Hopf bifurcation analysis in droop controlled islanded microgrids

The stability analysis of the microgrid has been carried out by several researchers. However, these studies have been limited to small signal (or linear) stability analysis. Such systems usually lose their stability via Hopf bifurcations. These bifurcations are either subcritical or supercritical. In case of subcritical bifurcations the stable region defined by small signal stability analysis may have unstable limit cycles. In other words, the region identified as stable for (infinitesimally) small signal may be unstable for slightly larger (finite) signal. Therefore, small signal analysis is not sufficient and it is imperative to identify type of Hopf bifurcation for a given system. In order to carry out stability analysis of the system, a generalised model is developed. This model is used for studying stability characteristics of a two bus system, modified IEEE 13 bus system and IEEE 33 bus system. Five different droop techniques from literature are compared with each other for relative stability. A non-dimensional index is proposed, which is used for comparing stability margin for each of these techniques using small signal stability analysis.