  In electric power systems delivering alternating current, it is essential to
maintain its synchrony of the phase with the rated frequency. The
synchronization stability that quantifies how well the power-grid system
recovers its synchrony against perturbation depends on various factors. As an
intrinsic factor that we can design and control, the transmission capacity of
the power grid affects the synchronization stability. Therefore, the transition
pattern of the synchronization stability with the different levels of
transmission capacity against external perturbation provides the stereoscopic
perspective to understand the synchronization behavior of power grids. In this
study, we extensively investigate the factors affecting the synchronization
stability transition by using the concept of basin stability as a function of
the transmission capacity. For a systematic approach, we introduce the
integrated basin instability, which literally adds up the instability values as
the transmission capacity increases. We first take simple 5-node motifs as a
case study of building blocks of power grids, and a more realistic IEEE 24-bus
model to highlight the complexity of decisive factors. We find that both
structural properties such as gate keepers in network topology and dynamical
properties such as large power input/output at nodes cause synchronization
instability. The results suggest that evenly distributed power generation and
avoidance of bottlenecks can improve the overall synchronization stability of
power-grid systems.
