## 2 Methodology
### Artificial Neural Network-Based Classification  
Artificial neural networks (ANNs) are effective for classification tasks involving nonlinear, non-stationary signals like voltage disturbances [40; 41]. This work employs a supervised ANN to identify and classify power quality events using features obtained from the Hilbert-Huang transform (HHT).  
The input to the network consists of six features derived from the first two intrinsic mode functions (IMFs) of each voltage signal window. Specifically, the feature vector includes the following:  
* The mean and standard deviation of the instantaneous amplitude of IMF1;
* The mean and standard deviation of the instantaneous amplitude of IMF2;
* The mean of the instantaneous frequency of IMF1;
* The mean of the instantaneous frequency of IMF2.  
These features capture the signal's energy content and spectral dynamics, providing a compact and discriminative representation for event classification. The ANN architecture consists of an input layer with 6 neurons, two hidden layers with 20 and 15 neurons, and a Softmax output layer with 4 neurons corresponding to the classes normal, sag, swell, and interruption. This topology is shown in Figure 1.  
The number of neurons in the hidden layers was determined empirically via multiple trials to maximize classification accuracy. However, no formal optimization method (e.g., grid search, Bayesian tuning, or genetic algorithms) was applied.  
Each hidden layer employed the Rectified Linear Unit (ReLU) activation function to enhance nonlinearity and improve convergence speed, while the output layer used the Softmax function for multi-class classification.  
The selection of this network structure was based on iterative experimentation. Several configurations were evaluated, including architectures with fewer neurons (e.g., 10-5) and those with additional hidden layers. Networks with fewer parameters exhibited under-fitting and reduced generalization, while larger or deeper models increased training time without substantial improvements in accuracy. The 20-15 topology was selected as it offered a favorable trade-off between classification performance and computational efficiency.  
No formal hyperparameter tuning methods (e.g., grid search or Bayesian optimization) were applied in this study as they were not part of this research objectives.  
The network was implemented and trained in MATLAB using the Levenberg-Marquardt backpropagation algorithm and a cross-entropy loss function. Training data were generated through voltage simulations in the IEEE 33-bus system under various disturbance types and durations (0.2 s, 0.4 s, and 0.8 s). The dataset was partitioned into 70% for training, 15% for validation, and 15% for testing.  
The proposed ANN configuration achieved a classification accuracy of 94.09% on the testing set, demonstrating strong generalization across different disturbance types and bus locations. Each input to the classifier corresponds to a 0.8 s window of voltage data, sampled at 10 kHz, resulting in 800 samples per event. Although the current implementation operates in offline mode, the compact feature set and lightweight network architecture are well suited for future integration into real-time disturbance monitoring systems.