Electric vehicles (EVs) are expected to become widespread in future years. Thus, it is foreseen that EVs will become the new high-electricity-consuming appliances in the households. The characteristics of the extra power load that they impose on the distribution grid follow the patterns of people's random usage behaviors. In this paper, we seek to provide answers to the following question: assigning real-world randomness to the EVs' availability in the households and their charging requirements, how can EVs' demand response (DR) help to minimize the peak power demand and, in general, shape the aggregated demand profile of the system? We present a general demandshaping problem applicable for limit order bids to a day-ahead (DA) energy market. We propose an algorithm for distributed DR of the EVs to shape the daily demand profile or to minimize the peak demand. Additionally, we put these problems in a game framework. Extensive simulations show that, for certain practical distributions of EVs' usage, it is possible to accommodate EVs for all the users in the system and yet achieve the same peak demand as when there is no EV in the system without any changes in the users' commuting behaviors.Index Terms-Day-ahead (DA) market, demand response (DR), electric vehicle (EV), flexible load, limit order bids, random usage patterns, residential load, smart grids, vehicle-to-grid (V2G).

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Electric vehicles (EVs) add significant load on the power grid as they become widespread. The characteristics of this extra load follow the patterns of people's driving behaviours. In particular, random parameters such as arrival time and charging time of the vehicles determine their expected charging demand profile from the power grid. In this paper, we first develop a model for uncoordinated charging power demand of an EV based on a stochastic process in order to characterize its expected daily power demand profile. Next, we illustrate it for different charging time distributions through simulations. This gives us useful insights into the long-term planning for upgrading the power systems' infrastructure to accommodate EVs. Then, we incorporate departure time as another random variable into this modelling and introduce an autonomous demand response (DR) technique to manage the EVs' charging demand. Our results show that, it is possible to accommodate a large number of EVs and achieve the same peak-to-average ratio (PAR) in daily aggregated power consumption of the grid as when there is no EV in the system without any change in the users' commuting behaviours. We also show that this peak value can be further decreased significantly when we add vehicle-to-grid (V2G) capability in the system.Index Terms-Demand response, electric vehicle, load model, residential load.

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