Bifurcation and chaos in power systems: A survey
- California Univ., Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences
- Cornell Univ., Ithaca, NY (United States). School of Electrical Engineering
The literature dealing with bifurcation and chaos in electric power systems is surveyed. A brief discussion of relevant mathematical concepts and results is included in order to make the presentation self-contained and readily accessible. The objective is to determine the extent and significance of power system behavior that can be understood by dynamic models exhibiting bifurcation and chaotic motion. Bifurcation denotes a qualitative change in system behavior. The study is divided into three parts dealing with static bifurcations, Hopf bifurcations, and chaos. Static bifurcation occurs when two or more equilibrium points coincide. Hopf bifurcation occurs when a periodic oscillation emerges from a stable equilibrium. These are both examples of local bifurcation - they are determined by the system behavior in a neighborhood of the equilibrium. Chaos emerges from a global bifurcation - a non-local change in the phase portrait of tile system. The following conclusions are reached. Even the simplest models of power systems exhibit both local and global bifurcations. Local bifurcations occur because power flow equations have multiple solutions. In models that only incorporate real power flow, the capacity of transmission systems is so large that local bifurcations although present are unlikely to be practically significant. However, in models where voltage is determined by reactive power flows, local bifurcations can dramatically shrink the stability region. These bifurcations may explain voltage collapse''. The simplest models also exhibit chaotic behavior. However, for analytical convenience, chaos has mostly been investigated in systems with unrealistic parameter values.
- Research Organization:
- Electric Power Research Inst., Palo Alto, CA (United States); California Univ., Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences; Cornell Univ., Ithaca, NY (United States). School of Electrical Engineering
- Sponsoring Organization:
- EPRI; Electric Power Research Inst., Palo Alto, CA (United States)
- OSTI ID:
- 7102359
- Report Number(s):
- EPRI-TR-100834
- Country of Publication:
- United States
- Language:
- English
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