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With the wide deployment of charging piles and the development of vehicle-to-grid technology, electric vehicles (EVs) will have more opportunities to participate in the operation and scheduling of electric power system through the EV aggregator (EVA), an intermediate agent between the power grid and EV users. Quantitatively evaluating the response capability (RC) of EVA, i.e., charging and discharging power ranges, is of fundamental importance for its trading with the operator of power grid. This article proposes a user-aware method to obtain a more accurate range of multitimescale RC considering the response willingness of EV users. First, a temporal RC evaluation model of a single EV considering charge-discharge state and state of charge (SOC) is established. Second, based on the user psychology model, which reflects the relationship between users' responsivity and incentive price, a multitimescale RC evaluation model of EVA considering users' willingness is built. The day-ahead RC of EVA is evaluated by the state prediction data of EVs. According to the control strategy which considers response time and SOC indicators comprehensively, the RC evaluation is updated intraday. Finally, using the statistical data from the EU MERGE project, the effectiveness of the proposed evaluation model is verified, and the impact of incentive price and scheduling time scale on the RC of EVA are analyzed. The results indicate that the proposed model can effectively track the scheduling goals of the system and realize the dynamic update of the RC of EVA. [ABSTRACT FROM AUTHOR]