A novel approach for transient stability using interval arithmetic and optimization methods

In this article, a new approach is proposed to include parametric uncertainties in the analysis of the transient stability of power systems by using intervals. Two methodologies based on the interval uncertainties were developed and implemented: (i) a robust extension of the potential energy boundary surface method combined with interval arithmetic and (ii) an optimization formulation for the transient stability problem. The interval uncertainties enable one to obtain closed-form expressions for stability assessment of uncertain systems, allowing a faster analysis. The results show that both methodologies can be used to find an accurate estimate of the critical clearing time for uncertain power systems more quickly than using the classical Monte Carlo approach.