Application of Bifurcation Analysis to Power Systems

Electric power systems are physically some of the largest and most complex nonlinear systems in the world. Bifurcations are rather mundane phenomena in power systems. The pioneer work on the local bifurcation analysis of power systems can be dated back to the 1970’s and earlier. Within the last 20 years or so nonlinear dynamical theory has become a subject of great interest to researchers and engineers in the power system community. Powerful computational tools for bifurcation analysis have been applied during this period to study important nonlinear problems arising in power systems, and in some cases, to relate this study to observed nonlinear phenomena in power systems. In this chapter, we will present an overview on the application of local bifurcation analysis and theory to (i) develop models explaining power system nonlinear behaviors and various power system instabilities such as voltage collapse and low-frequency oscillations, to (ii) develop a powerful global analysis tool based on continuation methods to trace power system quasi-steady-state behaviors due to load and generation variations in realistic power system models, and to (iii) develop performance indices for detecting and estimating local bifurcations of power systems. An overview on the extension of saddle-node bifurcation, Hopf bifurcation and limit-induced bifurcation to include the analysis of the system dynamics after the bifurcation is presented. In addition, the effects of un-modelled dynamics due to fast and slow variables on local bifurcations is presented.