not performed in step S43 of FIG. 6, and FIG. 10B is an example in which correction is performed once by the three-phase AC ETF method after the analysis of the second time step is completed in step S43. be.
As shown in the left diagram of FIG. 10A, when the initial value of the original coil current waveform is used, the starting value is originally close to the stationary solution. is obtained early.

The diagram on the right side of FIG. 10 is an enlarged diagram showing the vicinity of the peak of the waveform diagram on the left side of FIG. As can be seen from the diagram on the right side of FIG. 10A, the amplitude error of the three-phase coil current is ±1.6% without the correction in step S43. On the other hand, as shown in the diagram on the right side of FIG. 10B, when one correction is performed by the three-phase AC ETF method, the amplitude error of the coil current becomes ±0.04%, and a steady solution with higher accuracy is obtained. I know it can be done.

<Explanation of three-phase AC ETF method>
This three-phase AC ETF method is a method already disclosed in Japanese Unexamined Patent Application Publication No. 2014-142701 "Method for analyzing time-period nonlinear field and analysis program for time-period nonlinear field". The correction shown is implemented.

Here, the symbols U, V, and W are quantities that mean the three-phase components to be corrected, and U _new , V _new , and W _new are the values of U, V, and W after correction. dU, dV, and dW are the amounts of variation of U, V, and W from time step 1 to time step 2, respectively. Also, dθ is the amount obtained by converting the time step width into an electrical angle. Although α may be any value, a value of 1/2 is normally used.

So far, the first to fifth embodiments of the present invention have been described in order. The examples described here are merely embodiments, and the present invention is not limited to these. The present invention naturally includes other applications and modifications without departing from the scope of the claims.

1 computer, 2 display device, 3 storage medium, 4 input device, 10 input data file, 11 discretized data, 12 control data, 20 analysis process, 100 magnetic field analysis area including synchronous motor , 101... Motor coil, 200... Power supply

Claims (11)

causing a computer to read input data consisting of discretized data for numerically solving a differential equation and control data including coil current waveform data for controlling the analysis process;
using the input data to perform a transient magnetic field analysis with the computer using the coil current waveform data as a forced current;
A step of calculating a power supply voltage waveform from the coil induced voltage waveform obtained in the step of performing the transient magnetic field analysis and the coil current waveform data used as input data by the calculator, using a circuit equation in the power supply circuit;
Power supply voltage waveform calculation method including. 2. The step of calculating the power supply voltage waveform from the coil current waveform data by the calculator includes the step of calculating the power supply voltage waveform from the coil current waveform using a circuit equation using the potential of each point on the circuit. The described power supply voltage waveform calculation method. Furthermore, a step of storing the power supply voltage waveform, which is the analysis result calculated by the computer, in a storage device;
a step of displaying the analysis result on a display device by the computer;
The power supply voltage waveform calculation method according to claim 1 or 2, comprising: 3. The power supply voltage waveform calculation method according to claim 1, further comprising a step of calculating a power supply voltage basic sine wave voltage component or a PWM voltage waveform from the power supply voltage waveform by the calculator. causing a computer to read input data consisting of discretized data for numerically solving a differential equation and control data including coil current waveform data for controlling the analysis process;
using the input data to perform a transient magnetic field analysis with the computer using the coil current waveform data as a forced current;
A step of calculating a power supply voltage waveform from the coil induced voltage waveform obtained in the step of performing the transient magnetic field analysis and the coil current waveform data used as input data by the calculator, using a circuit equation in the power supply circuit;
a step of calculating a power supply voltage fundamental sinusoidal voltage component from the power supply voltage waveform by the calculator;
inputting the power supply voltage fundamental sinusoidal voltage component as a power supply voltage waveform into the calculator;
a step of performing a circuit coupled magnetic field analysis with the computer using the initial value of the coil current waveform input as the control data as the initial value of the coil current, which is an unknown variable;
A circuit coupled magnetic field analysis method including 6. The step of calculating the power supply voltage waveform from the coil current waveform data by the calculator includes the step of calculating the power supply voltage waveform from the coil current waveform using a circuit equation using the potential of each point on the circuit. The circuit coupled magnetic field analysis method described. Furthermore, after performing a transient analysis for at least two time steps with the computer, a step of performing correction once by the three-phase AC ETF method,
7. The circuit coupled magnetic field analysis method according to claim 5 or 6. a procedure for reading input data into a computer, which consists of discretized data for numerically solving a differential equation and control data for controlling the analysis process;
A procedure for performing a transient magnetic field analysis with the computer using the input data with the coil current waveform as a forced current;
Using circuit equations in a power supply circuit, a coil induced voltage waveform obtained in the procedure for performing the transient magnetic field analysis, and a procedure for calculating the power supply voltage waveform by the computer from the coil current waveform data used as input data;
is executed by the computer. 9. The step of calculating the power supply voltage waveform from the coil current waveform data by the computer includes the step of calculating the power supply voltage waveform from the coil current waveform using a circuit equation using the potential of each point on the circuit. program as described. Further, a step of calculating a power supply voltage fundamental sine wave voltage component from the power supply voltage waveform by the calculator;
a step of inputting the power supply voltage fundamental sinusoidal voltage component as a power supply voltage waveform using the calculator;
A step of performing circuit coupled magnetic field analysis by the computer using the initial value of the coil current waveform input as the control data as the initial value of the coil current, which is an unknown variable;
10. The program according to claim 8 or 9, for causing said computer to execute: A recording medium recording the program according to any one of claims 8 to 10.

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