F. Liu, W. Wei, and S. Mei (PR China)
Nonlinear System, Energy Function, Stability Region
The expansion of stability region estimation is an important tool for nonlinear system stability analysis. However, current literature has not provided a complete mathematical depict for it. This paper reveals that essentially the enlargement or compression of the estimated stability regions is a result from the diffeomorphism map induced by the flow contained in the stability region. As we prove that any integration algorithm with an order higher than one can approximately trace the flow of the system, a generalized methodology is proposed to construct various algorithms to realize the enlargement or compression of the estimated stability region. By using this methodology, a new algorithm with higher order based on symbolic calculation is suggested to reduce the computational burden. Furthermore, this methodology is applied to the transient stability analysis for power systems. Current algorithms based on symbolic calculation are infeasible for such complicated large-scale systems. Our generalized methodology, however, can provide a scalable numerical algorithm to calculate the Critical Clearing Time(CCT) of a power system for given faults. This algorithm is tested on the IEEE 39-bus system, and the results coincide with the step-by-step simulation with high accuracy.
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