Control of Initial-Sensitive Jumps and Angle Divergence of a Single-Machine Infinite-Bus Power System via Delayed Feedback

Initial-sensitive jumps and angle divergence are harmful dynamical behaviors in power systems, as they imply unreliability and insecurity of power systems. In this study, mechanisms of such phenomena of a typical Single-Machine Infinite-Bus (SMIB) power system under a harmonic disturbance power are discussed. Then, two types of delayed feedback are proposed to suppress these behaviors, and their control mechanisms and effect are investigated. The critical conditions for bistable responses and initial-sensitive angle divergence are analyzed via the method of multiple scales and the Melnikov method, respectively. Fractal erosion of basins of attraction and safe basin is employed to numerically simulate these initial-sensitive behaviors. The agreement of theoretical and numerical results shows the validity of the theoretical analysis. It follows that jumps between bistable responses owe to saddle-node bifurcation of the periodic solution, and the initial-sensitive angle divergence is due to homoclinic bifurcation of the system. Apart from these two phenomena, the period-[Formula: see text] response can also be detected which is a rare attractor. When the coefficient of the gain is positive, the two control strategies are both effective in eliminating jumps, the period-[Formula: see text] response and initial-sensitive angle divergence. The results may provide some theoretical reference in improving the performances of SMIB power systems.