  Network topology has significant impacts on operational performance of power
systems. While extensive research efforts have been devoted to optimization of
network topology for improving various system performances, the problem of how
to transition from the initial topology to the desired optimal topology
requires study. To address this problem, we propose the concept of optimal
topology transition (OTT). This aims to find the topology transition trajectory
from an initial topology to a desired terminal topology, which optimizes
certain transition performance and satisfies operational constraints. The OTT
problem is further formulated as a mixed-integer program under certain
assumptions. Next, we propose the formulation of transition-embedded topology
optimization that is capable of optimizing network topology and its transition
trajectory simultaneously. Considering the time complexity of directly solving
the mixed-integer programs, an efficient problem-specific solution algorithm is
developed. Finally, numerical studies demonstrate the effectiveness of the
proposed OTT and transition-embedded topology optimization models, as well as
the superiority of the obtained optimal transition trajectories compared to ad
hoc transition trajectories.
