  We present explicit sufficient conditions that guarantee the existence and
uniqueness of the feasible load-flow solution for distribution networks with a
generic topology (radial or meshed) modeled with positive sequence equivalents.
In the problem, we also account for the presence of shunt elements. The
conditions have low computational complexity and thus can be efficiently
verified in a real system. Once the conditions are satisfied, the unique
load-flow solution can be reached by a given fixed point iteration method of
approximately linear complexity. Therefore, the proposed approach is of
particular interest for modern active distribution network (ADN) setup in the
context of real-time control. The theory has been confirmed through numerical
experiments.
