## 1 Introduction  
During the process of delivering energy to final consumers, a substantial portion of energy is dissipated in the transmission and distribution systems, resulting in both technical and non-technical losses. Technical losses, which include inefficiencies in equipment and infrastructure, cause economic losses and environmental impacts on a national scale [1]. Therefore, optimizing these losses must be addressed comprehensively and nationally, regardless of the institutional structure of the electricity sector or the ownership of concessionary companies. The volume of losses in transmission and distribution systems is significant, typically ranging between 3% and 13%, highlighting their relevance to the efficiency of the system as a whole [1]. The analysis of electrical power systems often uses load flow calculation, a fundamental and widely used approach [2, 3, 4]. Many applications, from expansion planning to network reconfiguration and storage capacity, depend on these calculations [5, 6, 7]. The classical formulation based on [PERSON]'s method is commonly adopted due to its effectiveness in both transmission and distribution systems [8]. However, a significant drawback of this method is the need to construct and factorize the Jacobian matrix at each iteration, which can be computationally expensive, especially for large-scale systems [9, 10]. Continuation power flow (CPF) is an approach to determine the total losses of the electrical system for each load increment until reaching the critical point (CP). It is crucial to identify this point, as it marks the transition between the region of stability and the region of instability of the system. However, accurately obtaining this point can be challenging due to the singularity of the Jacobian matrix, requiring the use of parameterization techniques for its determination [11]. These additional techniques can significantly increase the computational cost of the process. In this context, it is desirable in engineering that even well-established energy systems analysis methods are revisited and eventually improved. In recent decades, an alternative formulation based on artificial neural networks (ANN) has been widely employed [12; 13; 14; 15; 16]. In [12], two artificial neural networks (ANN) were presented, the Multi-Layer Perceptron and the Radial-Based Perceptron, with the objective of estimating the magnitudes of voltages on the buses of electrical power systems, taking into account several parameters, such as the loading factor, the real and reactive power in the slack bus, and the contingent branch number. The results indicated that the Radial Base ANN was able to accurately estimate the desired output, presenting an error of around \(10^{-4}\). In [13], promising results were obtained in which an artificial neural network (ANN) reproduced the same results with high accuracy and speed compared to traditional voltage stability calculation methods. For this, the loading parameter and the voltage stability margin index were calculated using eight different input variables and fourteen different training functions. This approach allowed us to identify which training function was most efficient and offered the best ability to predict the loading margin and voltage stability index. In the study [14], artificial intelligence (AI) was used to identify predictive biomarkers relevant to the prognosis of diffuse large B-cell lymphoma. Two neural networks, using Multi-Layer Perceptron (MLP) and Function Network Radial Base (RBF), demonstrated an efficient methodology for identifying these biomarkers. In [15], an application of an MLP model for fast and automatic prediction of the geometry of finished products is presented. The results show that both the training and the tests carried out were highly accurate, with an accuracy rate that exceeded 92%, demonstrating the feasibility and effectiveness of the proposed method.