Simple certificate of solvability of power flow equations for distribution systems

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.