Improved parameter self-learning method for permanent magnet assisted synchronous reluctance motor with injected voltage

CN120512045BActive Publication Date: 2026-10-20HARBIN INST OF TECH
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Patent Information

Application Number
CN202510696918.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-05-28
Publication Date
2026-10-20
Estimated Expiration
2045-05-28

AI Technical Summary

Technical Problem

[0005]本申请是为了解决现有的电压注入技术限制了参数自学习方法的通用性,降低了所辨识的磁链-电流平面的准确性的问题,现提供改进注入电压的永磁辅助同步磁阻电机参数自学习方法,以提高辨识电机磁饱和平面的通用性和准确性

Benefits of technology

本申请所述的注入电压序列是基于频率比对注入数据分布影响提出的,所提出的电压注入序列具有零平均转矩,同时能够与现有的转子运动技术结合,实现了信号注入过程的转子静止或准静止。同时,所提注入序列是基于对数据分布的考虑设计的,因此所提的注入序列还具有良好的数据分布特性。

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Abstract

The application discloses an improved parameter self-learning method of a permanent magnet auxiliary synchronous reluctance motor with injected voltage, and relates to the technical field of motor control. The application is to solve the problem that the existing voltage injection technology limits the universality of the parameter self-learning method and reduces the accuracy of the identified flux-current plane. The application performs a flux self-saturation test on the permanent magnet auxiliary synchronous reluctance motor to obtain a current peak value and a corresponding flux peak value during single-axis injection; determines a flux boundary according to the flux peak value; determines an injected voltage amplitude according to the flux boundary; calculates a voltage signal of mutual saturation test according to the injected voltage amplitude; injects the voltage signal into the permanent magnet auxiliary synchronous reluctance motor, collects a current of the permanent magnet auxiliary synchronous reluctance motor during the injection process, and calculates a corresponding flux according to the current to realize parameter self-learning.
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Description

Technical Field

[0001] This application belongs to the field of motor control technology, and in particular relates to the identification of motor parameters. Background Technology

[0002] Permanent magnet-assisted synchronous reluctance motors (PMaSynRMs) have gained widespread attention in industrial drives and electric vehicles in recent years due to their advantages of low cost, high efficiency, and high power factor. However, to fully utilize the motor's reluctance torque, PMaSynRMs often exhibit significant magnetic saturation characteristics within their rated operating conditions. This leads to a significant saturation characteristic in the motor's flux linkage-current model, increasing the difficulty of motor control. Therefore, accurately identifying the motor's flux linkage-current model is crucial for achieving high-performance drive control.

[0003] Parameter self-learning methods are commonly used for identifying the magnetic saturation model of motors. This method involves injecting a signal while the motor is stationary and constructing a flux linkage-current plane based on the flux linkage-current data points obtained during the injection process. Hysteresis-based voltage signal injection is widely used in parameter self-learning due to its simple structure and lack of prior knowledge of motor parameters. To ensure both speed and accuracy of identification, the injected signal must provide sufficient effective data points while maintaining the motor's stationary state. Therefore, designing an efficient and reliable injection voltage signal is crucial for the parameter self-learning of permanent magnet assisted synchronous reluctance motors.

[0004] Existing voltage injection techniques often design voltage injection sequences based on the design requirement of zero average torque, which shows an effective rotor motion suppression effect. However, the amplitude of the injected voltage is selected empirically. Furthermore, different injection voltage amplitudes are often chosen for motors with different saturation levels, severely limiting the method's versatility. Simultaneously, existing methods often neglect the influence of the injected signal on data distribution during the injection process. This leads to random distribution of injected data points on its mapping plane, and even the existence of large data vacuum regions, reducing the accuracy of the identified flux linkage-current plane. Summary of the Invention

[0005] This application addresses the problem that existing voltage injection techniques limit the versatility of parameter self-learning methods and reduce the accuracy of the identified flux linkage-current plane. An improved parameter self-learning method for permanent magnet assisted synchronous reluctance motors based on injected voltage is provided to enhance the versatility and accuracy of identifying the motor's magnetic saturation plane.

[0006] This application provides a self-learning method for parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage, including: A flux self-saturation test was performed on a permanent magnet assisted synchronous reluctance motor to obtain the peak current and the corresponding peak flux during single-axis injection. The flux linkage boundary is determined based on the flux linkage peak value; The injection voltage amplitude is determined based on the magnetic flux boundary. The voltage signal for mutual saturation testing is calculated based on the injected voltage amplitude. The voltage signal is injected into the permanent magnet assisted synchronous reluctance motor, and the current of the permanent magnet assisted synchronous reluctance motor is collected during the injection process. The corresponding flux linkage is calculated based on the current to achieve parameter self-learning.

[0007] In one possible design, the above-mentioned flux linkage self-saturation test of the permanent magnet assisted synchronous reluctance motor to obtain the peak current during single-axis injection includes: The peak current is obtained based on the rated current of the permanent magnet assisted synchronous reluctance motor. , For the peak value of the current Taking the negative yields the lower peak current. .

[0008] In one possible design, determining the flux linkage boundary based on the flux linkage peak value includes: The flux linkage boundary is obtained according to the following formula: , in, and These represent the d-axis and q-axis flux linkage peak values ​​corresponding to the peak current during the self-saturation test. and These represent the d-axis and q-axis flux linkage peak values ​​corresponding to the peak current during the self-saturation test. and These are the upper and lower boundaries of the d-axis flux linkage, respectively. and These are the upper and lower boundaries of the q-axis flux linkage, respectively. It is a permanent magnet flux linkage.

[0009] In one possible design, determining the injection voltage amplitude based on the flux linkage boundary includes: d-axis and q-axis injection voltage amplitude and The specific expressions are as follows: , , in, The number of data points to be injected. For signal injection period, and All are coefficients. and These are the upper and lower boundaries of the d-axis flux linkage, respectively. and These are the upper and lower boundaries of the q-axis flux linkage, respectively.

[0010] In one possible design, the aforementioned magnetic linkage is divided into two stages, as detailed below: In the first stage: , , In the second phase: , , in, The frequency ratio of the injected flux linkage signal, and has .

[0011] In one possible design, the voltage signal for the mutual saturation test calculated based on the injected voltage amplitude includes: The voltage signal for the mutual saturation test is obtained using a hysteresis flux controller.

[0012] In one example, the expression for the hysteresis flux controller is: , in, Indicates time, , for The voltage signal used for mutual saturation testing of the shaft. for Shaft injection voltage amplitude, For stator resistance, for shaft current, for Axial magnetic flux, and They are respectively Minimum and maximum values ​​of axial flux linkage.

[0013] In one possible design, the magnetic flux calculated based on this current includes: The flux linkage corresponding to the current is calculated using the flux linkage calculation equation, which is expressed as follows: , , in, It is a permanent magnet flux linkage. and These are the magnetic flux linkages along the d-axis and q-axis, respectively. For stator resistance, and These are the voltages along the d-axis and q-axis, respectively. and These are the d-axis and q-axis currents, respectively.

[0014] In one possible design, the aforementioned self-learning method for permanent magnet assisted synchronous reluctance motor parameters with improved injection voltage also includes: The current and its corresponding flux linkage of the permanent magnet assisted synchronous reluctance motor are post-processed using fitting and interpolation algorithms to obtain an equally spaced grid of current-flux linkage.

[0015] In one possible design, the above-mentioned fitting and interpolation algorithms are used to post-process the current and its corresponding flux linkage of the permanent magnet assisted synchronous reluctance motor to obtain an equally spaced current-flux linkage grid, including: The matching relationship between the current and the corresponding flux linkage of the permanent magnet assisted synchronous reluctance motor is fitted to obtain the relationship curve between flux linkage and current. Based on the relationship curve, multiple magnetic flux links are selected at equal intervals as grid points within the range of the magnetic flux links; The current value corresponding to the grid point is calculated according to the interpolation algorithm, and the equidistant grid of current-magnetic flux is generated.

[0016] The beneficial effects of this application are: The injection voltage sequence described in this application is based on the influence of frequency ratio on the injection data distribution. The proposed voltage injection sequence has zero average torque and can be combined with existing rotor motion technology to achieve rotor stationary or quasi-stationary operation during the signal injection process. Furthermore, the proposed injection sequence is designed with data distribution in mind, thus exhibiting excellent data distribution characteristics.

[0017] The voltage injection method described in this application is based on a hysteresis flux linkage controller, which has the advantages of simple structure and ease of implementation. Furthermore, the proposed improved hysteresis flux linkage controller enables quantitative calculation of the injected voltage amplitude, avoiding the drawback of traditional methods that rely on empirical selection of the voltage injection amplitude.

[0018] The parameter self-learning method for permanent magnet assisted synchronous reluctance motors described in this application is based on an improved injection voltage, which fully considers the influence of data distribution and provides a design method for the injection voltage. Compared with traditional methods, this application avoids the problems of overlapping data point trajectories or large-area data vacuum, which improves the reliability of data post-processing and thus enhances the identification accuracy of the magnetic saturation model. Attached Figure Description

[0019] Figure 1 The plots show the distribution trajectories of flux linkage data along the d and q axes under different injection signal frequency ratios, where (a) to (f) represent the injection flux linkage signal frequency ratios, respectively. =1, 2, 2.5, 2.75, 3, 4; Figure 2 Flowchart of a self-learning method for parameters of a permanent magnet assisted synchronous reluctance motor to improve injection voltage; Figure 3 The experimental waveforms for the self-saturation test are shown in Figure 1, where (a) represents the experimental waveform of the d-axis self-saturation test and (b) represents the experimental waveform of the q-axis self-saturation test. Figure 4 Here are the flux linkage-current mapping diagrams of the self-saturation test results, where (a) represents the flux linkage-current mapping diagram of the d-axis self-saturation test and (b) represents the flux linkage-current mapping diagram of the q-axis self-saturation test. Figure 5 The signal waveform diagram shows the injection voltage amplitude and the corresponding real-time flux linkage result of the injection voltage sequence. Figure 6 The experimental waveform diagram for the mutual saturation test; Figure 7 The current-magnetic flux equally spaced grid surfaces are identified based on the magnetic saturation model. Among them, (a) is the d-axis current-magnetic flux equally spaced grid surface, and (b) is the q-axis current-magnetic flux equally spaced grid surface. Detailed Implementation

[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0021] Currently, the parameter self-learning technology for permanent magnet assisted synchronous reluctance motors still lacks consideration of data distribution, and the selection of voltage injection amplitude is empirical, which leads to a decrease in the universality of application and the identification accuracy of magnetic saturation models.

[0022] In view of this, the embodiments of this application provide an improved self-learning method for parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage, in order to solve the above-mentioned problems. The following will be discussed in conjunction with the appendix... Figure 2 The implementation scheme of this application will be described in detail.

[0023] Reference Figure 2This embodiment specifically describes the parameter self-learning method for a permanent magnet assisted synchronous reluctance motor with improved injection voltage, which includes: A flux self-saturation test was performed on a permanent magnet assisted synchronous reluctance motor to obtain the peak current and the corresponding peak flux during single-axis injection. The flux linkage boundary is determined based on the flux linkage peak value; The injection voltage amplitude is determined based on the magnetic flux boundary. The voltage signal for mutual saturation testing is calculated based on the injected voltage amplitude. The voltage signal is injected into the permanent magnet assisted synchronous reluctance motor, and the current of the permanent magnet assisted synchronous reluctance motor is collected during the injection process. The corresponding flux linkage is calculated based on the current to achieve parameter self-learning.

[0024] In one embodiment, the step of performing a flux self-saturation test on the permanent magnet assisted synchronous reluctance motor to obtain the peak current during uniaxial injection includes: obtaining the peak current based on the rated current of the permanent magnet assisted synchronous reluctance motor. For the peak value of the current Taking the negative yields the lower peak current. .

[0025] In one embodiment, determining the flux linkage boundary based on the flux linkage peak value includes: The flux linkage boundary is obtained according to the following formula: , in, and These represent the d-axis and q-axis flux linkage peak values ​​corresponding to the peak current during the self-saturation test. and These represent the d-axis and q-axis flux linkage peak values ​​corresponding to the peak current during the self-saturation test. and These are the upper and lower boundaries of the d-axis flux linkage, respectively. and These are the upper and lower boundaries of the q-axis flux linkage, respectively. It is a permanent magnet flux linkage.

[0026] In one embodiment, determining the injection voltage amplitude based on the flux linkage boundary includes: d-axis and q-axis injection voltage amplitude and The specific expressions are as follows: , , in, The number of data points to be injected. For signal injection period, and All are coefficients. and These are the upper and lower boundaries of the d-axis flux linkage, respectively. and These are the upper and lower boundaries of the q-axis flux linkage, respectively.

[0027] In one embodiment, the magnetic linkage is divided into two stages, which are as follows: In the first stage: , , In the second phase: , , in, The frequency ratio of the injected flux linkage signal, and has .

[0028] In one embodiment, the step of calculating the voltage signal for the mutual saturation test based on the injected voltage amplitude includes: obtaining the voltage signal for the mutual saturation test using a hysteresis flux linkage controller.

[0029] In one embodiment, the expression for the hysteresis flux controller is: , in, Indicates time, , for The voltage signal used for mutual saturation testing of the shaft. for Shaft injection voltage amplitude, For stator resistance, for shaft current, for Axial magnetic flux, and They are respectively Minimum and maximum values ​​of axial flux linkage.

[0030] In one embodiment, the step of calculating the corresponding flux linkage based on the current includes: The flux linkage corresponding to the current is calculated using the flux linkage calculation equation, which is expressed as follows: , , in, It is a permanent magnet flux linkage. and These are the magnetic flux linkages along the d-axis and q-axis, respectively. For stator resistance, and These are the voltages along the d-axis and q-axis, respectively. and These are the d-axis and q-axis currents, respectively.

[0031] In one embodiment, the improved self-learning method for parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage is characterized by further comprising: post-processing the current of the permanent magnet assisted synchronous reluctance motor and its corresponding flux linkage using fitting and interpolation algorithms to obtain an equidistant grid of current-flux linkage.

[0032] In one embodiment, the post-processing of the current and its corresponding flux linkage of the permanent magnet assisted synchronous reluctance motor using fitting and interpolation algorithms to obtain an equidistant grid of current-flux linkage includes: The matching relationship between the current of the permanent magnet assisted synchronous reluctance motor and its corresponding flux linkage is fitted to obtain the relationship curve between flux linkage and current. According to the relationship curve, multiple flux linkages are selected at equal intervals as grid points within the range of flux linkage. The current value corresponding to the grid point is calculated according to the interpolation algorithm to generate the equal-interval grid of current-flux linkage.

[0033] To further illustrate the implementation scheme of this application, this implementation scheme includes steps 1 to 8, wherein the numbering of each step does not necessarily limit the order in which they are executed. Each step is described in detail below: Step 1: Establish a mathematical model of the permanent magnet assisted synchronous reluctance motor and describe the motor's voltage and torque equations.

[0034] The specific expression for the voltage equation is: , , in, and These are the voltages along the d-axis and q-axis, respectively. and These are the d-axis and q-axis currents, respectively. For stator resistance, Electric angular velocity, and These are the magnetic flux linkages along the d-axis and q-axis, respectively.

[0035] The specific expression for the torque equation is as follows: , in, This represents the number of pole pairs of the motor. It is electromagnetic torque.

[0036] Step 2: Based on the static constraints, describe the calculation equations for the motor flux linkage.

[0037] The specific expression for the magnetic flux linkage calculation equation is as follows: , , in, It is a permanent magnet flux linkage.

[0038] Step 3: Design the injection flux linkage signal frequency ratio based on data dispersion considerations. .

[0039] In this embodiment, the frequency ratio of the injection flux linkage signals used in the two stages is selected as follows: .

[0040] Step 4, Figure 3 and Figure 4 The experimental waveforms of the self-saturation test and the corresponding flux linkage-current mapping diagrams are presented. As shown in the figure, the flux linkage self-saturation test was performed to obtain the current-flux linkage relationship during uniaxial injection, and the peak motor current was determined accordingly. and The corresponding flux linkage value.

[0041] Based on the selected 5.5kW permanent magnet assisted synchronous reluctance motor, the rated current... It is 14.7A, peak current. for: .

[0042] To ensure that the self-saturation test covers the rated current range of the motor, the threshold values ​​for the hysteresis current controllers on the d-axis and q-axis are selected as follows: .

[0043] Self-saturation testing does not require consideration of data distribution issues, therefore the selection of the injection voltage is flexible. The injection voltage amplitudes on the d and q axes... and Set to: , .

[0044] The d-axis self-saturation test can be passed. Figure 3 Find the peak motor current in the waveform diagram shown in (a). and The corresponding peak value on the d-axis flux linkage and lower peak In this embodiment, , .

[0045] The q-axis self-saturation test can be passed. Figure 3(b) shows the waveform diagram to identify the peak value of the motor current. and The corresponding peak value on the q-axis flux linkage and lower peak In this embodiment, , .

[0046] Step 5: Determine the flux linkage boundary of the mutual saturation injection based on the flux linkage value obtained from self-saturation.

[0047] Based on the selected 5.5kW permanent magnet assisted synchronous reluctance motor, the permanent magnet flux linkage The flux linkage boundary of the mutual saturation injection is determined to be 0.0629 Vs: , in, and These are the upper and lower boundaries of the d-axis flux linkage, respectively. and These are the upper and lower boundaries of the q-axis flux linkage, respectively.

[0048] Step 6: Based on the magnetic flux boundary and number of injection points of the mutual saturation injection, preliminarily determine the injection voltage amplitude.

[0049] d-axis and q-axis injected voltage amplitude and The specific expressions are as follows: , , in, The number of data points to be injected. For signal injection period, and All are coefficients. The magnetic flux linkage is divided into two stages, as detailed below: In the first stage: , , In the second phase: , , in, The frequency ratio of the injected flux linkage signal, and has In this embodiment, .

[0050] In the first stage, there are: , ; In the second stage, there are: , .

[0051] Based on the flux linkage boundary of mutual saturation injection obtained from the self-saturation test, and with the number of data points for both injection stages set to 400, the improved injection voltage amplitude is specifically as follows: , , , .

[0052] Step 7: Based on the determined injection voltage amplitude, a hysteresis flux linkage controller is used to inject the voltage signal for the mutual saturation test, and the motor current during the injection process is obtained through current sampling. The flux linkage value corresponding to each current sampling point is calculated according to the flux linkage calculation equation described in Step 2, ultimately obtaining the matching relationship between current and flux linkage.

[0053] In this embodiment, the specific expression for the hysteresis controller is: , in, To achieve the voltage signal for mutual saturation testing, , , Indicates the time.

[0054] Figure 5 The experimental waveform of the injection voltage for the mutual saturation test is given. Figure 6 The equally spaced grids corresponding to the mutual saturation test results are given.

[0055] Step 8: Perform data post-processing based on the current-magnetic flux relationship obtained from the injected signal to obtain an equally spaced grid of current-magnetic flux.

[0056] The data post-processing method is as follows: A fitting and interpolation algorithm is used to generate an equally spaced grid of current-magnetic flux linkage, as detailed below: The obtained current-magnetic flux matching relationship is fitted to obtain the relationship curve between magnetic flux and current. Based on this fitted relationship curve, a series of magnetic fluxes are selected as grid points at equal intervals within the range of magnetic flux. Then, the current values ​​corresponding to these grid points are calculated using an interpolation algorithm, thereby generating an equally spaced current-magnetic flux grid.

[0057] While specific embodiments of this application have been described herein with reference to them, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. An improved self-learning method for parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage, characterized in that, include: A flux self-saturation test was performed on a permanent magnet assisted synchronous reluctance motor to obtain the peak current and the corresponding peak flux during single-axis injection. The flux linkage boundary is determined based on the flux linkage peak value; The injection voltage amplitude is determined based on the magnetic flux boundary. The voltage signal for mutual saturation testing is calculated based on the injected voltage amplitude. The voltage signal is injected into the permanent magnet assisted synchronous reluctance motor, and the current of the permanent magnet assisted synchronous reluctance motor is collected during the injection process. The corresponding flux linkage is calculated based on the current to achieve parameter self-learning. The step of determining the injection voltage amplitude based on the magnetic flux boundary includes: d-axis and q-axis injection voltage amplitude and The specific expressions are as follows: , , in, The number of data points to be injected. For signal injection period, and All are coefficients. and These are the upper and lower boundaries of the d-axis flux linkage, respectively. and These are the upper and lower boundaries of the q-axis flux linkage, respectively. The magnetic linkage is divided into two stages, which are detailed below: In the first stage: , , In the second phase: , , in, The frequency ratio of the injected flux linkage signal, and has .

2. The method for self-learning parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage according to claim 1, characterized in that, The process of performing a flux self-saturation test on a permanent magnet assisted synchronous reluctance motor to obtain the peak current during single-axis injection includes: The peak current is obtained based on the rated current of the permanent magnet assisted synchronous reluctance motor. , For the peak value of the current Taking the negative yields the lower peak current. .

3. The method for self-learning parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage according to claim 1, characterized in that, The step of determining the flux linkage boundary based on the flux linkage peak value includes: The flux linkage boundary is obtained according to the following formula: , in, and These represent the d-axis and q-axis flux linkage peak values ​​corresponding to the peak current during the self-saturation test. and These represent the d-axis and q-axis flux linkage peak values ​​corresponding to the peak current during the self-saturation test. and These are the upper and lower boundaries of the d-axis flux linkage, respectively. and These are the upper and lower boundaries of the q-axis flux linkage, respectively. It is a permanent magnet flux linkage.

4. The method for self-learning parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage according to claim 1, characterized in that, The step of calculating the voltage signal for the mutual saturation test based on the injected voltage amplitude includes: The voltage signal for the mutual saturation test is obtained using a hysteresis flux controller.

5. The method for self-learning parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage according to claim 4, characterized in that, The expression for the hysteresis flux controller is: , in, Indicates time, , for The voltage signal used for mutual saturation testing of the shaft. for Shaft injection voltage amplitude, For stator resistance, for shaft current, for Axial magnetic flux, and They are respectively The lower and upper boundaries of the axial flux linkage.

6. The method for self-learning parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage according to claim 1, characterized in that, The calculation of the corresponding magnetic flux based on the current includes: The flux linkage corresponding to the current is calculated using the flux linkage calculation equation, the expression of which is: , , in, It is a permanent magnet flux linkage. and These are the magnetic flux linkages along the d-axis and q-axis, respectively. For stator resistance, and These are the voltages along the d-axis and q-axis, respectively. and These are the d-axis and q-axis currents, respectively.

7. The method for self-learning parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage according to any one of claims 1 to 6, characterized in that, Also includes: The current and its corresponding flux linkage of the permanent magnet assisted synchronous reluctance motor are post-processed using fitting and interpolation algorithms to obtain an equally spaced grid of current-flux linkage.

8. The method for self-learning parameters of a permanent magnet assisted synchronous reluctance motor with improved injection voltage according to claim 7, characterized in that, The post-processing of the current and its corresponding flux linkage of the permanent magnet assisted synchronous reluctance motor using fitting and interpolation algorithms to obtain an equally spaced current-flux linkage grid includes: The matching relationship between the current and the corresponding flux linkage of the permanent magnet assisted synchronous reluctance motor is fitted to obtain the relationship curve between flux linkage and current. Based on the relationship curve, multiple magnetic flux links are selected at equal intervals as grid points within the range of the magnetic flux links; The current value corresponding to the grid point is calculated according to the interpolation algorithm, and the equidistant grid of current-magnetic flux is generated.

Citation Information

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