## 1 Introduction
### Related Works  
There are many papers in the field of optimal scheduling of energy systems by considering EVs uncertain behaviors. In [9], chi-square and normal distributions are used to obtain the arrival and detention time of 30 EVs in the MG, respectively. However, the type of all EVs is considered homogenous. A linear robust optimization framework is proposed in [10] to take into account the worst-case load quantities of EVs charging stations for minimizing the MG operating cost. Each EV in the aggregation has the same battery type. The problem of distributed generation of optimal placement in the presence of EVs is solved in [11], and the triangular fuzzy numbers are used to model the uncertainty of plug-in electric vehicles' (PEVs) charging demand and another type of EVs, such as PHEVs, is not considered. In [12], the optimal operation of a virtual power plant, including EVs, wind turbines, photovoltaic (PV) system and conventional power plants, is presented. Uncertainty in the behavior of EVs is modeled by predicting their aggregated output power and calculating its deviation with the normal distribution without mentioning details about EVs. In [13], a new formulation for charging stations by considering their charging/discharging scheduling is presented for optimal planning. The scenario approach in the initial state of charge (SoC) of PHEVs batteries is used to consider their uncertainty. In this study the type of EVs and also the battery capacity of EVs are unknown. In [14], the bidding problem for a plug-in electric vehicle (PEV) aggregator in the day-ahead (DA) electricity market is investigated. The fleet is modeled as a virtual battery, clustering the batteries of PEVs connected to the grid, and there is no discussion about their different capacities and types. In [15], forecasting and modeling of load demand due to a large number of EVs fast chargers is investigated using a fitted fractional autoregressive integrated moving average model. This model is a high-quality forecasting model and includes the battery capacity and market sharing of them. However, the type of EVs and the level 2 EVs are not considered. In [16], the target for demand side management in a distribution grid including batteries and EVs is minimization of nodal, operational and power loss costs. The uncertainties lie in arrival time, departure time and energy demand of EVs, and are modeled with stochastic programming. The kernel density function is applied to model the distribution of these stochastic variables. In [17], a bi-level optimization is proposed for a fast charging station in order to maximize the profit of the station and EVs, simultaneously. Indeed, the station's operator aggregates its EVs to participate in joint energy and reserve market, but the uncertain behaviors of EVs are not considered. In [18], the uncertainty of EVs arrival times is considered in a supply cost minimization problem by the Lyapunov optimization technique, and the battery capacities of them are unknown. In [19], the uncertainties in arrival times, dwell times, SoC, walking ranges of drivers and demand of EVs are handled by stochastic programming. Although this model includes various uncertain parameters of EVs, further parameters such as battery capacity and type of EVs can be considered. In [20], an EVs charging station is designed aiming at increasing the profitability of fast charging stations. The uncertainties of arrival time and the SoC are modeled using the Monte Carlo simulation (MCS) method. The scenario-based approach is used in [21] to consider the several types of uncertainties in the planning of charging stations including charging station type, EVs growth rate and traffic flow. A DA optimization model is proposed in [22] to determine the charging/discharging power of EVs, as well as the capacity of up and down regulation that the EV fleet can provide. The start time of EVs connection, the trip duration and the energy use are modeled by normal distributions.