The increasing penetration of plug-in hybrid electric vehicles (PHEVs) imposes new challenges in low voltage distribution networks (LVDNs), due to worsening load imbalance, power losses, and increased probability of blackouts because of the overloads. To overcome these issues, PHEV charging must be performed in a coordinated fashion. In this context, there are several coordinated charging methods in the literature, none of which considers modeling neutral conductors of LVDN.This paper aims to present a mixed-integer linear programming model (MILP) for the PHEV charging problem in unbalanced LVDNs, considering the neutral conductor. In this regard, the main parameters of unbalanced LVDN, such as voltage profile and power loss, are examined with and without modeling the neutral conductor. The results indicate that it is required to consider the neutral conductor to achieve realistic values of the LVDN's parameters. The proposed model is applied to a 449-nodes smart distribution grid consisting of 31 nodes at a medium voltage (MV) level and 418 nodes at a low voltage (LV) level. To verify the performance of the proposed model, it is compared with two uncoordinated charging methods. The results show the effectiveness of the proposed strategy.