AC machine, its design method, manufacturing method and design support device

Abstract

To provide a design method of an AC machine capable of uniquely determining a structure without depending on a designer with respect to a stator slot.SOLUTION: A design method of an AC machine comprises a first step of performing approximating an absolute value of a sine wave function changing in a circumferential direction in a magnetic pole period of stators in the AC machine by a pulse function having a pulse width corresponding to an absolute value of a sine wave function to determine an area where the pulse function becomes on-pulse in a winding arrangement area; a second step of arranging a plurality of fine cross-sectional windings at equal intervals in the determined winding arrangement area; a third step of enlarging a cross-sectional area of each winding to produce a winding aggregate by synthesizing windings closest to each other when windings adjacent to each other are overlapped, or when a ratio of a portion where a winding out of a length in a circumferential direction of the stators; and a fourth step of determining an arrangement position of each winding aggregate at a position of a slot for storing each winding aggregate thereof, when the number of the resulting winding aggregates as a result obtained by enlarging the cross-sectional area of each winding reaches the desired number.SELECTED DRAWING: Figure 6

Description

[Technical Field]

[0001] The present disclosure relates to AC machines such as permanent magnet synchronous machines and induction machines, and to design methods, manufacturing methods, and design support devices for the same. [Background technology]

[0002] In order to reduce greenhouse gas emissions, there is an urgent need to improve the efficiency of rotating machines, which account for nearly half of the world's electricity consumption.

[0003] Various design methods have been proposed to achieve high efficiency for individual rotating machines. For example, Non-Patent Documents 1 and 2 disclose optimization methods that start from a widely used basic structural model and finely adjust dimensions such as the circumferential width of the stator slots as variables. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Hosokawa et al., "A Method for Optimizing the Efficiency of Permanent Magnet Motors - An Optimization Design Method Using GA and SA -," Transactions of the Institute of Electrical Engineers of Japan, Vol. 121, No. 2, 2001, pp. 171-177 [Non-patent document 2] Onishi et al., "Study on Design Method of IPM Motor Using Finite Element Method and Optimization Method," IEEJ Transactions on Industrial Applications, Vol. 121, No. 3, 2001, pp. 397-402 Summary of the Invention [Problem to be solved by the invention]

[0005] Dimensional optimization such as that described in Non-Patent Documents 1 and 2 above is difficult to expect to significantly improve efficiency because it depends on the topology of the initial shape of the AC machine. On the other hand, it is difficult to have a unified discussion regarding the structure of the stator slots or rotor bars, and designers may consider different structures to be optimal.

[0006] The present disclosure has been made in consideration of the above-mentioned background, and one of its objectives is to provide a design method for an AC machine that can determine a uniquely optimal structure for stator slots without relying on a designer. [Means for solving the problem]

[0007] A method for designing an AC machine according to one embodiment includes first to fourth steps. In the first step, a computer approximates the absolute value of a sine wave function that changes circumferentially with the magnetic pole period of the stator of the AC machine with a pulse function having a pulse width corresponding to the absolute value of the sine wave function, and determines a region where the pulse function becomes an on-pulse as a winding arrangement region. In the second step, the computer arranges multiple windings with small cross-sectional areas at equal intervals in the determined winding arrangement region. In the third step, the computer expands the cross-sectional area of ​​each winding. If adjacent windings overlap or if the proportion of the circumferential length of the stator where windings are arranged exceeds a predetermined ratio, the computer combines the closest windings to generate a new winding as a winding assembly. Here, the winding assembly is a winding having the total number of combined windings and the sum of the cross-sectional areas of the combined windings. Combining the first winding and the second winding includes placing the combined winding between the first winding and the second winding. In the fourth step, when the number of winding assemblies obtained as a result of enlarging the cross-sectional area of ​​each winding reaches a desired number, the computer determines the placement position of each winding assembly as the placement position of the slot that accommodates each winding assembly. [Effects of the Invention]

[0008] According to the above design method, the structure of the stator slot can be uniquely determined independently of the designer while maintaining the ideal sinusoidal electromagnetic field characteristics as much as possible. [Brief explanation of the drawings]

[0009] [Figure 1] 1 is a schematic diagram of the structure of a rotating machine that is addressed in the present disclosure. [Figure 2]10 is a flowchart showing a procedure for creating a line current model. [Figure 3] 1A and 1B are diagrams illustrating specific examples of modulated waves and carrier waves of PWM. [Figure 4] FIG. 4 is a diagram showing the number of windings in each winding arrangement region when the windings are evenly arranged in each winding arrangement region in the example of FIG. 3. [Figure 5] FIG. 5 is a diagram showing the magnetic flux density distribution at the center of the air gap region in the case of the winding arrangement of FIG. [Figure 6] 10 is a flowchart showing a procedure for designing a slot structure. [Figure 7] 10 is a diagram for explaining a method of combining a winding having a number of turns a1 and a cross-sectional area S1 with a winding having a2 and a cross-sectional area S2. FIG. [Figure 8] FIG. 10 is a diagram showing a specific example of a slot structure. [Figure 9] FIG. 9 is a diagram showing, in tabular form, the number of windings arranged in each of the slots SL1 to SL6 in FIG. 8, and the circumferential width and radial thickness of each slot. [Figure 10] FIG. 10 is a diagram showing the magnetic flux density distribution at the center of the air gap when the rotor is made of iron only in the slot structure of FIGS. 8 and 9. [Figure 11] 1 is a flowchart illustrating a method for designing a rotor of a permanent magnet synchronous motor. [Figure 12] FIG. 1 is a diagram showing an outline of a model of a permanent magnet synchronous motor. [Figure 13] 13 is a diagram showing the magnetic flux density distribution of the r component and the θ component on the rotor surface and the distribution of energy converted into torque in the model of FIG. 12. FIG. [Figure 14] FIG. 1 is a diagram for explaining a model in which the cross section of a rotor bar of an induction machine is minimized. [Figure 15] FIG. 2 is a diagram showing an equivalent circuit of an induction machine. [Figure 16] 1 is a flowchart showing a method for designing a rotor for a squirrel-cage induction machine. [Figure 17] FIG. 17 is a diagram showing the relationship between the output torque and the total number of rotor bars when the number of rotor bars is reduced according to the procedure of FIG. 16. [Figure 18] 1 is a flowchart illustrating an example of a method for manufacturing an AC machine. [Figure 19] FIG. 17 is a block diagram showing an example of the configuration of a computer for executing the design procedures shown in FIGS. 2, 6, 11, and 16. [Figure 20] FIG. 2 is a functional block diagram showing functions of a computer as a design support device. DETAILED DESCRIPTION OF THE INVENTION

[0010] Each embodiment will be described in detail below with reference to the drawings. First, a model of an ideal stator structure (referred to as an "ideal line current model") that ignores the shape of the stator slot is proposed as a premise for each embodiment. Next, in the first embodiment, the performance of the ideal line current model is maintained as much as possible, and the model is transformed into a realistic slot structure by continuous modification. This provides a method for designing a stator with a unique slot structure that is not dependent on the designer.

[0011] In a second embodiment, a method for designing the permanent magnet shape of a permanent magnet synchronous machine is proposed by combining an ideal line current model with a torque calculation method based on a Poynting vector. Furthermore, in a third embodiment, a method for designing the rotor of a squirrel-cage induction machine, particularly a method for optimizing the number of rotor bars, is proposed by combining an ideal line current model with a torque calculation method based on a Poynting vector. Note that the design methods of the second and third embodiments can also be implemented by using a stator having the slot structure described in the first embodiment instead of the ideal line current model.

[0012] In the following description, the same or corresponding parts are given the same reference symbols, and their descriptions may not be repeated.

[0013] <Regarding the stator design method that is the premise of the first to third embodiments> [Rotating machine structure] FIG. 1 is a schematic diagram of the structure of a rotating machine described in this disclosure. As shown in FIG. 1, the rotating machine has an inner rotor structure in which a rotor 12 is disposed inside a stator 11. The space between the stator 11 and the rotor 12 is referred to as an air gap 13. A cylindrical coordinate system is adopted in which the rotation axis of the rotor 12 is the z-axis, and the rotation direction of the rotor 12 is the θ-direction. Note that the following description deals with a case in which AC power is input to the stator 11, i.e., a case in which the rotating machine 10 is an AC machine. Furthermore, although a description will be given of a case in which the rotating machine 10 is an inner rotor type as shown in FIG. 1, an outer rotor type in which the rotor 12 is disposed outside the stator 11 can also be treated in the same manner.

[0014] [Line current model] The distribution of the rotating magnetic field generated by the stator winding contains many harmonic components due to the influence of the slot shape and arrangement. Therefore, in order to aim for a spatial distribution that approximately realizes an ideal sine wave, first, regarding the slot shape, the winding is assumed to be a line current and the cross-sectional shape of the slot is ignored. Regarding the slot arrangement, the concept of pulse width modulation (PWM) used in inverters, etc. is applied to space to generate an approximately sinusoidal magnetomotive force distribution. Because the magnetomotive force distribution by a single winding is a rectangular wave, it can be interpreted that the high state of the pulse wave (i.e., the on-pulse) corresponds to the arrangement of the winding.

[0015] Figure 2 is a flowchart showing the procedure for creating a line current model. Each step in Figure 2 is realized by a computer executing a program.

[0016] In step S100, the computer receives input of parameters such as the size of the rotating machine 10, the number of poles, the PWM modulation rate and carrier frequency, and the winding spacing from the user. The size of the rotating machine 10 refers to the physical size of the rotating machine 10. Specifically, the size of the rotating machine 10 includes the outer and inner diameters of the rotor 12, the outer and inner diameters of the stator 11, and the length in the z direction. As an example, in the example of the line current distribution arrangement shown in FIGS. 3 and 4, the stator outer diameter is 112 mm, the stator inner diameter is 56 mm, the rotor outer diameter is 55 mm, the rotor inner diameter is 16 mm, and the length in the z direction is 60 mm.

[0017] In the next step S110, the computer utilizes the concept of PWM to compare a sinusoidal function (corresponding to a PWM modulation wave) that changes circumferentially with the magnetic pole period of the stator of the AC machine with a periodic function (corresponding to a PWM carrier wave) that has an amplitude equal to or greater than that of the sinusoidal function and a spatial frequency significantly higher than that of the sinusoidal function, and approximates the absolute value of the sinusoidal function with a pulse function having a pulse width corresponding to the absolute value of the sinusoidal function. The computer determines the region where the approximated pulse function becomes an on-pulse as the winding arrangement region. Specifically, the section where the absolute value of the instantaneous value of the sinusoidal function is greater than the absolute value of the instantaneous value of the periodic function being compared is set as the on-pulse region (i.e., winding arrangement region). The periodic function being compared may be a triangular wave or a sawtooth wave, and is not particularly limited. When the number of magnetic poles of the stator is N, the period of the absolute value of the sinusoidal function is 360 / N degrees in mechanical angle (i.e., half the magnetic pole period).

[0018] Figure 3 is a diagram showing specific examples of PWM modulating waves and carrier waves. Figure 3 shows the U-phase winding layout region for a three-phase, four-pole configuration with a PWM modulation rate of 0.8, a sine wave modulating wave (with a magnetic pole period of 180 degrees mechanical angle), and a triangular wave period of 9.0 degrees (mechanical angle). To facilitate correlation with the winding layout, the on-pulse region is defined as the region where the absolute value of the instantaneous value of the modulating wave is greater than that of the carrier wave and where the absolute value of the instantaneous value of the opposite phase of the modulating wave is greater than that of the carrier wave.

[0019] The V-phase winding layout area is shifted by 120 electrical degrees (60 mechanical degrees for a three-phase, four-pole system) from the U-phase winding layout area. The W-phase winding layout area is shifted by -120 electrical degrees (-60 mechanical degrees for a three-phase, four-pole system) from the U-phase winding layout area. The modulation factor must be set to 1 or less.

[0020] Returning to FIG. 2, in the next step S120, the computer places many windings with small cross-sectional areas at equal intervals in the winding placement area determined in step S110. By setting the winding spacing to be equal, the number of wires in each winding placement area is approximated to an integer. For example, in the calculation of FIG. 3, the half cycle of the sine wave is divided into 10,000 parts, and the calculation is performed by sampling every 0.018 degrees. This sampling period can be used as the winding placement interval. However, depending on the cross-sectional area of ​​the winding, adjacent wires may overlap. In consideration of this, an example is shown below in which the winding placement interval is set wider than the sampling period.

[0021] FIG. 4 is a diagram showing the number of windings in each region when windings with small cross-sectional areas are uniformly arranged in each winding arrangement region in the example of FIG. 3. In FIG. 4, the winding arrangement interval is 0.39 degrees, the circumferential width of each winding is 0.01 degrees, and the radial thickness of each winding is 5.0 μm. In this case, the cross-sectional shape of each winding is approximately square. Note that the cross-sectional shape of each winding is not limited to square and may be rectangular or another cross-sectional shape. As shown in FIG. 4, 102 U-phase windings 14 are arranged within a range of 90 mechanical degrees (180 electrical degrees), which is half the magnetic pole period. Therefore, a total of 306 windings for the three phases are arranged within a range of 90 mechanical degrees.

[0022] Figure 5 shows the magnetic flux density distribution at the center of the air gap region in the case of the winding arrangement of Figure 4. Figure 5(a) shows the r component, and Figure 5(b) shows the magnetic flux density of the θ component after 0.125 seconds. The calculation was performed using the finite element method, with the voltage source set to 40 V, the power supply frequency set to 10 Hz, and the electrical conductivity of the stator winding set to 5.98 x 10 7S / m, the relative permeability of the stator material and rotor material was 10,000, the analysis step time was 0.005 seconds, and the number of analysis steps was 25.

[0023] As shown in Figure 5, both the r and θ components have distribution waveforms that are close to sine waves, but the θ component contains larger harmonic components. The orders of the harmonic components are 37th, 41st, 43rd, 77th, 79th, 83rd, 85th, etc., and are related to the period of the triangular wave that is the PWM carrier wave. The total harmonic distortion (THD) was 1.17% for the r component and 42.2% for the θ component.

[0024] To reduce THD, it is desirable to set the modulation rate to 1.0, increase the number of windings, and increase the spatial frequency of the carrier wave (shorten the triangular wave period).

[0025] <First Embodiment> In the calculation example of Figure 5 above, the winding current density is 1.64 x 10 5 A / mm 2 This is a realistic current density of 4.0 A / mm 2 Therefore, in the first embodiment, the cross-sectional area of ​​the windings is continuously increased while maintaining the magnitude of the current flowing through the windings, and adjacent windings are combined together. This allows the slot structure to be uniquely determined.

[0026] Figure 6 is a flowchart showing the design procedure for the slot structure. Each step in Figure 6 is realized by a computer executing a program. Note that when starting the procedure in Figure 6, it is assumed that the line current distribution has been created according to the flowchart in Figure 2.

[0027] In step S200, the computer determines whether the windings overlap each other. If the windings do not overlap each other (NO in step S200), in step S210, the computer determines whether the total winding width exceeds a predetermined percentage of the circumference. The predetermined percentage is, for example, 50% of the circumference. This condition is necessary to ensure sufficient magnetic permeance between the windings.

[0028] If the windings do not overlap each other (NO in step S200) and the total winding width does not exceed a predetermined percentage of the circumference (NO in step S210), the computer proceeds to step S220. In step S220, the computer increases the cross-sectional area of ​​the windings by the predetermined percentage, and then returns to step S200.

[0029] On the other hand, if the windings overlap each other (YES in step S200) or if the total winding width exceeds a predetermined percentage of the circumference (YES in step S210), the computer proceeds to step S230. In step S230, the computer searches for the most densely packed windings, and in the next step S240, combines the closest windings. The combined winding is also called a winding assembly. A winding assembly is a winding that has the total number of combined windings and the sum of the cross-sectional areas of the combined windings.

[0030] Specifically, the computer searches for the winding with the smallest total distance between the left and right windings among all windings (including winding assemblies) (this winding is designated as A). Next, the computer selects the winding on the left or right of winding A that is closer (this winding is designated as B) and combines windings A and B. As an example, the newly generated winding C is placed at a position that divides the distance between windings A and B in an inverse ratio of the cross-sectional areas of A and B. Winding C may also be placed at another position between windings A and B. Furthermore, the total cross-sectional area and total number of turns of windings A and B are inherited by winding C, and the cross-sectional shapes are maintained similar. The shape of each winding may be square, rectangular, or some other shape.

[0031] 7 is a diagram illustrating a method for combining a winding (i.e., a winding assembly) with a winding having a number of turns a1 and a cross-sectional area S1 and a winding (i.e., a winding assembly) with a winding having a2 and a cross-sectional area S2. As shown in FIG. 7, the combined winding has a number of turns a1+a2, a cross-sectional area S1+S2, and a cross-sectional shape similar to the cross-sectional shape before combining (in this case, approximately square). The position of the combined winding is obtained by dividing the distance between the position of the winding with cross-sectional area S1 and the position of the winding with cross-sectional area S2 by the inverse ratio of the cross-sectional areas S2:S1.

[0032] 6, in the next step S250, the computer determines whether the total number of winding assemblies in the entire stator is equal to the predetermined desired number of slots. If the total number of winding assemblies does not equal the desired number of slots (NO in step S250), the computer returns to step S200 and repeats the above-described process of increasing the winding cross section and combining the nearest windings.

[0033] If the total number of winding assemblies is equal to the desired number of slots (YES in step S250), the computer proceeds to step S260. In step S260, the computer determines the current density condition (i.e., the current density is 4.0 A / mm 2 The radial thickness of each winding is increased until the following condition is met. This completes the design procedure for the stator slot structure.

[0034] Next, we will explain a specific example of a slot structure created according to the flowchart in Figure 6. As an example, the PWM modulation rate is set to 1.0, and the period of the triangular carrier wave is set to 2.0 degrees. Other parameters are the same as in Figure 3. Also, assume that the initial winding spacing is 0.018 degrees, the winding width is 0.01 degrees, and the radial thickness of the winding is 5.0 μm. In this case, the cross-sectional shape of the winding is approximately square. The rotating machine is three-phase, four-pole, and there are six slots per 90 degrees of mechanical angle (180 degrees of electrical angle). Three-phase windings are inserted into each slot, and the area of ​​each phase within the slot is equivalent to the internal division of the slot, with the cross-sectional area proportional to the number of turns.

[0035] Fig. 8 is a diagram showing a specific example of the slot structure. Fig. 9 is a diagram showing, in tabular form, the number of windings arranged in each of the slots SL1 to SL6 in Fig. 8, as well as the circumferential width and radial thickness of each slot. In Fig. 9, a negative number of turns indicates that the current flows in the opposite direction to a positive number of turns.

[0036] As shown in Figures 8 and 9, windings for all phases are inserted into each slot, and the distance between the slots is approximately equal. Note that in Figure 8, the windings for each phase are arranged so that the phase with the fewer windings is closer to the inside of the slot, but this is not limited to this. For example, the windings for each phase may be arranged so that the phase with the greater number of windings is closer to the inside of the slot, or they may be arranged from the inside to the outside of the slot in the order of U phase, V phase, and W phase.

[0037] The winding distribution shown in Figures 8 and 9 is roughly as follows. Specifically, multiple slots formed in the stator are arranged circumferentially facing the rotor. U-phase windings, V-phase windings, and W-phase windings are wound around the multiple slots. Each slot houses windings for all phases, U, V, and W. If the number of stator poles is N, the number of U-phase windings housed in each slot changes circumferentially with a period of 360 / N mechanical degrees (half the magnetic pole period). The change in the number of U-phase windings housed in each slot within each period is approximated by a half-period sinusoidal curve. Within the same period, U-phase windings are arranged to pass current in the same direction, and in adjacent periods, U-phase windings are arranged to pass current in opposite directions. The distribution of the V-phase windings housed in each slot is obtained by shifting the distribution of the U-phase windings housed in each slot by 240 / N mechanical degrees in the circumferential direction. The distribution of the W-phase windings housed in each slot is the distribution of the U-phase windings housed in each slot, shifted by 240 / N mechanical degrees in the opposite direction to that of the V-phase windings.

[0038] Figure 10 shows the magnetic flux density distribution at the center of the air gap when the rotor is made of iron only in the slot structures of Figures 8 and 9. Figure 10(a) shows the r component, and Figure 10(b) shows the θ component. As shown in Figure 10, distortion occurs in both the r component and the θ component, and this distortion is mainly caused by the 11th and 13th harmonics corresponding to the slot arrangement period.

[0039] Furthermore, compared to a conventional example in which the same number of wires of the same phase are placed in each equally spaced slot, it has been confirmed that the slot structure of this embodiment has a smaller proportion of harmonic components, particularly a reduction in the seventh harmonic. Furthermore, the torque when permanent magnets (neodymium magnets) are placed on the surface of the rotor was compared with that of the above-mentioned conventional example. As a result, it was found that in the case of this embodiment, the torque is larger than that of the conventional example in the low load region (i.e., the region where the phase difference between current and voltage is small), and that it is highly efficient.

[0040] [Effects of the First Embodiment] As described above, according to the design method for an AC machine of the first embodiment, the slot arrangement is determined by expanding the line current model that provides a nearly ideal electromagnetic field distribution. Specifically, the cross section of each winding is continuously increased, and if one of the following two conditions is satisfied in the process, the windings that are closest to each other are combined.

[0041] Condition 1: The winding cross sections overlap each other.

[0042] Condition 2: The total cross-sectional width of the windings exceeds a predetermined ratio of the entire inner circumference of the stator.

[0043] In this way, each winding that has been approximated by a line current determines the distance between itself and the adjacent windings on the left and right and forms the slot structure, so the stator slot structure is determined by self-organization, so to speak. Therefore, the stator slot structure can be uniquely determined independently of the designer, while maintaining the electromagnetic field characteristics of an ideal sinusoidal wave as much as possible.

[0044] <Embodiment 2> In the second embodiment, a method for designing the arrangement of permanent magnets in the rotor of a permanent magnet synchronous machine using a line current model of the stator will be described. First, a method for calculating torque using the Poynting vector will be described.

[0045] [Torque calculation method] Using the electric field E, magnetic field H, current density J, vacuum permittivity ε0, and vacuum permeability μ0, the energy balance relationship for region V, whose surface is S, is expressed by the following equation (1). In the following equation (1), n ​​is the unit normal vector pointing outward with respect to the surface of region V. Vectors are written in bold.

[0046]

number

[0047] The right-hand side of equation (1) represents the change in energy per unit time in region V. The two terms on the left-hand side of equation (1) represent the energy converted from the electromagnetic field energy within region V. The first term on the left-hand side represents the energy flowing in or out through surface S, and the vector product of vector E and vector H (i.e., E × H) defines the Poynting vector.

[0048] The electromagnetic energy P that propagates from the stator through the air gap and flows into the rotor can be calculated by surface integrating the Poynting vector on the rotor surface S. The electric field E and magnetic field H are values ​​on the rotor surface in the stationary coordinate system. In the cylindrical coordinate system, the normal vector n=(1,0,0) T Therefore, the electromagnetic energy P is P r and is expressed by the following equation (2).

[0049]

number

[0050] The above equation (2) represents the energy flowing into the rotor as viewed from a stationary coordinate system, and corresponds to the energy converted into torque and the copper and iron losses in the rotor. On the other hand, the energy P flowing into the rotor as viewed from a rotating coordinate system that rotates in synchronization with the rotor is r ' is expressed by the following equation (3), where v is the rotational speed of the rotor surface and μ is the magnetic permeability. In the following equation (3), the prime represents a quantity seen from the rotating coordinate system.

[0051]

number

[0052] Since the above equation (3) is observed in a rotating coordinate system, the energy P r ' corresponds only to the loss in the rotor and does not include the energy converted into torque. r From the above equation (3), P r By subtracting ', the energy P converted into mechanical power, i.e., torque, torque Therefore, the energy P that is converted into torque from the energy flowing into the rotor (i.e., the Poynting vector) can be calculated as follows: torque is expressed by the following equation (4A): The energy p converted into torque flowing into the rotor per unit area of ​​the rotor surface is torque is a value before performing the surface integral of the following equation (4A), and is expressed by the following equation (4B).

[0053]

number

[0054] Torque T is calculated by P in the above equation (4A). torque The rotational angular velocity ω m In the following equation (5A), r represents the distance from the rotation axis to the rotor surface, and the rotational speed v of the rotor surface is calculated by dividing the rotational angular speed ω mThe torque τ acting per unit area of ​​the rotor surface is the value before performing the surface integral of the following equation (5A), and is expressed by the following equation (5B).

[0055]

number

[0056] [Rotor design method for permanent magnet synchronous motors] Next, the energy P converted into the torque mentioned above torque or p torque This section explains a rotor design method for a permanent magnet synchronous motor using the above method. Below, we will explain a rotor design method for a surface permanent magnet synchronous motor, but this design method can also be applied to interior permanent magnet synchronous motors.

[0057] 11 is a flowchart showing a method for designing a rotor of a permanent magnet synchronous motor. Each step in FIG. 11 is realized by a computer executing a program.

[0058] First, in step S300, the computer arranges windings on the surface of the stator 11 according to the procedure shown in the flowchart of the method for creating a line current model in FIG.

[0059] In the next step S310, the computer calculates the radial magnetic flux density B in the air gap near the surface of the rotor 12. r and the circumferential magnetic flux density B θ Calculate the following.

[0060] In the next step S320, the computer receives input of settings for the shape and / or arrangement of the permanent magnets. For example, in the case of a surface permanent magnet synchronous motor, the computer receives input of the circumferential width and radial thickness of the permanent magnets.

[0061] In the next step S330, the computer calculates the radial magnetic flux density B in accordance with the above-mentioned equation (4B). r , circumferential magnetic flux density Bθ , the energy p converted into torque per unit area by multiplying the inverse of the magnetic permeability μ by the circumferential speed v of the surface of the rotor 12. torque Furthermore, the computer calculates the energy per unit area p torque By surface integrating over the area of ​​the permanent magnet, the energy P converted into torque flowing into the entire permanent magnet is torque In this case, for example, the area near the edge of the permanent magnet and the other areas may be integrated separately. This allows the energy P converted into torque flowing into a specific area of ​​the permanent magnet to be calculated. torque In the above case, the computer may calculate the torque acting on the rotor.

[0062] In the next step S340, the computer calculates the energy P torque and / or p torque The calculation result is output to the user. For example, the computer displays the calculation result on a display.

[0063] In the next step S350, the computer receives a user input as to whether or not to change the shape and / or arrangement of the permanent magnets. If the user inputs that the shape and / or arrangement of the permanent magnets will be changed (YES in step S350), the computer returns to step S320. If the shape and / or arrangement of the permanent magnets will not be changed (NO in step S350), the computer ends the process.

[0064] [Energy converted into torque P torque Specific example of calculation of Hereinafter, the energy P that is converted into torque from the energy input to the rotor (i.e., the Poynting vector) is torque A specific example of the calculation of is explained below.

[0065] Figure 12 shows the outline of a model of a permanent magnet synchronous motor. The dimensions of the stator 11 and rotor 12 shown in Figure 12 are the same as those described in Figures 2 to 4. A permanent magnet 16 is disposed on the surface of the rotor 12. The radial thickness of the permanent magnet 16 is 1 mm, and its circumferential width is 45 degrees. A neodymium magnet with a radial magnetic flux density of 1.0 T is used as the permanent magnet 16. The permanent magnet is disposed so that the r-direction magnetic flux density distribution created by the permanent magnet coincides with the maximum and minimum positions of the r-direction magnetic flux density distribution generated when three-phase AC begins to flow through the stator windings. The modulation factor used to generate the stator winding distribution of the line current model is 0.8, the triangular wave period is 9.0 degrees (mechanical angle), and the total number of turns per phase is 408, all of which are the same as those described in Figures 2 to 4.

[0066] In the electromagnetic field calculation using the finite element method, the rotor is forced to rotate at a synchronous rotation speed of 300 rpm, with a position shifted 50 degrees in the opposite direction to the direction of rotation as the initial position. The voltage source is set to 40 V, the power supply frequency to 10 Hz, the resistance of one phase of the stator winding to 8 Ω, the analysis step time to 4.63 milliseconds, and the number of analysis steps to 60. The material of the rotor 12 does not generate iron loss, and because the electrical conductivity is set to 0, no copper loss occurs either. Therefore, all of the electromagnetic energy that flows into the rotor 12 is converted into torque.

[0067] Figure 13 shows the magnetic flux density distribution of the r component and the θ component on the rotor surface and the distribution of energy converted into torque in the model of Figure 12. These figures show values ​​0.208 seconds after the start of the analysis.

[0068] The magnetic flux density B of the r component on the rotor surface shown in Figure 13(a) r and the magnetic flux density B of the rotor surface θ component shown in Figure 13(b) θ is a value in the area of ​​the air gap 13 at a distance of 27.501 mm from the rotation axis, i.e., 0.001 mm from the rotor surface. Also, Fig. 13(d) shows the energy P converted into torque with respect to the mechanical angle shown in Fig. 13(c). torque 1 is a vertically enlarged view of the distribution of

[0069] The waveforms in Figures 13(a) and 13(b) are distortions of the waveforms in Figures 5(a) and 5(b) when no permanent magnet is present. In Figures 13(a) and 13(b), the sharply changing portions correspond to the edges of the permanent magnet. The magnetic flux density B of the r component r Although distortion occurs in the entire area where the permanent magnet 16 is arranged, the magnetic flux density B θ In this case, the distortion caused by the portions other than the edges of the permanent magnet 16 is small, and the distortion caused by the edge portions is the main portion.

[0070] From Fig. 13(c), the electromagnetic energy P torque It appears that most of the electromagnetic energy P flows into the rotor 12 from the edge portions of the permanent magnets 16, but from the enlarged view of FIG. 13(d), it can be seen that electromagnetic energy P flows from portions other than the edges of the permanent magnets 16. torque Assuming that the edge is the area with an angle width of 15 degrees from the edge as the starting point, the power flowing into the rotor 12 from the edge is 23.5 W. On the other hand, the electromagnetic energy P torque was 26.5W.

[0071] Next, when the radial thickness of the permanent magnet 16 was gradually increased from 1 mm, the power P torque decreases at the edge and increases at the non-edge parts, but the increase in the non-edge parts is larger, so the total increases. However, the increase gradually converges to 0, and the power P converted into torque torque The radial thickness when the upper limit of the permanent magnet thickness was 7 mm was therefore found to be the most efficient way for electromagnetic energy to flow into the rotor 12 and be converted into torque when the radial thickness of the permanent magnet 16 was 7 mm, given the above design parameters.

[0072] [Effects of the second embodiment] As described above, according to the design method for the permanent magnet synchronous machine of the second embodiment, the computer calculates the radial and circumferential magnetic flux densities B generated in the air gap based on the line current model having a nearly ideal electromagnetic field distribution. r ,B θ Calculate the radial and circumferential magnetic flux density B r ,B θ Based on the calculated torque or electromagnetic energy converted into torque, the user can repeatedly change the design of the shape and arrangement of the permanent magnets to obtain higher torque based on the output calculation results. As a result, it is possible to design a rotor for a permanent magnet synchronous machine that generates high torque. Note that the rotor design method of the second embodiment can also be implemented by using a stator with the slot structure described in the first embodiment instead of the stator of the line current model.

[0073] <Third Embodiment> In the third embodiment, we will explain a method for designing the rotor structure of a squirrel-cage induction machine by combining a stator line current model with a torque calculation method based on the Poynting vector. First, we will explain energy conversion when the cross section of the rotor bars is minimized and the influence of the rotor structure is ignored. Next, we will explain a method for determining the optimal number of rotor bars by increasing the cross section of the rotor bars while maintaining energy conversion performance as much as possible.

[0074] [Minimized rotor bar cross section model] Fig. 14 is a diagram illustrating a model in which the cross section of the rotor bar of an induction machine is minimized. In the squirrel-cage induction machine 10B shown in Fig. 14, a large number of bars 15, each with a square cross section and a very small cross section, are arranged at equal intervals. These large number of bars 15 are connected to end rings.

[0075] As an example, a model of a squirrel-cage induction machine 10B used for electromagnetic field calculations using the finite element method was determined as follows. First, the stator structure was the same as that of the line current model described with reference to Figures 2 to 4. The cross-sectional shape of the minimized bars 15 was approximately square, with a circumferential angular width of 0.1 degrees and a radial thickness of 50 μm. The cross-sectional shape of the bars 15 may be rectangular or another shape. The bars 15 were arranged on a circumference 50 μm away from the surface of the rotor 12. Furthermore, to ensure that the bars 15 were arranged at equal intervals in the circumferential direction, the magnetic path width between the bars was set to 0.1 degrees, the same as the circumferential width of the bars.

[0076] In the electromagnetic field calculation using the finite element method, the rotor is forced to rotate at a synchronous rotation speed of 300 rpm, slip of 0.17, and rotor rotation speed of 250 rpm. The voltage source is set to 40 V, the power supply frequency is set to 10 Hz, the resistance of one phase of the stator winding is set to 8 Ω, and the electrical conductivity of the rotor bar is set to 2.0 × 10 9 S / m, total end ring resistance 3.6×10 -7 Let's call it Ω.

[0077] It should be noted that, because the cross-sectional area of ​​the rotor bar 15 is small, the electrical conductivity of the rotor bar 15 must be set higher than usual to generate sufficient distortion in the rotating magnetic field. Therefore, the electrical conductivity of ordinary copper is 5.98×10 7 In this model, the electrical conductivity of the rotor bar 15 is set to 2.0×10 S / m, where the output torque reaches its maximum value. 9 It was set to S / m.

[0078] With the above setting values, the magnetic flux density B in the r direction in the air gap 13 near the rotor in the steady state r and magnetic flux density B in the θ direction θWhen the distribution of was calculated, it was confirmed that both the r-component and the θ-component were sinusoidal. Furthermore, when compared with the magnetic flux density distribution in the air gap 13 in a model in which no bars were placed on the rotor, it was confirmed that the addition of the rotor bars did not significantly change the r-component, but did increase the amplitude of the θ-component. Therefore, it is believed that the induced current flowing through the rotor bars significantly changes the magnetic flux density distribution, especially of the θ-component in the air gap, generating torque.

[0079] [How to determine the number of rotor bars] Next, a method for determining the optimum number of rotor bars by increasing the cross-sectional area of ​​the rotor bars while maintaining the energy conversion performance as much as possible will be described.

[0080] FIG. 15 is a diagram showing the equivalent circuit of an induction machine. The resistance and reactance of the stator winding (primary winding) of the induction machine are r1 and x1, and the resistance and reactance of the rotor winding (secondary winding) are r2 and x2. The excitation conductance is g0 and the excitation susceptance is b0. The primary voltage is V1 and the load resistance is R. In FIG. 15, the load resistance R and the secondary resistance r2 and secondary reactance x2 related to the rotor are converted into the load resistance R on the primary side. * and secondary resistance r2 * and secondary reactance x2 * When changing the shape of the rotor bars, these quantities related to the rotor are not changed. In this embodiment, the secondary reactance x2 * is assumed to be constant, and the secondary resistance r2 * The cross-sectional area of ​​the rotor bars is increased while keeping the value constant. This results in the same energy conversion in the equivalent circuit, so the output of the induction machine can be maintained.

[0081] Specifically, the resistance of one rotor bar r b [Ω] is the length l of the rotating machine in the z-direction [mm], and the cross-sectional area S of the rotor bar [mm 2 ] and the electrical conductivity of the rotor bar σ [S / m], it can be calculated as follows:

[0082]

number

[0083] The resistance of one rotor bar in equation (6) above is r b [Ω], total end ring resistance r r By using the rotor resistance [Ω], the number of rotor bars Z2, and the number of poles P, the secondary resistance r2 [Ω] can be calculated as follows:

[0084]

number

[0085] The total end ring resistance r r [Ω] is the electrical conductivity of the rotor bar σ r , end ring circumference l r [m], end ring cross-sectional area S r [m 2 ] can be calculated as follows:

[0086]

number

[0087] Furthermore, the primary side conversion factor α can be calculated as in the following equation (9A) using the total number m, the total number of series turns of the stator for one phase Z1, and the number of rotor bars Z2. Therefore, by multiplying the secondary resistance r2 shown in the above equation (7) by the primary side conversion factor α in the following equation (9A), the secondary resistance r2 converted to the primary side can be calculated. * can be calculated as follows:

[0088]

number

[0089] Secondary resistance r2 converted to the primary side of the above equation (9B) *The variables that can be changed in this calculation are the circumferential width of the bar θ [degrees], the radial thickness of the bar w [mm], the electrical conductivity σ [S / m], and the number of bars Z2. Therefore, as shown in the flowchart in Figure 16 below, the number of bars Z2 can be arbitrarily changed to calculate the secondary resistance r2 converted to the primary side. * Set other variables so that is a constant value.

[0090] Fig. 16 is a flowchart showing a method for designing a rotor for a squirrel-cage induction machine. Each step in Fig. 16 is realized by a computer executing a program.

[0091] First, in step S400 of Fig. 16, the computer calculates the output torque while changing the electrical conductivity σ in the rotor bar cross-section miniaturized model set by the user. The computer determines the electrical conductivity σ of the rotor bar when the output torque is maximized.

[0092] In the next step S410, the computer reduces the number of rotor bars Z2 by a factor of 1 / a, where a is a real number greater than 1.

[0093] In the next step S420, the computer increases the width θ and thickness w of the rotor bars in an inverse ratio to the change in the number of rotor bars Z2, i.e., by a factor a. This maintains the cross-sectional shape of the rotor bars as it was before the increase (in this example, a shape close to a square). Furthermore, in step S430, the computer determines the cross-sectional area S of the rotor bars from the changed width θ and thickness w of the rotor bars.

[0094] In the next step S440, the computer determines the electrical conductivity σ of the rotor bar using the number Z2 of the rotor bars, the width θ and thickness w of the rotor bar, and the cross-sectional area S of the rotor bar. The electrical conductivity σ is calculated by multiplying the secondary resistance r2 converted to the primary side. * It can be calculated from the constraint that is a constant value.

[0095] In the next step S450, the computer checks whether the electrical conductivity σ of the rotor bar calculated in step S440 is equal to or greater than the desired electrical conductivity (e.g., the electrical conductivity of copper, 5.98×10 7 S / m). If the electrical conductivity σ calculated in step S440 has reached the desired electrical conductivity (YES in step S450), the computer ends the process. On the other hand, if the electrical conductivity σ calculated in step S440 has not reached the desired electrical conductivity (NO in step S460), the computer returns the process to step S410 and further reduces the number of rotor bars Z2.

[0096] Fig. 17 shows the relationship between the output torque and the total number of rotor bars when the number of rotor bars is reduced according to the procedure in Fig. 16. The graph in Fig. 17 shows the results of an electromagnetic field calculation performed by the finite element method using the conditions described with reference to Fig. 14. In the case of Fig. 17, the number of bars was reduced while maintaining performance, and as a result, the electrical conductivity of the bars was reduced to 5.98 × 10 7 When the rotor reaches S / m, the total number of rotor bars is 52. However, in reality, the output torque decreases slightly as the total number of bars decreases, as shown in Figure 17. This decrease in output torque is thought to be due to the increase in leakage reactance caused by the enlargement of the cross-sectional area of ​​the bars.

[0097] [Effects of the Third Embodiment] As described above, according to the design method of the third embodiment, the radial and circumferential magnetic flux densities B generated in the air gap 13 are calculated based on the line current model having an ideal electromagnetic field distribution. r ,B θ Calculate the radial and circumferential magnetic flux density B r ,B θBased on this, the torque acting on the rotor bar when the cross section is minimized is calculated. Then, by increasing the cross section of the rotor bar while maintaining the conversion performance when the torque is at its maximum value, a rotor bar with an optimal structure is determined. As a result, a rotor of a squirrel-cage induction machine can be designed to generate high torque. Note that the rotor design method of the third embodiment can also be implemented by using a stator with the slot structure described in the first embodiment instead of the line current model stator.

[0098] <Manufacturing method of AC machine> Using the design methods described in the first to third embodiments above, an AC machine with a large output torque can be manufactured.

[0099] Specifically, as shown in FIG. 18, slots designed according to the design method of embodiment 1 (step S500) are formed in the stator, and the stator is manufactured by winding windings of each phase into the formed slots (step S510).

[0100] Furthermore, permanent magnets having an arrangement and shape designed according to the design method of embodiment 2 (step S500) are attached to the rotor to manufacture the rotor (step S520). The manufactured stator and rotor are assembled to manufacture a permanent magnet synchronous machine as an AC machine (step S530). Here, the design of the stator according to embodiment 1 and the design of the rotor according to embodiment 2 are performed in parallel (step S500), and the stator and rotor are designed as a single unit.

[0101] Alternatively, a squirrel-cage rotor having a structure designed according to the design method of the third embodiment (step S500) is manufactured (step S520). The manufactured stator and rotor are assembled to manufacture a squirrel-cage induction machine as an AC machine (step S530). Here, the design of the stator according to the first embodiment and the design of the rotor according to the third embodiment are carried out in parallel (step S500), and the stator and rotor are designed as a single unit.

[0102] <Design support equipment> Fig. 19 is a block diagram showing an example of the configuration of a computer for executing the design procedures shown in Fig. 2, Fig. 6, Fig. 11, and Fig. 16. As shown in Fig. 19, a computer 20 includes a CPU (Central Processing Unit) 21, a RAM (Random Access Memory) 22, a nonvolatile memory 23, a reader / writer 24 (or a reader only), a recording medium 25, a communication device 26, an input device 27, and a display device 28. These components are connected to each other via a bus 29.

[0103] The functions of the computer 20 as a design support device are realized by the CPU 21 executing a program. The RAM 22 is used as the main memory of the CPU 21. The non-volatile memory 23 stores the program executed by the CPU 21. The program is provided in a recording medium 25 and is read into the computer 20 via the reader / writer 24. Alternatively, the program may be provided via a network and imported into the computer 20 via the communication device 26.

[0104] The input device 27 includes a keyboard, a mouse, etc. for receiving user input. The display device 28 includes a liquid crystal display, an organic EL (Electroluminescence) display, etc. The input device 27 and the display device 28 may be integrated into one touch panel.

[0105] Fig. 20 is a functional block diagram showing the functions of computer 20 as a design support device. With reference to Fig. 20, functionally, design support device 30 comprises a winding arrangement region determination unit 31, a minute winding arrangement unit 32, and a winding synthesis unit 33. These elements can be considered to correspond to modules of a program executed by computer 20. Note that the division into modules is for convenience's sake, and for example, winding arrangement region determination unit 31 and minute winding arrangement unit 32 may be configured as a common module.

[0106] Specifically, the winding arrangement region determination unit 31 approximates the absolute value of a sine wave function that changes circumferentially with the magnetic pole period of the stator of the AC machine with a pulse function having a pulse width corresponding to the absolute value of the sine wave function. The winding arrangement region determination unit 31 determines the region where the pulse function becomes an on-pulse as the winding arrangement region.

[0107] The minute winding arrangement section 32 arranges a large number of windings with minute cross-sectional areas at equal intervals in the determined winding arrangement area.

[0108] The winding combining unit 33 expands the cross-sectional area of ​​each winding, and when adjacent windings overlap or when the proportion of the circumferential length of the stator where windings are arranged exceeds a predetermined ratio, combines the most adjacent windings to generate a new winding as a winding assembly. A winding assembly has the total number of combined windings and the sum of the cross-sectional areas of the combined windings. Combining the first winding and the second winding includes placing the combined winding between the first winding and the second winding. When the number of winding assemblies obtained as a result of expanding the cross-sectional areas of the windings reaches a desired number, the winding combining unit 33 determines the placement positions of each winding assembly as the placement positions of the slots that accommodate each winding assembly.

[0109] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of this application is defined by the claims, not the above description, and is intended to include all modifications within the meaning and scope of the claims. [Explanation of symbols]

[0110] 10 Rotating machine, 10A Permanent magnet synchronous machine, 10B Squirrel-cage induction machine, 11 Stator, 12 Rotor, 13 Air gap, 14 Winding, 15 Rotor bar, 16 Permanent magnet, 20 Computer, 21 CPU, 22 RAM, 23 Non-volatile memory, 24 Reader / writer, 25 Recording medium, 26 Communication device, 27 Input device, 28 Display device, 30 Design support device, 31 Winding placement area determination unit, 32 Microwinding placement unit, 33 Winding synthesis unit.

Claims

1. 1. A method for designing an AC machine, comprising: a step in which a computer approximates an absolute value of a sine wave function that changes in a circumferential direction with a magnetic pole period of a stator of the AC machine with a pulse function having a pulse width corresponding to the absolute value of the sine wave function, and determines a region where the pulse function becomes an on-pulse as a winding arrangement region; arranging a large number of windings each having a small cross-sectional area at equal intervals in the determined winding arrangement region; the computer enlarges the cross-sectional area of ​​each of the windings, and when adjacent windings overlap or when the proportion of the portion of the circumferential length of the stator where the windings are arranged exceeds a predetermined ratio, combines the windings that are closest to each other to generate a new winding as a winding assembly; The winding assembly has a total number of a plurality of combined windings and a total cross-sectional area of ​​the combined plurality of windings, and combining the first winding and the second winding includes disposing the combined winding between the first winding and the second winding, and further and when the number of winding assemblies obtained as a result of enlarging the cross-sectional area of ​​each of the windings reaches a desired number, determining by the computer an arrangement position of each of the winding assemblies to be an arrangement position of a slot that houses each of the winding assemblies.

2. 2. The method for designing an AC machine according to claim 1, wherein combining the first winding and the second winding includes arranging the combined winding at a position obtained by dividing a cross-sectional area of ​​the first winding to a cross-sectional area of ​​the second winding in an inverse ratio from the cross-sectional area of ​​the first winding to the cross-sectional area of ​​the second winding.

3. the AC machine is a permanent magnet synchronous machine, a step in which the computer calculates radial and circumferential magnetic flux densities generated in the air gap of the AC machine by currents flowing through the windings with small cross-sectional areas that are equally spaced in the winding arrangement region or the desired number of winding assemblies; a step in which the computer calculates a value obtained by dividing the product of the radial magnetic flux density, the circumferential magnetic flux density, and the rotational speed of the surface of the rotor of the AC machine by magnetic permeability as energy converted into torque acting on permanent magnets arranged in the rotor, out of energy input to the rotor; and receiving an input of a correction value for at least one of an arrangement and a shape of the permanent magnets by outputting, to a user, a calculation result of the energy converted into the torque or the torque based on the converted energy.

4. the AC machine is a squirrel-cage induction machine, a step in which the computer arranges a large number of rotor bars having minute cross-sectional areas at equal intervals as a rotor of the AC machine; the computer calculates radial and circumferential magnetic flux densities generated in the air gap of the AC machine by currents flowing through the windings of small cross-sectional area arranged at equal intervals in the winding arrangement region or the desired number of winding assemblies, and calculates torque acting on the rotor bars of small cross-sectional area based on the calculated radial and circumferential magnetic flux densities; The computer determines the electrical conductivity of the rotor bar when the calculated torque is maximized, using the electrical conductivity of the rotor bar as a variable; the computer reducing the number of the rotor bars and increasing the width and thickness of each of the rotor bars in inverse proportion to the change in the number of the rotor bars; The computer calculates the electrical conductivity of the rotor bars corresponding to the number of the rotor bars and the cross-sectional area of ​​each of the rotor bars after the change so as to satisfy the condition that the resistance of the rotor converted to the primary side is constant; and determining, by the computer, the number, width, and thickness of the rotor bars as design values ​​when the electrical conductivity of the rotor bars obtained as a result of reducing the number of the rotor bars reaches a desired value.

5. A method for manufacturing an AC machine, comprising the step of manufacturing the stator by forming the slots at the positions where the slots are to be arranged, which positions are determined according to the method for designing an AC machine according to claim 1 or 2.

6. manufacturing the stator by forming the slots at the slot placement positions determined in accordance with the method for designing an AC machine according to claim 3 or 4; and manufacturing the rotor to the rotor structure determined according to the AC machine design method.

7. A rotor; a stator having a plurality of slots arranged in a circumferential direction facing the rotor; a U-phase winding, a V-phase winding, and a W-phase winding wound in the plurality of slots, each of the plurality of slots accommodates windings of all phases, i.e., U-phase, V-phase, and W-phase; a thickness of each of the plurality of slots is equal to the sum of the thicknesses of the U-phase winding, the V-phase winding, and the W-phase winding housed in the respective slot, and the thickness varies depending on the position of the slot, with the thicknesses of adjacent slots being different from each other; the number of U-phase windings housed in each of the plurality of slots in the stator having N magnetic poles varies periodically in the circumferential direction with a period of 360 / N mechanical degrees, the change in the number of U-phase windings housed in each slot within each period is approximated by a sine curve of half a period, the U-phase windings are arranged in the same period for flowing current in the same direction, and the U-phase windings are arranged in adjacent periods for flowing current in opposite directions, a distribution of the V-phase windings housed in each of the plurality of slots is shifted by 240 / N mechanical degrees in the circumferential direction from a distribution of the U-phase windings housed in each of the plurality of slots, a distribution of the W-phase winding housed in each of the plurality of slots that is shifted by 240 / N mechanical degrees in the opposite direction to the distribution of the U-phase winding housed in each of the plurality of slots.

8. A design support device for an AC machine, comprising: a winding arrangement region determination unit that approximates an absolute value of a sine wave function that changes in a circumferential direction with a magnetic pole period of a stator of the AC machine with a pulse function having a pulse width corresponding to the absolute value of the sine wave function, and determines a region where the pulse function becomes an on-pulse as a winding arrangement region; a minute winding arrangement section that arranges a large number of windings with minute cross-sectional areas at equal intervals in the determined winding arrangement region; a winding combining unit that enlarges the cross-sectional area of ​​each of the windings, and combines the windings that are closest to each other when adjacent windings overlap or when the proportion of the portion of the circumferential length of the stator where the windings are arranged exceeds a predetermined ratio, thereby generating a new winding as a winding assembly; the winding assembly has a total number of a plurality of combined windings and a total cross-sectional area of ​​the combined plurality of windings, and combining the first winding and the second winding includes disposing the combined winding between the first winding and the second winding; When the number of winding assemblies obtained as a result of enlarging the cross-sectional area of ​​each of the windings reaches a desired number, the winding synthesis unit determines the arrangement position of each of the winding assemblies to be the arrangement position of a slot that accommodates each of the winding assemblies.

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