  As the penetration of wind generation increases, the uncertainty it brings
has imposed great challenges to power system operation. To cope with the
challenges, tremendous research work has been conducted, among which two
aspects are of most importance, i.e. making immune operation strategies and
accessing the power system's capability to accommodate the variable energy.
Driven and inspired by the latter problem, this paper will discuss the power
system's capability to accommodate variable wind generation in a probability
sense. Wind generation, along with its uncertainty is illustrated by a
polyhedron, which contains prediction, risk and uncertainty information. Then,
a three-level optimization problem is presented to estimate the lower
probability bound of power system's capability to fully accommodate wind
generation. After reformulating the inner \emph{max-min} problem, or
feasibility check problem, into its equivalent mixed-integer linear program
(MILP) form, the bisection algorithm is presented to solve this challenging
problem. Modified IEEE systems are adopted to show the effectiveness of the
proposed method.
