Analysis of a symmetrically stabilized three-phase oscillator and some of its applications

A nonlinearly stabilized three-phase oscillator model is treated in the present work. It is shown analytically and demonstrated by a computer solution of the equations that the oscillator equations possess a relatively large region, where stability of solutions is assured. All trajectories initiating or reaching this region are proved to approach a limit cycle solution. The three variables , and , representing the final Stable solution versus time, vary in time in a way similar to that of the three voltages of a balanced three-phase power generating System in steady state. The analysis of the relatively complicated third-order nonlinear system is made possible by transforming the original three-phase variables , and to new variables (introduced by Daboul) , and . The above oscillator has been applied earlier for the representation of power systems. The present thorough analysis of the model increases the authors\´ confidence that such representation of power systems is dependable.