The large-scale penetration of electric vehicles (EVs) into the power system will provoke new challenges needed to be handled by distribution system operators (DSOs). Demand response (DR) strategies play a key role in facilitating the integration of each new asset into the power system. With the aid of the smart grid paradigm, a day-ahead charging operation of large-scale penetration of EVs in different regions that include different aggregators and various EV parking lots (EVPLs) is propounded in this study. Moreover, the uncertainty of the related EV owners, such as the initial state-of-energy and the arrival time to the related EVPL, is taken into account. The stochasticity of PV generation is also investigated by using a scenario-based approach related to daily solar irradiation data. Last but not least, the operational flexibility is also taken into consideration by implementing peak load limitation (PLL) based DR strategies from the DSO point of view. To reveal the effectiveness of the devised scheduling model, it is performed under various case studies that have different levels of PLL, and for the cases with and without PV generation.