1. Introduction

2. Related Works

3. Theoretical Background

3.3. Performance Indices

The performance indices are elements used to quantify the behavior of the proposal in this work at different levels of complexity of PQDs and electrical generation systems with different architectures or scalability. The Table 2 shows the PQDs analysis, quantification, and regression task indices.

For the task of classifying PQDs by labels, indices were used, which are aided by the Confusion Matrix (CM) shown in the Figure 3. A CM is a table that evaluates a classification algorithm’s performance for a classification problem. It compares the predicted class labels to the actual class labels of a data set.

The rows of the CM represent the actual class labels, while the columns represent the predicted class labels. The CM main diagonal represents the correctly classified samples, while the off-diagonal elements represent the misclassified samples. A CM typically has four entries:

• True positives (TP): Corresponds to the samples correctly predicted as positive.
• False positives (FP): Corresponds to the incorrectly predicted as positive.
• True negatives (TN): Corresponds to the correctly predicted as negative.
• False negatives (FN): Corresponds to the incorrectly predicted as negative.

The CM provides valuable information of a classification algorithm, such as accuracy, precision, recall, and F1-score.

Table 3. Performance indices for data classification.

Table 3. Performance indices for data classification.

Performance indexes	Formula
Accuracy	$$Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$$
Recall	$$Recall=\frac{TP}{TP+FN}$$
Specificity	$$Specificity=\frac{TN}{TN+FP}$$

4. Materials And Methods

4.1. Synthesis Of Electrical Disturbances And Database

The electromagnetic phenomena used to test and develop the Multitasking Deep Neural Network model were made synthetically. Developing a synthesizer system of multiple electrical disturbances was carried out, the physical characteristics of which vary. However, the voltage signal without electrical disturbances has the following characteristics.

Table 4. General characteristics of synthesis of electrical disturbances.

Table 4. General characteristics of synthesis of electrical disturbances.

Parameter	Value
sample rate	16 kHz
Peak Voltage	180 V
Frequency	60 Hz

The synthesis of the different levels of electrical disturbances was based on different mathematical models, which are presented in Appendix A, these mathematical models are the scientific contribution of [29], and each electrical disturbance has different characteristics individually, such as duration time, disturbance severity characteristics such as p.u voltage rise or voltage loss, among other characteristics used in mathematical models for their correct synthesis. The Table 5 shows a fragment of the table in Appendix A with the first five levels of types of electrical disturbances. This table shows essential fields such as the name of the electrical disturbance and the numerical identifier, which is used as one of the output parameter elements of the Multitasking Deep Neural Network model. This identifier is associated with the level of complexity of the electrical disturbance. The table in Appendix A shows 29 different levels, and, as can be seen, the complexity increases as the value of the identifier increases.

Table 5. Fragment of the table in Appendix A of mathematical models of electrical disturbances.

Table 5. Fragment of the table in Appendix A of mathematical models of electrical disturbances.

Power quality disturbance	Identifier	Mathematical model	Synthesis parameters
Normal Signal	1	$v\left(t\right)=180sin(\omega t-\varphi )$	$\omega =2\pi *60\frac{rad}{s}$
Sag	2	$v\left(t\right)=180(1-\alpha (u(t-t_1)-u(t-t_2)))sin(\omega t-\varphi )$	$0.1\le \alpha \le 0.9$
Swell	3	$v\left(t\right)=180(1+\beta (u(t-t_1)-u(t-t_2)))sin(\omega t-\varphi )$	$0.1\le \beta \le 0.9$

Table 5 shows the mathematical model of the electrical disturbance, which was used to synthesize the multiple electrical disturbances and used in the development of the model and the different performance tests. Different parameters are shown in all formulas for electrical disturbances, such as the duration time where t is the total time, the parameter $t_1$, and the parameter $t_2$, which is the end of the electrical disturbance. Also have different synthesis parameters that represent the severity of the electrical disturbance. These values are determined randomly to have a diverse data set to develop the Multitasking Deep Neural Network model better. In addition, this multiple electrical disturbance synthesis system developed a data set for the training, validation, and testing of the Multitasking Deep Neural Network models. About 5000 different electrical disturbances were synthesized in aspects of a disturbance duration time, the severity of electrical disturbance, and synthesis parameters; the only fixed value is the sampling frequency of 16 kHz. In this way, 70% of the data set was used for training, equivalent to 3500 electrical disturbances. And 15% for the validation and test phases, the equivalent of 750 disturbances of the 29 levels of electrical disturbances with a great variety of syntheses.

4.2. Description of Power System

The microgrid model used is an island type grid with a photovoltaic system developed in the Matlab 2021b environment with the Simulink and AppDesigner tools and introducing different electrical disturbances with different levels of complexity, as shown in the previous section. A photovoltaic system mainly integrates the configuration of the island-type microgrid model shown in Figure 2. A user can manipulate the variables of temperature and solar irradiation through an interface developed in App Designer.

Figure 5. Photovoltaic power generator system for additional tests with multiple electrical disturbance injector system.

Figure 5. Photovoltaic power generator system for additional tests with multiple electrical disturbance injector system.

The solar photovoltaic system generate a maximum power of 250 kW in STC (cell temperature of 25 °C with solar irradiance of 1000 $\frac{W}{m^2}$). The system also has an integrated DC-DC Boost type charge controller and a DC-AC voltage source inverter (VSI). Maximum power point tracking (MPPT) controller with a DC-DC boost type voltage controller. The MPPT control helps to generate the proper voltage by extracting the maximum power and adjusting the duty cycle to avoid performance problems due to changes in temperature and solar irradiance that are simulated in the system. For the Voltage Source Inverter (VSI), a full bridge inverter works at 1000 Hz switching.

4.3 Deep neural network multitasking architecture

The Figure 6 shows the architecture used for multi-tasking learning. The following points show the description of each layer and discuss different issues, such as how the layer works and its objective in the deep neural network, among other important points discussed. To observe more straightforwardly the function and composition of the neural network and how the information flows, how the data are processed, and how they are normalized to reduce computational consumption.

• Batch Normalization: This layer is used to improve the training speed and stability of the model. The basic idea behind batch normalization is to normalize the input data of each layer [30]. This is done by subtracting the batch mean from each input data point and dividing it by the batch standard deviation. The batch means and standard deviation are estimated using the input data of a batch rather than the entire dataset [31]. Batch normalization helps to reduce the problem of internal covariate drift, which occurs when there is high variation in the input data. This can lead to slower convergence and overfitting [32]. Batch normalization is a powerful technique that improve the performance of deep neural networks [33].
• Convolutional layer or conv layer: is a crucial building block of convolutional neural networks (CNNs). It is designed to perform feature extraction from input data such as images, video, or audio. The basic idea behind convolutional layers is to apply a set of learnable filters (kernels or weights) to the input data to extract essential features [34]. Each filter performs a convolution operation on the input data, which involves sliding the filter over the input and computing the dot product between the filter weights and the local input values at each position [35]. In a Convolutional Neural Network (CNN) used for regression, the convolutional layers will be designed to extract relevant features from the input data that help predict the target values. The convolutional layers are an essential part of the network architecture for regression problems because they allow the network to capture important local patterns in the input data, which can be highly relevant for predicting the target values. By stacking multiple convolutional layers with increasing filter sizes, the network can learn increasingly complex and abstract features from the input data, making more accurate predictions [36].
• Polling: is used for down-sampling. The aim is to scale and map the data after feature extraction, reduce the dimension of the data and extract the important information, thus performing feature reduction efficiently within the neural architecture. Avoiding adding extra phases and reducing computational consumption. [37]. There are several types of pooling layers, but the most common ones are max pooling and average pooling. Max Pooling Layers in these layers reduce the spatial dimensions of the output from the convolutional layers by taking the maximum value within each pooling window [38].
• Dropout: randomly drops out some of the neurons in the previous layer during training, which helps prevent overfitting and improves the network’s generalization ability. The main idea behind dropout is that the network learns to rely on the remaining neurons to make accurate predictions. This forces the network to learn more robust features that are not dependent on any specific set of neurons [39].
• SoftMax: is a typical activation function used in neural networks, particularly in multi-class classification problems. The SoftMax function takes a vector of real-valued scores as input and normalizes them into a probability distribution over the classes [40].
• The flatten layer: is a layer that converts multidimensional inputs into a one-dimensional vector. This is often done to connect a convolutional layer to a fully connected layer, which requires one-dimensional inputs [41].
• Fully connected layer or dense layer: is a layer where each neuron is connected to every neuron in the previous layer. Each neuron performs a weighted sum of the activations from the previous layer and then applies an activation function to the sum to produce an output. The weights and biases are learned during training using backpropagation, where the gradients are propagated backward from the output to the input layer [42].

Figure 6. The architecture of a Novel Multitasking Deep Neural Network for Classification and Analysis of Multiple Electrical Disturbances.

Figure 6. The architecture of a Novel Multitasking Deep Neural Network for Classification and Analysis of Multiple Electrical Disturbances.

5. Analysis and Results

Figure 7. Feature extraction with EMD algorithm left) Spike right) Spike with noise.

Figure 7. Feature extraction with EMD algorithm left) Spike right) Spike with noise.

Figure 8. Feature extraction with EMD algorithm left) Notch right) Notch with noise.

Figure 8. Feature extraction with EMD algorithm left) Notch right) Notch with noise.

Figure 9. Feature extraction with EMD algorithm left) Oscillatory transient right) Oscillatory transient with noise.

Figure 9. Feature extraction with EMD algorithm left) Oscillatory transient right) Oscillatory transient with noise.

5.3 Analysis of Results

The Table 6 compares critical elements for classifying methodologies for multiple electrical disturbances. Such as the precision of the models, methodology to extract characteristics, classificatory methodology, levels of complexity of electrical disturbances, the noise levels used, and finally, if any of these proposals offer any other methodology for the analysis and quantification of electrical disturbances.

Table 6. Comparison of investigations with the contribution in this paper.

Table 6. Comparison of investigations with the contribution in this paper.

	Reference	[15]	[43]	[12]	[20]	Current
Characteristics
Accuracy percentage		79.14% - 83.66%	90%	88% - 98%	91.3% - 99%	98% -99%
Feature extraction methodology		short time Fourier Transform	Higher-Order Statistics	1-D convolutional	Wavelet Transform	Empirical Mode Decomposition (EMD)
Classification methodology		Convolutional Neural Networks Long Short-Term Memory	Multi-layer perceptron (MLP) Support Vector Machine (SVM)	Deep convolutional neural network	Support Vector Machine (SVM)	Multitasking Deep Neural Network
Electrical disturbance levels		7 levels	2 levels, Sags, and swells	15 levels	5 levels	28 levels
Noise levels		Without noise	40 dB to 60 dB	40 dB to 60 dB	Without noise	10 dB to 50 dB
Qualitative analysis of electrical disturbance		Does not perform quantification or analysis	Does not perform quantification or analysis	Does not perform quantification or analysis	Does not perform quantification or analysis	Quantitative analysis of the different electrical disturbances

With this comparative table, exciting points are inferred. First, the percentage of precision is not very variable among the classification proposals, and most remain above 90%. However, there is beginning to be a high concentration in the following attributes, feature extraction, and classification methodologies based on deep learning or machine learning. Artificial intelligence is a discipline that has played a significant role in various contexts in the analysis and monitoring of electrical disturbances. The levels of electrical disturbances see how some are reduced to sags and swell, with five levels of disturbances or 15 levels. These contributions present a notable bias to classify disturbances that emerge from the amplitude. This is because working with frequency disturbances could often be complex and challenging if noise is added. This element in which is compare this proposal, although the range oscillates between 40 dB and 60 dB This advantage is because it represents less noise than 10 dB or 20 dB. The level of complexity increases as the signal is noisier. It is important. Furthermore, it can note how none of these proposals works with quantifying and analyzing electrical disturbances. They only give a taxonomy with labels for the type of disturbance that occurs. It is essential to mention that measuring and analyzing the main quality and energy factors develops more direct and informative energy quality reports. In summary, the following important points of the proposed model can be highlighted.

1.

Extraction of adaptive multi-resolution features of the signal

2.

Processing, signal classification analysis

3.

The noise affects the classification of the signal; however, due to the analysis task, it helps to identify the affectations on the quality of the electric wave.

4.

Introducing the analysis and quantification of primary elements to quantify the quality of electrical energy. An opportunity to make more visually appealing power quality reports with data science tools is outlined, in addition to performing the compensation of electrical disturbances intelligently.

6. Conclusions

Abbreviations

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