A Sufficient Condition for Multiple Load Flow Solutions Existence in Three Phase Unbalanced Active Distribution Networks

This brief proposes an explicit sufficient condition which guarantees the existence of multiple power flow solutions 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 node voltage has been plotted into a closed contour region where the power flow solution exists. Different cases of system unbalance have been studied to analyze their effect over multiple power flow solutions. As the proposed method depends only on 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.