The thesis utilizes the analogy in dynamic equations between a mechanical and an electrical system to convert the steam-turbine, micro-turbine, wind-turbine and hydro-turbine generator mechanical model to equivalent electrical circuit models respectively. And based on the round rotor type and permanent magnetic rotor type synchronous generators¡¦ dynamic equations, as well as their electromagnetic torque equations, the equivalent electrical interface circuits were derived respectively. By using the interface circuit, the circuit model of synchronous generator and the equivalent electrical circuit model of turbine-generator mechanism can thus be combined into the electromechanical integrated circuit model (Thevenin¡¦s analogy circuit model and Norton's analogy circuit model). The electromechanical integrated circuit model is helpful for analyzing the energy conversion, power transmission and interactions between the mechanical and electrical systems for a turbine generator unit. In order to learn about these electromechanical interactions by using the proposed electromechanical integrated circuit model, the thesis has made a study on the torsional vibrations for a small gas turbine generator unit and for a large steam turbine generator unit respectively. By way of the frequency scanning and eigenvalue calculation, it is found that the torsional mode frequencies can be changed due to the electromechanical integration. Moreover, the small unit was more affected by the electromechanical integration than the large unit. Finally, we studied the effect of operations of an Electric Arc Furnaces (EAF) on torsional vibrations of a low capacity turbine generator. The electric system studied belongs to a practical steel plant in an industrial park. Based on the electromechanical integrated equivalent circuit model, a flywheel coupling shaft was designed. It is found by simulations that the coupling shaft can be quite effective in alleviating vibrations caused by the system unbalance arising from the EAF operations.