  Voltage instability is one of the main causes of power system blackouts.
Emerging technologies such as renewable energy integration, distributed energy
resources and demand responses may introduce significant uncertainties in
analyzing of system-wide voltage stability. This paper starts with summarizing
different known voltage instability mechanisms, and then focuses on a class of
voltage instability which is induced by the singular surface of the algebraic
manifold. We argue and demonstrate that this class can include both dynamic and
static voltage instabilities. To determine the minimum distance to the point of
voltage collapse, a new formulation is proposed on the algebraic manifold. This
formulation is further converted into an optimal control framework for
identifying the path with minimum distance on the manifold. Comprehensive
numerical studies are conducted on some manifolds of different power system
test cases and demonstrate that the proposed method yields candidates for the
local shortest paths to the singular surface on the manifold for both the
dynamic model and the static model. Simulations show that the proposed method
can identify shorter paths on the manifold than the paths associated with the
minimum Euclidean distances. Furthermore, the proposed method always locates
the right path ending at the correct singular surface which is responsible for
the voltage instability; while the Euclidean distance formulation can
mistakenly find solutions on the wrong singular surface. A broad range of
potential applications using the proposed method are also discussed.
