Existence of Explicit and Unique Necessary Conditions for Power Flow Insolvability in Power Distribution Systems

This paper proposes an explicit necessary condition which guarantees the existence and uniqueness of power flow insolvability in the active distribution networks. Compared to the existing methods, the proposed condition shows better result for the power flow solution space boundary limit. The solution space for each node voltage has been plotted into a closed contour region, where the power flow solution exists. Based on derived solution criteria, a new index is presented to analyze the sensitivity of the system with load change in case of power flow solution. As the proposed method depends only on the present set of data, hence it can be used as a tool for real-time power flow analysis with lesser computational burden. The proposed theoretical derivation has been confirmed with numerical experiments over IEEE 13, 123 bus benchmark distribution systems and a real Indian distribution grid system.