Study of the periodic ferroresonance in the electrical power networks by bifurcation diagrams

The principal contribution of this article is to determine the existence zones of the various periodic ferroresonant modes (fundamental, harmonic and subharmonic) intervening in the electrical power network. The bifurcation diagrams are used for this purpose. To be able to plot a bifurcation diagram of a particular solution, it is initially necessary to locate this solution and then to follow it according to a bifurcation parameter. The developed computation code, resulting from the implementation of the Galerkin method jointly with the pseudo-arclength continuation method, has proved to be a powerful and reliable tool to construct these bifurcation diagrams. Indeed, it enables the electrical power network operators to better understand the problems of the phenomenon which had been observed in its network and to foresee new ferroresonance cases.Applied to the single-phase ferroresonant circuits, both series and parallel, we have been able to easily calculate the existence zones of these modes, as well as the stability limits of the system on ranges of broad variation of the parameters.Several results obtained numerically by software MATLAB, as from the real cases, are presented and commented upon.