BIFURCATIONS AND CHAOS IN ELECTRIC-POWER SYSTEMS - NUMERICAL-STUDIES

In the first part of this paper, we show via computer simulation the e xistence of chaos in two electric networks over a range of lending con ditions. These two power systems, which were derived and simplified fr om physical power networks, are four-dimensional and 11-dimensional re spectively, and both exhibit a period-doubling transition to chaos. Th e existence of chaos is confirmed though Lyapunov exponents, power spe ctra, and inspection of Poincare maps. The effect of system damping fa ctors on bifurcations and complicated behaviors is also examined. Our studies indicate that some phenomena not appearing in small test syste ms can appear in larger systems. These simulations favor the claim tha t bifurcation and chaos can occur in a real power. system, motivating a future investigation of the nature, extent, and significance of thes e phenomena in realistic power system models. We present a survey of e xisting work On the application of continuation methods to realistic p ower system models-which may contain thousands of nonlinear equations, some with hard limits on certain state variables. An emphasis is plac ed on the package CPFLOW, to illustrate, on a 3493-bus power system, t he computational requirements and difficulties to be overcome in attem pts to develop tools for realistic power. system bifurcation and chaos studies. In addition to the review, this paper presents some new work in the interpretation of dynamical phenomena observed in power system s using qualitative results about bifurcation and chaos theory.