Vulnerability assessment for voltage stability based on solvability regions of decoupled power flow equations

This paper proposes a novel method of identifying buses vulnerable to power system voltage instability. Unlike traditional sensitivity and modal analysis methods, the proposed method can preserve the nonlinearity of power flow equations, and visually pinpoint the vulnerable buses in advance for any possible load increasing scenarios. Based on the power flow equations on decomposed two-bus equivalent channels from the power network, a vulnerability index is introduced and visualized for each channel in the solvability region of its decoupled power flow equations bounded by a parabola. It is found that the arrival at the parabolic boundary indicates a potentially vulnerable bus but not necessarily results in voltage collapse. Thus, a criterion on the gradient of vulnerability index trajectory is proposed to discover and differentiate two types of potentially vulnerable buses: one type has trajectories that are tangent to the boundary but stay inside the solvability region; the other type has trajectories crossing the boundary to result in unsolvable power flow equations, which are identified as the vulnerable buses. The proposed method is validated on the IEEE 14-bus, IEEE 118-bus, and New England power systems with comparison to the traditional methods, and the test results show that the proposed method performs better than the traditional methods with satisfactory robustness under voltage fluctuation. In particular, the proposed method is 33.3% and 66.7% more accurate than the voltage sensitivity method in prospective operating conditions on the IEEE 14-bus and 118-bus systems, respectively.