Load flow fractals

The use of Newton-Raphson load flows to locate type-one equilibria for determining domains of attraction for transient stability analysis or for examining voltage collapse has become common. It is known that Newton's method for real equations can produce true fractals behavior. Using the Cornell National Supercomputing Facility, the domains of attraction of the various equilibria of a three-machine power system are investigated and shown to be fractal. The set analogous to a Julia set for the fractal is the closure of the preimages of the points at which the Jacobian is singular. The implication of the fractal in locating the boundary of the domains of attraction is discussed. A modification of the rectangular load flow which is free of the fractal domains is introduced.<>