### Abstract

Fast parallel algorithms to compute unstable equilibria in the state space of a large electric power system are introduced and analyzed. The approach utilizes cluster separation. The algorithm proposed for finding stable equilibria is novel and is much faster in parallel implementation then the sparse Newton-Raphson technique. The algorithm proposed for finding unstable equilibria is not only novel but is the only available algorithm for computing unstable equilibria. Necessary and sufficient conditions for stability and instability checking have been developed. These conditions give some indications how the (N-1) unstable equilibria can be located through cluster structures. Simulation results are also given to show the convergence of the algorithms. Time-complexity analysis of parallel implementation is described and shows the potential of the algorithms.

Original language | English |
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Journal | Proceedings of the IEEE Conference on Decision and Control |

Publication status | Published - 1 Dec 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality