Elimination of Chaos in both Integer and Fractional Order Single-Machine-Infinite-Bus Power System using Lyapunov based Controller

The nonlinear dynamics of an integer order as well as fractional order single-machine-infinite-bus (SMIB) power system model is analysed numerically as well as the dynamical behaviours of the system is studied by means of modern nonlinear theories such as bifurcation and chaos. The study illustrates that the system undergoes a chaotic oscillations whenever the value of the system parameters or the order of dynamics of the system fall into a particular ranges. Here a simple Lyapunov based control method is applied which controls the random chaotic oscillation of the system and hence chaotic oscillation is converted into periodic motion. The controller is designed for both integer order and fractional order type SMIB system. Simulation outcomes are acquired numerically for the stability analysis of the system under certain initial conditions.