With the emergence of the Electric Vehicle, there is an awareness in the power system community to utilize this opportunity for the grid's benefit. Vehicle to Grid (V2G) idea could come into realization through the bidirectional procedure, allowing higher penetration of renewable energy and electric vehicles. One of options is employing V2G as frequency support with inertia control. It is crucial to analyze how uncertainties (e.g. location, time, and condition of EVs) will impact the state of the grid. This research is trying to analyze this impact. Moreover, the battery as the core of V2G has behavior which highly related to its State of Charge (SoC). First, the SoC-dependent battery is modeled. Then, the complex power system is simplified by two area systems. Optimum gains are attained by Gradient Descent-Square Quadrature Program (GD-SQP). Finally, the outcome are tested by several scenarios. It is revealed that SoC-dependent EV's characteristic forces a condition where an improper assortment of gain value sets could produce system instability.