The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized Lyapunov function to solve the problems. Also, a new synchronization definition is introduced and characterized by frequency boundedness and angle cohesiveness, the latter of which requires angles of any two connected nodes rather than any two arbitrary nodes to stay cohesive. It allows to take power fluctuations into explicit account as disturbances and can lead to less conservative stability condition. Applying the analysis framework, we derive two algebraic stability conditions for power systems that relate the underlying network topology and system parameters to the stability. Finally, to authors best knowledge, we first explicitly give the estimation of region of attraction for power systems. The analysis is verified via numerical simulation showing that two stability conditions can complement each other for predicting the stability.
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