A multi-objective robust optimization method for interior permanent magnet synchronous motor

Abstract

This invention discloses a multi-objective robust optimization method for an embedded cascaded permanent magnet synchronous motor, belonging to the technical field of modular cascaded embedded permanent magnet motors for electric vehicles. Based on the 6σ robust design method and differential evolution algorithm, this invention proposes an improved multi-objective optimization design algorithm for permanent magnet motors. The optimization objectives are to maximize average torque and efficiency, and minimize manufacturing cost and product performance instability. This optimizes product performance while improving product competitiveness. Furthermore, this invention uses Taylor expansion instead of Monte Carlo analysis, reducing the robustness analysis time. After obtaining the electromagnetic parameters, this invention also establishes a thermal resistance network model of the motor to verify its multi-physics integrated performance.

Description

Technical Field

[0001] This invention relates to a multi-objective robust optimization method for built-in cascaded permanent magnet synchronous motors, belonging to the technical field of modular cascaded built-in permanent magnet motors for electric vehicles. Background Technology

[0002] Built-in permanent magnet motors (IPMs) are widely used in electric and hybrid vehicles due to their high efficiency, high torque density, and wide speed range. Meanwhile, the rapid development of electromagnetic analysis technology in recent years has made it possible to accurately design and optimize IPM motors. However, traditional optimization design processes and performance analyses for permanent magnet motors are typically based on deterministic parameters, neglecting the impact of manufacturing deviations. This can lead to significant variations in product performance, affecting the reliability and quality of the motor in mass production.

[0003] To improve the reliability and robustness of permanent magnet motors (PMMs), robust optimization design that considers manufacturing uncertainties, material diversity, and performance sensitivity to parameters during the design and simulation stages has gained increasing attention in recent years. For example, the Taguchi robust design algorithm can account for the impact of manufacturing tolerances in PMMs, achieving robust performance in areas such as back EMF and torque. However, traditional robust optimization design for motors often focuses solely on electromagnetic performance optimization, neglecting the verification of PMM thermal performance. Furthermore, the large computational load and long computation time in robust optimization design of motors are current bottlenecks. Therefore, improving optimization algorithms and accelerating robust optimization design is a core issue in robust design research. Summary of the Invention

[0004] This invention proposes a multi-objective robust optimization method for built-in cascaded permanent magnet synchronous motors. The optimization objectives are to maximize average torque and efficiency, and minimize manufacturing cost and product performance instability, thereby improving product performance and competitiveness. Furthermore, a Taylor expansion method is used instead of Monte Carlo analysis, reducing the robustness analysis time and addressing problems existing in prior art.

[0005] A robust multi-objective optimization method for built-in cascaded permanent magnet synchronous motors includes the following steps:

[0006] Step 1: Based on the design requirements and constraints of the motor, establish the deterministic optimization objective equation for the motor;

[0007] Step 2: Establish a parametric model of the motor and define the optimization design range for each parameter of the motor [x] l ,x u ];

[0008] Step 3: Considering the range of uncertain parameters of the motor, modify the deterministic optimization objective equation of the motor into a robust optimization objective equation of the motor;

[0009] Step 4: Based on the deterministic parameters of the motor, calculate the motor torque T using the finite element method. ave Efficiency P eff Cost, torque ripple (T) rip And slot full rate sf;

[0010] Step 5: Based on the fluctuation range of the machining process parameters, generate a motor model that considers machining factors, and calculate the motor torque T under the influence of machining deviation using Taylor series expansion. ave Efficiency P eff Cost, torque ripple (T) rip The mean and standard deviation of the slot fill factor sf, i.e., the average torque μ(T) ave ), average efficiency μ(P) eff ), average cost μ(cost), average torque ripple μ(T) rip ), average slot fill factor μ(sf) and standard deviation of torque σ(T) ave ), efficiency standard deviation σ(P) eff ), cost standard deviation σ(cost), torque ripple standard deviation σ(T) rip ) and the standard deviation of the fill factor σ(sf);

[0011] Step 6: Using the robust optimization objective equation of the motor, find the optimal solution of the design parameters so that the optimization objective value and constraints of the motor meet the design conditions;

[0012] Step 7: Calculate the motor losses based on the optimal solution of the optimized parameters;

[0013] Step 8: Establish a thermal network model of the motor and calculate the temperature rise of the motor.

[0014] Furthermore, in step two, the deterministic optimization objective equation for the motor is expressed as:

[0015]

[0016] stg1(x)=T rip -0.1≤0

[0017] g2(x)=sf-0.75≤0

[0018] g3(x)=T ave -15≥0

[0019] x l ≤x≤x u

[0020] In the formula, T ave P is the motor torque. effT represents motor efficiency, cost represents motor cost, and T represents the motor efficiency. rip sf represents the motor torque pulsation, and sf represents the motor slot fill factor.

[0021] Furthermore, in step three, the objective equation for the robust optimization design of the motor is expressed as follows:

[0022] min:{F k =μ fk (x)+σ fk (x), k = 1, 2, 3}

[0023] stμ Trip (x)+6σ Trip (x)≤0.1

[0024] μ sf (x)+6σ sf (x)≤0.75

[0025] μ Tave (x)-6σ Tave (x)≥15

[0026] x l +6σ x ≤μ x ≤x u -6σ x

[0027] μ fk -6σ fk ≥LSL

[0028] μ fk +6σ fk ≤USL

[0029] In the formula, μ(T) ave ) represents the average value of the motor torque, μ(P) eff ) represents the average motor efficiency, μ(cost) represents the average motor cost, and μ(T) represents the average motor cost. rip ) represents the average value of the motor torque ripple, μ(sf) represents the average value of the motor slot fill factor, and σ(T) represents the average value of the motor slot fill factor. ave ) represents the standard deviation of the motor torque, σ(P) eff σ(cost) represents the standard deviation of motor efficiency, and σ(T) represents the standard deviation of motor cost. rip ) represents the standard deviation of motor torque ripple, and σ(sf) represents the standard deviation of motor slot fill factor.

[0030] Furthermore, the cost in step four is expressed as:

[0031]

[0032] In the formula, p mFor the price of the component, M m Q represents the quality of the component, and Q represents the quantity purchased.

[0033] Furthermore, the Taylor expansion in step five is expressed as:

[0034]

[0035] Therefore, the average product performance is

[0036] μ y =Y(μ) x )

[0037] The standard deviation of product performance is

[0038]

[0039] In the formula, i is the variable number, and j is the number of uncertain parameters.

[0040] Furthermore, the improved parameters in the multi-objective robust optimization algorithm in step six are expressed as follows:

[0041]

[0042] F = F0·2 fr

[0043] In the formula, f r For the adaptive mutation operator, F0 is the initial mutation operator, and G is the G... m G represents the maximum iteration step size, and G represents the current iteration number.

[0044] Furthermore, the motor losses in step seven are expressed as follows:

[0045] P core =P h +P e +P c

[0046] =C h fB 2 +C e f 2 B 2 +C c f 1.5 B 1.5

[0047] In the formula, P core For iron loss, P h For hysteresis loss, P e For eddy current losses, P c For additional losses, C h C is the hysteresis loss coefficient. e C is the eddy current loss coefficient. cHere, f is the additional loss coefficient, f is the frequency, and B is the magnetic flux density of each finite element.

[0048] P copper =mI 2 R

[0049] In the formula, P copper R is the copper loss, R is the resistance of each phase winding, I is the effective value of the phase current, and m is the number of phases.

[0050] Furthermore, the thermal resistance of the thermal resistance network model in step eight is expressed as:

[0051]

[0052]

[0053] In the formula, R p For flat-plate thermal resistance, R c Let L be the length of the cylindrical thermal resistor, λ be the thermal conductivity of the plate thermal resistor, S be the cross-sectional area of ​​the plate thermal resistor, and r1 and r2 be the inner and outer diameters of the cylindrical thermal resistor.

[0054] To model the complex thermal resistance of the winding region, we solve for the equivalent thermal conductivity of this region. The equivalent thermal conductivity is expressed as:

[0055] k mix =θ*k ins +(1-θ)k imp

[0056] In the formula, k mix k is the equivalent thermal conductivity. ins k is the thermal conductivity and insulation coefficient of copper wire material. imp θ represents the impregnation thermal conductivity, and θ is the ratio of the winding insulation area to the total slot area.

[0057] The beneficial effects of this invention are as follows: This invention provides a robust multi-objective optimization method for a built-in cascaded permanent magnet synchronous motor. It overcomes the shortcomings of traditional deterministic optimization methods that cannot consider uncertain parameters during motor manufacturing. By combining intelligent genetic optimization algorithms with robust design algorithms, it takes into account the uncertain parameters in the motor. Through robust optimization design, the performance consistency of motor products during mass production is improved. Furthermore, this invention proposes improved measures to accelerate algorithm convergence, resulting in shorter optimization time and higher optimization efficiency. Finally, this invention establishes an equivalent thermal resistance network for the motor, realizing a comprehensive robust design of the motor under multi-physics fields, laying a solid foundation for multi-physics optimization design that couples electromagnetic and thermal analysis of the motor. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the embedded cascaded permanent magnet motor structure of the present invention;

[0059] Figure 2 This is a flowchart of the multi-objective robust optimization method for embedded cascaded permanent magnet motors of the present invention;

[0060] Figure 3 The improved genetic algorithm flow of this invention;

[0061] Figure 4 This is the optimized result of the embedded cascaded permanent magnet motor of the present invention;

[0062] Figure 5 This is a schematic diagram of the flat plate thermal resistance model of the present invention;

[0063] Figure 6 This is a schematic diagram of the cylindrical thermal resistance model of the present invention;

[0064] Figure 7 This is a schematic diagram of the equivalent winding model of the present invention;

[0065] Figure 8 This is a model diagram of the embedded cascaded permanent magnet motor thermal resistance network of the present invention;

[0066] Figure 9 The temperature calculation results for the embedded cascaded permanent magnet motor of this invention are shown.

[0067] In this designation, 1 is the stator, 2 is the permanent magnet, 3 is the rotor, 10 is the stator winding, 11 is the stator core, 20 is the N-pole permanent magnet, 21 is the S-pole permanent magnet, 30 is the rotor core, and 31 is the shaft. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] In the accompanying drawings of specific embodiments of the present invention, in order to better and more clearly describe the working principle of each component in the system and show the connection relationship of each part in the device, only the relative positional relationship between each component is clearly distinguished. It does not constitute a limitation on the signal transmission direction, connection sequence, or size, dimension, and shape of each part within the component or structure.

[0070] like Figure 1 As shown, the rare-earth permanent magnet motor with a double-layer tangential magnetic pole structure of the present invention consists of a stator 1, permanent magnets 2, and a rotor 3. It includes a stator winding 10 and a stator core 11; the permanent magnets include an N-pole permanent magnet 20 and an S-pole permanent magnet 21; and the rotor includes a rotor core 30 and a shaft 31.

[0071] The stator core 11 has winding slots to house the stator winding 10. The rotor core 30 has permanent magnet slots to house permanent magnets 20 and 21. The permanent magnets 20 and 21 are neodymium iron boron permanent magnets and are arranged at intervals.

[0072] Once the basic dimensions and stator / rotor topology of the motor are determined, a finite element simulation model of the motor can be established using finite element software. Based on the motor's design requirements and manufacturing factors, the optimization parameters, objectives, and constraints are determined, and a multi-objective robust optimization equation for the motor is established.

[0073] This implementation case uses the motor's torque, efficiency, cost, torque ripple, and slot fill factor as design parameters to illustrate the multi-objective robust optimization design of the motor. For example... Figure 2 The flowchart shown is a multi-objective robust optimization design method for motors, which includes the following steps:

[0074] Step 1: Based on the motor's design requirements [f1,f2,f3,…] and constraints [g1,g2,…], establish the motor's optimization objective equation.

[0075] Step 2: Establish a parametric model of the motor and define the optimization design range for each parameter of the motor [x] l ,x u ].

[0076]

[0077] stg1(x)=T rip -0.1≤0

[0078] g2(x)=sf-0.75≤0

[0079] g3(x)=T ave -15≥0

[0080] x l ≤x≤x u

[0081] In the formula, T ave P is the motor torque. eff T represents motor efficiency, cost represents motor cost, and T represents the motor efficiency. rip sf represents the motor torque pulsation, and sf represents the motor slot fill factor.

[0082] Step 3: Considering the range of uncertain parameters of the motor, modify the deterministic optimization objective equation of the motor into a robust optimization objective equation of the motor.

[0083] min:{F k =μ fk (x)+σ fk(x), k = 1, 2, 3}

[0084] stμ Trip (x)+6σ Trip (x)≤0.1

[0085] μ sf (x)+6σ sf (x)≤0.75

[0086] μ Tave (x)-6σ Tave (x)≥15

[0087] x l +6σ x ≤μ x ≤x u -6σ x

[0088] μ fk -6σ fk ≥LSL

[0089] μ fk +6σ fk ≤USL

[0090] In the formula, μ(T) ave ) represents the average value of the motor torque, μ(P) eff ) represents the average motor efficiency, μ(cost) represents the average motor cost, and μ(T) represents the average motor cost. rip ) represents the average value of the motor torque ripple, μ(sf) represents the average value of the motor slot fill factor, and σ(T) represents the average value of the motor slot fill factor. ave ) represents the standard deviation of the motor torque, σ(P) eff σ(cost) represents the standard deviation of motor efficiency, and σ(T) represents the standard deviation of motor cost. rip ) represents the standard deviation of motor torque ripple, and σ(sf) represents the standard deviation of motor slot fill factor.

[0091] Step 4: Based on the deterministic parameters of the motor, calculate the motor torque T using the finite element method. ave Efficiency P eff Cost, torque ripple T rip The motor's torque, efficiency, torque ripple, and slot fill factor (sf) can all be obtained directly through finite element model simulation. The cost of the motor can be calculated as follows:

[0092]

[0093] In the formula, p m For the price of the component, M m Q represents the quality of the component, and Q represents the quantity purchased.

[0094] Step 5: Based on the fluctuation range of the machining process parameters, generate a motor model that considers machining factors, and calculate the motor torque T under the influence of machining deviation using Taylor series expansion. ave Efficiency P eff Cost, torque ripple T rip And the average and standard deviation of the slot fill factor sf, i.e., the average torque μ(T) ave ), average efficiency μ(P) eff ), average cost μ(cost), average torque ripple μ(T) rip The average slot fill factor μ(sf) and the standard deviation of torque σ(T) ave ), efficiency standard deviation σ(P) eff Cost standard deviation σ(cost), torque ripple standard deviation σ(T) rip The standard deviation of slot fill factor σ(sf). The mean and standard deviation of each optimization objective and constraint of the motor can be calculated using the following formula:

[0095]

[0096] Therefore, the average performance of the product can

[0097] μ y =Y(μ) x )

[0098] The standard deviation of product performance is

[0099]

[0100] In the formula, i is the variable number, and j is the number of uncertain parameters.

[0101] Step Six: Using the multi-objective robust optimization design algorithm proposed in this invention, find the optimal solution for the design parameters, ensuring that the optimization objective value and constraints of the motor meet the design conditions. The optimization process mainly includes population initialization, mutation, and crossover. During the population mutation process, this invention proposes an adaptive mutation operator to improve the algorithm's optimization capability, such as... Figure 3 As shown. The adaptive mutation operator can be expressed as:

[0102]

[0103] F = F0·2 fr

[0104] In the formula, f r For the adaptive mutation operator, F0 is the initial mutation operator, and G is the G... m G represents the maximum iteration step size, and G represents the current iteration number.

[0105] After crossover and mutation, the finite element method (FEM) is used to calculate the optimization objective and constraints of each individual, and to determine if the motor performance meets the requirements. If the requirements are not met, the individual is discarded to save computational resources and accelerate the solution. If the requirements are met, the mean and variance of the individual's optimization objective and constraints are calculated, and the variance of the individual is checked to ensure it meets the requirements. If the requirements are not met, the individual is discarded to save computational resources. If the requirements are met, the excellent individual is retained, and the algorithm is checked to see if the iteration termination condition is met. If the iteration termination condition is not met, optimization continues. If the termination condition is met, the result is output, such as... Figure 4 As shown.

[0106] Step 7: Based on the optimal solution of the optimized parameters, calculate the motor losses. The main losses in the motor are iron losses, copper losses, and permanent magnet eddy current losses. The motor losses can be expressed as:

[0107] P core =P h +P e +P c

[0108] =C h fB 2 +C e f 2 B 2 +C c f 1.5 B 1.5

[0109] In the formula, P core For iron loss, P h For hysteresis loss, P e For eddy current losses, P c For additional losses, C h C is the hysteresis loss coefficient. e C is the eddy current loss coefficient. c Here, f is the additional loss coefficient, f is the frequency, and B is the magnetic flux density of each finite element.

[0110] Copper loss can be expressed as:

[0111] P copper =mI 2 R

[0112] In the formula, P copper R is the copper loss, R is the resistance of each phase winding, I is the effective value of the phase current, and m is the number of phases.

[0113] Step 8: Establish a thermal network model of the motor and calculate its temperature rise. Based on the shape of the motor components, the thermal resistance of different regions of the motor can be simplified equivalently to flat plate thermal resistance and cylindrical thermal resistance. Among them, the flat plate thermal resistance is as follows: Figure 5As shown, it can be represented as:

[0114]

[0115] In the formula, R p Let L be the length of the flat plate thermal resistor, λ be the thermal conductivity of the flat plate thermal resistor, and S be the cross-sectional area of ​​the flat plate thermal resistor.

[0116] Cylindrical thermal resistance such as Figure 6 As shown, it can be represented as:

[0117]

[0118] In the formula, R c It is a cylindrical thermal resistor, where r1 and r2 are the inner and outer diameters of the cylindrical thermal resistor.

[0119] Furthermore, for modeling the complex thermal resistance of the winding region, it can be done by solving for the equivalent thermal conductivity of that region, such as... Figure 7 As shown. The equivalent thermal conductivity can be expressed as:

[0120] k mix =θ*k ins +(1-θ)k imp

[0121] In the formula, k mix k is the equivalent thermal conductivity. ins k is the thermal conductivity and insulation coefficient of copper wire material. imp θ represents the impregnation thermal conductivity, and θ is the ratio of the winding insulation area to the total slot area.

[0122] The final equivalent heat network model is as follows: Figure 8 As shown.

[0123] Based on the equivalent heat network model in this case, the results are as follows: Figure 9 As shown. Throughout the entire motor design process, not only electromagnetic performance but also the motor's temperature robustness were considered, achieving a comprehensive and robust design of the motor under multiple physical fields.

[0124] The aforementioned motor optimization algorithm can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated.

[0125] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and these modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A multi-objective robust optimization method for a built-in cascaded permanent magnet synchronous motor, characterized in that, Includes the following steps: Step 1: Based on the design requirements and constraints of the motor, establish the deterministic optimization objective equation for the motor; Step 2: Establish a parametric model of the motor and define the optimization design range for each parameter of the motor [x] l ,x u ]; Step 3: Considering the range of uncertain parameters of the motor, the deterministic optimization objective equation of the motor is modified into a robust optimization design objective equation of the motor. The robust optimization design objective equation of the motor is expressed as follows: ； Step 4: Based on the deterministic parameters of the motor, calculate the motor torque using the finite element method. T ave ,efficiency P eff Cost, Torque ripple T rip Slot fill rate sf ; Step 5: Based on the fluctuation range of the machining process parameters, generate a motor model that considers machining factors, and calculate the motor torque under the influence of machining deviations using Taylor series expansion. T ave ,efficiency P eff Cost, Torque ripple T rip Slot fill rate sf The average value and standard deviation, i.e., the average torque value Average efficiency μ ( P eff ), average cost μ (Cost), Average Torque Ripple Average Slot Fill Rate With torque standard deviation Efficiency Standard Deviation σ ( P eff ), cost standard deviation σ (Cost), Torque Ripple Standard Deviation Standard deviation of fill factor ; Step 6: Using the robust optimization design objective equation of the motor, find the optimal solution of the design parameters so that the optimization objective value and constraints of the motor meet the design conditions; Step 7: Calculate the motor losses based on the optimal solution of the optimized parameters; Step 8: Establish a thermal resistance network model of the motor based on the motor losses, and calculate the temperature rise of the motor.

2. The multi-objective robust optimization method for a built-in cascaded permanent magnet synchronous motor according to claim 1, characterized in that, In step one, the deterministic optimization objective equation for the motor is expressed as: In the formula, T ave This is the motor torque. P eff For motor efficiency, Cost is the cost of the motor. T rip For motor torque pulsation, and sf This represents the motor slot fill factor.

3. The multi-objective robust optimization method for a built-in cascaded permanent magnet synchronous motor according to claim 2, characterized in that, The cost in step four is expressed as: In the formula, p m For the price of the components, M m For the quality of the components, Q This refers to the quantity purchased.

4. The multi-objective robust optimization method for a built-in cascaded permanent magnet synchronous motor according to claim 3, characterized in that, The Taylor expansion in step five is expressed as follows: Therefore, the average product performance is The standard deviation of product performance is In the formula, i For the variable number, j The number of uncertain parameters.

5. A multi-objective robust optimization method for a built-in cascaded permanent magnet synchronous motor according to claim 4, characterized in that, The improved parameters in the multi-objective robust optimization algorithm in step six are expressed as follows: In the formula, fr For adaptive mutation operators, F 0 represents the initial mutation operator. G m For the maximum iteration step size, G This represents the current iteration number.

6. A multi-objective robust optimization method for a built-in cascaded permanent magnet synchronous motor according to claim 5, characterized in that, The motor losses in step seven are expressed as follows: In the formula, P core For iron loss, P h For hysteresis loss, P e For eddy current losses, P c For additional losses, C h This is the hysteresis loss coefficient. C e The eddy current loss coefficient is... C c For additional loss coefficient, f For frequency, B Let be the magnetic flux density of each finite element; In the formula, P copper For copper loss, R The resistance of each phase winding, I This is the effective value of the phase current. m The phase number.

7. A multi-objective robust optimization method for a built-in cascaded permanent magnet synchronous motor according to claim 6, characterized in that, The thermal resistance of the thermal resistance network model in step eight is expressed as follows: In the formula, R p It is a flat thermal resistor. R c It is a cylindrical thermal resistor. L For flat plate thermal resistance length, λ The thermal conductivity of the flat-plate thermal resistance is... S Let be the cross-sectional area of ​​the flat-plate thermal resistor. r 1. r 2 represents the inner and outer diameters of the cylindrical thermal resistor. To model the complex thermal resistance of the winding region, we solve for the equivalent thermal conductivity of this region. The equivalent thermal conductivity is expressed as: In the formula, k mix For equivalent thermal conductivity, k ins The thermal conductivity of copper wire material is its insulation coefficient. k imp For impregnation thermal conductivity, θ It is the ratio of the winding insulation area to the total slot area.

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