Blue sky bifurcations caused by unstable limit cycle leading to voltage collapse in an electric power system

Computer simulations of an electric power system have been carried out to determine the possible bifurcations which lead to voltage collapse. Depending on the value of a capacitor, three kinds of the bifurcations are observed; blue sky disappearance of a chaotic attractor, of a limit cycle (via cyclic fold), or of a stable equilibrium (via subcritical Hopf) leads to voltage collapse. It is confirmed that an unstable limit cycle causes these bifurcations for almost all cases. A variety of nonlinear phenomena, including chaotic attractors and multiple coexisting limit cycles, are observed. From the point of view of an electric power system, voltage collapse studied in this paper will be the most possible phenomenon as compared with previous studies because condition of the system before voltage collapse is closer to a normal operation.