2.1. WT and Feature Analysis of Transformer Transient Signals

The upper block is assigned a lower time interval and therefore a higher frequency, while the lower block is assigned a longer time interval and a lower frequency. The characteristics of the power transformer under consideration are given in Table 1. Figure 2 shows the secondary winding current of studied transformer under two-phase short circuit condition.

In this case, DWT was used to find the short circuit fault in the studied transformer. The resulting secondary current was transferred to the wavelet program and the following results were obtained. Figures 3(a) and 3(b) show the decomposition current obtained by applying the Daubechies5 (DB5) wavelet to the transformer under normal operating conditions and two-phase short circuit, respectively.

The S signal is decomposed by the DWT process into an equal number of low-frequency components, i.e., approximations (A), and high-frequency components, i.e., details (D). Based on these results, Figures 4(a) and 4(b) show the DB5 Level 5 wavelet in normal and faulty condition, respectively.

Figures 5(a) and 5(b) show the energy of the DB5 Level 5 wavelet in the normal and faulty condition. FFT-Spectrum analyzer was used to see how the energy changes in which frequency range and in which frequency range it is more intense. The FFT spectrum shows how much power and energy the signal has at which frequency. This is a widely used method to analyze the frequency components of the signal and identify important frequency components. It can be seen in the figure that the transformer in the normal operation condition first shows a small increase, then the energy increases to the maximum level and with a sudden decrease it reaches a value close to zero and continues at a value close to zero. This shows that a normally functioning transformer has a stable energy distribution. In the faulty condition, a slight increase is observed at first and then a decrease. This is different from the normal situation and indicates an abnormal change in energy distribution. Such changes in fault-mode power dissipation may indicate potential problems in transformer performance. Therefore, analysis of energy graphs is an important tool for fault detection and preventive maintenance. After continuing this process several times, the energy reaches its peak and then suddenly decreases, and these processes are repeated several times periodically. Following these periodic increases and decreases, the energy value continues to be close to zero after a certain period of time. This indicates the existence of a certain periodic pattern. Such periodic increases and decreases can provide information about the stability of the system or irregularities in its functioning. Especially sudden drops or periodic changes in the energy level may indicate possible malfunctions or imbalances in the operation of the system. Therefore, monitoring and analyzing such periodic changes in energy values can provide valuable information about the state of the system and enable necessary interventions. The flowchart of short circuit fault detection using DWT is shown in Figure 6.

2.2. Fault Diagnosis Model of Transformer With DL Method

In this section, two different DL methods are used to predict the short circuit fault of the transformer. The architecture of the first model, the FCN model, is given in Figure 7.

This function gives a zero value if the input value is negative, and if it is positive, the input value is given directly to the output. This simple function can increase the learning ability of neural networks. It can provide faster learning compared to activation functions such as sigmoid or tanh. Batch normalization is a technique used to normalize the output of layers in a neural network. This can speed up the training process and provide better generalization ability. It helps the model learn better by reducing the risk of overfitting. While the proposed wavelet-CNN method is inherently less sensitive to noise due to the properties of WTs, its performance may still be affected by high noise levels. Therefore, implementing noise reduction techniques—such as filtering, wavelet thresholding, and adaptive methods—can enhance the robustness and reliability of the fault detection process. Employing these techniques ensures that the model can effectively differentiate between genuine fault signals and noise, leading to more accurate diagnostics in power transformers. If the original study did not cover these techniques, they could be considered for future work or exploratory research to further improve the method’s performance. WTs are known for their ability to separate signal components based on frequency. This property makes them particularly effective in distinguishing between meaningful signal features (e.g., those related to faults) and noise. By focusing on specific frequency bands, the WT can preserve important low-frequency signal information while attenuating high-frequency noise. The method’s use of both approximation and detail coefficients allows for a comprehensive analysis at different scales, which can help to identify and mitigate the effects of noise. After applying the WT, coefficients can be manipulated through thresholding methods. In this approach, detail coefficients that fall below a certain threshold (indicating noise rather than signal) can be set to zero (hard thresholding) or reduced in magnitude (soft thresholding). This technique helps to keep significant features while eliminating noise. Global average pooling is a technique that generally helps to reduce the size of the feature map and summarize the features. It can replace the mostly used fully connected layers and help the model learn more general features. Convolutional layers are DL layers used in visual data processing. In the first scenario, 1 neuron was used in each convolution layer, and in the second scenario, 10 neurons were used in the first convolution layer, 20 neurons were used in the second convolution layer, and 30 neurons were used in the third convolution layer. In the third scenario, 32 neurons were used in the first convolution layer, 64 neurons were used in the second convolution layer, and 128 neurons were used in the third convolution layer. MLP was used as the second model. The architecture of this model is shown in Figure 8.

Dense layer is a basic layer used in neural network models. It is a fully connected layer where each neuron is connected to all neurons in the previous layer. Flatten layer is a layer used to flatten multidimensional data. This layer is most commonly used to flatten 2D or 3D data structures, such as image data. It converts all elements of input data into a single flattened vector, which is usually connected to consecutive dense layer. Dropout is one of the regularization techniques used to reduce overfitting that allows disabling randomly selected connections during the training. This helps the model avoid being overly dependent on a particular neuron and increases its generalization ability. In order to get optimum results in the MLP model, the number of neurons in the convolution layers was changed and the results were observed.

In the first scenario, 1 neuron was used in each fully connected layer, and in the second scenario, 10 neurons were used in the first fully connected layer, 20 neurons were used in the second fully connected layer, and 30 neurons were used in the third fully connected layer. In the third scenario, one fully connected layer and 32 neurons were used in that layer. Increasing the number of neurons in the convolutional layers of an FCN model has a direct impact on computational cost and training time. While more neurons can enhance the model’s capacity to learn complex features, they also introduce significant computational overhead and extend training duration. Proper tuning and experimentation are essential to strike the right balance between model complexity and training efficiency for optimal performance in specific applications, such as fault detection in transformers.

Each neuron (or filter) in a convolutional layer corresponds to a set of weights. Increasing the number of neurons directly increases the total number of parameters in the model. More parameters lead to higher memory requirements for storage and will be more computationally intensive during both the forward and backward passes through the network. As the number of neurons increases, this computational cost escalates, leading to longer processing times for both training and inference. While more neurons can potentially allow the model to learn more complex features, they can also lead to slower convergence. This occurs due to the increased complexity of the loss landscape, where more parameters might result in more intricate and potentially more challenging optimization problems. As the model becomes more complex, it may also require more epochs to converge to an optimal solution, further extending training time.

The dataset obtained in the wavelet analysis was transferred to FCN and MLP models and trained separately, and transformer short circuit faults were detected with these models. It was examined how the accuracy changed by changing the number of neurons in both models, and the model with the highest accuracy was selected for fault detection. The first FCN model has three convolutional layers, each one created using only one neuron. Looking at the training and validation losses of the model in Figure 9, it is seen that the training loss does not fall below 0.69. This situation shows that the model cannot perform as expected. It is observed that the training loss is gradually increasing according to the verification losses.

In order to reduce the training and validation loss, the number of neurons in the layers is increased in the FCN model. 32 neurons were used in the first convolution layer, 64 neurons in the second convolution layer, and 128 neurons in the third convolution layer. Since the model has a more complex structure, it aims to achieve better results. Figure 10(a) shows that the training and validation losses gradually decrease and reach a value close to 0.5. This means that the model is well learned and has a high generalization ability. Looking at Figure 10(b), it can be seen that the training accuracy is 92% and the validation accuracy is 97%. These results show that the model successfully fulfills the given task.

In this section, the MLP method is used as the second model to predict transformer short circuit fault. The first MLP model used 1 neuron in each of three fully connected layers. According to the training and validation losses of the model in Figure 11(a), it is seen that both training and validation losses are not at acceptable values. Looking at Figure 11(b), it can be seen that the training accuracy exhibits a wavy graph. It is seen that the training accuracy is 43% and the validation accuracy is 50%. This is definitive proof that the model has not learned anything.

In the second scenario, 10 neurons were used in the first layer of the three fully connected layers in the MLP model, 20 neurons were used in the second layer, and 30 neurons were used in the third layer. According to the results, it was not observed that as the number of epochs increased, the training loss decreased compared to the first model. A decrease was observed when looking at verification losses. However, it seems that the model still cannot learn well enough. It is seen that the training accuracy is 57% and the validation accuracy is 50%. This shows that the model still cannot learn better. For this reason, in the third MLP model, only one fully connected layer was used and 32 neurons were placed in this layer. According to the results obtained in Figure 12(a), it is seen that the training and validation losses are gradually decreasing compared to other models. Both training and validation losses are close to 0.5. It can be seen in Figure 12(b) that the training accuracy is 78% and the validation accuracy is 75%. These results show that the model starts to learn better and reduces the overlearning problem.