Parallel (quasi-periodic) ferroresonant oscillations in electrical power systems

Quasi-periodic oscillation, hitherto unobserved in power systems, was first experienced in the French grid. Besides obtaining the numerical solution of a set of differential equations or using the method of circle maps, there are no known simple analytical tools available to study conditions for the occurrence of quasi-periodic oscillations. In this paper, quasi-periodic oscillations are analyzed by first neglecting all losses which in effect reduces the dimension of the system. The unperturbed solution for the reduced system is obtained using the method of harmonic balance. The effect of perturbations (losses) on the unperturbed solution are then considered one at a time by using Melnikov function. The geometrical interpretation is confirmed by numerical solution on the original set of differential equations