Bifurcation behavior and coexisting motions in a time-delayed power system**Project supported by the National Natural Science Foundation of China (Grant Nos. 51475246 and 51075215), the Natural Science Foundation of Jiangsu Province of China (Grant No. Bk20131402), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China (Grand No. [2012]1707).

Abstract

With the increase of system scale, time delays have become unavoidable in nonlinear power systems, which add the complexity of system dynamics and induce chaotic oscillation and even voltage collapse events. In this paper, coexisting phenomenon in a fourth-order time-delayed power system is investigated for the first time with different initial conditions. With the mechanical power, generator damping factor, exciter gain, and time delay varying, the specific characteristic of the time-delayed system, including a discontinuous “jump” bifurcation behavior is analyzed by bifurcation diagrams, phase portraits, Poincaré maps, and power spectrums. Moreover, the coexistence of two different periodic orbits and chaotic attractors with periodic orbits are observed in the power system, respectively. The production condition and existent domain of the coexistence phenomenon are helpful to avoid undesirable behavior in time-delayed power systems.