Mathematical model-based simulation, characterization analysis, and control device for synchronous motor generating iron loss

Abstract

To provide a mathematical model that can be used for simulation, characterization-analysis, and control for a three-phase synchronous motor that generates iron loss in a stator, as well as a simulating device, characterization analysis device, or control device for a synchronous motor.SOLUTION: A mathematical model solves a problem regarding a stator reaction flux and rotor flux constituting a stator flux by providing an equivalent iron loss resistance so that iron losses occur in the stator reaction flux, while the iron losses does not occur in the rotor flux, and a voltage drop due to the equivalent iron loss resistance and a back electromotive force due to the stator reaction flux are roughly equal.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] This invention relates to a mathematical model-based simulator, characteristic analyzer, and controller for three-phase synchronous motors in which the rotor rotates at the same average electrical speed as the stator power frequency, particularly for synchronous motors that generate iron loss. Known types of synchronous motors include permanent magnet synchronous motors with only permanent magnets as the rotor field, wound field synchronous motors with only a field winding, and hybrid field synchronous motors with both permanent magnets and a field winding.

[0002] In the present invention, the portion of a synchronous motor on which a winding through which an AC current flows is called a "stator." In the present invention, the "stator" is synonymous with the "armature."

[0003] Terms such as "stator flux" and "stator flux linkage" are widely used synonymously to refer to the total magnetic flux that links with the stator winding. In the present invention, this magnetic flux is generally referred to as stator flux. Terms such as "armature reaction flux" and "stator reaction flux" are widely used synonymously to refer to the magnetic flux that is generated by the stator current and that links with the stator winding. In the present invention, this magnetic flux is generally referred to as stator reaction flux.

[0004] In the present invention, the magnetic flux generated by the rotor field and interlinked with the stator winding is referred to as the "rotor magnetic flux." According to the definition of terms used in the present invention, the stator reaction magnetic flux can also be rephrased as "magnetic flux obtained by removing the rotor magnetic flux from the stator magnetic flux."

[0005] In the present invention, the inductance of the stator winding is simply referred to as inductance. For simplicity, the d-axis stator inductance and the q-axis stator inductance are referred to as d-axis inductance and q-axis inductance, respectively.

[0006] In the present invention, two-dimensional space (plane) is considered in polar coordinates, and the three terms angle, spatial position, and spatial phase are used interchangeably. These units are "radians (rad)" or "degrees (degree)." The positive direction of angle, spatial position, and spatial phase in the present invention may be defined as either left-handed (counterclockwise) or right-handed (clockwise). However, in this specification, to maintain simplicity of explanation, the positive direction of angle, spatial position, and spatial phase will be defined as left-handed (counterclockwise) to explain the present invention. This does not cause a loss of generality of the present invention.

[0007] In the present invention, in principle, in a dq synchronous coordinate system (described later in detail using FIG. 1) consisting of two orthogonal axes, the d axis and the q axis, parameters, physical quantities, etc. associated with each axis are indicated with the subscripts d and q to clearly indicate their relationship with each axis. [Background technology]

[0008] The three-phase synchronous motor targeted by this invention is a synchronous motor that has a rotor field and generates rotor magnetic flux. Examples of this type of synchronous motor include permanent magnet synchronous motors, wound-field synchronous motors, and hybrid field synchronous motors. This invention is applicable to all three-phase synchronous motors that generate rotor magnetic flux. However, the core of this invention lies in the mathematical modeling of iron loss that occurs in the stator. For this simple explanation, a permanent magnet synchronous motor with only a permanent magnet in the rotor as the rotor field is suitable. With this in mind, the following explanation will primarily use a permanent magnet synchronous motor as the three-phase synchronous motor to clearly explain the core of this invention.

[0009] Prior inventions relating to the mathematical model of a synchronous motor that is the subject of the present invention, as well as simulators, characteristic analyzers, and controllers based on the mathematical model, are listed in, for example, Non-Patent Documents 1 to 3.

[0010] Before explaining the mathematical model used in Non-Patent Document 1 and elsewhere, let us first explain the coordinate system in which the mathematical model is defined. Consider Figure 1. The rotor phases θα and θγ of a permanent magnet synchronous motor are the phases of the rotor magnetic flux (north pole phase). The figure depicts three two-axis Cartesian coordinate systems for a permanent magnet synchronous motor: the dq synchronous coordinate system, which rotates at an electrical speed ω2n and is synchronized with the rotor without phase difference; the αβ fixed coordinate system; and the γδ generalized coordinate system, which rotates at an arbitrary speed ωγ. In the figure, the direction from the base axis to the counter axis is defined as the positive direction. Therefore, the counter axis is π / 2 rad ahead of the main axis. The rotor phases θα and θγ are based on the α axis and the γ axis, respectively. The γδ generalized coordinate system is the most general coordinate system, encompassing the αβ fixed coordinate system and the dq synchronous coordinate system as special cases. The position of the base axis (α axis) of the αβ fixed coordinate system, which is the basis for phase calculation, is generally selected to be the center position of the u-phase winding of the uvw three-phase winding.

[0011] To drive a synchronous motor, it is necessary to minimize losses caused by the stator current. Typical examples of this type of loss are copper loss and iron loss. Generally, iron loss is dominant in speed regions above the rated speed. A mathematical model is required to generate a stator current that generates the desired torque while minimizing the total loss consisting of copper loss and iron loss at any speed. In other words, a mathematical model is essential for building a simulator, characteristic analyzer, and controller for a synchronous motor that contributes to the rational generation of stator current. It is common practice to "model iron loss, which is loss in the magnetic circuit, using an equivalent iron loss resistance in the electric circuit in a mathematical model" (see Non-Patent Documents 1 to 3).

[0012] The "conventional mathematical model that takes iron loss into consideration" for a permanent magnet synchronous motor, which is a typical synchronous motor, is characterized by "arranging an equivalent iron loss resistance in parallel with the stator magnetic flux that is composed of the stator flux linkage and the rotor magnetic flux" (see Non-Patent Documents 1 to 3).

[0013] Fig. 7 shows the state of the equivalent iron loss resistance Rc arranged in parallel to the stator magnetic flux φ1 as a virtual vector circuit using 2 × 1 physical quantities (current, magnetic flux) defined on a γδ general coordinate system for a permanent magnet synchronous motor (see Non-Patent Documents 1 to 3). The main points of the parallel arrangement in the figure can also be described using formulas as follows:

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[0014] D(s,ωγ) in equation (1b) is a 2×2 matrix with the time differential operator s as its diagonal element, and is defined as follows when I is a 2×2 unit matrix:

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[0015] When minimizing total loss based on the conventional "mathematical model that takes iron loss into account," the stator current is controlled to reduce iron loss caused by rotor magnetic flux. As a result, even when no torque is generated, a non-zero current is required to be generated according to the speed.

[0016] For efficient driving by the flow of stator current, it is important to reduce iron loss caused by the stator current, that is, iron loss caused by stator reaction flux. In other words, from the perspective of efficient driving by the flow of stator current, iron loss caused by rotor flux that can occur without the need for current can be ignored.

[0017] Based on previous mathematical models, the flow of stator current that reduces iron loss due solely to stator reaction flux requires separating iron loss due to stator reaction flux from iron loss due to rotor flux. However, this separation is not easy. To achieve this, a new mathematical model based on the premise that "only stator reaction flux generates iron loss" is developed. Based on this mathematical model, a realistic approach is to generate a stator current that minimizes the total loss, consisting of copper loss and iron loss, while still generating the desired torque. In other words, to develop a simulator, characteristic analyzer, or controller for a three-phase synchronous motor that contributes to the rational generation of a stator current that minimizes the total loss, consisting of copper loss and iron loss, a new mathematical model based on the premise that "rotor flux does not generate iron loss, and only stator reaction flux generates iron loss" is essential. [Prior art documents] [Non-patent literature]

[0018] [Non-Patent Document 1] Shinji Shinnaka: "Vector Control of Permanent Magnet Synchronous Motors", ISBN 978-4-274-22950-3, Ohmsha, pp.176-233(2022-10) [Non-patent document 2] Shinji Shinnaka: "Construction of a new mathematical model with parallel iron loss terms for salient-pole synchronous motors based on a unified stator model," Transactions of the Society of Instrument and Control Engineers, Vol. 36, No. 2, pp. 223-225 (2000-02) [Non-patent document 3] Shinji Shinnaka: "Block diagram of AC motor with stator iron loss using general coordinate vector signals", Transactions of the Institute of Electrical Engineers of Japan, Vol. 120, No. 12, pp. 1492-1500 (2000-12) [Non-patent document 4] Shinnaka Shinji: "Detailed Explanation of Vector Control Technology for Synchronous Motors", ISBN 978-4-501-11820-4, Tokyo Denki University Press, pp. 404-470 (2019-6) Summary of the Invention [Problem to be solved by the invention]

[0019] The present invention has been made under the above circumstances. The object of the present invention is to establish and provide a new mathematical model for a three-phase synchronous motor that requires consideration of iron loss, which is based on the premise that "rotor flux does not generate iron loss, and only stator reaction flux generates iron loss," based on the recognition that "it is practical to generate a stator current that minimizes the total loss consisting of copper loss and iron loss while generating a desired torque, based on a mathematical model that assumes that only stator reaction flux generates iron loss," and further to provide a new simulator, characteristic analyzer, or controller based on this model. [Means for solving the problem]

[0020] In order to achieve the above object, the invention of claim 1 is a mathematical model stand-type simulator, characteristic analysis device, or control device for a three-phase synchronous motor having a field formed by a permanent magnet or field winding in the rotor and generating iron loss in the stator having a stator winding, characterized in that the stand-type mathematical model is provided with an equivalent iron loss resistance that equivalently simulates the iron loss generated in the stator, and the equivalent iron loss resistance is provided so that the voltage drop due to the equivalent iron loss resistance and the back electromotive force due to the stator reaction magnetic flux are approximately equal.

[0021] The invention of claim 2 is a mathematical model standpoint simulator, characteristic analyzer, or controller for a three-phase synchronous motor according to claim 1, in which the main axis is the γ axis, the secondary axis is the δ axis, and the phase of the main axis is advanced by π / 2 [rad] relative to the main axis, and a two-axis orthogonal coordinate system that rotates at an arbitrary speed ωγ is defined as a γδ generalized coordinate system, and in the γδ generalized coordinate system, the stator current of a 2×1 vector quantity is expressed as i1, and a part of the stator current that does not contribute to the generation of the stator reaction magnetic flux and that contributes to the generation of iron loss together with the equivalent iron loss resistance is expressed as i2. The stator iron loss current, which is a 2×1 vector quantity that contributes equivalently, is expressed as iR; the stator load current, which is a part of the stator current and does not contribute to the generation of stator iron loss but contributes to the equivalent generation of the stator reaction flux, is expressed as iL; the stator reaction flux, which is a 2×1 vector quantity that is equivalently generated by the stator load current, is expressed as φi; the equivalent iron loss resistance is expressed as Rc; the time differential operator is expressed as s; the 2×2 unit matrix is ​​expressed as I; and the 2×2 symmetric matrix expressed as J is defined as follows:

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[0022] The effects of the present invention will now be explained. Iron loss, which is loss in a magnetic circuit, is known to be proportional to the square of the magnetic flux flowing through the magnetic circuit. It is also well known to those skilled in the art that the dominant losses that make up iron loss are eddy current loss and hysteresis loss. It is known that eddy current loss and hysteresis loss are proportional to the square and absolute value of the current frequency, respectively. In a three-phase synchronous motor, the current frequency is essentially equal to the electrical speed ω2n. Mathematical models for simulating, analyzing, or controlling electric motors must be compact enough for these purposes. To ensure compactness, mathematical models of electric motors model iron loss, which is loss in the magnetic circuit, equivalently as loss in the electric circuit. The electric circuit element that can generate loss is resistance. In mathematical models of electric motors, an equivalent iron loss resistance is introduced, and iron loss is expressed as loss due to the equivalent iron loss resistance. The loss due to equivalent iron loss resistance is best expressed as the original characteristics of iron loss, "proportional to the square of the magnetic flux" and "proportional to the square of the frequency or absolute frequency."

[0023] According to the invention of claim 1, the mathematical model includes an equivalent iron loss resistance that simulates the iron loss generated by a three-phase synchronous motor, and the equivalent iron loss resistance is provided so that the voltage drop due to the equivalent iron loss resistance is approximately equal to the back electromotive force due to the stator reaction flux of the three-phase synchronous motor. As a result, the loss due to the equivalent iron loss resistance according to the invention of claim 1 can be expressed as "proportional to the square of the stator reaction flux" and "proportional to the squared frequency or absolute frequency," similar to the original characteristics of iron loss. This will be demonstrated in detail using mathematical formulas when explaining the first embodiment (see the explanation using Figure 3 and equations (11) to (13) below). Due to the novel characteristic of "proportional to the square of the stator reaction flux," the mathematical model based on claim 1 exhibits characteristics consistent with empirical knowledge of actual motors, namely, "the optimal stator current when no torque is generated is zero, regardless of the speed of the synchronous motor." Furthermore, according to the invention of claim 1, it is possible to utilize a mathematical model that is applicable over a wide speed range from low speeds to speeds exceeding the rated speed and that reflects actual iron loss characteristics, and as a result, it is possible to construct an actual simulator, characteristic analyzer, or controller for a three-phase synchronous motor based on this mathematical model.

[0024] Next, we will explain the effects of the invention of claim 2. A mathematical model that can be used in a three-phase synchronous motor simulator, characteristic analyzer, or controller must not be complex in terms of practicality. It must be simple. The requirements of the invention of claim 1 are constructed and expressed in the simplest form as two mathematical equations in the invention of claim 2, namely, equation (5). Moreover, this equation is constructed in the most general γδ coordinate system. Consequently, the invention of claim 2 has the effect of enabling the construction of a mathematical model that can be used in a three-phase synchronous motor simulator, characteristic analyzer, or controller in the simplest and most versatile form, and further enabling the construction of these mathematical model-based devices in a simple and versatile form. As a result, the invention of claim 2 also has the effect of enhancing the effects of the invention of claim 1. [Brief explanation of the drawings]

[0025] [Figure 1] "Diagram showing the relationship between three types of two-axis Cartesian coordinate systems" [Figure 2] "Diagram showing a virtual vector circuit with an equivalent core loss resistance according to the present invention for a three-phase synchronous motor" [Figure 3] "Diagram showing a detailed configuration example of equivalent iron loss resistor" [Figure 4] "A diagram showing an example of the configuration of a simulator or characteristic analyzer on a γδ generalized coordinate system according to the present invention" [Figure 5] "A diagram showing an example of response by a simulator or characteristic analyzer on a dq synchronous coordinate system according to the present invention" [Figure 6] "A diagram showing an example of the configuration of a drive system using a control device according to the present invention" [Figure 7] "Diagram showing an example of a virtual vector circuit with equivalent iron loss resistance according to a prior invention for a three-phase synchronous motor" DETAILED DESCRIPTION OF THE INVENTION

[0026] Preferred embodiments of the present invention will now be described in detail with reference to the drawings. [Example]

[0027] A three-phase synchronous motor is a type of electrical circuit. Therefore, a mathematical model of such a motor must include a circuit equation (first basic equation) that models its dynamic characteristics as an electrical circuit. A three-phase synchronous motor is also a torque generator, which generates torque. Therefore, a mathematical model of such a motor must include a torque generation equation (second basic equation) that models its torque generation characteristics. A three-phase synchronous motor is also an energy converter, which converts electrical energy into mechanical energy. Therefore, a mathematical model of such a motor must include an energy transfer equation (third basic equation) that models the dynamic characteristics of energy conversion. The three basic equations that make up the mathematical model are mathematical models of the same three-phase synchronous motor from three different perspectives: electrical circuit, torque generator, and energy converter. The subject of the mathematical model is the same three-phase synchronous motor. Consequently, the three basic equations must be mathematically consistent. Hereinafter, this consistency will be referred to as "self-consistency."

[0028] A self-consistent mathematical model for a three-phase synchronous motor using the inventions of claims 1 and 2 is shown below. According to the inventions of claims 1 and 2, that is, "an equivalent iron loss resistance that simulates iron loss equivalently is provided," and "an equivalent iron loss resistance is provided so that the voltage drop due to the equivalent iron loss resistance and the back electromotive force due to the stator reaction flux are roughly equal." Alternatively, this requirement can be formulated and expressed in a simple form as equation (5), which can be used. Applying these claimed requirements to a permanent magnet synchronous motor, a representative three-phase synchronous motor, allows for the creation of a virtual vector circuit in the γδ generalized coordinate system shown in Figure 2.

[0029] From FIG. 2, the following equation can be constructed as a mathematical model (particularly, the circuit equation (first basic equation)) on the γδ general coordinate system.

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[0030] In the above mathematical model, the 2x1 vector signals v1, i1, φi, and φm are the stator voltage, stator current, stator reaction flux, and rotor flux defined in the γδ generalized coordinate system. Also, iR and iL are the stator iron loss current that generates iron loss equivalently, and the stator load current that contributes to the stator reaction flux, respectively. Q(θγ) and u(θγ) are a 2x2 mirror matrix and a 2x1 unit vector, respectively, defined as follows:

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[0031] The above equation (6), i.e., equations (6b) and (6c) constituting the circuit equation (first basic equation), are completely identical to the two equations (5a) and (5b) of the invention of claim 2, which are constructed and formulated in a simplified form from the invention of claim 1. This fact is particularly pointed out.

[0032] According to the inventions of claims 1 and 2, the following equation is constructed as a torque generation equation (second basic equation) in the γδ general coordinate system that should be consistent with the circuit equation of equation (6), when the number of pole pairs is expressed as Np.

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[0033] According to the inventions of claims 1 and 2, the following equation is constructed as an energy transfer equation (third basic equation) in the γδ general coordinate system, which should be consistent with the circuit equation (first basic equation) of equation (6) and the torque generation equation (second basic equation) of equation (9).

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[0034] The self-consistency of the three basic equations that make up the mathematical model (circuit equation (6), torque generation equation (9), and energy transfer equation (10)) can be mathematically and rigorously proven by following the procedure below. The instantaneous input power, which is the left side of equation (10), is processed and calculated using equation (6), the first basic equation. In the processing stage, the mechanical output is calculated using torque using equation (9), the second basic equation. This allows the third basic equation (10) to be derived. The self-consistency of the three basic equations mathematically demonstrates that all three basic equations (circuit equation (6), torque generation equation (9), and energy transfer equation (10)) comply with the inventions of claims 1 and 2.

[0035] Equation (10), i.e., the energy transfer equation (third basic equation), means the following. The left side of the equation represents the instantaneous power input to the three-phase motor. The first term on the right side of the equation represents the copper loss due to the resistance of the stator winding, the second term represents the iron loss due to the equivalent iron loss resistance, the third term represents the differential value of the magnetic energy stored in the stator inductance, and the fourth term represents the mechanical power (unit: watts, instantaneous value of shaft output) output from the rotating shaft. The right side of equation (10) does not contain any unclear terms that could raise doubts. In other words, the mathematical model according to the inventions of claims 1 and 2 (a mathematical model consisting of three basic equations) incorporates iron loss in a manner that leaves no room for doubt.

[0036] The dominant losses that make up iron loss are eddy current loss and hysteresis loss. We will show below that the mathematical model according to the present invention can appropriately express eddy current loss and hysteresis loss. First, some preparation is required. When the norm of the stator reaction flux is constant and the instantaneous frequency of the stator reaction flux is ω1f, the following relationship holds:

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[0037] With the above preparations in place, we move on to a detailed evaluation of the loss expression. The iron loss due to the equivalent iron loss resistance shown as the second term on the right-hand side of equation (10) can be evaluated as follows, taking equations (11) and (12) into consideration:

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[0038] When the conditions of the dq synchronous coordinate system (θγ=0, ωγ=ω2n) are applied to the mathematical model of the γδ general coordinate system, the model becomes a mathematical model on the dq synchronous coordinate system (see Figure 1).Furthermore, when the conditions of the αβ fixed coordinate system (θγ=θα, ωγ=0) are applied to the mathematical model of the γδ general coordinate system, the model becomes a mathematical model on the αβ fixed coordinate system (see Figure 1). [Example]

[0039] Three-phase synchronous motors include permanent magnet synchronous motors with only permanent magnets as rotor field magnets, wound field synchronous motors with only field windings, and hybrid field synchronous motors with both permanent magnets and field windings. The difference between the three types of three-phase synchronous motors lies in the rotors, and the stators of the three types of three-phase synchronous motors are fundamentally the same. The present invention, as set forth in claims 1 and 2, relates to modeling of iron loss that occurs in a stator with stator windings. As is clear from the above, there is no difference among the three types of three-phase synchronous motors in terms of modeling of iron loss that occurs in the stator.

[0040] For example, the circuit equations of a hybrid field synchronous motor, which has a permanent magnet and field winding in the field, are essentially the same as equations (6a) to (6e) for the stator, which generates iron loss. On the other hand, equation (6f) for the rotor magnetic flux φm caused by the rotor can be rewritten as follows:

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[0041] Details of the mathematical models relating to the rotor field of a hybrid field synchronous motor and a wound field synchronous motor are well known to those skilled in the art through, for example, Non-Patent Document 4, and therefore further explanation will be omitted. As is clear from the above explanation, the parts relating to the iron loss generated in the stator remain unchanged, regardless of the type of three-phase synchronous motor, in the circuit equation (6), the torque generation equation (9), and the energy transfer equation (10). [Example]

[0042] An example of a new embodiment based on the invention of claims 1 and 2 is shown below. The circuit equation (first basic equation) of equation (6) can be modified as follows: In other words, the structure described by the following equation can be given.

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[0043] If we use equations (15) and (16), we obtain Figure 4, which shows a simulation device or characteristic analysis device for a three-phase synchronous motor on the γδ general coordinate system. The various signals and parameters in this figure have already been explained in relation to the related equations. For reference, in this figure, the mechanical load system consisting of the rotor and the load connected to it is represented by a dashed block, with its mechanical dynamic characteristics being assumed to be approximately expressed by the following equation:

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[0044] Using a simulator or characteristic analyzer constructed on the γδ generalized coordinate system in Figure 4, it is possible to simulate and analyze the instantaneous values ​​of the stator current i1, stator load current iL, stator iron loss current iR, and various magnetic fluxes related to these currents, in response to the applied stator voltage v1. It is also possible to simulate and analyze the instantaneous value of the generated torque. Furthermore, by applying these simulated and analyzed physical quantities to equation (10), it is possible to simulate and analyze the instantaneous values ​​of copper loss, iron loss, magnetic energy, and mechanical power. [Example]

[0045] Applying the conditions of the dq synchronous coordinate system (θγ = 0, ωγ = ω2n) to the simulator or characteristic analysis device constructed on the γδ generalized coordinate system in Figure 4 results in a simulator or characteristic analysis device constructed on the dq synchronous coordinate system. Figure 5 shows examples of instantaneous responses of various physical quantities obtained by the simulator or characteristic analysis device constructed on the dq synchronous coordinate system. The illustrated responses are at the rated speed, specifically, a mechanical speed of 180 rad / s. The number of pole pairs Np of the synchronous motor under test is Np = 3. Figures 5(a), (b), and (c) show the current response, torque response, and loss response, respectively. The instantaneous responses of all physical quantities are displayed synchronized in time. The waveforms in Figure 5(a) represent, from top to bottom, the q-axis element iq of the stator current, the q-axis element iLq of the stator load current, the q-axis element iRq of the stator iron loss current, the d-axis element iLd of the stator load current, the d-axis element iRd of the stator iron loss current, and the d-axis element id of the stator current.The waveforms in Figure 5(b) represent, from top to bottom, the total torque τ, the magnet torque τm, and the reluctance torque τr.The waveforms in Figure 5(c) represent, from top to bottom, the iron loss and copper loss.

[0046] It should be noted that the instantaneous response of the rated speed in Figure 4 shows a response that supports the effect of the invention of claim 1, which states that "regardless of the speed of a synchronous motor, the best stator current when no torque is generated is zero," as explained in the "Effectiveness of the Invention" section. [Example]

[0047] If the conditions of the αβ-fixed coordinate system (θγ = θα, ωγ = 0) are applied to the simulator or characteristic analysis device constructed on the γδ general coordinate system in Figure 4, it becomes a simulator or characteristic analysis device constructed on the αβ-fixed coordinate system. Depending on the purpose of using the simulator or characteristic analysis device, constructing it on the αβ-fixed coordinate system may be the most useful. [Example]

[0048] An example of an embodiment of a control device based on the inventions of claims 1 and 2 is shown below. An example of a drive system using a control device based on the inventions of claims 1 and 2 is shown in Fig. 6. Fig. 6 illustrates the entire drive system including the control device. The drive system is broadly composed of a synchronous motor 1, a power conversion device 2 (shown as a dashed block), and a control device 3 (shown as a dashed block). The power conversion device is composed of a power converter 21 and a current detector 22. The control device 3 is broadly composed of a command converter 31 and a current control unit 32 (shown as a dashed block). The current control unit 32 includes a three-phase to two-phase converter 321a, a two-phase to three-phase converter 321b, vector rotators 322a and 322b, and a current controller 323 to perform current control. The current control unit also includes a phase detector (resolver, encoder, etc.) 324 for detecting the rotor phase, a speed detector 325 for detecting the rotor speed by performing approximate differentiation of the rotor phase obtained by the phase detector, and a cosine / sine signal generator 326 for processing the rotor phase obtained by the phase detector and generating cosine and sine signals. For simplicity, in the figure, multiple scalar signals are treated as a single vector signal, and multiple scalar signal lines are represented by a single thick signal line. The three-phase signal (i.e., 3x1 vector signal) on the right side of the three-phase to two-phase converter and two-phase to three-phase converter, and the two-phase signal (i.e., 2x1 vector signal) on the left side are represented by a single thick signal line. The subscripts t, r, and s on the vector signals indicate the signal in the uvw coordinate system, the signal in the αβ fixed coordinate system, and the signal in the dq synchronous coordinate system, respectively. The core of this embodiment lies in the command converter 31. The devices other than this device are basically the same as those in the prior invention (see Non-Patent Document 1) and are well known to those skilled in the art, so a description of these devices will be omitted. Next, the command converter, which is the core of this embodiment, will be described.

[0049] The command converter 31 is responsible for generating the stator current command value i1* from the torque command value τ*. For example, as shown in the torque generation equation (9), there are an infinite number of stator currents that generate the same torque. Among the infinite number of stator currents, the most important one is the current that minimizes the sum of copper loss and iron loss (total loss) contained in the energy transfer equation (third basic equation) corresponding to the torque generation equation (second basic equation). The torque generation equation (second basic equation) (9) corresponds to the energy transfer equation (third basic equation) (10). In equation (10), the first term on the right-hand side represents copper loss, and the second term represents iron loss. The command converter 31 generates a current command value that minimizes the sum of copper loss and iron loss (total loss) from the torque command value, using the relationship in the circuit equation (first basic equation) (6) as well as the torque generation equation (second basic equation) and energy transfer equation (third basic equation) that constitute the mathematical model.

[0050] When configuring the command converter 31, the relationship between three currents, stator current, stator load current, and stator iron loss current, is utilized by utilizing the circuit equation (first basic equation) of equation (6) which is directly based on the inventions of claims 1 and 2. The relationship between the three currents on the γδ general coordinate system is derived and organized as follows from the circuit equation (first basic equation) of equation (6):

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[0051] The drive system configuration in Fig. 6 is intended for a permanent magnet synchronous motor as the three-phase synchronous motor. When a wound field synchronous motor or a hybrid field synchronous motor is intended for the three-phase synchronous motor, a field circuit including a DC inverter for generating a field is required. The configuration of the field circuit in a motor drive system is well known to those skilled in the art, as seen in Non-Patent Document 4 and the like, and therefore a description thereof will be omitted.

[0052] In wound-field synchronous motors and hybrid-field synchronous motors, the magnetic flux strength of the rotor magnetic flux becomes variable due to the presence of a field circuit (see equation (14)). If the variability of magnetic flux strength is taken into consideration, there is no essential change in the configuration of the command converter, whether or not there is a field circuit. In other words, the configuration of a command converter for wound-field synchronous motors and hybrid-field synchronous motors is basically the same as the configuration of a command converter for a permanent magnet synchronous motor. [Industrial Applicability]

[0053] The present invention is suitable for use in simulators, characteristic analyzers, and controllers for three-phase synchronous motors in applications requiring efficient drive over a wide range (from low speeds to speeds exceeding the rated speed), such as main drive motors for battery electric vehicles, fuel cell electric vehicles, and hybrid electric vehicles, and high-speed motors for home appliances. [Explanation of symbols]

[0054] 1 synchronous motor 2. Power conversion device 21 Power Converter 22 Current detector 3. Control device 31 Command converter 32 Current control section 321a Three-phase to two-phase converter 321b Two-phase to three-phase converter 322a Vector Rotator 322b Vector Rotator 323 Current Controller 324 Phase Detector 325 Speed ​​Detector 326 Cosine and Sine Signal Generator

Claims

1. A mathematical model-based simulator, characteristic analyzer, or controller for a three-phase synchronous motor having a rotor with a permanent magnet or a field winding and generating iron loss in a stator having a stator winding, The mathematical model of the base is an equivalent iron loss resistor that equivalently simulates iron loss occurring in the stator; The equivalent iron loss resistance is provided so that the voltage drop due to the equivalent iron loss resistance and the back electromotive force due to the stator reaction magnetic flux are approximately equal. A mathematical model-based simulator, characteristic analyzer, or controller for a three-phase synchronous motor.

2. The main axis is the γ axis, and the secondary axis is the δ axis, which is at a phase lead of π / 2 [rad] relative to the main axis. A two-axis Cartesian coordinate system that rotates at an arbitrary speed ωγ is called the γδ general coordinate system. In the γδ generalized coordinate system, the stator current, which is a 2×1 vector quantity, is expressed as i1; the stator iron loss current, which is a part of the stator current, which does not contribute to the generation of the stator reaction flux and which contributes equivalently to the generation of iron loss together with the equivalent iron loss resistance, is expressed as iR; the stator load current, which is a part of the stator current, which does not contribute to the generation of stator iron loss and contributes to the equivalent generation of the stator reaction flux, is expressed as iL; and the stator reaction flux, which is a 2×1 vector quantity and which is generated equivalently by the stator load current, is expressed as φi; The equivalent iron loss resistance is expressed as Rc, the time differential operator is expressed as s, the 2×2 unit matrix is ​​expressed as I, and the 2×2 symmetric matrix expressed as J is defined as follows: When the 2 × 2 matrix expressed by D(s, ωγ) is defined as follows: The mathematical model is expressed by the relationship between the following two equations:

2. The mathematical model-based simulator, characteristic analyzer, or controller for a three-phase synchronous motor according to claim 1, wherein the mathematical model-based simulator, characteristic analyzer, or controller is configured to satisfy at least the following:

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