  Power flow solvable boundary plays an important role in contingency analysis,
security assessment, and planning processes. However, to construct the real
solvable boundary in multidimensional parameter space is burdensome and time
consuming. In this paper, we develop a new technique to approximate the
solvable boundary of distribution systems based on Banach fixed point theorem.
Not only the new technique is fast and non-iterative, but also the approximated
boundary is more valuable to system operators in the sense that it is closer to
the feasible region. Moreover, a simple solvable criterion is also introduced
that can serve as a security constraint in various planning and operational
problems.
