An Efficient Three Phase Four Wire Radial Power Flow Including Neutral-Earth Effect

This article presents a new methodology to solve the power flow problem for radial three phase four wire distribution networks considering neutral grounded, based on a backward/forward procedure. An equivalent circuit of these elements is introduced involving the neutral to earth effects. Additionally, the power flow algorithm is improved by the Anderson mixing scheme, which stabilizes the algorithm convergence. The proposed methodology is easier to implement than the Newton Raphson Algorithm, both of which have the same response values. Moreover, it allows expanding a \(3\times 3\) matrix to \(4\times 4\) representation; therefore, both the neutral wire and earth wire effects are explicit throughout the procedure, providing the advantage of close examination of the grounding system. Furthermore, the convergence problem of the traditional methods when the slack bus is not solidly grounded, is solved. The methodology was applied on several case studies, and the results show differences in loss evaluation regarding Kron’s reduction. This new approach gives utilities a clearer vision of the operational state of their systems.