Any alternating electric power supply is always characterized by three reference quantities, which are voltage, electric power and frequency. The generators of power stations are synchronous machines. The present work is based on the modelling of the synchronous machine for a study of the stability of the electricity transmission network. The example considered is a thermal power station of the national network. i.e., Algiers port power station. We have developed a computer program based on MATLAB to simulate the calculations of our multi-variable system. The study presented in this article examines the static stability of a thermal power plant. To make this study a reality, it is necessary to model the synchronous machine. We present the three models of the synchronous machine by emphasizing the role of the shock absorbers and the smoothness of the model with three windings. This work is supported by a spectral analysis based on the eigenvalues of the system.