Power distribution system's security is often jeopardized by network uncertainties, usually caused by the recent increase in intermittent power injections from renewable energy sources, and non-traditional energy demands. Naturally, there is an ever increasing need for a tool for assessing distribution system security. This paper presents a fast and reliable tool for constructing \emph{inner approximations} of steady state voltage stability regions in multidimensional injection space such that every point in our constructed region is guaranteed to be solvable. Numerical simulations demonstrate that our approach outperforms all existing inner approximation methods in most cases. Furthermore, the constructed regions are shown to cover substantial fractions of the true voltage stability region. The paper will later discuss a number of important applications of the proposed technique, including fast screening for viable injection changes, constructing an effective solvability index and rig 查看全文>>