Vehicle to grid systems (V2Gs) are complex interfaces that coordinate the energy flow between the grid and the connected EVs. The nonlinear dynamic model of the entire V2G system is developed in a manner that permits a rigorous stability analysis. The resulting complexity of the numerous EVs that connect to the grid through their bidirectional converters is compensated by adopting a novel aggregate model for the battery-converter pairs. In the proposed configuration, a LCL filter, an inverter that couples the grid with the dc-side of the system and the battery-converter pairs of all the connected EVs are involved. In order to operate the V2G system in a reliable and desired manner cascaded mode PI controllers are adopted, due to their simple design and robust behavior. The controller schemes are appropriately modified for the present case, in order to prove stability of the entire system. To that end suitable Lyapunov techniques are applied to prove input to state stability (ISS) of the system and convergence to a nonzero equilibrium at steady state. The conducted simulations verify the effectiveness of the proposed controllers, the validity of the developed nonlinear model for the entire V2G system and confirm the attained theoretical results.