Electric vehicles (EVs) in Vehicle-to-Grid (V2G) systems act as distributed energy resources that support grid stability. Centralized coordination such as the extended State Space Model (eSSM) enhances scalability and estimation efficiency but may introduce new cyber-attack surfaces. This paper presents a stealthy False Data Injection Attack (FDIA) targeting eSSM-based V2G coordination. Unlike prior studies that assume attackers can disrupt physical charging or discharging processes, we consider an adversary who compromises only a subset of EVs, and limiting their influence to the manipulation of reported State of Charge (SoC) and power measurements. By doing so, the attacker can deceive the operator's perception of fleet flexibility while remaining consistent with model-based expectations, thus evading anomaly detection. Numerical simulations show that the proposed stealthy FDIA can deteriorate grid frequency stability even without direct access to control infrastructure. These findings highlight the need for enhanced detection and mitigation mechanisms tailored to aggregated V2G frameworks

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