A hierarchical optimization method for permanent magnet synchronous motor based on response surface

Abstract

The application discloses a layered optimization method of a permanent magnet synchronous motor based on a response surface, innovatively proposes the concept of 'bidirectional' and 'unidirectional' parameters, and divides the parameters into layers based on the concept, and the layer with higher average sensitivity is used as the first layer. For the 'bidirectional' parameter layer, a Latin hypercube sampling method is used, and enough sample points are given, then a kriging response surface is fitted; for the 'unidirectional' parameter layer, a central composite experimental design (CCD) or a Box-henven experimental design is used, and a full second-order polynomial response surface is fitted. On the basis of the response surface, a multi-objective optimization algorithm NSGA2 is used for optimization, after a Pareto front is obtained, a simple weight aggregation method is used to screen an optimal point into the next layer optimization. The layered optimization method of the permanent magnet synchronous motor based on the response surface greatly improves the fitting precision of the response surface, and improves the optimization efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of motor parameter optimization design, and particularly relates to a parameter layered optimization method of a permanent magnet synchronous motor. BACKGROUND

[0002] Permanent magnet synchronous motor (PMSM) is widely used in ship propulsion, wind power generation, mine hoisting and other fields due to its high efficiency, high power density and other advantages. In order to further improve the comprehensive performance of the motor, multi-objective optimization is necessary. In view of the problems of high parameter dimension and slow finite element model calculation speed in the multi-objective optimization process, many scholars have proposed parameter layering and response surface surrogate model construction methods. The layered optimization method divides parameters into several layers according to the sensitivity size relationship, and optimizes layer by layer, solving the problems of high parameter dimension and easy convergence to local optimum. The response surface constructs surrogate models such as full second-order polynomial response surface and kriging response surface through a small number of samples, and optimizes on this basis. Although this method solves the problem of slow finite element calculation speed, the accuracy of the constructed response surface is poor. In order to improve the accuracy of the response surface, the number of sample points must be increased significantly, which leads to low optimization efficiency. The currently popular method of combining layered optimization and response surface surrogate model can improve the fitting accuracy of the response surface to a certain extent, but the accuracy is still poor when dealing with harmonic relationships such as cogging torque and torque ripple. SUMMARY

[0003] In view of the deficiencies of the prior art, the purpose of the present application is to overcome the problems of high parameter dimension and poor accuracy of the response surface surrogate model in the motor optimization process, and a layered optimization method of a permanent magnet synchronous motor based on a response surface is proposed. This method innovatively proposes the concepts of "bidirectional" parameters and "unidirectional" parameters, and divides the parameters into "bidirectional" parameter layers and "unidirectional" parameter layers according to these concepts. Then different sampling methods and surrogate models are used for the two types of parameters, taking into account the speed and accuracy.

[0004] A layered optimization method of a permanent magnet synchronous motor based on a response surface, comprising the following steps:

[0005] Step one: select the optimization objectives according to the motor performance requirements, and determine the upper and lower limits of each design parameter;

[0006] Step two: determine the constraint conditions in the motor optimization process;

[0007] Step three: sensitivity analysis, calculate the sensitivity of the parameters to each target and the comprehensive sensitivity to all targets;

[0008] Step four: divide the parameters into two categories of bidirectional and unidirectional according to the specific influence of the parameters on the targets;

[0009] Step 5: Divide all parameters into two layers: one layer for bidirectional parameters and another layer for unidirectional parameters;

[0010] Step 6: Use different sampling methods and response surface construction methods for bidirectional and unidirectional parameters, and use a multi-objective optimization algorithm to find the optimal solution. The optimal solution obtained at each layer is used as the basis for the next layer of optimization.

[0011] Step 7: After the last layer of optimization is completed, determine whether the convergence criterion has been met. If it is not met, return to step 6; if it is met, stop the loop.

[0012] Furthermore, the constraint selected in step two is the set threshold value of the fundamental wave amplitude of the air gap magnetic flux density.

[0013] Furthermore, the sensitivity analysis method in step three is as follows:

[0014]

[0015] Where S ij f is the interval sensitivity of the i-th parameter to the j-th target, k is the index of the interval sensitivity, and f j and △f j These are the value and change of the j-th target, respectively, z i and △z i These are the values ​​and changes of the i-th design parameter. Sensitivity analysis is performed on only one parameter at a time. When all other parameters are at their center values, the current parameter is changed according to a set step size. Each parameter change yields an interval sensitivity. The final sensitivity for a target is the average of all interval sensitivities. The calculation formula is as follows:

[0016]

[0017] l is the total number of interval sensitivities.

[0018] Furthermore, the method for calculating the overall sensitivity in step three is as follows:

[0019]

[0020] Where S i It is the overall sensitivity of the i-th parameter, ω j It is the weight of the j-th objective.

[0021] Furthermore, the criteria for classifying parameters into bidirectional and unidirectional categories in step four are as follows:

[0022]

[0023] is the maximum or minimum value of all interval sensitivities of a certain parameter, and S ij The sign is opposite, when the interval sensitivity satisfies the above formula, it is judged that the influence of the parameter on the target is bidirectional, otherwise it is unidirectional.

[0024] Further, the parameter layering method in step five is specifically:

[0025] All bidirectional parameters are a layer, and all unidirectional parameters are another layer, and the layer with larger average sensitivity of the parameters is set as the first layer, for the bidirectional parameter layer, if the parameters in the layer are too many, the layer can be further layered according to the sensitivity.

[0026] Further, the response surface construction method in step six is specifically:

[0027] For unidirectional parameters, a sampling method based on CCD or Box-henven is used for sampling, and a full second-order polynomial response surface is constructed; for bidirectional parameters, a Latin hypercube sampling method is used for encryption sampling, and a kriging response surface is constructed.

[0028] Further, the multi-objective optimization algorithm in step six is a non-dominated sorting genetic algorithm II (NSGA2).

[0029] Further, the convergence criterion in step seven is:

[0030]

[0031] F is a standard for selecting the optimal point, △F is the change value of F in two iterations, and target f j By default, minimization.

[0032] Beneficial effects:

[0033] The application innovatively proposes the concepts of unidirectional and bidirectional parameters, which are used as the basis for parameter layering. For unidirectional parameters, a Box-Behnken, CCD or other sampling method with fewer sample points is used to construct a full second-order polynomial response surface, and for bidirectional parameters, an encryption sampling method such as a Latin hypercube sampling method is used to construct a kriging response surface. The method effectively solves the problem of insufficient precision of the hierarchical optimization method based on the response surface proxy model, and improves the optimization efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a flow chart of a hierarchical optimization method of a permanent magnet synchronous motor based on a response surface;

[0035] Figure 2 is a topology diagram of a low-speed large-torque permanent magnet synchronous motor;

[0036] Figure 3 is a comprehensive sensitivity analysis result diagram;

[0037] Figure 4 is the response surface of the first layer parameter to torque;

[0038] Figure 5 is the response surface of the first layer parameter to torque ripple;

[0039] Figure 6 is the response surface of the first layer parameter to efficiency;

[0040] Figure 7 is the Pareto front of the first layer, and the red dot is the optimal point;

[0041] Figure 8 is the response surface of the second layer parameter to torque;

[0042] Figure 9 is the response surface of the second layer parameter to torque ripple;

[0043] Figure 10 is the response surface of the second layer parameter to efficiency;

[0044] Figure 11 is the Pareto front of the second layer, and the red dot is the optimal point. DETAILED DESCRIPTION

[0045] The application will be described in further detail below with reference to the drawings and embodiments. It is obvious that the described embodiments are only a part of the embodiments of the application, but not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application.

[0046] The application is a layered optimization method for permanent magnet synchronous motors based on response surfaces, comprising the following steps:

[0047] Step one: select the optimization target according to the motor performance requirements, and determine the upper and lower limits of each design parameter;

[0048] Step two: determine the constraint conditions in the motor optimization process;

[0049] Step three: sensitivity analysis, calculate the sensitivity of the parameters to each target and the comprehensive sensitivity to all targets;

[0050] Step four: according to the specific influence of the parameters on the targets, the parameters are divided into two categories: bidirectional and unidirectional;

[0051] Step five: divide all parameters into two layers, bidirectional parameters for one layer, and unidirectional parameters for another layer;

[0052] Step six: different sampling methods and response surface construction methods are used for bidirectional parameters and unidirectional parameters, and a multi-objective optimization algorithm is used for optimization, and the optimal solution obtained at each layer is used as the basis for optimization at the next layer;

[0053] Step seven: after the last layer of optimization is completed, it is judged whether the convergence criterion is met, if not, return to step six, if yes, stop the cycle.

[0054] Further, the constraint condition selected in step two is a set threshold value of the fundamental amplitude of the air gap magnetic flux density.

[0055] Further, the sensitivity analysis method in step three is specifically:

[0056]

[0057] Where S ij is the interval sensitivity of the i-th parameter to the j-th target, k is the serial number of the interval sensitivity, f j and△f j are the value and change value of the j-th target, z i and△z i are the value and change value of the i-th design parameter, the sensitivity analysis is performed on only one parameter at a time, when the other parameters are all central values, the current parameter is changed according to the set step size, an interval sensitivity is obtained for each parameter change, the final sensitivity of a certain target is the average value of all interval sensitivities, and the calculation formula is as follows:

[0058]

[0059] l is the total number of interval sensitivities.

[0060] Further, the method for calculating the comprehensive sensitivity in step three is:

[0061]

[0062] Where S i is the comprehensive sensitivity of the i-th parameter, and ω j is the weight of the j-th target.

[0063] Further, the judgment standard for dividing the parameters into bidirectional and unidirectional in step four is:

[0064]

[0065] is the maximum value or minimum value of all interval sensitivities of a certain parameter, and S ij signs are opposite, when the interval sensitivity meets the above formula, it is judged that the influence of the parameter on the target is bidirectional, otherwise it is unidirectional.

[0066] Further, the parameter hierarchical method in step five is specifically:

[0067] All bidirectional parameters are as a layer, and all unidirectional parameters are another layer, the layer with greater average parameter sensitivity is set as the first layer, for the bidirectional parameter layer, if the parameters in the layer are too many, the layer can be further divided according to the sensitivity.

[0068] Further, the response surface construction method in step six is specifically:

[0069] For unidirectional parameters, a sampling method based on CCD or Box-henven is used for sampling, and a full second-order polynomial response surface is constructed; for bidirectional parameters, a Latin hypercube sampling method is used for encryption sampling, and a kriging response surface is constructed.

[0070] Further, the multi-objective optimization algorithm in step six is a non-dominated sorting genetic algorithm II (NSGA2).

[0071] Further, the convergence criterion in step seven is:

[0072]

[0073] F is the standard for selecting the optimal point, △F is the change value of F in two iterations, the target f j The default is minimization.

[0074] The steps of the present application will be described in detail below with reference to the accompanying drawings: Figure 2 The low-speed large-torque magnetic type permanent magnet synchronous motor rotor structure optimization shown in the low-speed large-torque magnetic type permanent magnet synchronous motor rotor structure optimization will be described in detail. Step 1: This type of motor is commonly used in mine hoisting, ship propulsion and other fields, and high requirements are put forward for torque density, efficiency and torque ripple, therefore, torque, torque ripple and efficiency are selected as the three objectives of this optimization. Figure 2 All design parameters of the rotor are labeled, and table 1 gives the specific meanings, ranges and initial values of all parameters.

[0075] Table 1 Motor design parameters

[0076]

[0077] Step 2: The design parameters include parameters related to permanent magnets, in order to ensure that the magnetic load of the motor is within a reasonable range, the air gap flux density fundamental wave amplitude is limited to not more than 1.02T, and at the same time, it is also not less than 0.9T.

[0078] Step 3: Sensitivity analysis, each design parameter is divided into 10 intervals, when performing sensitivity analysis on a certain parameter, other parameters are kept at the center value, the following takes the rotor height coefficient khr as an example to illustrate, table 2 shows the sensitivity analysis process of khr on torque ripple.

[0079] Table 2 Sensitivity analysis of rotor height coefficient khr

[0080]

[0081] Table 2 (continued)

[0082]

[0083]

[0084] The average value of the sensitivity of khr to torque ripple is -0.85, and the sensitivity of khr to torque and efficiency is -0.38 and -0.015 respectively, using the same method as table 2. In order to calculate the comprehensive sensitivity of this parameter to all targets, the weight of each target also needs to be determined. For simplicity, the weight of torque and efficiency is taken as 0.4, and the weight of torque ripple is taken as 0.2, so the comprehensive sensitivity of khr is 0.33, Figure 3 The results of the comprehensive sensitivity analysis are shown.

[0085] Step 4: Determine the reference for bidirectional and unidirectional parameters:

[0086]

[0087] According to this standard, it is found that all the remaining parameters are bidirectional parameters except for the air gap length g, the permanent magnet width bm, the eccentricity length offset and the rotor width br, which also illustrates the complex harmonic relationship inside the motor. The ordinary parameter layering and response surface optimization method has already been difficult to ensure the accuracy of the optimization result.

[0088] Step 5: According to the parameter type, six bidirectional parameters are one layer, and four unidirectional parameters are one layer. Since the bidirectional parameter layer still has a large number of parameters, a threshold value δ = 0.1 is set, and the bidirectional parameter layer is further layered with δ as the boundary. The bidirectional parameters with a comprehensive sensitivity higher than δ are one layer, and the bidirectional parameters with a comprehensive sensitivity lower than δ are another layer. Therefore, all parameters are finally divided into three layers, arranged in descending order of average sensitivity, as shown in table 3. The first layer is three bidirectional parameters, the second layer is four unidirectional parameters, and the third layer is three bidirectional parameters. This optimization will optimize the parameters of each layer in order, and the optimization result of the previous layer will be the optimization basis for the next layer.

[0089] Table 3 Final layering results

[0090]

[0091] Step 6: Latin hypercube sampling method is used to sample the bi-directional parameters of the first layer, the sample number is set to 100, and the kriging response surface is fitted, on this basis, the NSGA2 algorithm is used to search for the optimal solution, Figures 4-6 is the response surface of the first layer parameters, Figure 7 is the Pareto front of the first layer, in order to select an optimal solution on the Pareto front, we define the following parameters:

[0092]

[0093] T and T' are the initial torque values, T ripple and T r ' ipple are the torque ripple and the initial torque ripple, n and n' are the efficiency and the initial efficiency, and ω1, ω2 and ω3 are weight coefficients, which are the same as the values used in calculating the comprehensive sensitivity. The F value of all individuals in the Pareto front is calculated, and the minimum value is selected into the next layer optimization, and the optimal point of the first layer has been marked in Figure 7 .

[0094] Based on the optimization results of the first layer, the second layer parameters are optimized. Central composite experimental design is used to sample the second layer parameters and fit the full quadratic polynomial response surface. Unlike the kriging response surface, the full quadratic polynomial response surface has poor flexibility and adaptive ability, often resulting in poor fitting accuracy, which is manifested in a small determination coefficient R2. However, through the new parameter layering strategy proposed in this patent, the parameters in the second layer are all unidirectional parameters, and the response surface does not need to have strong adaptive ability. In this optimization process, the determination coefficients of the full quadratic polynomial response surface for the three objectives are 0.9999, 0.9989 and 0.9999, which indicates that the fitting quality of the response surface is very high, Figures 8-10 gives part of the response surface of the second layer parameters. Similarly, the Pareto front is obtained using the NSGA2 algorithm and the optimal point is selected, Figure 11 gives the Pareto front of the second layer.

[0095] Finally, the same method as the first layer parameters is used to complete the optimization of the last layer parameters, Table 4 shows the changes of each objective in each iteration process, and the error between the fitted value and the simulation value of each layer optimal point is compared. The small error value greatly improves the convergence speed of the layered optimization.

[0096] Table 4 Changes of objectives in the iteration process

[0097]

[0098] Step 7: The optimization is performed for three iterations, and the F value of each iteration is 0.8762, 0.8661 and 0.8669. According to the convergence judgment basis proposed previously, the optimization process ends after the third iteration is completed. Since the local search capability of the NSGA2 algorithm is not strong, the result of the third iteration is slightly worse than that of the second iteration, and therefore the result of the second iteration is taken as the final optimization result. Table 5 is a comparison of the motor parameters and performance before and after optimization.

[0099] Table 5 Comparison of motor parameters and performance before and after optimization

[0100]

[0101] The preferred embodiments of the present application have been described above by referring to the drawings, and are not intended to limit the present application. Various modifications and changes can be made by those skilled in the art to the present application without departing from the spirit and principles of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A layered optimization method for permanent magnet synchronous motor based on response surface, characterized in that, The method comprises the following steps: Step 1: selecting optimization targets according to motor performance requirements, and determining upper and lower limits of each design parameter; Step 2: determining constraint conditions in the motor optimization process; Step 3: sensitivity analysis, calculating the sensitivity of parameters to each target and the comprehensive sensitivity to all targets; the sensitivity analysis method in step 3 is specifically as follows: where S ij is the interval sensitivity of the ith parameter to the jth objective, k is the serial number of the interval sensitivity, f j and△f j are the value and change value of the jth objective, z i and△z i are the value and change value of the ith design parameter, the sensitivity analysis is performed on one parameter at a time, when the other parameters are all at the center value, the current parameter is changed according to the set step, an interval sensitivity is obtained for each parameter change, and the final sensitivity of an objective is the average of all interval sensitivities, and the calculation formula is as follows: l is the total number of interval sensitivities; The method for calculating the comprehensive sensitivity is as follows: where S i is the overall sensitivity of the ith parameter, ω j is the weight of the jth objective; Step 4: according to the specific influence of parameters on targets, the parameters are divided into two categories of bidirectional and unidirectional; the judgment standard for dividing the parameters into bidirectional and unidirectional is as follows: is the maximum or minimum value of all interval sensitivities of a certain parameter, and S ij The sign is opposite. When the interval sensitivity satisfies the above formula, it is determined that the influence of the parameter on the target is bidirectional, otherwise it is unidirectional. Step 5: all parameters are divided into two layers, bidirectional parameters are one layer, and unidirectional parameters are another layer; Step 6: different sampling methods and response surface construction methods are used for bidirectional parameters and unidirectional parameters, and a multi-objective optimization algorithm is used for optimization, and the optimal solution obtained by each layer is used as the basis for optimization of the next layer; Step 7: after the optimization of the last layer is completed, it is judged whether the convergence standard is reached, if not, it returns to step 6, and if yes, the cycle is stopped.

2. The response surface based layered optimization method of a permanent magnet synchronous motor according to claim 1, wherein, The constraint condition selected in step 2 is a set threshold of the fundamental amplitude of air gap flux density.

3. The response surface based layered optimization method for permanent magnet synchronous motor according to claim 1, wherein, The parameter layering method in step 5 is specifically as follows: All bidirectional parameters are one layer, and all unidirectional parameters are another layer, the layer with larger average sensitivity of parameters is set as the first layer, for the bidirectional parameter layer, if the parameters in the layer are too many, the layer can be further layered according to the sensitivity.

4. The response surface based layered optimization method of a permanent magnet synchronous motor according to claim 1, wherein, The response surface construction method in step 6 is specifically as follows: For unidirectional parameters, CCD or Box-henven sampling method is used for sampling, and a full second-order polynomial response surface is constructed; for bidirectional parameters, Latin hypercube sampling method is used for encryption sampling, and a kriging response surface is constructed.

5. The response surface based layered optimization method of permanent magnet synchronous motor according to claim 1, wherein, The multi-objective optimization algorithm in step 6 is a non-dominated sorting genetic algorithm II (NSGA2).

6. The response surface based layered optimization method of a permanent magnet synchronous motor according to claim 1, wherein, The convergence standard in step 7 is as follows: F is the criterion for selecting the optimal point, AF is the change in F between two iterations, and the target f j Default minimization.

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