Analytical load flow solution for radial distribution networks

This paper proposes an analytical method to solve the load flow problem for radial single and multi-feeder power distribution networks in three-phase balanced conditions. The Analytical Load Flow (ALF) formulation relies on a single assumption for the estimation of line losses and accounts for line susceptances. A set of comparative tests performed on a total active and passive 33 nodes benchmark network allowed showing that the accuracy of the proposed method is extremely high, if compared with the alternative numerical solution. Furthermore, a specific analysis is proposed to evaluate the impact of the approximation on the losses in the determination of the nodal voltage phasors. Finally, ALF is validated in a realistic scenario with high integration of Renewable Energy Sources (RESs), considering seasonal variations in production and consumption. In this context, it is shown that the proposed method outperforms existing approximate analytical approaches, such as the industrial voltage drop method. The ALF approach, being fully analytical, does not require any numerical solver and can be applied as a valid alternative to existing numerical and analytical methods in balanced multi-feeder networks.