Ferroresonance in networks - Modeling and applications to circuit typology

Ferroresonance is a non-linear resonance phenomenon that can affect electricity transmission and distribution networks. It refers to all oscillatory phenomena, most often harmonic but also pseudo-periodic or even chaotic in extreme cases, which occur in an electrical circuit comprising, on the one hand, one or more non-linear inductors (including saturable ferromagnetic materials) and, on the other hand, a network comprising at least one capacitor supplied by one or more generally sinusoidal voltage sources.

The essential and characteristic property of such a phenomenon is to present at least two stable regimes for the same excitation. Classically, in electrical engineering, the electrical characteristics of components are considered to be linear, which implies that the steady state reached is unique and independent of initial conditions. Here, the presence of inductances with non-linear characteristics can lead to radically different and even surprising behavior for electrical engineers. Several different permanent regimes can occur in a given circuit, depending on initial conditions (remanent flux, switch-on times, etc.). Generally speaking, one of these is the one we usually expect, while the others are abnormal and sometimes even dangerous for electrical equipment, as they present overvoltages or overcurrents.

The non-linear phenomena encountered here in electrical engineering are also the subject of growing interest in many fields of physics. The best-known example is meteorology, with its sensitivity to initial conditions (butterfly effect) and the difficulty of predicting over a horizon of more than a few days.

After presenting the nonlinear ferroresonance phenomena observed in our first dossier [D 91] , this dossier [D 92] looks at the modelling and tools used to study them, as well as applications to different circuit topologies.

Calculation methods for these phenomena encountered in electrical engineering are specific to non-linear circuits. Progress since the 1980s has provided us with the mathematical framework and numerical tools needed to study these phenomena. These theories and tools enable us to better understand and study ferroresonance...