## 1 Introduction  
The rapid growth in urban mobility and the corresponding increase in energy use, greenhouse gas emissions, (GHG), air quality [1], and their externalities have driven more people to switch from their conventional cars to cleaner fleets, electric cars. The population of plug-in electric vehicles (PEVs) increased drastically over the past decade [2]. The PEVs are equipped with a large battery bank and the need for fast charging of these batteries and range anxiety issues impose an enormous load demand on the residential and distribution networks and this made many operation problems for the distribution system operator. Two approaches might be considered when the charging infrastructure is needed. First is developing a charging infrastructure and increasing the capacity of the network which requires further investment in grid peak capacity. The second approach is managing the demand by considering the driving behaviors and charging schedules for cars and predicting the load pattern that the PEVs force on a daily basis. In this approach, if the pricing and rate structure are correctly planned, the demand for additional peak capacity investment will be declined and the cost of PEVs charging will be reduced, in one hand. It also improves the stability of the grid, on the other hand. Grid-to-vehicle (G2V), and vehicle-to-grid (V2G) are the two solutions suggested to avoid the loss of the power grid by supplying the network demand in a peak load period. G2V is the common type of PEV charging procedure, where power goes from grid to vehicle, but V2G, which has various applications in the power system auxiliary services, transfers power from vehicle to grid. In G2V and V2G, the aggregator can control and operate a group of PEVs and these vehicles act like storage systems. There is a body of literature that proposed various managed PEV charging methods [3; 4; 5; 6; 7]. Prior studies in the area of PEVs and electric grid are based on the models, since the actual data of PEVs in a large scale are limited. However, the results of some of the studies are hampered because of much uncertainty surrounding the drivers' behaviors. For example, the current trend in the literature is to use a simplified PEV travel profile by mapping the travel behavior of conventional vehicles, which might introduce bias into the results. In addition, considering only a single PEV fleet in the simulation as a proof of concept or assuming that all vehicles have the same features are other shortcomings of prior studies [8; 9; 10; 11; 12]. The limitations of the distribution network are essential to be considered in the modeling framework, while they are neglected in some prior studies [13; 14; 15]. On-peak charging might cause serious problems such as voltage instability, reserve capacity, and voltage collapse, voltage insecurity, and power loss. In addition, while dynamic electricity price is critical in a smart charging system, the availability of accurate electricity price is an area of concern in a realistic optimization problem [16; 17; 18]. Dynamic pricing can encourage PEV owners to charge their vehicles at a lower rate. In this study, we compare the uncoordinated, smart G2V versus V2G charging mode for a set of PEV fleets in a sample distribution network to understand which charging mode has supremacy over the others. We integrated wind energy into the power grid to consider using renewable energy resources in the grid. To fill the existing gap in the literature, the uncertainties of load, wind speed, electricity price, and travel behavior are studied in the PEV-grid model. A detailed driving pattern including the arrival and departure time and travel distance of PEVs drivers are taken into account. The Monte Carlo simulation with scenario reduction task is also conducted to model the stochastic nature of PEVs' travel behavior. The probabilistic economic dispatch is also applied to optimize the charging/discharging problem.