A method for proving the global stability of a synchronous generator connected to an infinite bus

We consider a grid connected synchronous generator (SG), having a constant field current and driven by a prime mover with constant torque. The grid is regarded as an "infinite bus", i.e., a three-phase AC voltage source. The problem of interest is verifying if, for a given set of SG parameters, the angular velocity of the SG rotor converges to the angular velocity of the grid, irrespectively of the SG initial conditions. We pose this problem as a question of almost global asymptotic stability of a fourth order nonlinear system. In a recent work, we derived an integro-differential equation, which resembles the forced pendulum equation, and showed that the fourth order system is almost globally asymptotically stable if and only if the same holds for this equation. In this paper, it is shown that this equation is almost globally asymptotically stable if a real-valued nonlinear map defined on a finite interval is a contraction. For any given set of SG parameters, it is straight forward to check numerically if this map is a contraction. An example demonstrating our results is included.