Optimal design method of high-frequency transformer based on LS-SVM and NSGA

Abstract

The present invention discloses a high-frequency transformer optimization design method based on LS-SVM and NSGA. First, the electrical and structural parameters of the HFT are input, and the optimization design variables and their value ranges are determined. Then, a sample space is constructed based on optimal Latin hypercube sampling and the calculated response values, and an LS-SVM model is established. When the accuracy meets the design requirements, the HFT electromagnetic thermal parameters are calculated using this model. Secondly, the core and winding dimensions, as well as the insulation distance between the primary and secondary windings, are calculated based on the electrical parameters, fixed parameters, and optimized variables, and it is determined whether the temperature rise and insulation distance meet the requirements. Finally, the electromagnetic thermal parameters are calculated using the LS-SVM model, and the NSGA-II algorithm is used to search for the optimal solution within the design variable space, thereby obtaining the optimal HFT design result. The present invention can achieve the efficient, accurate, and reliable optimization design goals of the HFT, which is of great significance to the performance improvement of the HFT itself and the system to which it belongs.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic thermal characteristic analysis and optimization design of magnetic components, and particularly relates to a high-frequency transformer optimization design method based on LS-SVM and NSGA. Background Art

[0002] A power electronic transformer (PET), also known as a solid-state transformer (SST), is a new type of power transformer that combines power electronics technology with a high-frequency transformer (HFT). It offers a range of functions and advantages, including power regulation and control, power quality control, and smart device communication. As a key component of a power electronic transformer, the HFT plays an important role in voltage conversion and isolation throughout the entire circuit. Compared to traditional industrial frequency transformers, HFTs offer advantages such as small size, light weight, and high power density, making them widely applicable in areas with limited size and weight, such as electric locomotives and offshore wind power. Therefore, accurately optimizing the design of the HFT is of great significance for improving the performance of both the HFT itself and the system to which it belongs.

[0003] The compact design and high operating frequency of HFTs significantly increase core and winding losses, leading to heat dissipation difficulties. Furthermore, leakage inductance parameters also have a significant impact on the performance of the HFT system. Therefore, the impact of electromagnetic thermal parameters on the design scheme should be comprehensively considered during the optimization process. Currently, HFT optimization design methods mainly include free parameter scanning, artificial intelligence optimization algorithms, and the core area product formula method. These methods primarily use analytical empirical formulas to calculate the electromagnetic thermal parameters of HFTs. However, due to the presence of multiple simplifying assumptions, analytical models have low calculation accuracy and a narrow application range, resulting in low accuracy and reliability of the optimization design results and schemes.

[0004] For example, the Chinese invention "A DAB inductor loss calculation method based on the characteristic value of the inductor current" with publication number CN114417767A uses the generalized Steinmetz formula to solve the core loss. However, under high-frequency excitation, the magnetic flux density of the core is usually unevenly distributed. The Steinmetz series of empirical formulas only calculate the core loss based on the average magnetic flux density of the core, making it difficult to use for accurate calculation of the core loss. For another example, the Chinese invention "A three-dimensional fast calculation method for high-frequency loss of circular Litz wire" with publication number CN116720404A uses the Tourkhani model and finite element simulation to calculate the winding loss. However, this model has low calculation accuracy at high frequencies, and because it uses finite elements to calculate the external magnetic field distribution of the winding, the calculation amount is large, making it unsuitable for real-time optimization design of HFT. Thermal network models are easy to parameterize and quickly solve, making them the primary method for calculating HFT temperature rise. The Chinese invention patent application, "A Method and System for Analytical Calculation of Temperature Fields in High-Frequency Magnetic Components," with publication number CN117610335A, divides high-frequency magnetic components into their actual structures and constructs an equivalent thermal network model. This method uses iterative calculations to determine the steady-state temperature of these components. The actual temperature distribution within windings and cores is nonlinear, and this method only predicts temperature by constructing a lumped parameter thermal network model with a limited number of nodes. Therefore, this model fails to accurately reflect the overall temperature distribution of the actual HFT.

[0005] In summary, the current methods for calculating HFT electromagnetic heating parameters mostly use analytical methods. Although these analytical formulas have a fast calculation speed, their accuracy is low, which leads to low accuracy and reliability of the results obtained. Summary of the Invention

[0006] The present invention addresses the shortcomings of existing high-frequency transformer design methods and provides a new method for calculating the electromagnetic thermal parameters of high-frequency transformers based on least squares support vector machines (LS-SVM) and utilizing a non-dominated sorting genetic algorithm (NSGA-II) to achieve optimal design of high-frequency transformers. This method solves the problem that the existing analytical model has low precision, which leads to low accuracy and reliability of the obtained results.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] The high-frequency transformer optimization design method based on LS-SVM and NSGA includes the following steps:

[0009] Step 1: Obtain the electrical parameters and structural parameters of the high-frequency transformer, and determine the design variables of the high-frequency transformer and their value ranges;

[0010] Step 2: Based on the design variables determined in step 1, the optimal Latin hypercube sampling and finite element simulation method are used to establish a sample design space within their value range, fit the initial least squares support vector machine model, and train the least squares support vector machine model. The model is then used as a tool to calculate the electromagnetic thermal parameters of the high-frequency transformer.

[0011] Step 3: Based on the electrical parameters, structural parameters, and design variables in step 1, calculate the core and winding dimensions of the high-frequency transformer and the insulation distance between the primary and secondary windings, and determine whether the insulation distance meets the requirements; and use the least squares support vector machine model to determine whether the temperature rise of the high-frequency transformer meets the requirements, and establish an optimization mathematical model with efficiency and power density as optimization objectives;

[0012] Step 4: Use the least squares support vector machine model to calculate the electromagnetic thermal parameters of the high-frequency transformer, and then calculate the objective function value of the high-frequency transformer. Use the non-dominated sorting genetic algorithm to search for the best in the design variable space, and finally obtain the design result of a high-efficiency, high-power density high-frequency transformer.

[0013] Furthermore, in step 1, electrical parameters and structural parameters of the high-frequency transformer are determined according to the design specifications of the high-frequency transformer.

[0014] Preferably, in step 1, the core arm width is selected A , core thickness B , Number of turns per winding layer N , Primary winding diameter d 1. Secondary winding diameter d 2 as the design parameter of the high-frequency transformer.

[0015] Furthermore, in step 2, based on the design variables determined in step 1, optimal Latin hypercube sampling and finite element simulation methods are used to establish a sample design space within their value range, fit an initial LS-SVM model, and train the model. This model is used to calculate the electromagnetic thermal parameters of the high-frequency transformer.

[0016] When training the LS-SVM model, given N Group HFT design parameters and electromagnetic heating parameter data D ={( x k , y k ) , x k ∈ R n , y k ∈ R},k =1,2,3,…, N , x k For the k The design variables of the training sample input, y k For the k The electromagnetic thermal parameters output by the training sample group, n is the dimension of the design variables, R represents the real number space, R n express n dimensional real number space.

[0017] The LS-SVM model function is:

[0018] (1)

[0019] Where: ω represents the weight vector; φ ( x ) represents the kernel space mapping function, which can transform the nonlinear function estimation problem in the original low-dimensional space of the design variables into the linear function estimation problem in the high-dimensional space; b Indicates the amount of deviation.

[0020] According to the structural risk minimization, the LS-SVM model can be transformed into solving the following optimal problem:

[0021] (2)

[0022] Where: J represents the optimization objective; γ represents the penalty factor; e k ∈ R The relaxation factor representing the insensitive loss function is the deviation between the electromagnetic thermal parameters of the training sample and the regression result. Based on the optimization function and the constraints, the Lagrange function is defined to solve the above optimal problem:

[0023] (3)

[0024] Where: α k ∈ R represents the Lagrange multiplier.

[0025] According to the KKT optimal condition, it can be transformed into the problem of finding the minimum value of the Lagrangian function:

[0026] (4)

[0027] By making L right ω 、 b 、 e k 、 α k The partial derivative of is equal to zero, eliminating the variable ω 、 e k Get the LS-SVM model:

[0028] (5)

[0029] Mode K ( ) represents the Gaussian radial basis kernel function,

[0030] (6)

[0031] Where: σ Represents the kernel function width, and exp( ) represents the exponential function with e as the base.

[0032] In the LS-SVM model, γ Penalty factor and σ The kernel function width affects the generalization ability of the model and the distribution of training parameters, and is closely related to the accuracy of the output HFT electromagnetic thermal parameters.

[0033] Preferably, when establishing the LS-SVM model, the particle swarm optimization algorithm is used to optimize the penalty factor. γ and kernel width σ Optimize and get γ The optimal value and σ The optimal value of .

[0034] Furthermore, in step 3, the core and winding sizes are calculated based on the electrical parameters, structural parameters, and design variables in step 1, and the insulation distance between the primary and secondary windings is calculated based on the leakage inductance design requirements to control the leakage inductance. At the same time, the insulation distance between the primary and secondary windings is also determined to determine whether the insulation distance meets the requirements, and the LS-SVM model is used to determine whether the HFT temperature rise meets the requirements.

[0035] A mathematical model with efficiency and power density as optimization goals is established, and the objective function is:

[0036] (7)

[0037] Where: P n Indicates rated capacity; V box Indicates volume; P total Indicates the total loss.

[0038] In order to ensure that the maximum temperature rise of the transformer is within the allowable temperature rise range and take into account the withstand voltage level between the primary winding and the secondary winding, the constraints of the objective function are:

[0039] (8)

[0040] Where: x i represents the i-th design parameter to be optimized; x imin Indicates the lower limit of the design parameter value; x imax Indicates the upper limit of the design parameter value; Indicates temperature rise; Indicates the maximum allowable temperature rise; d iso 、 d iso_min Respectively represent the actual insulation distance and the minimum allowable insulation distance between the primary winding and the secondary winding.

[0041] Preferably, in step 4, the NSGA-II algorithm is used to solve the optimization mathematical model, and the HFT electromagnetic heating parameters are calculated according to the LS-SVM model established in step 2 to thereby solve the objective function value. By searching within the design parameter range, the optimal Pareto solution set is obtained and the final optimal design result is determined.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1) This invention utilizes the LS-SVM model to construct a mapping between high-frequency transformer design parameters and electromagnetic thermal parameters, enabling rapid and accurate calculation of high-frequency losses and temperatures. Using the LS-SVM as a fast calculation model for core loss, winding loss, and temperature, and using HFT efficiency and power density as optimization targets for high-frequency transformer design, and maximum temperature rise and the insulation distance between the primary and secondary windings as constraints, the optimal design parameter combination is determined, resulting in a high-frequency transformer with optimal performance. This proposed model achieves higher accuracy in calculating electromagnetic thermal parameters, resolving the issue of unreliable optimization results due to large calculation errors in analytical models.

[0044] 2) The LS-SVM model of the present invention is an improvement on the standard support vector machine based on regularization theory. It adopts the least square error as the loss function and transforms the quadratic programming problem into a linear equation system that can be solved by the least squares method by using equality constraints. This reduces the complexity of the algorithm and thus improves the solution speed without changing the original kernel function mapping relationship and global optimality.

[0045] 3) This paper uses the NSGA-II algorithm to solve the optimization mathematical model, which reduces the computational complexity of the non-dominated sorting. The NSGA-II algorithm introduces an elitist strategy to expand the sampling space, thereby improving the accuracy of the optimization results. The congestion operator evenly distributes the solutions across the entire Pareto domain, ensuring solution diversity. Therefore, the NSGA-II algorithm ensures more reliable HFT optimization results. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0047] Figure 1 Schematic diagram of the flow of the high-frequency transformer optimization design method according to an embodiment of the present invention.

[0048] Figure 2 This is a front view of a high-frequency transformer according to an embodiment of the present invention.

[0049] Figure 3 FIG. 4 is a top view of a high-frequency transformer according to an embodiment of the present invention.

[0050] Figure 4 This is a comparison chart of the core loss calculated by the LS-SVM model of the present invention and other methods.

[0051] Figure 5 This is a comparison chart of the winding losses calculated by the LS-SVM model of the present invention and other methods.

[0052] Figure 6 This is a comparison chart of transformer temperature calculated by the LS-SVM model of the present invention and other methods.

[0053] Figure 7 This is a comparison chart of the prediction accuracy of the LS-SVM model of the present invention and DNN and RNN.

[0054] Figure 8 A schematic diagram of the Pareto solution set solved by an embodiment of the present invention.

[0055] Figure 9 This is a loss density distribution diagram of the optimally designed high-frequency transformer obtained in an embodiment of the present invention.

[0056] Figure 10 This is the temperature field distribution diagram of the optimally designed high-frequency transformer obtained in an embodiment of the present invention.

[0057] Figure 11 This is the leakage magnetic field distribution diagram of the optimally designed high-frequency transformer obtained in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] like Figure 1As shown in FIG, the high-frequency transformer optimization design method based on LS-SVM and NSGA includes the following steps:

[0059] Step 1: Obtain the electrical and structural parameters of the HFT, as shown in Table 1. Select the core arm width A , core thickness B , Number of turns per winding layer N , Primary winding diameter d 1. Secondary winding diameter d 2 is used as a design parameter, and its value range is shown in Table 2. Figure 2 、 Figure 3 Shown are the front and top views of the HFT structure, where green represents the primary winding and orange represents the secondary winding.

[0060] Table 1 HFT electrical and structural parameters

[0061]

[0062] Table 2 HFT design parameter constraints

[0063]

[0064] Step 2: Based on the design variables determined in step 1, Latin hypercube sampling and finite element simulation are used to establish the LS-SVM design space within their value ranges, and the LS-SVM model is trained as a tool for HFT electromagnetic heating parameter calculation;

[0065] Given N Group HFT design parameters and electromagnetic heating parameter data D ={( x k , y k ) , x k ∈ R n , y k ∈ R}, k =1,2,3,…, N , x k For the k The design variables of the training sample input, y k For the k The electromagnetic thermal parameters output by the training sample group, n is the dimension of the design variables. The LS-SVM model function is:

[0066] (1)

[0067] Where: ω represents the weight vector; φ ( x ) represents the kernel space mapping function, which can transform the nonlinear function estimation problem in the original low-dimensional space of the design variables into the linear function estimation problem in the high-dimensional space; b represents the deviation.

[0068] According to the structural risk minimization, the LS-SVM model can be transformed into solving the following optimal problem:

[0069] (2)

[0070] Where: J represents the optimization objective; γ represents the penalty factor; e k ∈ R The relaxation factor representing the insensitive loss function is the deviation between the electromagnetic thermal parameters of the training sample and the regression result. Based on the optimization function and the constraints, the Lagrange function is defined to solve the above optimal problem:

[0071] (3)

[0072] Where: α k ∈ R is the Lagrange multiplier.

[0073] According to the KKT optimal condition, it can be transformed into the problem of finding the minimum value of the Lagrangian function:

[0074] (4)

[0075] By making L right ω 、 b 、 e k 、 α k The partial derivative of is equal to zero, eliminating the variable ω 、 e k Get the LS-SVM model:

[0076] (5)

[0077] Formula K( ) represents the Gaussian radial basis kernel function,

[0078] (6)

[0079] Where: σRepresents the kernel function width, and exp( ) represents the exponential function with e as the base.

[0080] In the LS-SVM model, γ Penalty factor and σ The kernel width affects the generalization ability of the model and reflects the distribution of training parameters, and is therefore closely related to the accuracy of the output HFT electromagnetic thermal parameters. Therefore, the present invention uses a particle swarm optimization algorithm to optimize these two parameters when establishing the LS-SVM model.

[0081] The present invention introduces the deep neural network DNN model and the recurrent neural network RNN ​​model to compare with the LS-SVM model, and analyzes the fitting results and determination coefficients of the training samples and test samples. R 2 The comparison verifies that the method proposed in the present invention has higher accuracy. Figure 4 、 Figure 5 、 Figure 6 The prediction results of HFT core loss, winding loss and hot spot temperature by LS-SVM, DNN and RNN models are shown respectively. It can be seen that the fitting effect of LS-SVM model is better than that of DNN and RNN models.

[0082] In order to compare the fitting accuracy of the three models, the present invention introduces the coefficient of determination R 2 , which indicates the degree of fit between the proxy model and the original model:

[0083] (7)

[0084] Where: cov represents covariance; var represents variance; f ( x ) represents the true value; Represents the predicted value. R 2 The closer it is to 1, the higher the accuracy of the model. Figure 7 It can be seen that the determination coefficient of the test set samples of the LS-SVM model proposed in this invention is R 2 Closer to 1, it means better accuracy, while DNN and RNN R 2 Both are lower than the LS-SVM model of the present invention, so the fitting accuracy is lower than LS-SVM.

[0085] Step 3: Calculate the core and winding dimensions based on the electrical parameters, fixed parameters, and design variables in step 1. Calculate the insulation spacing between the primary and secondary windings based on the leakage inductance design requirements to control the leakage inductance. Also, determine whether the insulation spacing between the primary and secondary windings meets the requirements. Use the LS-SVM model in step 2 to determine whether the HFT temperature rise meets the requirements. Establish a mathematical model with efficiency and power density as optimization objectives. The constraints and mathematical model are as follows:

[0086] (8)

[0087] Where: P n Indicates rated capacity; V box Indicates volume; P total Indicates the total loss.

[0088] In order to ensure that the maximum temperature rise of the transformer is within the allowable temperature rise range and take into account the withstand voltage level between the primary winding and the secondary winding, the constraints of the objective function are:

[0089] (9)

[0090] Where: x i represents the i-th design parameter to be optimized; x imin Indicates the lower limit of the design parameter value; x imax Indicates the upper limit of the design parameter value; Indicates temperature rise; Indicates the maximum allowable temperature rise; d iso 、 d iso_min Respectively represent the actual insulation distance and the minimum allowable insulation distance between the primary winding and the secondary winding.

[0091] Step 4: Calculate the HFT electromagnetic heating parameters based on the LS-SVM model and use the NSGA-II algorithm to optimize within the design variable space. The specific parameters of the NSGA-II algorithm are set to 100 population size, 300 iterations, 0.2 crossover probability, 0.2 mutation probability, and 0.02 mutation probability. Finally, a high-efficiency, high-power-density HFT design result is obtained. The optimal Pareto solution set for HFT efficiency and power density is obtained according to this algorithm, as shown in the following figure: Figure 8 As shown, the blue mark is the final optimal design point, where the HFT efficiency is 99.2% and the power density is 13.2MW / m 3The corresponding design parameter combinations are shown in Table 3. Finally, the optimal high-frequency transformer loss, temperature and leakage magnetic field obtained in the finite element simulation embodiment are as follows: Figure 9-11 As shown in Table 4, the accuracy and efficiency of the obtained optimization design scheme are verified. In addition, the calculated values ​​of the traditional HFT parameter analytical model are compared with the calculated values ​​of the proposed model and the finite element results, which proves that the traditional HFT optimization design method has defects.

[0092] Table 3 HFT design parameter values

[0093]

[0094] Table 4 Comparison of HFT design results

[0095]

Claims

1. A high-frequency transformer optimization design method based on LS-SVM and NSGA is characterized by: The following steps are involved: Step 1: Obtain the electrical parameters and structural parameters of the high-frequency transformer, and determine the design variables of the high-frequency transformer and their value ranges; Step 2: Based on the design variables determined in step 1, the optimal Latin hypercube sampling and finite element simulation method are used to establish the sample design space within the value range of the design variables, fit the initial least squares support vector machine model, and train the least squares support vector machine model; Step 3: Based on the electrical parameters, structural parameters, and design variables in step 1, calculate the core and winding dimensions of the high-frequency transformer and the insulation distance between the primary and secondary windings, and determine whether the insulation distance meets the requirements; and use the least squares support vector machine model to determine whether the temperature rise of the high-frequency transformer meets the requirements, and establish an optimization mathematical model with efficiency and power density as optimization objectives; Step 4: Use the least squares support vector machine model to calculate the electromagnetic thermal parameters of the high-frequency transformer, and then calculate the objective function value of the high-frequency transformer. Use the non-dominated sorting genetic algorithm to search for the best in the design variable space, and finally obtain the design result of a high-efficiency, high-power density high-frequency transformer.

2. The high-frequency transformer optimization design method according to claim 1, characterized in that: In step 1, electrical parameters and structural parameters of the high-frequency transformer are obtained according to the design specifications of the high-frequency transformer, and the optimized design variables of the high-frequency transformer and their value ranges are determined. The optimized design variables include the core arm width, the core thickness, the number of turns per layer of the winding, the primary winding strand diameter, and the secondary winding strand diameter.

3. The high-frequency transformer optimization design method according to claim 2, characterized in that: In step 2, the least squares support vector machine design space is established using optimal Latin hypercube sampling and finite element simulation, and the least squares support vector machine model is trained. The least squares support vector machine model function is: (1) Where: ω represents the weight vector; φ ( x ) represents the kernel space mapping function; b Indicates the amount of deviation; x represents the optimization design variable; y( x ) represents the electromagnetic heating parameter function; According to the principle of structural risk minimization, the least squares support vector machine is transformed, the Lagrangian function is defined according to the optimization function and constraints, and the minimum value of the Lagrangian function is obtained to further obtain the least squares support vector machine model: (2) Mode K ( ) represents the Gaussian radial basis kernel function, N Indicates the number of training samples; k Indicates the sequence number of the training sample; x k Indicates the k The design variables of the training samples; (3) Where: σ represents the kernel function width, and exp() represents the exponential function.

4. The high-frequency transformer optimization design method according to claim 3, characterized in that: In step 3, the core and winding sizes are calculated based on the electrical parameters, structural parameters and design variables, and the high-frequency transformer power density is selected. P s and efficiency η As optimization objectives, the range of design variables, hotspot temperature rise, and insulation distance between primary and secondary windings are taken as constraints; The objective function of the optimization mathematical model is: (4) Where: P n Indicates rated capacity; V box Indicates volume; P total Indicates the total loss.

5. The high-frequency transformer optimization design method according to claim 4, characterized in that: In step 3, the constraints of the optimization mathematical model are: (5) Where: x i Indicates the i design parameters to be optimized; x imin Indicates the lower limit of the design parameter value; x imax Indicates the upper limit of the design parameter value; Indicates temperature rise; Indicates the maximum allowable temperature rise; d iso 、 d iso_min Respectively represent the actual insulation distance and the minimum allowable insulation distance between the primary winding and the secondary winding.

6. The high-frequency transformer optimization design method according to claim 4 or 5, characterized in that: In step 4, after the electromagnetic thermal parameters of the high-frequency transformer are calculated using the least squares support vector machine model, the non-dominated sorting genetic algorithm II is used to solve the optimization mathematical model in step 3; The solution process of the non-dominated sorting genetic algorithm II includes: An initial population is randomly generated according to the optimization variables and parameters of the high-frequency transformer, and non-dominated sorting and crowding calculation are performed on it. Selection, crossover, and mutation operations are performed based on the non-dominated sorting values ​​and crowding sizes of the individuals in the initial population to generate a new population. Non-dominated sorting and crowding calculation are then performed on the new population. The better individuals are selected from the new population for the next round of iteration. This process is repeated until the maximum number of iterations is reached to obtain the optimal design result of the high-frequency transformer.

Images