Permanent magnet synchronous motor all-condition design method considering driver constraint

Abstract

The invention relates to a permanent magnet synchronous motor full-working-condition design method considering driver constraints, and belongs to the technical field of permanent magnet synchronous motor design, and the method comprises the following steps: building a mathematical model of a permanent magnet synchronous motor; calculating the electromagnetic relation of the motor in the constant torque maximum torque / current control mode; calculating the electromagnetic relation of the motor under the constant-power weak magnetic control; and according to the model and the electromagnetic relationship, carrying out full-condition design on the motor. Based on the mathematical model and the control mode of the permanent magnet synchronous motor, by analyzing the influence of the direct current bus voltage and the inverter circuit output current on the maximum rotating speed, the maximum torque and the current density of the motor, the constraint condition of the driver performance on the motor design can be determined. According to the method, whether the electromagnetic performance of the design scheme reaches the standard or not can be calculated and analyzed more quickly, and the design efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet synchronous motor design, and relates to a full-operating-condition design method for a permanent magnet synchronous motor taking driver constraints into consideration. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in new energy vehicles, industrial drives, and other fields due to their high efficiency, high power density, and excellent dynamic performance. However, the actual operating performance of a motor depends not only on its design but is also significantly constrained by the performance of its driver. Parameters such as the driver's DC bus voltage and inverter circuit output current directly limit the motor's operating boundaries (such as maximum speed and maximum torque). Traditional motor design methods typically design the motor itself first and then design a suitable driver for that motor. However, this design process focuses solely on the electromagnetic performance of the motor itself and ignores the impact of driver performance constraints. This makes it difficult for the design scheme to meet system requirements in actual applications and increases the difficulty of driver design. Therefore, it is of great significance to propose a permanent magnet synchronous motor design method that considers driver constraints. Summary of the Invention

[0003] In view of this, an object of the present invention is to provide a full-operating-condition design method for a permanent magnet synchronous motor taking into account drive constraints, aiming to maximize the performance of the permanent magnet synchronous motor in a wide speed and torque range.

[0004] In order to achieve the above object, the present invention provides the following technical solutions:

[0005] A full-operation-condition design method for a permanent magnet synchronous motor considering drive constraints comprises the following steps:

[0006] Establish a mathematical model of permanent magnet synchronous motor;

[0007] Calculate the electromagnetic relationship of the motor under constant torque maximum torque / current control mode;

[0008] Calculate the electromagnetic relationship of the motor under constant power flux weakening control;

[0009] Based on the above model and electromagnetic relationship, the motor is designed for all working conditions.

[0010] Furthermore, the mathematical model of the permanent magnet synchronous motor is as follows:

[0011] According to the voltage equation of the permanent magnet synchronous motor in the ABC three-phase stationary coordinate system, after performing Clark transformation and Park transformation, the voltage equation in the dq axis rotating coordinate system is obtained as follows:

[0012]

[0013] The motor torque equation in the dq axis rotating coordinate system is:

[0014]

[0015] u d 、u q are the stator d and q axis voltages respectively; i d 、i q are the stator d-axis and q-axis currents respectively; ψ d , ψ q are the stator d-axis and q-axis flux respectively; L d , L q are the d-axis and q-axis inductances of the stator winding respectively; i f is the equivalent excitation current of the permanent magnet; ψ f is the flux linkage generated by the fundamental magnetic field of the permanent magnet in the stator winding; p is the number of motor pole pairs;

[0016] Expressing formula (1) and formula (2) in space vector form, we get the space vector diagram of the permanent magnet synchronous motor, which includes the stator current vector i s and stator voltage vector u s .

[0017] Furthermore, the calculation of the electromagnetic relationship of the motor under the constant torque maximum torque / current control mode specifically includes:

[0018] The limit value U of the effective phase voltage of the permanent magnet synchronous motor lim Due to the limitation of the inverter DC bus voltage, the effective value of the motor phase current is limited to I lim Limited by the maximum output current of the inverter; when the DC side voltage of the inverter is U d When , the maximum effective value of the fundamental voltage of the motor in the dq axis coordinate system is:

[0019]

[0020] When the motor is running stably, the voltage and current meet the following requirements:

[0021]

[0022] Where u s is the amplitude of the stator voltage, i s is the effective value of the stator current;

[0023] Substituting formula (1) into formula (4), the expression of the rotational speed is obtained as follows:

[0024]

[0025] The electromagnetic torque of the motor is expressed as:

[0026]

[0027] For salient-pole permanent magnet synchronous motors, d -i q In the plane, its maximum torque / current trajectory satisfies formula (7):

[0028]

[0029] Solving equations (4) and (7) together, we can obtain the following equation: the permanent magnet synchronous motor adopts maximum torque / current control and the current reaches the limit value i lim The expressions of the quadrature and direct axis currents are:

[0030]

[0031] where i lim Indicates the maximum effective value of the inverter output current;

[0032] When the maximum torque / current control is used in the constant torque control range, the voltage limit ellipse, current limit circle, and maximum torque / current trajectory will converge at point A as the speed continues to increase. This is the maximum speed of the motor in the constant torque range, that is, the turning speed, and its expression is:

[0033]

[0034] Where,

[0035] Furthermore, the calculation of the electromagnetic relationship of the motor under constant power flux weakening control specifically includes the following steps:

[0036] For salient-pole permanent magnet synchronous motors, the control strategy is optimized based on the speed range, subject to the constraints of a certain inverter capacity. Below the breakover speed, maximum torque-to-current ratio control is used to maximize torque output and optimize servo control performance. Above the breakover speed, constant power operation is achieved through field weakening control, thereby expanding the motor's speed range.

[0037] For embedded permanent magnet synchronous motors, since the quadrature axis inductance is greater than the direct axis inductance, the motor’s salient pole ratio ρ>1;

[0038] when i lim <ψ f / L d When the speed increases continuously in the initial constant torque stage, the voltage limit ellipse gradually decreases and finally converges at point A. The turning speed at this time is ω bAt this time, the motor terminal voltage reaches the limit value, and weak magnetic control must be used to continue to increase the speed. The control current vector increases along the current limit circle, and the demagnetization direct axis current moves from point A to point B. At point B, the direct axis demagnetization current is the largest and reaches the highest speed. In the AB weak magnetic control stage, as the demagnetization direct axis current increases, the motor will run to the maximum electromagnetic power point P, and the quadrature and direct axis currents i corresponding to the maximum power point of the motor are obtained. dP 、i qP and speed ω P Power P emP for:

[0039]

[0040] when i lim =ψ f / L d When , since the center of the voltage limit ellipse is on the current limit circle, the quantities corresponding to point D are as follows, and the corresponding weak magnetic capacity is infinite at this time:

[0041]

[0042] where i dD 、i qD Respectively represent the quadrature and direct axis currents at point D, ω D Indicates the speed at point D, P emD Indicates the power at point D;

[0043] when i lim >ψ f / L d When , the center of the voltage limit ellipse is inside the current limit circle, the motor power reaches its maximum at point C, and then maintains constant power to run to the highest speed point, and the highest speed and weak magnetic capability are infinite; the quantities corresponding to the motor maximum power point C are written as:

[0044]

[0045] where i dC 、i qC Respectively represent the cross-axis and direct-axis currents at point C, ω C Indicates the speed at point C, T emC Indicates the torque at point C.

[0046] Furthermore, the full-operating-condition design of the motor specifically includes:

[0047] Design the motor's technical specifications, including rated parameters, peak parameters, DC bus voltage, peak current, torque ripple, motor stator outer diameter, axial length, and cooling method;

[0048] In order to meet the maximum speed requirement in the constant torque area, the turning speed is calculated using formula (9);

[0049] In order to meet the peak torque requirement, the electromagnetic torque is calculated using formula (6);

[0050] In order to meet the speed requirement of the constant power zone under peak working conditions, formulas (10), (11), and (12) are used to calculate the quadrature and direct axis currents, shaft speed, torque, and power corresponding to the maximum power point of the motor.

[0051] The beneficial effects of the present invention are:

[0052] (1) Based on the mathematical model and control method of permanent magnet synchronous motor, by analyzing the influence of DC bus voltage and inverter circuit output current on the maximum speed, maximum torque and current density of the motor, the constraints of drive performance on motor design can be clearly defined.

[0053] (2) Compared with the direct motor design method, this method can more quickly calculate and analyze whether the electromagnetic performance of the design scheme meets the standards, thereby improving design efficiency.

[0054] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0056] Figure 1 It is the space vector diagram of permanent magnet synchronous motor;

[0057] Figure 2 is the maximum torque / current trajectory of the salient-pole permanent magnet synchronous motor;

[0058] Figure 3 Schematic diagram of the voltage limit ellipse and current limit circle trajectory; (a) is i lim <ψ f / L d Case (b) is i lim =ψ f / L d Case, (c) is i lim >ψ f / L d Condition;

[0059] Figure 4is the effective value of current at different torque and speed;

[0060] Figure 5 is the line voltage amplitude at different torque and speed;

[0061] Figure 6 is the motor efficiency at different torque and speed. DETAILED DESCRIPTION

[0062] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0063] It should be noted that the illustrations provided in the following embodiments are merely schematic illustrations of the basic concept of the present invention. Therefore, the illustrations only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0064] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the embodiments of the present invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring the embodiments of the present invention.

[0065] Example 1:

[0066] The present invention provides a full-operation-condition design method for a permanent magnet synchronous motor taking into account driver constraints, comprising the following steps:

[0067] Establish a mathematical model of permanent magnet synchronous motor;

[0068] Calculate the electromagnetic relationship of the motor under constant torque maximum torque / current control mode;

[0069] Calculate the electromagnetic relationship of the motor under constant power flux weakening control;

[0070] Based on the above model and electromagnetic relationship, the motor is designed for all working conditions.

[0071] Example 2:

[0072] The present invention provides a full-operation-condition design method for a permanent magnet synchronous motor taking into account driver constraints, comprising the following steps:

[0073] 1. Establish a mathematical model of permanent magnet synchronous motor

[0074] According to the voltage equation of the permanent magnet synchronous motor in the ABC three-phase stationary coordinate system, after performing Clark transformation and Park transformation, the voltage equation in the dq axis rotating coordinate system can be obtained as follows:

[0075]

[0076] The motor torque equation in the dq axis rotating coordinate system is:

[0077]

[0078] u d 、u q are the stator d and q axis voltages respectively; i d 、i q are the stator d-axis and q-axis currents respectively; ψ d , ψ q are the stator d-axis and q-axis flux respectively; L d 、L q are the d-axis and q-axis inductances of the stator winding respectively; i f is the equivalent excitation current of the permanent magnet; f is the flux linkage generated by the fundamental magnetic field of the permanent magnet in the stator winding; p is the number of motor pole pairs.

[0079] Expressing formula (1) and formula (2) in space vector form, we can get Figure 1 The permanent magnet synchronous motor space vector diagram is shown in Fig. s is the stator current vector, u s is the stator voltage vector.

[0080] 2. Calculate the electromagnetic relationship of the motor under constant torque maximum torque / current control mode

[0081] Maximum torque / current control is also called maximum torque per unit current output control, which is mostly used to control salient pole permanent magnet synchronous motors in the constant torque operation range. Since the operation of the permanent magnet synchronous motor is directly affected by the driver used, the limit value of the effective value of the motor phase voltage U lim Due to the limitation of the inverter DC bus voltage, the effective value of the motor phase current is limited to I lim It is limited by the maximum output current of the inverter. When the DC side voltage of the inverter is U d When , the maximum fundamental voltage effective value of the motor in the dq axis coordinate system can be expressed as:

[0082]

[0083] When the motor is running stably, the voltage and current should meet the following requirements:

[0084]

[0085] Where u s is the amplitude of the stator voltage, i s is the effective value of the stator current.

[0086] Substituting formula (1) into formula (4), the expression of the rotational speed can be obtained as follows:

[0087]

[0088] The electromagnetic torque of the motor can be expressed as:

[0089]

[0090] For salient-pole permanent magnet synchronous motors, d -i q In the plane, the maximum torque / current trajectory must satisfy the following formula (7), and its trajectory is as follows Figure 2 As shown:

[0091]

[0092] Solving equations (4) and (7) together, we can obtain the following equation: lim The expressions of the quadrature and direct axis currents are:

[0093]

[0094] When the maximum torque / current control is used in the constant torque control range, the voltage limit ellipse, current limit circle, and maximum torque / current trajectory will converge at point A as the speed continues to increase. This is the maximum speed of the motor in the constant torque range, that is, the turning speed, and its expression is:

[0095]

[0096] Where,

[0097] 3. Calculate the electromagnetic relationship of the motor under constant power weak magnetic control

[0098] Once the motor speed reaches the breakover speed, further increases in speed require a field-weakening control strategy. This requirement stems from the inherent characteristics of permanent magnet synchronous motors: their permanent magnet magnetomotive force is generated by the permanent magnets and cannot be directly adjusted. For salient-pole permanent magnet synchronous motors, the control strategy must be optimized across the speed range, within the constraints of a specific inverter capacity. Below the breakover speed, maximum torque-to-current ratio control is employed to maximize torque output and optimize servo control performance. Above the breakover speed, field-weakening control achieves constant power operation, thereby extending the motor's speed range.

[0099] For the embedded permanent magnet synchronous motor, since its quadrature axis inductance is greater than the direct axis inductance, the motor salient ratio ρ>1, and its corresponding voltage limit ellipse and current limit circle are as follows: Figure 3 shown.

[0100] when i lim <ψ f / L d When, such as Figure 3 As shown in (a), in the initial constant torque stage, the speed continues to increase, the voltage limit ellipse gradually decreases, and finally converges at point A. The turning speed at this time is ω b At this point, the motor terminal voltage reaches its limit, and field weakening control must be used to continue increasing the speed. The control current vector increases along the current limit circle, moving the demagnetizing direct-axis current from point A to point B. At point B, the direct-axis demagnetizing current is maximum and reaches the highest speed. During the AB field weakening control stage, as the demagnetizing direct-axis current increases, the motor will run to the maximum electromagnetic power point P. Because the motor speed is high during field weakening operation, the stator resistance copper and iron losses can be ignored. The quadrature and direct-axis currents and power corresponding to the motor's maximum power point can be obtained as:

[0101]

[0102] when i lim =ψ f / L d When, such as Figure 3 As shown in (b), since the center of the voltage limit ellipse is on the current limit circle, the corresponding quantities of point D are as follows. At this time, the corresponding weak magnetic capacity is infinite:

[0103]

[0104] when i lim >ψ f / L d When, such as Figure 3 As shown in (c), the center of the voltage limit ellipse is inside the current limit circle. The motor power reaches its maximum at point C, and then maintains constant power until it reaches the highest speed point, where the maximum speed and weak magnetic capability are infinite. The quantities corresponding to the motor's maximum power point C can be written as:

[0105]

[0106] 4. Full-operation motor design

[0107] The performance requirements of the permanent magnet synchronous motor designed in this case are shown in Table 1:

[0108] Table 1

[0109]

[0110] During the design process, in order to meet the maximum speed requirement of 7000 rpm in the constant torque zone, formula (9) was used to calculate the design scheme; in order to meet the peak torque requirement of 22 Nm, formula (6) was used to calculate the design scheme; in order to meet the requirement that the constant power zone under peak working conditions should reach 13000 rpm, formulas (10), (11), and (12) were used to calculate the design scheme.

[0111] 5. Motor performance simulation analysis

[0112] In order to verify whether the performance of the designed permanent magnet synchronous motor meets the standards, finite element simulation software is used to analyze its electromagnetic performance.

[0113] The effective value of the phase current required at different torque and speed is as follows: Figure 4 It can be seen that the effective value of the current under rated conditions is 84A, and the motor reaches a peak torque of 22Nm when excited by a sinusoidal current of 204A.

[0114] Figure 5 The figure shows the variation in line voltage amplitude at different torque and speed conditions. In the constant torque region, the line voltage amplitude increases proportionally with speed. When the speed exceeds the breakover speed, the line voltage reaches the maximum value provided by the DC bus. Further speed increases require field weakening control, and the motor enters the constant power region. At the peak constant power maximum speed, the line voltage amplitude is 71V, meeting the 72V DC bus supply voltage requirement.

[0115] Figure 6 The efficiency distribution at different torque and speed levels is shown. In the low-speed range, motor efficiency gradually increases with increasing torque, reaching a peak at medium load. As speed increases, efficiency remains high in the constant-torque range, but gradually decreases as speed enters the constant-power range due to increased iron loss and windage losses. The highest efficiency, reaching 98%, occurs in the low-to-medium speed and medium-to-high load ranges, with a broad high-efficiency range. The overall efficiency distribution meets design expectations and meets the requirements for efficient motor operation.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A full-operation-condition design method for a permanent magnet synchronous motor considering drive constraints, characterized by: The following steps are involved: Establish a mathematical model of permanent magnet synchronous motor; Calculate the electromagnetic relationship of the motor under constant torque maximum torque / current control mode; Calculate the electromagnetic relationship of the motor under constant power flux weakening control; Based on the above model and electromagnetic relationship, the motor is designed for all working conditions.

2. The full-operating-condition design method for a permanent magnet synchronous motor considering driver constraints according to claim 1 is characterized in that: The mathematical model of the permanent magnet synchronous motor is as follows: According to the voltage equation of the permanent magnet synchronous motor in the ABC three-phase stationary coordinate system, after performing Clark transformation and Park transformation, the voltage equation in the dq axis rotating coordinate system is obtained as follows: The motor torque equation in the dq axis rotating coordinate system is: u d 、u q are the stator d and q axis voltages respectively; i d 、i q are the stator d-axis and q-axis currents respectively; ψ d , ψ q are the stator d-axis and q-axis flux respectively; L d 、L q are the d-axis and q-axis inductances of the stator winding respectively; i f is the equivalent excitation current of the permanent magnet; ψ f is the flux linkage generated by the fundamental magnetic field of the permanent magnet in the stator winding; p is the number of motor pole pairs; Expressing formula (1) and formula (2) in space vector form, we get the space vector diagram of the permanent magnet synchronous motor, which includes the stator current vector i s and stator voltage vector u s .

3. The full-operating-condition design method for a permanent magnet synchronous motor considering driver constraints according to claim 1 is characterized in that: The calculation of the electromagnetic relationship of the motor under the constant torque maximum torque / current control mode specifically includes: The limit value U of the effective phase voltage of the permanent magnet synchronous motor lim Due to the limitation of the inverter DC bus voltage, the effective value of the motor phase current is limited to I lim Limited by the maximum output current of the inverter; when the DC side voltage of the inverter is U d When , the maximum effective value of the fundamental voltage of the motor in the dq axis coordinate system is: When the motor is running stably, the voltage and current meet the following requirements: Where u s is the amplitude of the stator voltage, i s is the effective value of the stator current; Substituting formula (1) into formula (4), the expression of the rotational speed is obtained as follows: The electromagnetic torque of the motor is expressed as: For salient-pole permanent magnet synchronous motors, d -i q In the plane, its maximum torque / current trajectory satisfies formula (7): Solving equations (4) and (7) together, we can obtain the following equation: the permanent magnet synchronous motor adopts maximum torque / current control and the current reaches the limit value i lim The expressions of the quadrature and direct axis currents are: where i lim Indicates the maximum effective value of the inverter output current; When the maximum torque / current control is used in the constant torque control range, the voltage limit ellipse, current limit circle, and maximum torque / current trajectory will converge at point A as the speed continues to increase. This is the maximum speed of the motor in the constant torque range, that is, the turning speed, and its expression is: Where, 4. The full-operating-condition design method for a permanent magnet synchronous motor considering driver constraints according to claim 1 is characterized in that: The calculation of the electromagnetic relationship of the motor under constant power flux weakening control specifically includes the following steps: For salient-pole permanent magnet synchronous motors, the control strategy is optimized based on the speed range, subject to the constraints of a certain inverter capacity. Below the breakover speed, maximum torque-to-current ratio control is used to maximize torque output and optimize servo control performance. Above the breakover speed, constant power operation is achieved through field weakening control, thereby expanding the motor's speed range. For embedded permanent magnet synchronous motors, since the quadrature axis inductance is greater than the direct axis inductance, the motor’s salient pole ratio ρ>1; when i lim <ψ f / L d When the speed increases continuously in the initial constant torque stage, the voltage limit ellipse gradually decreases and finally converges at point A. The turning speed at this time is ω b At this time, the motor terminal voltage reaches the limit value, and weak magnetic control must be used to continue to increase the speed. The control current vector increases along the current limit circle, and the demagnetization direct axis current moves from point A to point B. At point B, the direct axis demagnetization current is the largest and reaches the highest speed. In the AB weak magnetic control stage, as the demagnetization direct axis current increases, the motor will run to the maximum electromagnetic power point P, and the quadrature and direct axis currents i corresponding to the maximum power point of the motor are obtained. dP 、i qP and speed ω P , power P emP for: when i lim =ψ f / L d When , since the center of the voltage limit ellipse is on the current limit circle, the quantities corresponding to point D are as follows, and the corresponding weak magnetic capacity is infinite at this time: where i dD 、i qD Respectively represent the quadrature and direct axis currents at point D, ω D Indicates the speed at point D, P emD Indicates the power at point D; when i lim >ψ f / L d When the center of the voltage limit ellipse is inside the current limit circle, the motor power reaches its maximum at point C, and then maintains constant power to the highest speed point, where the maximum speed and weak magnetic capability are infinite. The quantities corresponding to the motor maximum power point C are written as: where i dC 、i qC Respectively represent the cross-axis and direct-axis currents at point C, ω C Indicates the speed at point C, T emC Indicates the torque at point C.

5. The full-operating-condition design method for a permanent magnet synchronous motor considering driver constraints according to claim 1 is characterized in that: The full-operating-condition design of the motor specifically includes: Design the motor's technical specifications, including rated parameters, peak parameters, DC bus voltage, peak current, torque ripple, motor stator outer diameter, axial length, and cooling method; In order to meet the maximum speed requirement in the constant torque area, the turning speed is calculated using formula (9); In order to meet the peak torque requirement, the electromagnetic torque is calculated using formula (6); In order to meet the speed requirement of the constant power zone under peak working conditions, formulas (10), (11), and (12) are used to calculate the quadrature and direct axis currents, shaft speed, torque, and power corresponding to the maximum power point of the motor.

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