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Nowadays, the increasing penetration of renewable energies often leads to system frequency variation due to the intermittent outputs, which limits the utilization of renewable electricity and brings higher requirements to frequency regulation. Aggregated electric vehicles (EVs) are suggested to be used as good regulation resources because of the vehicle-to-grid (V2G) capability and quick response characteristic. However, the participation of EVs inevitably leads to cyber delays due to their underlying communication infrastructure and scheduling, which may cause instability. To guarantee the system stability, this paper investigates the stability of a grid frequency regulation system with electric vehicle (EV) aggregators embedded by cyber delays in the cyber system. A comprehensive stability assessment method is proposed in this paper based on the discrete spectrum iteration. A stability assessment method flow is designed with only five stages: 1) system initialization and modeling; 2) spectrum transformation; 3) Chebyshev discretization; 4) Krylov subspace projection dimension reduction; 5) Newton correction. Comprehensive case studies are performed on the cyber regulation systems with single, double, and three EV aggregators to extract the stability region and to validate the proposed approach. It is revealed that the controller gain, the ratio between the participation ratios of each aggregator, and that between EV and grid are important factors for determining the stability of the regulation system at a given controller gain. Besides, the criterion of the stability region changing with the three factors is proposed. It is found that the mass utilization of electric vehicles in the frequency control disrupts system stability due to the aggregation delay and thus the stability region can be divided into several intervals and presents periodicity. It is expected that the proposed criteria can help to guide the determination of delay requirements for EV aggregators participating in frequency regulation service.

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Discrete Spectrum Iteration Based Comprehensive Stability Assessment Method for the Delayed Cyber-Physical System With Electric-Vehicle Frequency Regulation