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Bifurcations are performed for a power system model consisting of two generators feeding a load, which is represented by an induction motor in parallel with a capacitor and a combination of constant power and impedance PQ load. The constant reactive power and the coefficient of the reactive impedance load are used as the control parameters. The response of the system undergoes saddle-node, subcritical and supercritical Hopf, cyclic-fold, and period-doubling bifurcations. The latter culminate in chaos. The chaotic solutions undergo boundary crises. The basin boundaries of the chaotic solutions may consist of the stable manifold of a saddle or an unstable limit-cycle. A nonlinear controller is used to control the subcritical Hopf and the period-doubling bifurcations and hence mitigate voltage collapse.

This paper demonstrates a phase tunable holographic fabrication of three-dimensional photonic lattice structures using a single optical element. A top-cut four-side prism is employed to generate five-beam three-dimensional interference patterns. A silica glass slide is inserted into the optical path to adjust the phase of one interfering beam relative to other four beams. The phase control of the interfering laser beam renders the lattice of the interference pattern from a face-center tetragonal symmetry into a high contrast, interconnecting diamondlike symmetry. This method provides a flexible approach to fabricating three-dimensional photonic lattices with improved photonic band structures.

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