This project seeks to model and simulate the synchronous machine using a classic model and adding an automatic voltage regulator and / or a stabilizing power system connected to an infinite bus using the advance technology for the stability analysis of power systems. The stability analysis considers the performance of generators and its ability to maintain synchronism under sudden changes in the power system, the response is non-linear and its analysis must include the variables behavior as deviations of rotor angles, rotor speeds, power flows in the system and voltages at machine's terminals. The use of computational tools is proposed in previous works, aiming for fast and effective solutions under high disturbances, however simulation times was not efficient. Due to this, trapezoidal integration rule is used to solve the model's equations and the computing is accomplished using Graphic Processing Units (GPU) technology. The algorithm is implemented in MATLAB® and its main goal is to simulate the behavior of electrical power systems, looking to satisfy with real time requirements and to decrease simulation time using parallel processing technology. Given the technological advances that have occurred, it has been possible to reach faster simulations by using computational tools.