Power flow and power system stability: Evolution of analysis methods

This document explores in depth the calculation of power flow in electrical networks, which is crucial for determining the voltages, currents and active and reactive powers in order to maintain the stability and efficiency of the network. It examines the evolution of calculation techniques, from the early manual methods to algorithms similar to Gauss-Seidel and Newton-Raphson, discussing their advantages and limitations. It highlights the challenges related to convergence and accuracy in large networks, as well as the importance of more modern methods such as machine learning techniques. The paper also addresses contemporary approaches based on numerical optimization and machine learning, which offer flexible and efficient solutions for managing increasingly complex electrical grids, particularly in the context of the integration of renewable energies and smart grids. These advances allow for improved accuracy of model and optimal management of electrical networks to meet the growing needs for precision and integration of renewable energies.