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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.
Small-signal instability of grid-connected power converters may arise when the converters use a phase-locked loop (PLL) to synchronize with a weak grid. Commonly, this stability problem (referred as PLL-synchronization stability in this paper) was st
One of the fundamental concerns in the operation of modern power systems is the assessment of their frequency stability in case of inertia-reduction induced by the large share of power electronic interfaced resources. Within this context, the paper p
We show that an introduction of a phase parameter ($alpha$), with $0 le alpha le pi/2$, in the interlayer coupling terms of multiplex networks of Kuramoto oscillators can induce explosive synchronization (ES) in the multiplexed layers. Along with the
For the high-dimensional Kuramoto model with identical oscillators under a general digraph that has a directed spanning tree, although exponential synchronization was proved under some initial state constraints, the exact exponential synchronization
Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and thus groun