## 1 Introduction  
Electric vehicles are the result of recent developments in modern transportation due to the growing concerns over carbon and greenhouse effects and reduce carbon emissions [1, 2]. EVs became an essential approach to solve environmental problems because they have zero emissions and low noise [3]. The increase in the number of EVs is welcomed by green energy supporters [4]. However, uncoordinated EV charging results in undesirable impacts on the operation and performance of electrical systems [5, 6, 7]. In consequence, the EVs charging process is managed to reduce congestion or to balance the load and achieve peak load shaving [8]. Various studies have been reported to explore the effects of EVs charging on electrical power systems [9, 10, 11, 12, 13, 14, 15, 16, 17]. As an example, EV charging could lead to voltage variation, increase the load, and increase power losses of electrical grids [18]. Moreover, EV charging could affect the generation scheduling of the thermal generation units as well as the wind power plants [19]. The random nature of the EV state plays the main role in developing the EV model. The EV charging profile is determined in terms of several factors [11]: (1) the number of EVs, (2) the battery type, (3) the initial state of charge (SOC) at the beginning of the charging process, (3) the start time of EV charging process, and (4) type and location of chargers [20]. The initial SOC of EVs' batteries always subject to an element of randomness, but the general pattern is influenced by the battery usage. The charge rate of EV batteries during the charging process should also follow the general charging characteristics determined by the battery type and the charging mode [21]. The normal and quick EV charging on regular weekdays and off-peak days in both summer and winter have been studied in [22]. Several statistical models have been proposed based on the random SOC that depended on the vehicle traveled distance. A statistical model was presented based on the National Travel Survey data [23]. The EV's battery capacity, SOC, and energy consumption are used to model the EVs charging to assess their impact on the residential loads [24]. The probabilistic using Monte Carlo simulation of EVs has been developed with considering two EVs random variables: the time for vehicle arrival and energy demand [25]. The uncertainties characteristic of the EV is fully exploited whereas the transportation data have been used to extract the probability density function (pdf) [26]. The coordination of EV charging is very important to avoid many severe effects on power grids. Many control schemes have been proposed to overcome the negative impacts of EV charging. A control strategy using data-driven models has been implemented to relax power system components and prevent excessive loading due to EV charging demand [27; 28; 29]. Demand side management (DSM) works to guarantee EVs' demand satisfaction in all grid situations and certifies grid stability [30; 31; 32; 33; 34]. At a low voltage transformer, DSM is used to shave the daily load while satisfying the EV charging process [35]. Real-time energy management is developed to reduce the EVs charging cost, and eliminate the charging impact with the existence of a photovoltaic (PV) system [36]. A control strategy is also developed for dynamic peak shaving at various scenarios considering the EV owner preferences [17]. A smart charging strategy with a two-stage optimization technique is applied to minimize the total energy loss at different penetration levels of EVs whereas the reactive power compensation from vehicle to grid (V2G) mode is utilized to reduce the energy losses [37]. A bi-directional charging power control of aggregated EV is analyzed in time series to assess generation modes [38]. A mathematical model-based M/M/s queue is presented using the fluid dynamic model to forecast the charging demand [39]. The model of EVs is used in the probabilistic load flow and the queueing theory to obtain the charging load of multiple EVs [40].