Abstract
The expansion of the estimated stability region plays an important role in the stability analysis of nonlinear systems. However, current literatures have not provided a complete mathematical description for this problem. This paper reveals that essentially the enlargement or the compression of the estimated stability region results directly from the diffeomorphism map, which is induced by the flow contained in the stability region. By proving 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 the compression of the estimated stability region. With this methodology, two new algorithms based on symbolic calculation are suggested to reduce the computational burden. Furthermore, this methodology is applied to construct a scalable numerical algorithm to calculate the critical clearing time (CCT) of the power system for given faults. Tests on the IEEE 10-machine 39-bus system show that the computational results coincide well with the step-by-step simulation with high accuracy.
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