## 2 Related Work  
There have been many studies on the V2G concept since its introduction [5]. Most of them focus primarily on the technical aspects of this concept. A study in [11] defined a controller that for generation-consumption balance in a system utilizes a fleet of EVs. The application of the V2G concept in this study is very simplified since there are only three discrete possible charging rates: charging or discharging at a constant rate and idle. Authors in [12] focus on frequency regulation in more detail. They presented an algorithm for primary and secondary frequency control using one or a group of five EVs and verified simulation results with the experiment. The results demonstrated the effectiveness of V2G-based frequency control. Unlike previous studies, the authors in [13] also incorporate the uncertainty of EV availabilities.  
A few studies also utilize the V2G concept in voltage regulation. A study in [17] presented a charging and discharging coordination strategy considering transformer loading and bus voltage profiles. The application of the proposed system on the test network showed a reduction in voltage fluctuations.  
In addition to decreasing the impact of EV charging on the electric grid, many studies deal with power supply from RES for charging stations in order to reduce the EVs' charging carbon footprint. Authors in [20] formulated a stochastic optimization problem for EV charging supplied from the time-varying renewable energy source. The study considers EVs' charging requests as well as the intermittent character of the source. Researchersin [21] also incorporated a discharge strategy to support mismatching between load and renewable energy generation.  
Previous studies dealt with the technical aspect of the V2G concept. In a few studies, the electric grid or charging station costs are also considered along with technical limits. A study in [31] defined optimal charging of electric vehicles by considering the microgrid's cost for purchasing energy from the external grid. Researchers in [32] presented a scheduling scheme for EV charging that minimizes electricity cost at the utility company while maximizing the payoff of charging stations within the grid.  
However, for this concept to be successful, it needs to be accepted by EV drivers [10]. Factors influencing acceptance of this concept by EV drivers in the Netherland were presented in [8]. The study [8] showed some reservations and caution regarding this concept caused mainly by range anxiety, battery degradation, or discomfort experienced by participation in such service. So lately, there have been an increasing number of studies that consider not just the technical limits but the cost minimization of EV drivers as well. Authors in [25] focus on charging coordination that deals with the tradeoff between total generation cost and accumulated battery degradation cost. Researchers in [33] studied the electric vehicle-based system, where vehicle control charging led to higher revenues for their owner. Similarly, a study in [34] presents a mechanism that computes optimal charging schedules that maximize the social welfare of all users with their given preferences. However, both studies consider automatic enrollment of all participants.  
Therefore, the authors in [30] proposed an incentive mechanism that ensures that participation, as well as truth-telling, is an optimal strategy for each EV driver. However, the charging control policy is defined for a specific charging horizon, so the participants cannot vary at the charging terminal or change their preferences during this time.  
To the best of our knowledge, no previous works have defined an online V2G algorithm that takes into account technical limits as well as cost functions of EV drivers and charging station operators with an incentive mechanism ensuring social welfare maximization. Further, in contrast to the work presented so far, in this paper, we represent a cost function of the EV drivers based on empirical data.