Electric Vehicles(EVs) and Plug-in Hybrid Electric Vehicles(PHEVs) which have the grid connection capability, represent an important power system issue of charging demands. Analyzing impacts EVs charging demands of the power system such as increased peak demands, developed by means of modeling a stochastic distribution of charging and a demand dispatch calculation. Optimization processes proposed to determine optimal demand distribution portions so that charging costs and demand can possibly be managed. In order to solve the problems due to increasing charging demand at the peak time, alternative electricity rate such as Time-of-Use(TOU) rate has been in effect since last year. The TOU rate would in practice change the tendencies of charging time at the peak time. Nevertheless, since it focus only minimizing costs of charging from owners of the EVs, loads would be concentrated at times which have a lowest charging rate and would form a new peak load. The purpose of this paper is that to suggest a scenario of load leveling for a power system operator side. In case study results, the vehicles as regular load with time constraints, battery charging patterns and changed daily demand in the charging areas are investigated and optimization results are analyzed regarding cost and operation aspects by determining optimal demand distribution portions.