Due to environmental problems in the world, the need for electric vehicles is increasing. While the transition to Electric Vehicles continues, the acceleration of this process plays an important role in reducing environmental problems. In order to accelerate this transition, charging units should become widespread and charging time should be reduced. Higher power charging units are needed to reduce charging time. This is where DC (Direct Current) fast charging units come into play. In this study, the charging process of electric vehicles, the behavior of the DC fast charging unit on the battery and the control systems are modeled in MATLAB/Simulink environment. The designed model represents the electric power system that will charge electric vehicles and is suitable for more than one electric vehicle to be included in the DC fast charging system. The simulation is integrated according to the DC level-2 charging conditions. The system model consists of 1 AC(AC Current)/DC converter, 1 DC busbar, 2 DC/DC converters to charge electric vehicles and multiple EV batteries. The system model includes the design methods (AC/DC-DC/DC) design and different control strategies) and descriptions of these components. The simulation result shows that the filter and control system integrations in the electrical power system exhibit more stable behavior by correcting the negative effects on the power system. Thus, it offers positive outputs about the integration of DC fast charging units, which will increase rapidly in the future, into the power system and how this process should be established.