The stability of a synchronous generator with a prime mover connected to a resistive load

We present the stability analysis of a system which contains a synchronous generator (SG) with its prime mover and a resistive load. Inductive transmission lines connect between these. The model of the SG and its prime mover includes a frequency droop loop that acts through the prime mover and its governor, with its own dynamics. The SG model takes into account the variation of the inductances with the rotor angle. We derive a mathematical model of the system that takes into account a simplified model of the damper windings and is a fifth order nonlinear system. We present sufficient conditions on the model's parameters to insure local stability for the system. We strive to find sufficient conditions that are easy to verify. We use Lyapunov functions and the port-Hamiltonian representation.