A solvability condition for reactive power flow

A central question in the analysis and operation of power networks is the feasibility of a unique high-voltage solution to the power flow equations satisfying operational constraints. For planning, monitoring, and contingency analysis in transmission networks, the high-voltage solution of these nonlinear equations can be constructed only numerically or roughly approximated using a linear DC power flow. In this work we analytically study the solvability of the nonlinear decoupled reactive power flow equations, and present a solvability condition relating the existence of a unique high-voltage solution to the spatial distribution of loading and the effective impedances between load buses. We validate the accuracy and applicability of our results through standard power network test cases.