Three routes to chaos in power systems

In this paper routes to chaotic oscillation in power systems are deeply studied. Using a three-bus simple system, three routes which may cause chaos in power systems are presented, illustrated and discussed. They are the route of cascading period doubling bifurcation (PDB), torus bifurcation route and directly initiated by large disturbance route. PDB is caused by a real Floquet multiplier (FM) moving counter to the real axis and going out of the unit circle from a point (-1,0) in the complex plane. The route of cascading PDB is a typical route to chaos and has been studied deeply in many nonlinear systems. In this paper, we give a full bifurcation diagram of PDB and discuss some of its detail structure. Torus bifurcation (TB) is also a typical route to chaos. TB is caused by a couple of conjugate Floquet multipliers (FM) going out of the unit circle with a nonzero imaginary part in the complex plane. Chaos caused by TB has some interesting features, such as self-organizing phenomenon, coexistence of divergent subspace and chaotic subspace. These features are helpful to deeply understand various modes of power system instability. The last route, which is directly initiated by a large disturbance, is reported and studied for the first time to the authors' knowledge. All studies told us that chaos in power systems is in fact caused by some kind of external disturbances.