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Power flow analysis of distribution networks incorporating LV consumer representation needs to be cognizant of an unbalanced load structure and the grounding network between the consumer and network operator (TNC-S earthing). In this paper, the asymmetrical 3-phase (and neutral) power flow problem is solved by a correction current injection methodology applied to a system represented by a complex admittance matrix. The correction current injection technique is adopted to adjust the power exchange of shunt elements, whose nominal admittances are included in the system admittance matrix, through suitable fringing currents in the iteration process. This methodology offers an improved and more robust alternative for asymmetrical network scenarios under unbalanced power flow conditions when compared to the standard power flow methodologies, such as the Newton-Raphson or the forward-backward sweep approaches. These well-known methods may encounter convergence issues as a consequence of the specific consumer/network earthing arrangements especially when they need to be defined throughout the network. The algorithm presented here has been applied to a 4-wire representation of a suburban distribution network within Dublin city,