An optimization design method of a modular axial flux permanent magnet synchronous wind generator

Abstract

The application relates to an optimal design method of a modular axial flux permanent magnet synchronous wind generator, and belongs to the field of wind power generation. The generator comprises a stator and a rotor; torque pulsation and torque density are used as optimization targets, and stator slot depth, rotor permanent magnet thickness and rotor permanent magnet pole arc coefficient are used as to-be-optimized design variables; constraint conditions of the design variables are determined, a Latin hypercube sampling experiment is carried out, a DNN proxy model of the optimization target and the to-be-optimized design variables is established; a Bayesian optimization algorithm is used to optimize hyperparameters of the proxy model, and optimal hyperparameters are obtained; the proxy model adopting the optimal hyperparameters is trained to obtain an optimal proxy model, and based on the optimal proxy model, an NSGA-II optimization algorithm is used to optimize the to-be-optimized design variables, and finally, an optimal combination of the to-be-optimized design variables is determined. The application can reduce modeling errors, improve calculation efficiency, robustly process multi-target trade-off under complex parameter coupling conditions, and effectively improve the performance of the modular generator.

Description

TECHNICAL FIELD

[0001] The application relates to an optimal design method of an axial flux permanent magnet synchronous wind generator, in particular to an optimal design method of a modular axial flux permanent magnet synchronous wind generator, and belongs to the technical field of wind power generation. BACKGROUND

[0002] The permanent magnet synchronous wind generator has become one of mainstream models in the field of wind power generation, because it has the following advantages: 1) without a complex mechanical gear box and its lubrication system, the failure rate and maintenance cost are low; 2) high energy conversion efficiency. In addition to the above advantages, the axial flux permanent magnet synchronous wind generator also has the advantages of small size, light weight, good heat dissipation, low operation noise, etc., especially can meet the environmental protection requirements of the wind farm, and has a broad market prospect.

[0003] However, most of the traditional axial flux permanent magnet synchronous wind generators (AFPMSG) adopt an overall iron core structure, the iron core cannot adopt a radial motor lamination type iron core, the manufacturing process is complex, the cost is high, and the development of the axial flux motor is limited.

[0004] Therefore, the AFPMSG modularization is a promising alternative solution to the above problems. The modular AFPMSG has the advantages of convenient and fast maintenance, only needs to replace the faulty module, and has strong fault tolerance. Therefore, the modular axial flux permanent magnet synchronous wind generator (MAFPMSG) is more and more concerned in the field of wind power generation, and is one of the development directions of future wind power.

[0005] However, modularization also brings new problems, such as the existence of contact reluctance between modules, which leads to the reduction of magnetic flux density and power density, and magnetic field distortion, and the magnetic field distortion leads to the increase of harmonics. Therefore, the optimal design of the modular AFPMSG is particularly important. However, it is worth pointing out that these new problems make the optimization process more difficult and complex, because the optimal design of the modular axial flux permanent magnet synchronous wind generator involves multi-dimensional and discrete parameter type optimization, and is essentially a complex nonlinear multi-objective optimization problem with multiple constraints, and there is usually no optimal solution that satisfies multiple performance indicators at the same time.

[0006] In the existing literature, some propose a design method based on equivalent magnetic circuit method and multi-objective optimization, but its accuracy is insufficient when dealing with the coupling effect of multiple permanent magnets and the dynamic change of magnetic performance. Some use a multi-level optimization strategy combined with response surface method to optimize the design of modular motor to balance torque performance and fault tolerance. However, the optimization process needs to carefully weight different targets, and may not fully capture the interaction of all complex parameters. Some propose a new semi-analytical method combined with artificial intelligence to suppress the cogging torque of modular permanent magnet motor, but due to the complexity of finite element model and the number of design variables, the optimization process using genetic algorithm and artificial neural network may require a large amount of computation. Some propose a modular motor design method based on analytical method and genetic algorithm to optimize geometric parameters to obtain maximum volume and weight torque density. However, this method does not fully solve the interdependence and constraints of parameters, limiting its applicability under different conditions. Some propose a multi-objective optimization method for modular motor based on surrogate-assisted multi-objective optimization (SAMOO) algorithm to achieve accurate Pareto front, however, in large-scale design, its high computational cost and sensitivity to initial sampling point distribution can lead to unsatisfactory results. In summary, existing methods still face major challenges in solving the non-linear change of air gap reluctance caused by the modular structure and the optimization of multi-physical field coupling.

[0007] Therefore, the present application proposes a modular axial flux permanent magnet synchronous wind generator optimization design method combined with deep neural network (DNN), Bayesian optimization and second generation non-dominated sorting genetic algorithm (NSGA-II), which integrates three key components of DNN, Bayesian optimization and NSGA-II to handle complex nonlinear multi-objective optimization problems, optimizes the structural parameters of the modular axial flux permanent magnet synchronous wind generator to maximize the torque density and minimize the torque ripple, thereby ensuring the performance of the modular axial flux permanent magnet synchronous wind generator while improving design efficiency, reducing computation time, and reducing design and manufacturing costs, and promoting the continuous progress of wind power technology. SUMMARY

[0008] The main purpose of the present application is to provide a modular axial flux permanent magnet synchronous wind generator optimization design method that takes into account performance, efficiency and cost during the optimization process, effectively improves the performance of the modular AFPMSG, meets the design requirements, and provides a new solution for modular AFPMSG optimization design.

[0009] In order to achieve the above object, the modular axial flux permanent magnet synchronous wind generator comprises a stator and a rotor, the stator comprises a stator core and a stator winding, and the rotor comprises a rotor permanent magnet and a rotor core. The stator and the rotor are designed in a modular manner, the stator core module and the rotor core module are trapezoidal modules, and the rotor core module is pasted with the permanent magnet.

[0010] The optimization design method of the modular axial flux permanent magnet synchronous wind generator comprises the following steps:

[0011] Step 1, according to the performance requirements of the modular axial flux permanent magnet synchronous wind generator, the average torque density T a , the torque ripple T ri are selected as the optimization targets; three structure parameters of the modular axial flux permanent magnet synchronous wind generator are selected as the to-be-optimized design variables, the three structure parameters are: the stator slot depth h s , the rotor permanent magnet thickness h c , and the rotor permanent magnet pole arc coefficient α p , then the vector x of the to-be-optimized design variables can be expressed as: x = [x1, x2, x3] = [h s , h c , α p ];

[0012] Step 2, the constraint conditions of the to-be-optimized design variables of the modular axial flux permanent magnet synchronous wind generator are determined, that is:

[0013] (1)

[0014] Wherein, h sl and h su are the lower limit and the upper limit of the stator slot depth respectively; h cl and h cu are the lower limit and the upper limit of the rotor permanent magnet thickness respectively; α pl and α pu are the lower limit and the upper limit of the rotor permanent magnet pole arc coefficient respectively.

[0015] Step 3, Latin hypercube sampling (LHS) experiment is carried out to establish the required sample space:

[0016] 31) divide each design variable into M subintervals between the upper and lower limits of its own constraint condition (i.e. the value range), and then randomly select a point in each subinterval;

[0017] 32) randomly combine the points selected in all subintervals of each design variable to obtain a total of M sample data groups (h sm , h cm , α pm), i.e. M combinations of design variables, where m = 1, 2, 3, …, M;

[0018] 33) Obtain the actual value T of the optimization objective of each sample data set through finite element simulation a, m and T ri, m .

[0019] Step 4, establish a deep neural network DNN proxy model, which contains an input layer, a hidden layer and an output layer; the input layer has three neurons, i.e. three design variables to be optimized; the output layer has two neurons, which are the predicted values of two optimization objectives (T a , T ri ) respectively; the number of layers of the hidden layer is 3.

[0020] The input H s and the output HO s of the s-th neuron of the first hidden layer are respectively:

[0021] (2)

[0022] (3)

[0023] In the formula, w is is the connection weight value between the i-th neuron x i of the input layer and the s-th neuron of the first hidden layer, a s is the threshold value of the s-th neuron of the first hidden layer, s = 1, 2, …, N (1) ; f1(·) is the excitation function of the first hidden layer, which is a ReLU function (Rectified Linear Unit function), and has: f(x) = max(x, 0);

[0024] The input H j and the output HO j of the j-th neuron of the second hidden layer are respectively:

[0025] (4)

[0026] (5)

[0027] In the formula, w sj is the connection weight value between the s-th neuron of the first hidden layer and the j-th neuron of the second hidden layer, a j is the threshold value of the j-th neuron of the second hidden layer, j = 1, 2, …, N (2) ; f2(·) is the excitation function of the second hidden layer, which is a ReLU function (Rectified Linear Unit function);

[0028] Input H of the u-th neuron of the third hidden layer u , output HO u , respectively

[0029] (6)

[0030] (7)

[0031] where w ju is the connection weight between the j-th neuron of the second hidden layer and the u-th neuron of the third hidden layer, a u is the threshold value of the u-th neuron of the third hidden layer, u = 1, 2, …, N (3) ; f3(·) is the activation function of the third hidden layer, which is a ReLU function (Rectified Linear Unit function);

[0032] Input of the l-th neuron of the output layer is:

[0033] (8)

[0034] Output of the l-th neuron of the output layer, i.e. the predicted value of the optimization objective is:

[0035] (9)

[0036] where w ul is the connection weight between the u-th neuron of the third hidden layer and the l-th neuron of the output layer, b l is the threshold value of the l-th neuron of the output layer, l = 1, 2; f o (·) is the activation function of the output layer, which is a ReLU function (Rectified Linear Unit function); , ;

[0037] Step 5: using the Bayesian optimization algorithm to optimize the hyperparameters of the DNN surrogate model to obtain the optimal hyperparameters.

[0038] Step 6: training the DNN surrogate model based on the optimal hyperparameters obtained in step 5.

[0039] Step 7: based on the optimal DNN surrogate model obtained in step 6, using the NSGA-II optimization algorithm to optimize the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine, and determining the optimal combination of the design variables to be optimized of the modular axial flux permanent magnet synchronous wind turbine, so that the modular axial flux permanent magnet synchronous wind turbine obtains the optimal performance.

[0040] The specific method of step 5 is:

[0041] 51) The objective function of Bayesian optimization is designed as:

[0042] (10)

[0043] (11)

[0044] In the formula, T N is the rated torque of the modular axial flux permanent magnet synchronous wind power generator.

[0045] 52) The hyperparameter vector of Bayesian optimization of the modular axial flux permanent magnet synchronous wind power generator is defined as:

[0046] The hyperparameter vector h has 8 parameters, defined as: h={η, B, N (1) , N (2) , N (3) , p, γ,T drop}; wherein η is the initial learning rate, B is the batch size, i.e. the number of samples, N (1) , N (2) , N (3) are the number of nodes of the first layer, the second layer and the third layer of the hidden layer of the DNN respectively; p is the signal loss probability, γ is the learning rate, and T drop is the learning rate decay period.

[0047] 53) Initialize the sample set, i.e. initialize the hyperparameter space:

[0048] Determine the value range of each hyperparameter, based on Latin hypercube sampling (LHS) experiment, divide each hyperparameter into M subintervals in its value range, then randomly select a point in each subinterval to obtain M-dimensional components, and establish an 8×M initial sample space of the required hyperparameters; set the maximum number of iterations T;

[0049] 54) An improved Mariton 5 / 2-ARD (Automatic Relevance Determination) hybrid kernel function is used as the covariance function of the Gaussian process GP to construct a Gaussian process surrogate model:

[0050] (12)

[0051] In the formula, f(h) is the target value corresponding to h, μ(h) is the expectation function of the Gaussian process, and k(h p , h q) is the covariance function of Gaussian process, defined as:

[0052] (13)

[0053] where h p , h q are two different hyperparameters, p = 1, 2, …, 8, q = 1, 2, …, 8; σ f is the signal variance; r 2 is defined as:

[0054] (14)

[0055] where l m is the Hamming distance correction term, l m = αδ(h p,m , h q,m ), which is suitable for discrete parameters; α is the scaling factor of discrete parameters; δ is the difference function related to discrete parameters; h p,m and h q,m represent the mth-dimensional component values of h p , h q , respectively.

[0056] 55) Calculate the expected function EI(h):

[0057] (15)

[0058] (16)

[0059] where f , σ are the predicted mean and predicted standard deviation of the target function by the Gaussian process surrogate model, respectively; f(h + ) is the optimal target value observed at present; t, T are the current cycle number and the maximum cycle number, respectively; is the dynamic exploration factor; Φ(Z), ϕ(Z) are the cumulative distribution function and probability density function of the standard normal distribution, respectively; Z is the improvement degree of the predicted value of the current target value to the current optimal target value, which has:

[0060] (17)

[0061] 56) Evaluate the performance of the Gaussian process surrogate model: calculate the coefficient of determination R² and the root mean square error RMSE, whose expressions are:

[0062] (18)

[0063] (19)

[0064] 57) If the coefficient R 2 > 0.9, and the root mean square error RMSE < ε, ε is a positive real number close to 0, output the optimal hyperparameters, and go to step 6; otherwise, go to step 58);

[0065] 58) Determine whether the maximum number of cycles is reached, if yes, output the optimal hyperparameters, and go to step 6; otherwise, update the sample point h value, and return to step 54).

[0066] The specific method of step 6 is:

[0067] 61) Initialize the DNN, including: initializing the connection weights w is , w sj , w ju , w ul and the threshold values a s , a j , a u , b l ;

[0068] 62) Define the loss function J as:

[0069] (20)

[0070] 63) Update the connection weights and threshold values using the Adam optimizer:

[0071] A1. Create an Adam optimizer object: DNN proxy model parameters, set the initial learning rate η;

[0072] A2. Data loading and preprocessing;

[0073] A3. Zero the gradient of the loss function;

[0074] A4. Perform forward propagation calculation according to formulas (2)~(9) to obtain the predicted value of the optimization target , l = 1, 2, i.e.: and ;

[0075] A5. Calculate the loss function J according to formula (20);

[0076] A6. Perform backpropagation to calculate the gradient of the loss function J with respect to the connection weights g t (W) and the gradient with respect to the threshold values g t (B):

[0077] (21)

[0078] where W is the connection weight vector, defined as: W = {wis , w sj , w ju , w ul}; B is the threshold vector, defined as: B={a s , a j , a u , b l};

[0079] A7. Update the connection weights W and threshold B:

[0080] (twenty two)

[0081] (twenty three)

[0082] In the formula, the variables with subscripts t+1, t, and t-1 represent the values ​​of the variable in the next cycle, the current cycle, and the previous cycle, respectively; β1 and β2 are exponential decay rates, and β1, β2∈[0,1].

[0083] A8. Has the number of iterations t reached the maximum number of iterations T? If so, end and proceed to step 7; otherwise, proceed to step A9.

[0084] A9. Does the loss function J no longer decrease? If so, end and proceed to step 7; otherwise, return to step A2.

[0085] The specific method for step 7 is as follows:

[0086] 71) Parameter initialization, including: setting the population size; selection, crossover, and mutation parameters; and the maximum number of iterations K.

[0087] 72) Randomly generate the initial parent population P0, and modify the infeasible solution through constraint processing.

[0088] 73) Through iterative evolution, the objective function value is sorted, feasible solutions are determined, fast non-dominated sorting is performed, and crowding is calculated.

[0089] 74) Selection operation: Based on non-dominance level and crowding degree, select a portion of individuals as the parent population P. k .

[0090] 75) Crossover and mutation operations: For the selected parent population P k Individuals in the population undergo crossover and mutation operations to generate a progeny population Q. k And correct infeasible solutions.

[0091] 76) Population merging: Combining the parent and offspring populations to form a new population R. k , for R kReapply fast non-dominated sorting and crowdedness comparison to determine the new parent population P k+1 .

[0092] 77) If the iteration number k does not reach the maximum iteration number K and the accuracy does not meet the pre-set value, the iteration number k is increased by 1, that is, k=k+1, and returning to step 73); otherwise, output the Pareto optimal solution set and determine the optimal solution.

[0093] The beneficial effects of the application are:

[0094] 1) The physical constraint model based on the deep neural network DNN reduces the modeling error; the Bayesian hyperparameter optimization improves the search efficiency through the probability exploration of the optimization space, thereby minimizing the redundant evaluation and improving the calculation efficiency; the dynamic constraint of the NSGA-II algorithm retains the Pareto front diversity and can robustly handle the multi-objective trade-off under the condition of complex parameter coupling.

[0095] 2) The performance, efficiency and cost in the optimization process are considered, the performance of the modular AFPMSG is effectively improved, and a new solution is provided for the design of the modular AFPMSG. BRIEF DESCRIPTION OF DRAWINGS

[0096] Figure 1 It is a schematic diagram of the stator and rotor topology structure of the modular axial flux permanent magnet synchronous wind generator.

[0097] Figure 2 It is a schematic diagram of the stator core module of the modular axial flux permanent magnet synchronous wind generator.

[0098] Figure 3 It is a DNN-Bayesian-NSGA-II collaborative optimization framework diagram.

[0099] Figure 4 It is a flowchart of the optimization design method.

[0100] Figure 5 It is a Bayesian hyperparameter optimization flowchart.

[0101] Figure 6 It is an NSGA-II multi-objective optimization design flowchart.

[0102] Figure 7 It is a Latin hypercube sampling experimental result diagram.

[0103] Figure 8 It is a DNN proxy model of the optimization design method.

[0104] Figure 9The Pareto front diagram of the optimized objective generated by the modular axial flux permanent magnet wind turbine of the present invention after optimization by NSGA-II.

[0105] Figure 10 The image shows the torque curves of the modular axial flux permanent magnet synchronous wind turbine generator before and after optimization according to the present invention.

[0106] Wherein, 1-stator; 2-rotor; 11-stator core; 12-stator winding; 21-rotor permanent magnet; 22-rotor core. Detailed Implementation

[0107] The present invention will now be described in further detail with reference to the accompanying drawings.

[0108] like Figure 1 , Figure 2 As shown, the modular axial flux permanent magnet synchronous wind turbine of the present invention includes a stator 1 and a rotor 2, etc. The stator 1 includes a stator core 11 and a stator winding 12, and the rotor 2 includes a rotor permanent magnet 21 and a rotor core 22. The inner and outer diameters of the stator core 11 and the rotor core 22 are the same. Both the stator 1 and the rotor 2 adopt a modular design. Both the stator core module and the rotor core module are trapezoidal modules, and permanent magnets are attached to the rotor core module.

[0109] like Figure 3 , Figure 4 As shown, the present invention provides an optimized design method for a modular axial flux permanent magnet synchronous wind turbine, comprising the following steps:

[0110] Step 1: Based on the performance requirements of the modular axial flux permanent magnet synchronous wind turbine generator, select the average torque density T. a Torque pulsation T ri To optimize the objective, three structural parameters of the modular axial flux permanent magnet synchronous wind turbine generator were selected as design variables to be optimized, namely: stator slot depth h. s Rotor permanent magnet thickness h c Rotor permanent magnet pole arc coefficient α p The vector x representing the design variables to be optimized is: x = [x1, x2, x3] = [h s , h c , α p ];

[0111] Step 2: Determine the constraints of each design variable to be optimized in the modular axial flux permanent magnet synchronous wind turbine, namely:

[0112] (1)

[0113] Among them, h sl h surespectively, are lower and upper bounds of stator slot depth; h cl , h cu respectively, are lower and upper bounds of rotor permanent magnet thickness; α pl , α pu respectively, are lower and upper bounds of rotor permanent magnet pole arc coefficient.

[0114] Step 3, Latin hypercube sampling (LHS) experiment is carried out to establish the required sample space:

[0115] 31) Divide each design variable to be optimized between the upper and lower bounds of its own constraint condition (i.e. the value range) into M subintervals, and then randomly select a point in each subinterval;

[0116] 32) Randomly combine the points selected in all subintervals of each design variable to be optimized to obtain a total of M sample data groups (h sm , h cm , α pm ), i.e. M combinations of design variables to be optimized, wherein m = 1, 2, 3, …, M;

[0117] 33) Obtain the optimization target values T a, m and T ri, m corresponding to each sample data group through finite element simulation.

[0118] Step 4, a deep neural network DNN proxy model is established, which contains an input layer, a hidden layer and an output layer; the input layer has three neurons, i.e. three design variables to be optimized; the output layer has two neurons, which are the predicted values of two optimization targets (T a , T ri ); the number of layers of the hidden layer is 3.

[0119] The input H s and output HO s of the s-th neuron of the first hidden layer are respectively:

[0120] (2)

[0121] (3)

[0122] In the formula, w is is the connection weight value between the i-th neuron x i of the input layer and the s-th neuron of the first hidden layer, a s is the threshold value of the s-th neuron of the first hidden layer, s = 1, 2, …, N (1) ; f1(·) is the excitation function of the first hidden layer, which is a ReLU function (Rectified Linear Unit function), and has: f(x) = max(x, 0);

[0123] The input H of the j-th neuron in the second hidden layer j Output HO j They are respectively:

[0124] (4)

[0125] (5)

[0126] In the formula, w sj It is the connection weight between the s-th neuron in the first hidden layer and the j-th neuron in the second hidden layer, a j Let be the threshold of the j-th neuron in the second hidden layer, where j = 1, 2, …, N. (2) f2(·) is the activation function of the second hidden layer, which is the ReLU function (corrected linear unit function).

[0127] The input H of the u-th neuron in the third hidden layer u Output HO u They are respectively:

[0128] (6)

[0129] (7)

[0130] In the formula, w ju It is the connection weight between the j-th neuron in the second hidden layer and the u-th neuron in the third hidden layer, a u Let be the threshold of the u-th neuron in the third hidden layer, where u = 1, 2, …, N. (3) f3(·) is the activation function of the third hidden layer, which is the ReLU function (corrected linear unit function).

[0131] The input to the l-th neuron in the output layer is:

[0132] (8)

[0133] The output of the l-th neuron in the output layer is the predicted value of the optimization target. for:

[0134] (9)

[0135] In the formula, w ul b is the connection weight coefficient between the u-th neuron in the third hidden layer and the l-th neuron in the output layer. l f is the threshold of the l-th neuron in the output layer, where l = 1, 2; o(·) is an excitation function of an output layer, and is a ReLU function (Rectified Linear Unit function); , ;

[0136] Step 5, in order to obtain optimal performance of the modular axial flux permanent magnet synchronous wind power generator, while improving the average torque, the effect of reducing torque ripple is achieved, as shown in formula (10), the Bayesian optimization algorithm is used to optimize the hyperparameters of the established DNN proxy model, and the optimal hyperparameters are obtained, and the specific method is as follows: Figure 5

[0137] 51) the objective function of Bayesian optimization is designed as:

[0138] (10)

[0139] (11)

[0140] In the formula, T N is the rated torque of the modular axial flux permanent magnet synchronous wind power generator.

[0141] 52) the hyperparameter vector of the Bayesian optimization of the modular axial flux permanent magnet synchronous wind power generator is defined as:

[0142] The hyperparameter vector h has 8 parameters, which are defined as: h={η, B, N (1) , N (2) , N (3) , p, γ,T drop}; wherein η is the initial learning rate, B is the batch size, i.e. the number of samples, N (1) , N (2) , N (3) are the number of nodes of the first layer, the second layer and the third layer of the hidden layer of the DNN respectively; p is the signal loss probability, γ is the learning rate, and T drop is the learning rate decay period.

[0143] 53) initialize the sample set, i.e. initialize the hyperparameter space:

[0144] Determine the value range of each hyperparameter, based on Latin hypercube sampling (LHS) experiment, divide each hyperparameter into M subintervals in its value range, then randomly select a point in each subinterval, obtain M-dimensional components, establish an 8×M required hyperparameter initial sample space, and set the maximum number of cycles T;

[0145] ​54) A modified Marton 5 / 2 - ARD (Automatic Relevance Determination) hybrid kernel function is used as the covariance function of the Gaussian process GP to construct a Gaussian process surrogate model:

[0146] (12)

[0147] where f(h) is the target value corresponding to h, μ(h) is the expectation function of the Gaussian process, k(h p , h q ) is the covariance function of the Gaussian process, defined as:

[0148] (13)

[0149] where h p , h q are two different hyperparameters, p = 1, 2, …, 8, q = 1, 2, …, 8; σ f is the signal variance; r 2 is defined as:

[0150] (14)

[0151] where l m is the Hamming distance correction term, l m = αδ(h p,m , h q,m ), which is suitable for discrete parameters; α is the scaling factor of the discrete parameter; δ is the difference function related to the discrete parameter; h p,m and h q,m represent the mth-dimensional component values of h p , h q , respectively.

[0152] 55) Calculate the expectation function EI(h):

[0153] (15)

[0154] (16)

[0155] where , are the predicted mean and predicted standard deviation of the target function by the Gaussian process surrogate model, respectively; f(h + ) is the optimal target value currently observed; t, T are the current cycle number and the maximum cycle number, respectively; is a dynamic exploration factor; Φ(Z), ϕ(Z) are the cumulative distribution function and probability density function of the standard normal distribution respectively; Z is the predicted value of the current target value; the improvement degree of the predicted value to the current optimal target value is

[0156] (17)

[0157] 56) Evaluate the performance of the Gaussian process surrogate model: calculate the coefficient of determination R² and the root mean square error RMSE, whose expressions are:

[0158] (18)

[0159] (19)

[0160] 57) If the coefficient of determination R²>0.9 and the root mean square error RMSE<ε, where ε is a positive real number close to 0, output the optimal hyperparameters and go to step 6; otherwise, go to step 58);

[0161] 58) Determine whether the maximum number of iterations is reached. If yes, output the optimal hyperparameters and go to step 6; otherwise, update the value of the sample point h and return to step 54).

[0162] Step 6, based on the optimal hyperparameters obtained in step 5, train the DNN surrogate model, the specific method is:

[0163] 61) Initialize the DNN surrogate model, including: initialize the connection weights w is , w sj , w ju , w ul and the threshold values a s , a j , a u , b l ;

[0164] 62) Define the loss function J as:

[0165] (20)

[0166] 63) Update the connection weights and threshold values using the Adam optimizer:

[0167] A1. Create an Adam optimizer object: DNN surrogate model parameters, set the initial learning rate η=0.001;

[0168] A2. Data loading and preprocessing;

[0169] A3. Set the gradient of the loss function to zero;

[0170] A4. Perform forward propagation calculation according to formula (2)-(9) to obtain the predicted value of the optimization target , l = 1, 2, i.e. and ;

[0171] A5. Calculate the loss function J according to formula (20);

[0172] A6. Perform back propagation calculation of the gradient g t (W) of the loss function J on the connection weight value and the gradient g t (B) on the threshold value:

[0173] (21)

[0174] In the formula, W is a connection weight value vector, defined as: W = {w is , w sj , w ju , w ul}; B is a threshold value vector, defined as: B = {a s , a j , a u , b l};

[0175] A7. Update the connection weight value W and the threshold value B:

[0176] (22)

[0177] (23)

[0178] In the formula, the variables with subscripts t+1, t, t-1 represent the values of the next cycle, the current cycle, and the previous cycle of this variable, respectively; β1, β2 are exponential decay rates, and β1, β2 ∈ [0, 1], β1 = 0.9, β2 = 0.999.

[0179] A8. Is the cycle number t reached the maximum cycle number T? If yes, end and enter step 7, otherwise enter step A9;

[0180] A9. Is the loss function J no longer decreasing? If yes, end and enter step 7, otherwise return to step A2.

[0181] Step 7, if Figure 6As shown, based on the optimal DNN agent model obtained in step 6, the NSGA-II optimization algorithm is used to optimize the to-be-optimized design variables of the modular axial flux permanent magnet synchronous wind power generator, and the optimal combination of the to-be-optimized design variables of the modular axial flux permanent magnet synchronous wind power generator is determined, so that the modular axial flux permanent magnet synchronous wind power generator obtains the optimal performance. The specific method is:

[0182] 71) Parameter initialization, including: setting the population size; selecting, crossing, and mutating parameters; maximum iteration number K = 1000.

[0183] 72) Randomly generate an initial parent population P0, and modify infeasible solutions through constraint processing.

[0184] 73) Through iterative evolution, perform target function value sorting, feasible solution judgment, and fast non-dominated sorting and crowdedness calculation.

[0185] 74) Selection operation: based on non-dominated level and crowdedness, select part of the individuals as the parent population P k .

[0186] 75) Crossing and mutation operation: cross and mutate the individuals in the selected parent population P k , generate the offspring population Q k , and correct infeasible solutions.

[0187] 76) Population merging: merge the parent population and the offspring population to form the population R k , and reapply fast non-dominated sorting and crowdedness comparison to the R k to determine the new parent population P k+1 .

[0188] 77) If the iteration number k has not reached K and the accuracy does not meet the pre-set value, increase the iteration number k, i.e. k = k + 1, and return to step 73); otherwise, output the Pareto optimal solution set and determine the optimal solution.

[0189] The application will be further described below with one preferred embodiment.

[0190] Taking a 2kW modular axial flux permanent magnet synchronous wind power generator as an example, the technical parameters are shown in Table 1.

[0191] Table 1 Technical parameters of the modular axial flux permanent magnet synchronous wind power generator Table 2 shows the initial values and value ranges of the to-be-optimized design variables, based on which the Latin hypercube sampling experiment is performed.

[0192] Table 2 Initial values and value ranges of the to-be-optimized design variables

[0193]

[0194] The results of the Latin hypercube sampling experiment are as follows: Figure 7 As shown. By Figure 7 It can be seen that the sample points are highly uniformly distributed and mutually independent in the three-dimensional parameter space. Finite element analysis (FEA) was performed on 50 experiments collected by the LHS method to establish a sample dataset.

[0195] A DNN surrogate model is constructed from the sampled data, and its structure is as follows: Figure 8 As shown in Table 3, the hyperparameters of the DNN surrogate model and their value ranges are also shown.

[0196] Table 3. Hyperparameters of the DNN surrogate model and their value ranges

[0197]

[0198] The Bayesian optimization algorithm was used to tune the hyperparameters of the established DNN surrogate model to obtain the optimal hyperparameters and the optimal number of hidden layer neurons N. (1) N (2) N (3) The values ​​are 256, 128, and 64 respectively; the signal loss probability p is 0.45; and the initial learning rate η is 0.0032.

[0199] After training the DNN surrogate model, RMSE(T) a The RMSE (T) decreased from 5.4927 to 4.7984. ri The RMSE values ​​decreased from 0.012881 to 0.011299, indicating that the DNN surrogate model has a good prediction effect and can be further optimized.

[0200] Figure 9 The Pareto front plot is shown for the optimization objective after optimization for NSGA-II. The marked points in the plot are selected from the solution set as the optimal solutions to this multi-objective optimization problem, and the optimized values ​​of the design variables and the results of the optimization objective are shown in Table 4.

[0201] Table 4 Optimal values ​​and target values ​​of the design variables to be optimized

[0202]

[0203] Simulations were performed using the optimized design variables. Table 5 shows the optimized structural parameters of the modular axial flux permanent magnet synchronous wind turbine generator from Table 1, and its torque curves before and after optimization are as follows. Figure 10 As shown.

[0204] Table 5 Optimized Structural Parameters of Modular Axial Flux Permanent Magnet Synchronous Wind Turbine

[0205]

[0206] From Figure 10 It can be seen that the optimized torque level is significantly improved, and the torque ripple is also significantly reduced. Table 6 gives the comparison of the related performance parameters of the modular axial flux permanent magnet synchronous wind generator before and after optimization. The results show that the average torque T a is increased by 10.43%; the torque ripple T ri is reduced by 25.8%. Compared with the technical requirements in Table 1, after optimization by the NSGA-II algorithm, the error of the average torque is 1.22%, and the error of the torque ripple is 1.26%, both of which meet the design requirements.

[0207] Table 6 Comparison of results before and after optimization

[0208]

[0209] In summary, the present application integrates a deep neural network DNN agent model, a Bayesian hyperparameter tuning, and an NSGA-II multi-objective optimization algorithm to provide an optimization design method for a modular axial flux permanent magnet synchronous wind generator, which takes into account the performance, efficiency and cost during the optimization process, can effectively improve the performance of the modular axial flux permanent magnet synchronous wind generator, meets the design requirements, and provides a new solution for the optimization design of the modular axial flux permanent magnet synchronous wind generator.

Claims

1. A method for optimal design of a modular axial flux permanent magnet synchronous wind generator, the modular axial flux permanent magnet synchronous wind generator comprising: A stator and a rotor, the stator comprising a stator core and a stator winding, the rotor comprising a rotor permanent magnet and a rotor core; The stator and the rotor are both modularized, the stator core module and the rotor core module are both trapezoidal modules, and the rotor core module is pasted with a permanent magnet; characterized by comprising the following steps: Step 1, according to the performance requirements of the modular axial flux permanent magnet synchronous wind generator, the average torque density T a , torque ripple T ri is selected as the optimization target; three structural parameters of the modular axial flux permanent magnet synchronous wind generator are selected as the design variables to be optimized, the three structural parameters are: stator slot depth h s , rotor permanent magnet thickness h c , rotor permanent magnet pole arc coefficient α p , then the vector x of the design variables to be optimized can be expressed as: x=[x1, x2, x3]=[ h s , h c , α p ] Step 2, determining the constraint conditions of each optimization design variable of the modular axial flux permanent magnet synchronous wind power generator, namely: （1） wherein h sl , h su are the lower and upper bounds of the stator slot depth, respectively; h cl , h cu are the lower and upper bounds of the rotor permanent magnet thickness, respectively; a pl , a pu are the lower and upper bounds of the rotor permanent magnet pole arc coefficient, respectively. Step 3, performing Latin hypercube sampling LHS experiment to establish the required sample space: 31) dividing each optimization design variable into M subintervals between the upper and lower bounds of its own constraint condition, and then randomly selecting a point in each subinterval; 32) randomly combine the selected points of all sub-intervals of each design variable to be optimized to obtain a total of M sample data groups (h sm , h cm , α pm ), that is, M design variable combinations, wherein m = 1, 2, 3, …, M; h sm , h cm , α pm are the stator slot depth h s , the rotor permanent magnet thickness h c , and the rotor permanent magnet pole arc coefficient α p in the mth sample data group, respectively; 33) The actual value T of the optimization objective of each sample data set is obtained by finite element simulation a, m and T ri, m ; wherein T a, m , T ri, m are the actual value of the average torque density T a, , the actual value of the torque fluctuation T ri of the mth sample data set respectively; Step 4, a deep neural network (DNN) proxy model is established, which contains an input layer, a hidden layer and an output layer; the input layer has three neurons, i.e. three design variables to be optimized; the output layer has two neurons, which are the predicted values of two optimization objectives (T a , T ri ); the number of layers of the hidden layer is 3; the input H of the s-th neuron of the first hidden layer s , the output HO s respectively: （2） （3） wherein w is is the connection weight between the i-th neuron x i of the input layer and the s-th neuron of the first hidden layer, a s is the threshold value of the s-th neuron of the first hidden layer, s = 1, 2, …, N (1) ; f1(·) is the activation function of the first hidden layer, which is a ReLU function (Rectified Linear Unit function) and has: f1(x) = max(x, 0). the input H of the jth neuron of the second hidden layer j , the output HO j respectively: （4） （5） where w sj is a connection weight between the s-th neuron of the first hidden layer and the j-th neuron of the second hidden layer, a j is a threshold value of the j-th neuron of the second hidden layer, j = 1, 2, …, N (2) ; f2(·) is an activation function of the second hidden layer, which is a ReLU function (Rectified Linear Unit function). The input H of the u-th neuron of the third hidden layer u , the output HO u are respectively: （6） （7） where w ju is a connection weight between the jth neuron of the second hidden layer and the u neuron of the third hidden layer, a u is a threshold value of the u neuron of the third hidden layer, u = 1, 2, …, N (3) ; f3(·) is an activation function of the third hidden layer, which is a ReLU function (Rectified Linear Unit function). The input of the lth neuron of the output layer is: （8） the output of the lth neuron of the output layer, i.e. the predicted value of the optimization objective is: （9） wherein w ul is a connection weight coefficient between the u-th neuron of the third hidden layer and the l-th neuron of the output layer, b l is a threshold value of the l-th neuron of the output layer, l = 1, 2; f o is an activation function of the output layer, and is a ReLU function (Rectified Linear Unit function); , ; wherein, , are respectively a predicted value of an optimization target of the m-th sample data group, i.e., a predicted value of the average torque density T a , a predicted value of the torque fluctuation T ri . Step 5, using the Bayesian optimization algorithm to optimize the hyperparameters of the DNN surrogate model to obtain the optimal hyperparameters; Step 6, training the DNN surrogate model based on the optimal hyperparameters obtained in step 5; Step 7, based on the optimal DNN surrogate model obtained in step 6, using the NSGA-II optimization algorithm to optimize the optimization design variables of the modular axial flux permanent magnet synchronous wind power generator, to determine the optimal combination of the optimization design variables of the modular axial flux permanent magnet synchronous wind power generator, so that the modular axial flux permanent magnet synchronous wind power generator obtains the optimal performance.

2. The method for optimal design of a modular axial flux permanent magnet synchronous wind generator according to claim 1, wherein, The specific method of step 5 is: 51) the objective function of Bayesian optimization is designed as: （10） （11） In the formula, T N is the rated torque of the modular axial flux permanent magnet synchronous wind power generator; T a (x), T ri (x) are the average torque density T a and the torque ripple T ri corresponding to the design variable x, respectively; 52) define the hyperparameter vector of Bayesian optimization of the modular axial flux permanent magnet synchronous wind power generator: The super parameter vector h has 8 parameters, defined as: h={η, B, N (1) , N (2) , N (3) , p, γ, T drop}; wherein η is an initial learning rate, B is a batch size, i.e., a number of samples, N (1) , N (2) , N (3) are respectively numbers of nodes of first, second, and third layers of hidden layers of the DNN; p is a signal loss probability, γ is a learning rate, and T drop is a learning rate decay period. 53) initialize the sample set, that is, initialize the hyperparameter space: Determine the value range of each hyperparameter, based on the Latin hypercube sampling (LHS) experiment, divide each hyperparameter into M subintervals in its value range, then randomly select a point in each subinterval, get M-dimensional components, establish an 8xM required initial sample space of hyperparameters; set the maximum number of iterations T; 54) use the improved Marton 5 / 2-ARD, Automatic Relevance Determination mixed kernel function as the covariance function of Gaussian process GP to construct a Gaussian process surrogate model: （12） where f(h) is a target value corresponding to h, μ(h) is an expectation function of the Gaussian process, and k(h p , h q ) is a covariance function of the Gaussian process, defined as: （13） where h p , h q are two different hyperparameters, p = 1, 2, …, 8, q = 1, 2, …, 8; σ f is the signal variance; r 2 is defined as: （14） wherein l m is a Hamming distance correction term, l m = aD(h p,m , h q,m ), which is applicable to discrete parameters; a is a scaling factor of the discrete parameters; D is a difference function related to the discrete parameters; h p,m and h q,m represent component values of the mth dimension of h p and h q , respectively. 55) calculate the expected function EI(h): （15） （16） where, , are the predictive mean and predictive standard deviation of the objective function by the Gaussian process surrogate model, respectively; f(h + ) is the current observed optimal objective value; t, T are the current cycle number and the maximum cycle number, respectively; is the dynamic exploration factor; Φ(Z), are the cumulative distribution function and the probability density function of the standard normal distribution, respectively; Z is the improvement of the predictive value of the current objective value over the current optimal objective value, which has: （17） 56) evaluate the performance of the Gaussian process surrogate model: calculate the determination coefficient R² and the root mean square error RMSE, whose expressions are: （18） （19） where f(h p ) is the target value corresponding to h p . 57) If the coefficient R 2 > 0.9, and the root mean square error RMSE < ε, ε is a positive real number close to 0, then output the optimal hyperparameters, go to step 6; otherwise go to step 58); 58) determine whether the maximum number of iterations is reached, if yes, output the optimal hyperparameters, and enter step 6; otherwise, update the sample point h value and return to step 54).

3. The method of claim 1, wherein the method is characterized by: The specific method of step 6 is: 61) initializing the DNN, including: initializing connection weights w is , w sj , w ju , w ul , and thresholds a s , a j , a u , b l ; 62) define the loss function J as: （20） 63) use the Adam optimizer to update the connection weights and threshold values: A1. Create an Adam optimizer object: DNN surrogate model parameters, set the initial learning rate η; A2. Data loading and preprocessing; A3. Zero the gradient of the loss function; A4. Perform forward propagation calculation according to formula (2)-(9) to obtain the predicted value of the optimization target , l = 1, 2, i.e. and ; A5. Calculate the loss function J according to formula (20); A6. Perform backpropagation to compute the gradient g of the loss function J with respect to the connection weights t (W) and the gradient g with respect to the threshold t (B): （21） In the formula, W is a connection weight vector, defined as: W={w is , w sj , w ju , w ul}; B is a threshold value vector, defined as: B={a s , a j , a u , b l}. A7. Update the connection weights W and the threshold value B: （22） （23） In the formula, the variables with subscripts t+1, t, t-1 represent the values of the variable in the next cycle, the current cycle, and the previous cycle, respectively; β1, β2 are exponential decay rates, and β1, β2 ∈ [0, 1]; m w,t , are the exponential moving average and the estimated value of the gradient g t (W) of the connection weight, respectively; v w,t , are the exponential moving average and the estimated value of the square of the gradient g t (W) of the connection weight, respectively; m b,t , are the exponential moving average and the estimated value of the gradient g t (B) of the threshold, respectively; v b,t , are the exponential moving average and the estimated value of the square of the gradient g t (B) of the threshold, respectively. A8. Is the number of cycles t reached the maximum number of cycles T? If yes, end, go to step 7, otherwise go to step A9; A9. Is the loss function J not getting smaller anymore? If yes, end, go to step 7, otherwise go back to step A2.

Images