  In this paper, we study the monitoring and control of long-term voltage
stability considering load tap-changer (LTC) dynamics. We show that under
generic conditions, the LTC dynamics always admit a unique stable equilibrium.
For the stable equilibrium, we characterize an explicit inner approximation of
its region of attraction (ROA). Compared to existing results, the computational
complexity of the ROA characterization is drastically reduced. A quadratically
constrained linear program formulation for the ROA characterization problem is
proposed. In addition, we formulate a second-order cone program for online
voltage stability monitoring and control exploiting the proposed ROA
characterization, along with an ADMM-based distributed algorithm to solve the
problem. The efficacy of the proposed formulations and algorithms is
demonstrated using a standard IEEE test system.
