Layered optimization method of permanent magnet synchronous motor based on response surface

Abstract

The invention discloses a permanent magnet synchronous motor layered optimization method based on a response surface, which innovatively proposes the concept of'bidirectional 'and'unidirectional' parameters, and layering the parameters on the basis of the concept, and takes a layer with higher average sensitivity as a first layer. A Latin hypercube sampling method is used for a'bidirectional 'parameter layer, enough sample points are given, and then a kriging response surface is fitted; center composite experimental design (CCD) or Box-open experimental design is used for the one-way parameter layer, 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 optimizing, and after a Pareto leading edge is obtained, a simple weight aggregation method is used for screening an optimal point to enter next-layer optimization. According to the permanent magnet synchronous motor layered optimization method based on the response surface, the fitting precision of the response surface is greatly improved, and the optimization efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the field of motor parameter optimization design, and in particular relates to a parameter hierarchical optimization method for a permanent magnet synchronous motor. Background Art

[0002] Permanent Magnet Synchronous Motor (PMSM) is widely used in ship propulsion, wind power generation, mine hoisting and other fields due to its advantages such as high efficiency and high power density. In order to further improve the comprehensive performance of the motor, multi-objective optimization is a necessary process. In view of the high parameter dimension and slow calculation speed of the finite element model in the multi-objective optimization process, many scholars have proposed parameter stratification and response surface proxy model construction methods. The stratified optimization method divides the parameters into several layers according to the sensitivity size relationship, and optimizes them layer by layer, which solves the problem of high parameter dimension and easy convergence to local optimum; the response surface constructs proxy models such as full second-order polynomial response surface and kriging response surface through a small number of samplings, 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 greatly increased, which leads to low optimization efficiency. The currently popular method of combining stratified optimization with the response surface proxy model can improve the fitting accuracy of the response surface to a certain extent, but the accuracy is still poor for targets with complex harmonic relationships such as cogging torque and torque pulsation. Summary of the invention

[0003] In view of the shortcomings of the prior art, the purpose of the present invention is to overcome the problems of high parameter dimension and poor accuracy of response surface proxy model in the motor optimization process, and proposes a hierarchical optimization method of permanent magnet synchronous motor based on response surface. This method innovatively proposes the concepts of "bidirectional" parameters and "unidirectional" parameters, and divides the parameters into "bidirectional" parameter layer and "unidirectional" parameter layer based on this, and then adopts different sampling methods and proxy models for the two parameters, taking into account both speed and accuracy.

[0004] A hierarchical optimization method for a permanent magnet synchronous motor based on a response surface comprises the following steps:

[0005] Step 1: Select the optimization target according to the motor performance requirements and determine the upper and lower limits of each design parameter;

[0006] Step 2: Determine the constraints in the motor optimization process;

[0007] Step 3: Sensitivity analysis, calculating the sensitivity of the parameters to each target and the comprehensive sensitivity to all targets;

[0008] Step 4: According to the specific impact of the parameters on the target, the parameters are divided into two categories: bidirectional and unidirectional;

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

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

[0011] Step 7: After the last layer is optimized, determine whether the convergence standard is met. If not, return to step 6. If so, stop the loop.

[0012] Furthermore, the constraint condition selected in step 2 is a set threshold value of the air gap magnetic density fundamental wave amplitude.

[0013] Furthermore, the sensitivity analysis method in step 3 is specifically as follows:

[0014]

[0015] Where S ij is the interval sensitivity of the ith parameter to the jth target, k is the sequence number of the interval sensitivity, and f j and ∆f j are the value and change of the jth target, z i and △z i is the value and change of the i-th design parameter. The sensitivity analysis is performed on only one parameter at a time. When other parameters are at the center value, the current parameter is changed according to the set step size. Each time the parameter changes, an interval sensitivity is obtained. The final sensitivity of a certain 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 comprehensive sensitivity in step 3 is:

[0019]

[0020] Where S i is the comprehensive sensitivity of the ith parameter, ω j is the weight of the j-th target.

[0021] Furthermore, the judgment criteria for dividing the parameters into bidirectional and unidirectional in step 4 are:

[0022]

[0023] It is the maximum or minimum value of the sensitivity of all intervals of a parameter and is related to S ij The signs are 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] Furthermore, the parameter stratification method in step 5 is specifically as follows:

[0025] All bidirectional parameters are taken as one layer, and all unidirectional parameters are taken as another layer. The layer with the larger average parameter sensitivity is set as the first layer. For the bidirectional parameter layer, if there are too many parameters in the layer, it can be further stratified according to the sensitivity.

[0026] Furthermore, the response surface construction method described in step 6 is specifically as follows:

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

[0028] Furthermore, the multi-objective optimization algorithm described in step six is ​​a second-generation non-dominated sorting genetic algorithm NSGA2.

[0029] Furthermore, the convergence criterion in step 7 is:

[0030]

[0031] F is the criterion for selecting the optimal point, △F is the change in F between two iterations, and the target f j Minimized by default.

[0032] Beneficial effects:

[0033] The present invention innovatively proposes the concepts of unidirectional and bidirectional parameters, which are used as the basis for parameter stratification. For unidirectional parameters, a sampling method such as Box-Behnken and CCD with fewer sample points is adopted and a full second-order polynomial response surface is constructed. For bidirectional parameters, an encrypted sampling method such as Latin hypercube sampling method is adopted, and a kriging response surface is constructed. This 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 THE DRAWINGS

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

[0035] Figure 2 It is the topology diagram of low speed and high torque permanent magnet synchronous motor;

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

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

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

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

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

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

[0042] Fig. 9 is the response surface of the second layer parameters to torque ripple;

[0043] Fig.10 is the response surface of the second-layer parameters to efficiency;

[0044] Fig.11 It is the Pareto frontier of the second layer, and the red point is the optimal point. DETAILED DESCRIPTION

[0045] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] The present application is a hierarchical optimization method for a permanent magnet synchronous motor based on a response surface, comprising the following steps:

[0047] Step 1: Select the optimization target according to the motor performance requirements and determine the upper and lower limits of each design parameter;

[0048] Step 2: Determine the constraints in the motor optimization process;

[0049] Step 3: Sensitivity analysis, calculating the sensitivity of the parameters to each target and the comprehensive sensitivity to all targets;

[0050] Step 4: According to the specific impact of the parameters on the target, the parameters are divided into two categories: bidirectional and unidirectional;

[0051] Step 5: Divide all parameters into two layers, bidirectional parameters as one layer and unidirectional parameters as another layer;

[0052] Step 6: Different sampling methods and response surface construction methods are used for bidirectional parameters and unidirectional parameters, and the multi-objective optimization algorithm is used to find the optimal solution. The optimal solution obtained at each layer is used as the basis for the optimization of the next layer.

[0053] Step 7: After the last layer is optimized, determine whether the convergence standard is met. If not, return to step 6. If so, stop the loop.

[0054] Furthermore, the constraint condition selected in step 2 is a set threshold value of the air gap magnetic density fundamental wave amplitude.

[0055] Furthermore, the sensitivity analysis method in step 3 is specifically as follows:

[0056]

[0057] Where S ij is the interval sensitivity of the ith parameter to the jth target, k is the sequence number of the interval sensitivity, and f j and ∆f j are the value and change of the jth target, z i and △z i is the value and change of the i-th design parameter. The sensitivity analysis is performed on only one parameter at a time. When other parameters are at the center value, the current parameter is changed according to the set step size. Each time the parameter changes, an interval sensitivity is obtained. The final sensitivity of a certain target is the average of all interval sensitivities. The calculation formula is as follows:

[0058]

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

[0060] Furthermore, the method for calculating the comprehensive sensitivity in step 3 is:

[0061]

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

[0063] Furthermore, the judgment criteria for dividing the parameters into bidirectional and unidirectional in step 4 are:

[0064]

[0065] It is the maximum or minimum value of the sensitivity of all intervals of a parameter and is related to S ij The signs are 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.

[0066] Furthermore, the parameter stratification method in step 5 is specifically as follows:

[0067] All bidirectional parameters are taken as one layer, and all unidirectional parameters are taken as another layer. The layer with the larger average parameter sensitivity is set as the first layer. For the bidirectional parameter layer, if there are too many parameters in the layer, it can be further stratified according to the sensitivity.

[0068] Furthermore, the response surface construction method described in step 6 is specifically as follows:

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

[0070] Furthermore, the multi-objective optimization algorithm described in step six is ​​a second-generation non-dominated sorting genetic algorithm NSGA2.

[0071] Furthermore, the convergence criterion in step 7 is:

[0072]

[0073] F is the criterion for selecting the optimal point, △F is the change in F between two iterations, and the target f j Minimized by default.

[0074] The following will introduce each step of this application in detail with reference to the accompanying drawings: Figure 2 The present invention is described in detail by taking the rotor structure optimization of the low-speed, high-torque magnetic-concentrated permanent magnet synchronous motor shown in the figure as an example. Step 1: This type of motor is commonly used in the fields of mine hoisting, ship propulsion, etc., and has high requirements on torque density, efficiency and torque pulsation. Therefore, torque, torque pulsation and efficiency are selected as the three goals of this optimization. Figure 2 All the design parameters of the rotor are marked, 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 motor magnetic load is within a reasonable range, the air gap magnetic density fundamental wave amplitude is limited to no more than 1.02T and no 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 as the center value. The rotor height coefficient khr is used as an example for explanation. Table 2 shows the sensitivity analysis process of khr to torque pulsation.

[0079] Table 2 Rotor height coefficient khr sensitivity analysis

[0080]

[0081] Table 2

[0082]

[0083]

[0084] The average sensitivity of khr to torque ripple is -0.85. Using the same method as in Table 2, the sensitivity of khr to torque and efficiency is -0.38 and -0.015 respectively. In order to calculate the comprehensive sensitivity of this parameter to all targets, the weight of each target needs to be determined. For simplicity, the weight of torque and efficiency is 0.4, and the weight of torque ripple is 0.2. Therefore, the comprehensive sensitivity of khr is 0.33. Figure 3 Comprehensive sensitivity analysis results are presented.

[0085] Step 4: The criteria for determining whether the parameter is bidirectional or unidirectional are:

[0086]

[0087] Based on this standard, it is found that except for the air gap length g, permanent magnet width bm, eccentric pole length offset and rotor width br, the other parameters are bidirectional parameters. This also explains the complex harmonic relationship inside the motor. The ordinary parameter layering and response surface optimization method can hardly guarantee the accuracy of the optimization results.

[0088] Step 5: According to the parameter type, six bidirectional parameters are in one layer, and four unidirectional parameters are in one layer. Since there are still many parameters in the bidirectional parameter layer, the threshold δ is set to 0.1. The bidirectional parameter layer is further stratified with δ as the boundary. The bidirectional parameters with a comprehensive sensitivity higher than δ are in one layer, and the bidirectional parameters with a comprehensive sensitivity lower than δ are in another layer. Therefore, all parameters are finally divided into three layers, arranged from large to small according to the 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 sequence, and the optimization result of the previous layer will serve as the optimization basis for the next layer.

[0089] Table 3 Final stratification results

[0090]

[0091] Step 6: Use the Latin hypercube sampling method to sample the bidirectional parameters of the first layer, set the number of samples to 100, and fit the kriging response surface. On this basis, use the NSGA2 algorithm to search for the optimal solution. Figures 4 to 6 is the response surface of the first layer parameters, Figure 7 is the Pareto frontier of the first layer. In order to select an optimal solution on the Pareto frontier, 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 value of torque ripple, n and n' are the efficiency and the initial value of efficiency, ω1, ω2 and ω3 are the weight coefficients, which are the same as the values ​​used in calculating the comprehensive sensitivity. Calculate the F value of all individuals on the Pareto frontier, select the minimum value to enter the next level of optimization, and the optimal point of the first level is already Figure 7 Winning bid.

[0094] Based on the optimization results of the first layer, the parameters of the second layer are optimized. The central composite experimental design is used to sample the second layer parameters and fit the full second-order polynomial response surface. Unlike the kriging response surface, the full second-order polynomial response surface has poor flexibility and adaptability, and often has problems with poor fitting accuracy, which is specifically manifested in the small determination coefficient R2. However, through the new parameter stratification strategy proposed in this patent, the parameters of the second layer are all unidirectional parameters, and the response surface does not need to have strong adaptive capabilities. During this optimization process, the determination coefficients of the full second-order polynomial response surface for the three targets were 0.9999, 0.9989 and 0.9999, respectively, which means that the fitting quality of the response surface is very high. Figures 8 to 10 The partial response surface of the second layer parameters is given. Similarly, the NSGA2 algorithm is used to obtain the Pareto frontier and select the optimal point. Fig.11 The Pareto front of the second level is given.

[0095] Finally, the third layer parameters are optimized using the same method as the first layer parameters. Table 4 shows the changes in each target during each iteration. At the same time, the errors between the optimal fitting value and the simulation value of each layer are compared. The small error value greatly improves the convergence speed of hierarchical optimization.

[0096] Table 4. Target changes during iteration

[0097]

[0098] Step 7: This optimization was performed three times in total, and the F value of each iteration was 0.8762, 0.8661 and 0.8669. According to the convergence judgment criteria proposed earlier, the optimization process ended after the third iteration. Due to the weak local search capability of the NSGA2 algorithm, the result of the third iteration was slightly worse than that of the second iteration, so the result of the second iteration was taken as the final optimization result. Table 5 is a comparison of motor parameters and performance before and after optimization.

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

[0100]

[0101] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A hierarchical optimization method for permanent magnet synchronous motor based on response surface, characterized in that: The following steps are involved: Step 1: Select the optimization target according to the motor performance requirements and determine the upper and lower limits of each design parameter; Step 2: Determine the constraints in the motor optimization process; Step 3: Sensitivity analysis, calculating the sensitivity of the parameters to each target and the comprehensive sensitivity to all targets; Step 4: According to the specific impact of the parameters on the target, the parameters are divided into two categories: bidirectional and unidirectional; Step 5: Divide all parameters into two layers, bidirectional parameters as one layer and unidirectional parameters as another layer; Step 6: Different sampling methods and response surface construction methods are used for bidirectional parameters and unidirectional parameters, and the multi-objective optimization algorithm is used to find the optimal solution. The optimal solution obtained at each layer is used as the basis for the optimization of the next layer. Step 7: After the last layer is optimized, determine whether the convergence standard is met. If not, return to step 6. If so, stop the loop.

2. The response surface-based permanent magnet synchronous motor hierarchical optimization method according to claim 1, characterized in that: The constraint condition selected in step 2 is the set threshold of the air gap magnetic density fundamental wave amplitude.

3. The method for hierarchical optimization of permanent magnet synchronous motor based on response surface according to claim 1, characterized in that: The sensitivity analysis method in step 3 is as follows: Where S ij is the interval sensitivity of the i-th parameter to the j-th target, k is the sequence number of the interval sensitivity, and f j and ∆f j are the value and change of the jth target, z i and △z i is the value and change of the i-th design parameter. The sensitivity analysis is performed on only one parameter at a time. When other parameters are at the center value, the current parameter is changed according to the set step size. Each time the parameter changes, an interval sensitivity is obtained. The final sensitivity of a certain target is the average of all interval sensitivities. The calculation formula is as follows: l is the total number of interval sensitivities.

4. The method for hierarchical optimization of a permanent magnet synchronous motor based on a response surface according to claim 1, characterized in that: The method for calculating the comprehensive sensitivity in step 3 is: Where S i is the comprehensive sensitivity of the ith parameter, ω j is the weight of the j-th target.

5. The method for hierarchical optimization of permanent magnet synchronous motor based on response surface according to claim 1, characterized in that: The criteria for classifying parameters into bidirectional and unidirectional in step 4 are: It is the maximum or minimum value of the sensitivity of all intervals of a parameter and is related to S ij The signs are 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.

6. The method for hierarchical optimization of a permanent magnet synchronous motor based on a response surface according to claim 1, characterized in that: The parameter stratification method in step 5 is as follows: All bidirectional parameters are taken as one layer, and all unidirectional parameters are taken as another layer. The layer with the larger average parameter sensitivity is set as the first layer. For the bidirectional parameter layer, if there are too many parameters in the layer, it can be further stratified according to the sensitivity.

7. The response surface-based permanent magnet synchronous motor hierarchical optimization method according to claim 1, characterized in that: The response surface construction method described in step 6 is specifically as follows: For unidirectional parameters, sampling is performed based on CCD or Box-henven sampling methods, and a full second-order polynomial response surface is constructed; for bidirectional parameters, Latin hypercube sampling method is used to encrypt sampling and construct kriging response surface.

8. The method for hierarchical optimization of a permanent magnet synchronous motor based on a response surface according to claim 1, characterized in that: The multi-objective optimization algorithm described in step six is ​​the second generation non-dominated sorting genetic algorithm NSGA2.

9. The method for hierarchical optimization of a permanent magnet synchronous motor based on a response surface according to claim 1, characterized in that: The convergence criteria described in step 7 are: F is the criterion for selecting the optimal point, △F is the change in F between two iterations, and the target f j Minimized by default.

Images