Electric vehicles (EVs) have gained traction and have become a viable option in recent years, providing cleaner alternatives to traditional vehicles. This has led to significant strides in research on the various aspects of electric vehicle charging stations (EVCSs) and electric vehicle charging infrastructures (EVCIs). As more and more EVs are adopted, the need for fast charging stations and multiple charge points arises, which further increases the burden on the grid. One of the key areas of research is the optimal placement of EVCIs in the distribution system (DS) to reduce the impact on the utility grid. In this work, we provide an in-depth analysis of how the placement of EVCI impacts the grid and how EVCIs with high loads due to fast chargers or multiple chargers could affect the load flow analysis in obtaining the optimal placement in DS. We analyze the distribution load flow (DLF) for all possible combinations of EVCI allocated at different points in the DS and propose a new schema for performing DLF for high EVCI loads. The proposed DLF algorithm is used with a modified multi-objective particle swarm optimization (MOPSO) algorithm to obtain the optimal locations of five EVCIs in the distribution system. Our analysis provides the preferred choice of bus locations for EVCI placement and also the combinations of buses with EVCI for which the DLF does not converge.