Research on digital twins (DTs) in the power system field has mainly focused on implementing DTs for specific resources, while few studies on electric vehicle (EV)-based DT implementation have considered integration and interoperability between systems. This study introduces a DT-based EV system operation framework to address the aforementioned research gap. The framework implements individual EVs, charging stations, and charging station operators (CPOs) as DTs, enabling integrated operation with the power grid. The DT-based EV agent supports independent decision-making on power service participation by considering location information, distance, charging amount, spare time, and incentives. In addition, the CPO can establish an optimal incentive strategy to induce EV users to participate in grid power services. The proposed DT systems map information between EVs, charging stations, and the grid, enabling analysis and verification of the impact of participants on charging station operation, grid stability, and economic efficiency in an independent environment. The effectiveness and usability of the proposed framework were verified through a case study on an incentive-based demand response program.