More load flow fractals

The existence of fractal domains of attraction of solutions of the load flow equations using the Newton-Raphson iteration is investigated as a function of load level. Using constant impedance loads, the size of the fractal region is seen to be essentially independent of load level. The three-machine system used by J.S. Thorp and S.A. Naqavi (1989) when they first demonstrated these fractals is modified to produce a system with fractal domains and large regions of initial conditions where the Newton load flow oscillates. By adding a strong tie between the two machines in the three machine example, a system has been produced which has an unstable limit cycle (on a torus) for the reduced order dynamical system and a large area of eventually periodic initial conditions (with period two) in the Newton load flow. It is not clear whether these phenomena are related, but the example demonstrates the potentially complicated behavior that can be expected from the Newton load flow when the initial condition is not near a solution