Parasitic Parameter Prediction for Planar Transformers Based on Neural Network

Parasitic parameters such as leakage inductance and distributed capacitance of planar transformers have a direct impact on the performance and efficiency of transformers. Traditional methods for parasitic parameter prediction are commonly based on empirical formulas or simulation software, but they have problems of high computational complexity, time-consuming and low accuracy. In this paper, a method for predicting parasitic parameters of planar transformers based on a multilayer perceptron (MLP) under a specific winding structure is proposed, which can improve the efficiency of transformer design. The experiments demonstrate that the model can effectively predict the leakage inductance, distributed capacitance, and AC loss of planar transformers.


Introduction
As a power transmission device in power electronics, planar transformers are often used in switching power supplies.Parasitic parameters such as leakage inductance, distributed capacitance, and AC losses have a direct impact on the performance of planar transformers [1].Leakage inductance and distributed capacitance lead to lower transformer efficiency and damage switching tubes by forming voltage spikes and current spikes on the primary side.AC losses are significant at high frequencies and can degrade transformer efficiency.Therefore, accurate prediction of parasitic parameters can evaluate transformer performance, losses, and efficiency in advance, thus optimizing design solutions and improving power system effectiveness.
The main methods for parameter prediction during transformer design include 1-D electronmagnetic analysis (1-D EM) [2,3] and 3-D finite-element analysis (3-D FEA) [4,5].However, due to the complexity of modelling and high simulation time cost, several methods have been proposed for better prediction of parasitic parameters, including curve fitting [6] and evolutionary algorithms [7].An algorithm based on differential evolution to effectively predict the leakage inductance and impedance of planar transformers is proposed [8].
Neural networks are commonly used in the field of data prediction due to their strong learning ability and ability to handle nonlinear relationships, etc. [9].This paper builds a neural network-based model for predicting the parasitic parameters of planar transformers with fixed winding structure, which can predict the leakage inductance, distributed capacitance and winding loss more accurately.

Windings structure model for planar transformers
During the design and analysis of planar transformers, the winding structure of a planar transformer has an important impact on the prediction of its parasitic parameters [10].By understanding the

Data pre-processing
The experimental data are obtained by simulation with the electromagnetic simulation software, and there are 130 groups, where the features include primary winding width, primary winding turns, winding spacing and layer spacing, and the target values are leakage inductance, AC loss and distributed capacitance.Table 1 shows the part of experimental data, and Table 2 shows the statistical information of the target values.
Before training a neural network model, the feature data needs to be normalized.The purpose of normalization is to eliminate the difference in magnitude between features, thus making the training process more stable and faster.In this paper, the Min-Max normalization method is used to scale the value of each feature to the range of [0, 1], which is calculated as follows: where denotes the normalized data, N indicates the number of samples, F means the sample dimension, X represents the original data, and m ax X and m in X denote the maximum and minimum values of the original data, respectively.In this paper, N is set to 130, and F is set to 7.   ( 2 ) where W and b denote the learnable weight parameters and bias parameters, respectively, which are updated with the iterative training of the model; X denotes the input of the current layer; Y denotes the output of the current layer, and denotes the activation function, whose role is to limit the output of the layer to between (-1, 1) by a nonlinear function.The activation function used in this paper is Re ( ) LU x , which is calculated as follows: Based on the above theoretical analysis, this paper establishes an MLP-based model for predicting parasitic parameters of planar transformers, which involves an input layer, three hidden layers and an output layer.Among them, the number of the input layer nodes is 4, which matches 4 features, and the number of the output layer nodes is 3, which matches 3 target values.The number of nodes in each hidden layer is set to 32, 64 and 32.

Experimental setup
In this section, the data set is separated into training and testing sets in the ratio of 8:2, where 104 sets of data are used as the training set and 26 sets of data are used as the testing set.The model training in this paper is performed on a single PC.The settings of the experimental hyperparameters are shown in Table 3.

Name
Parameters Batch Size 32 Dropout 20% Optimizer A d a m Learning Rate 0.01 The mean square error is chosen as the value of the loss function with the following formula: where i y denotes the true parasitic parameter value, and ^i y denotes the predicted value.For the prediction of the three parasitic parameters evaluated by three metrics: Mean Absolute Error (MAE), Mean Absolute Percentage (MAP) and Root Mean Square Error (RMSE), which are calculated as follows: where i y denotes the real parasitic parameter value, ^i y denotes the predicted value, and N denotes the number of samples.

Experimental results and analysis
Figure 4, Figure 5 and Figure 6 show the comparison between the predicted and real values of the parasitic parameters of planar transformers.As can be seen from the three figures, the predicted and real values of the three parasitic parameters are basically the same, indicating that the model built in this paper has high accuracy and reliability, and it also shows that the MLP has good prediction performance in predicting the parasitic parameters of planar transformers.prediction errors of the three parasitic parameters are small and the accuracies are high, which proves the high accuracy and reliability of the model proposed in this paper.

Conclusion
Planar transformers are one of the common electrical devices in power systems, and the accurate prediction of their parasitic parameters is crucial to the stable operation and performance optimization of power systems.In this paper, a neural network-based parasitic parameter prediction model for planar transformers is proposed, which can predict leakage inductance, distributed capacitance and AC loss more accurately, and the effectiveness of the model is proved by experiments.

3. 2
Parasitic parameter prediction model buildingMultilayer Perceptron (MLP) is an artificial neural network model, which consists of multiple neuron layers, where the neurons in each layer are connected to the neurons in the next layer, and the structure of MLP is shown in Figure3.

Figure 3 .
Figure 3.The structure of MLP Each layer in MLP can be represented by a nonlinear function: ( ) Y f WX b  

Table 1 .
Part of the experimental data.