The eigenvalues analysis method is generally applied to synchronous machines by using d,q-components. This paper presents the application of this method on an equivalent model for the synchronous machine based on phase variables a,b,c instead of d,q-components. The advantages of this approach, essential for programs using phase variables as state variables, are presented. The application of this method to a complete hydroelectric production site including hydraulic components (pump-turbine, penstock, gallery, reservoir…), permits the study and analysis of the interactions between the hydraulic, electric and regulation parts of the system. Results coming from the proposed eigenvalues analysis method and the numerical simulations confirm the interest of the presented approach.