The growing integration of intermittent renewable energy sources (RESs), such as wind and solar, into power grids presents significant operational challenges, particularly in maintaining grid stability and managing generation forecasting errors. This study underscores the critical role of Electric Vehicles (EVs) as a flexible load in providing ancillary services, especially for secondary frequency regulation, to address these challenges. Moreover, a novel scheduling model for EV aggregators is introduced that aims to optimize frequency regulation and cost efficiency. This model strategically manages the State of Charge (SOC) to ensure EV owner satisfaction while minimizing operational costs. Employing Mixed-Integer Linear Programming (MILP), solved via CPLEX-GAMS in both deterministic and stochastic scenarios, the proposed approach evaluates various EV integration strategies, demonstrating potential reductions in charging costs and enhancing owner participation by considering parking constraints. This research highlights the importance of innovative grid management solutions in the era of renewable energy proliferation, offering significant insights into cost-effective and reliable energy practices. The results in the deterministic show that by considering the EV parking constraint, the total charging cost will be increased by about 20%. Also, by applying the proposed strategy to the down-regulation value of 18%, the total cost of EV charging is decreased to 11,400 $ which shows about a 5% decrement in comparison with the down-regulation value of 32%.