An optimization method for reducing power consumption of induction motors considering uncertainty

Abstract

Firstly, the influence of rotor size on the performance of the motor was analyzed based on the equivalent circuit method and electromagnetic finite element method. Then, the proxy models of total loss, starting torque and starting current were constructed based on the radial basis function neural network. Finally, in order to reduce the influence of rotor slot manufacturing tolerance, a reliability optimization model considering the uncertainty of rotor manufacturing process was established. In the optimization process, the adaptive weighted response surface method was used to adaptively approximate the limit state function, the Monte Carlo simulation method was used for reliability analysis, and the sequential quadratic programming algorithm was used to solve the optimization model.

Description

Technical Field

[0001] The present invention relates to the technical field of motors, and in particular to an induction motor power consumption reduction optimization method taking uncertainty into consideration. Technical Background

[0002] As the power source of electric vehicles (EVs), the design optimization of motors has become a research hotspot. It is a key component that converts electrical energy into mechanical energy, and its selection plays an important role in the performance of EVs. In general, the improvement of motor efficiency provides greater possibilities for energy saving, which is closely related to structural design and starting control strategy and can be enhanced by deterministic optimization. However, performance reliability cannot be guaranteed by deterministic optimization alone, because there are various uncertainties in the design and manufacturing process, which may lead to deviations between actual performance and expected performance. Performance deviations are not only reflected in the performance degradation compared with the initial design, but may also lead to the failure of constraints, which in turn leads to reduced starting ability or thermal runaway. Therefore, by exploring the uncertainty of the motor manufacturing process, the motor performance is improved. Summary of the invention

[0003] The purpose of the present invention is to reduce the influence of manufacturing tolerance on the starting performance of the motor. Under the condition of meeting the starting torque and starting current of the motor, a reliability-based design method is used to design the slot size of the rotor using the adaptive weighted response surface method of the induction motor, and an induction motor consumption reduction optimization method considering uncertainty is established.

[0004] The technical solution adopted to achieve the purpose of the present invention is as follows, that is, an induction motor power consumption optimization method considering uncertainty, comprising the following steps:

[0005] Step 1: Analyze the factors that affect the performance of the induction motor from the structural aspect, and establish a proxy model of the total motor loss, starting torque and starting current with the motor rotor slot size as a variable;

[0006] Step 2: Taking the total motor loss as the target, the slot size of the motor rotor as the random optimization variable, the starting torque and starting current values ​​as the reliability constraints, an induction motor consumption reduction optimization model considering uncertainty is established based on the radial basis function neural network;

[0007] Step 3: Use the sequential quadratic programming algorithm to solve the optimization model. In the optimization process, the adaptive weighted response surface method is used to approximate the limit state function, and the Monte Carlo simulation method is combined to perform reliability analysis.

[0008] In step 1, the process of establishing the proxy model is:

[0009] (1) By analyzing the factors affecting performance from the structural aspect, the notch height H is selected. s0 , Slot height H s2 、Upper groove width Bs1 , Lower groove width B s2 are the design variables, and the total loss, starting torque and starting current are the research objectives;

[0010] (2) Latin hypercube sampling is used to sample in the design space to obtain the total loss, starting torque and starting current parameter values ​​of the motor;

[0011] (3) Establish proxy models of total loss, starting torque, and starting current based on radial basis function neural network;

[0012] In step 2, the optimization model established is:

[0013] (1) Design variables:

[0014] Rotor slot size: slot height H s0 , Slot height H s2 、Upper groove width B s1 , Lower groove width B s2 ;

[0015] (2) Objective function:

[0016] min P loss (H s0 ,H s2 ,B s1 ,B s2 )

[0017] Among them, P loss is the total loss;

[0018] (3) Constraints:

[0019] Starting torque and starting current are used as reliability constraints to impose process constraints on the slot size of the rotor;

[0020]

[0021] Among them, P represents probability, T st is the starting torque, I st Indicates the starting current, R 1 is the starting torque reliability, R 2 For starting current reliability, The actual value of the variable affected by uncertainty is subject to Distribution, H s0L and H s0U H s0 The minimum and maximum values ​​of

[0022] The actual value of the variable affected by uncertainty is subject to Distribution B s1L and B s1U For Bs1 The minimum and maximum values ​​of The actual value of the variable affected by uncertainty is subject to Distribution, H s2L and H s2U H s2 The minimum and maximum values ​​of The actual value of the variable affected by uncertainty is subject to Distribution, B s2L and B s2U For B s2 The minimum and maximum values ​​of

[0023] In step 3, the process of solving the optimization model is as follows:

[0024] (1) The present invention adopts an adaptive weighted response surface method to approximate the limit state function:

[0025] 1) The limit state function is approximated by the adaptive weighted response surface method as follows:

[0026]

[0027] in, is the response surface function value, X i is the i-th random design variable, β 0 is a constant term, β i is the coefficient of the linear term, β ij The coefficient of the cross term, N is the number of random variables;

[0028] 2) Get the weight coefficient:

[0029] Give higher weights to experimental points closer to the limit state function:

[0030] y best =min|G(x l )|

[0031] D(x l )=G(x l )-y best l=1,2K,L

[0032]

[0033] Among them, y best is defined as the distance to the closest point to the limit state function, L represents the number of experimental points in each iteration, G(x) represents the performance function, and D(X l ) is the distance from the remaining experimental points to the nearest experimental point, w l is the weight coefficient;

[0034] The weight matrix is ​​obtained through the least squares regression method:

[0035]

[0036] The coefficient matrix can be expressed as:

[0037] β=[x T W(x)x] -1 x T W(x)y

[0038] Where x is an N-dimensional vector of random variables, and W(x) is a diagonal matrix of weights;

[0039] 3) Update the center point of the experimental design and use saturated design sampling at the center of the new experimental design:

[0040]

[0041] Among them, x m New center point, x D is the current design point, is the variable mean;

[0042] (2) Using the Monte Carlo simulation method for reliability analysis, when considering the uncertainty of the system, a disturbance design beyond the feasible domain will be generated Therefore, the jth constraint G j The reliability of (X) is expressed as:

[0043]

[0044]

[0045] Where N is the number of test samples in the Monte Carlo simulation, is the indicator function, N is large enough to ensure the accuracy of reliability calculation;

[0046] (3) Use sequential quadratic programming algorithm to solve the optimization model.

[0047] Compared with the existing induction motor design, the beneficial effects of the present invention are:

[0048] The present invention proposes an induction motor consumption reduction optimization model considering uncertainty, and establishes a proxy model of the total loss, starting torque, and starting current of the induction motor; the optimization model takes the slot size of the rotor as the optimization variable, the slot size of the rotor as the size constraint, and the starting torque and starting current values ​​as the reliability constraints, and takes the minimum total motor loss as the target, which is conducive to realizing the reliability optimization design of the induction motor consumption reduction; quadratic programming is used to calculate the gradient, and Monte Carlo simulation and adaptive weighted response surface method are used for reliability analysis; the final optimization results show that the design optimization method proposed by the present invention can effectively reduce the total loss of the induction motor, improve the reliability of the starting torque and starting current, and verify the reliability of the optimization results. The present invention performs reliability optimization design for the rotor slot size of the induction motor, which has a positive effect on the design scheme of the induction motor. Considering the manufacturing tolerance of the rotor from the design stage, it can further reduce the total loss of the machine tool and improve the reliability of the motor. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 An optimization process for reducing power consumption of induction motors considering uncertainty

[0050] Figure 2 Induction motor model (a) Physical model (b) Configuration of the induction motor and initial shape of the rotor slots

[0051] Figure 3 Induction motor single phase equivalent circuit

[0052] Figure 4 Performance of different slot sizes (a) H s0 (b)H s2 (c)B s1 (d)B s2

[0053] Figure 5 Flowchart of reliability design optimization algorithm combined with AWRSM DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with the accompanying drawings and embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to common technical knowledge and customary means in the field, which should all be included in the protection scope of the present invention.

[0055] This embodiment takes a certain type of induction motor as a research object and performs energy-saving reliability design optimization of the induction motor.

[0056] Physical models such as Figure 2(a) and its specifications are shown in Table 1. Technically, the size of the conductor bar is smaller than the size of the rotor slot. In the invention, in order to facilitate the finite element simulation, the size of the slot and the conductor bar are considered to be the same. The rotor configuration and the initial shape of the rotor slot are shown in Figure 2 (b) as shown.

[0057] Table 1 Induction motor parameters

[0058]

[0059] For the selected slot size H s0 , H s2 , B s1 , B s2 Independent variable, the induction motor is equivalent to Figure 3 The single-phase equivalent circuit shown is s and are the currents flowing through the stator and rotor windings, R s is the stator resistance, is the stator resistance calculated from the rotor, L sσ is the stator leakage inductance, is the stator leakage inductance calculated by the rotor, and s is the slip ratio.

[0060] Rotor bar cross-sectional area A r is considered as a function of the slot size and is expressed as

[0061] A r =f(H s0 ,H s2 ,B s1 ,B s2 )

[0062] Combine the following

[0063]

[0064] Calculate rotor resistance The influence of the slot size is

[0065]

[0066] In the formula, Is the skin effect coefficient of the rotor relative to the stator side, which is related to the configuration parameters of the motor. If the skin effect is not considered, it is constant. Rotor resistance R r By rotor rod R bar and end ring R end The resistance composition of R end is considered as a constant. ρ is the resistivity, l b is the length of the conductor bar, A r is the cross-sectional area of ​​the rotor bars. s0 , Hs2 , B s1 , B s2 is the slot size of the rotor.

[0067] Combination Definition and λ u Definition

[0068]

[0069] Where, L rσ is the rotor leakage inductance, μ 0 is the vacuum permeability, λ u and λ end is the magnetic permeability coefficient of the rotor slot and the squirrel cage end ring. u is closely related to the slot type and the corresponding size, and if the slot size changes, then λ end is constant.

[0070] Calculate rotor resistance The influence of the slot size is

[0071]

[0072] Based on the above rotor resistance calculation, combined with the electromagnetic torque analytical formula of the induction motor

[0073]

[0074] Calculate the starting torque T st and starting current I st The influence of the slot size is

[0075]

[0076] According to the motor efficiency and total loss expression

[0077]

[0078] P loss =P iron +P sCu +P rCu +P me +P stray

[0079] It can be seen that the total loss P loss The total loss, starting torque and starting current are further analyzed by electromagnetic finite element analysis. Figure 4 As shown. When the slot size fluctuates around the initial value, there is a certain performance deviation. s1 , under the deviation of 0.6mm, the total loss P lossThe deviation is as high as nearly 200W, the starting current deviation is as high as 60A, and the starting torque deviation is as high as 10N·m, which has considerable fluctuations on the stable operation and safety of the motor.

[0080] The present invention adopts a proxy model method to construct an implicit relationship between the rotor slot size and the total loss, starting torque and starting current, and selects the Latin hypercube method (LHS) for sampling.

[0081] The radial basis function (RBF) neural network is used to establish the surrogate model. In order to verify the effectiveness of RBF, it is compared with Kriging and response surface method (RSM). The median absolute deviation (MAD), maximum absolute error (MAE), root mean square error (RMSE) and R-square are used to verify the accuracy of the model. The accuracy data are shown in Table 2. It can be seen that the RBF predicted values ​​of the three performances have a more accurate approximation effect compared with the observed values.

[0082] Table 2. Evaluation index values ​​of proxy models

[0083]

[0084] Based on this surrogate model, a reliability design optimization model is established to manage the uncertainty caused by the manufacturing tolerance of the induction motor rotor slot. The adaptive weighted response surface method (AWRSM) is combined with the Monte Carlo simulation (MCS) method to

[0085] Reliability calculation of reliability optimization design.

[0086] The reliability optimization design model is usually expressed as:

[0087] minf(X)

[0088]

[0089] Four slot dimensions H s0 , H s2 , B s1 , B s2 The range is the size constraint. During the manufacturing process, the slot size usually deviates from the design value, and the actual value varies around the nominal value. The design variables are independent random variables and obey the normal distribution X~N(u,σ 2 ). The tolerance is usually close to ±2% of the nominal size value, so the value of the standard deviation σ in the optimization is set to 0.02u; the starting current and starting torque are reliability constraints; the total loss P loss As the optimization target, the reliability design optimization mathematical model can be expressed as follows:

[0090] min P loss (H s0 ,Hs2 ,B s1 ,B s2 )

[0091]

[0092] Where R 1 and R 2 is the target reliability, set to 0.9505, is the actual value of the variable affected by uncertainty. The properties of the random variable are shown in Table 3.

[0093] Table 3. Distributions and bounds of random design variables

[0094]

[0095] To solve the established optimization model, sequential quadratic programming (SQP) is used to calculate the gradient. Figure 5 As shown in the figure, during the optimization process, AWRSM is used to adaptively approximate the limit state function, and the MCS method is used for reliability analysis.

[0096] The process of solving the optimization model is as follows:

[0097] (1) The present invention adopts an adaptive weighted response surface method to approximate the limit state function:

[0098] 1) The limit state function is approximated by the adaptive weighted response surface method as follows:

[0099]

[0100] in, is the response surface function value, X i is the i-th random design variable, β 0 is a constant term, β i is the coefficient of the linear term, β ij The coefficient of the cross term, N is the number of random variables;

[0101] 2) Get the weight coefficient:

[0102] Give higher weights to experimental points closer to the limit state function:

[0103] y best =min|G(x l )|

[0104] D(x l )=G(x l )-y best l=1,2K,L

[0105]

[0106] Among them, y best is defined as the distance to the closest point to the limit state function, L represents the number of experimental points in each iteration, G(x) represents the performance function, and D(X l ) is the distance from the remaining experimental points to the nearest experimental point, w l is the weight coefficient;

[0107] The weight matrix is ​​obtained through the least squares regression method:

[0108]

[0109] The coefficient matrix can be expressed as:

[0110] β=[x T W(x)x] -1 x T W(x)y

[0111] Where x is an N-dimensional vector of random variables, and W(x) is a diagonal matrix of weights;

[0112] 3) Update the center point of the experimental design and use saturated design sampling at the center of the new experimental design:

[0113]

[0114] Among them, x m New center point, x D is the current design point, is the variable mean;

[0115] (2) Using the Monte Carlo simulation method for reliability analysis, when considering the uncertainty of the system, a disturbance design beyond the feasible domain will be generated Therefore, the jth constraint G j The reliability of (X) is expressed as:

[0116]

[0117] Where N is the number of test samples in the Monte Carlo simulation, is the indicator function, N is large enough to ensure the accuracy of reliability calculation;

[0118] (3) Use sequential quadratic programming algorithm to solve the optimization model.

[0119] Comparing the deterministic design and the reliability design, the optimization results and initial values ​​of the two designs are shown in Table 4. The optimization design of the reliability design can meet the reliability requirements, while the deterministic design fails for two constraints with reliability values ​​of 0.479 and 0.503, respectively. Constraint failure means that due to the uncertainty of the manufacturing process, the probability that the starting torque may be less than 156.25N·m is 52.1%, and the probability that the starting current is greater than 1150A is 49.7%. The results of the two optimization models are better than the initial plan in terms of target values, and their total losses are reduced by 6.74W and 80.8W, respectively.

[0120] Table 4 Optimization results of induction motor

[0121]

[0122] The optimization results are reconstructed and the design variables are brought into the electromagnetic finite element analysis (FEA) simulation module for verification. The comparison between the optimized value and the verified value of the total loss is shown in Table 5. The total loss P after bringing the optimized design variables of the reliability design into the simulation loss The total loss P after simulation is 5990.1W, which is only 0.0176% error compared with the optimized value. loss The value is 5918.9W, and the error compared with the optimized value is only 0.0304%, which shows that the optimal result is accurate enough.

Claims

1. A method for optimizing induction motor power consumption reduction considering uncertainty, comprising the following steps: Step 1: Analyze the factors that affect the performance of the induction motor from the structural aspect, and establish a proxy model of the total motor loss, starting torque and starting current with the motor rotor slot size as a variable; Step 2: Taking the total motor loss as the target, the slot size of the motor rotor as the random optimization variable, the starting torque and starting current values ​​as the reliability constraints, an induction motor consumption reduction optimization model considering uncertainty is established based on the radial basis function neural network; Step 3: Use the sequential quadratic programming algorithm to solve the optimization model. In the optimization process, the adaptive weighted response surface method is used to approximate the limit state function, and the Monte Carlo simulation method is combined to perform reliability analysis. In step 1, the process of establishing the proxy model is: (1) By analyzing the factors affecting performance from the structural aspect, the notch height H is selected. s0 , Slot height H s2 、Upper groove width B s1 , Lower groove width B s2 are the design variables, and the total loss, starting torque and starting current are the research objectives; (2) Latin hypercube sampling is used to sample in the design space to obtain the total loss, starting torque and starting current parameter values ​​of the motor; (3) Establish proxy models of total loss, starting torque, and starting current based on radial basis function neural network; In step 2, the optimization model established is: (1) Design variables: Rotor slot size: slot height H s0 , Slot height H s2 、Upper groove width B s1 , Lower groove width B s2 ; (2) Objective function: min P loss (H s0 ,H s2 ,B s1 ,B s2 ) Among them, P loss is the total loss; (3) Constraints: Starting torque and starting current are used as reliability constraints to impose process constraints on the slot size of the rotor; Among them, P represents probability, T st is the starting torque, I st Indicates starting current, R1 is starting torque reliability, R2 is starting current reliability, The actual value of the variable affected by uncertainty is subject to Distribution, H s0L and H s0U H s0 The minimum and maximum values ​​of The actual value of the variable affected by uncertainty is subject to Distribution B s1L and B s1U For B s1 The minimum and maximum values ​​of The actual value of the variable affected by uncertainty is subject to Distribution, H s2L and H s2U H s2 The minimum and maximum values ​​of The actual value of the variable affected by uncertainty is subject to Distribution, B s2L and B s2U For B s2 The minimum and maximum values ​​of In step 3, the process of solving the optimization model is as follows: (1) Adopting adaptive weighted response surface method to approximate the limit state function: 1) The limit state function is approximated by the adaptive weighted response surface method as follows: in, is the response surface function value, X i is the i-th random design variable, β0 is a constant term, β i is the coefficient of the linear term, β ij The coefficient of the cross term, N is the number of random variables; 2) Get the weight coefficient: Give higher weights to experimental points closer to the limit state function: y best =min|G(x l )| D(x l )=G(x l )-y best l=1,2K,L Among them, y best It is defined as the distance to the closest point of the limit state function, L represents the number of experimental points in each iteration, G(x) represents the performance function, and D(X l ) is the distance from the remaining experimental points to the nearest experimental point, w l is the weight coefficient; The weight matrix is ​​obtained through the least squares regression method: The coefficient matrix can be expressed as: β=[x T W(x)x] -1 x T W(x)y Where x is an N-dimensional vector of random variables, and W(x) is a diagonal matrix of weights; 3) Update the center point of the experimental design and use saturated design sampling at the center of the new experimental design: Among them, x m New center point, x D is the current design point, is the variable mean; (2) Using the Monte Carlo simulation method for reliability analysis, when considering the uncertainty of the system, a disturbance design beyond the feasible domain will be generated Therefore, the jth constraint G j The reliability of (X) is expressed as: Where N is the number of test samples in the Monte Carlo simulation, is the indicator function, N is large enough to ensure the accuracy of reliability calculation; (3) Use sequential quadratic programming algorithm to solve the optimization model.

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