Cyber-physical modelling operator and multimodal vibration in the integrated local vehicle-grid electrical system

The interaction of the individual user and the electrical are deeply strengthened with wireless communication and internet of things development. In the region of urban, the growing penetration of electric vehicles and the corresponding fast charging techniques not only emerge an effective interface for the virtual power plant, but also emerge the vulnerable points for the cyber attack. Facing the complexity of the physical vehicle-grid system and the uncertainty of the communication network, the unified modelling with a cyber-physical operator is established in this work. By the implicit Runge-Kutta method, the cyber-physical dynamics of the vehicle-grid electrical system is narrowed in the finite-dimensional space, which mimics the latency and denial-of-service attacks with a discretized matrix. After that, the techniques of space transformation and the subspace mapping are introduced to further approximate the hybrid system by a reduced cyber-physical operator. The resulting operator simultaneously preserves the system structure and reduces the dimensions, which provides the opportunity for the extraction of dynamic indexes and the participation factor. The proposed cyber-physical operator has experimentally verified in the case studies as well as the disclosure of the multimodal vibration. It is found that the interface of open cyber network and the lower-inertia batteries inside the electric vehicles might become the potential attacking points for the integrated local energy system. By the malicious cyber attacks, the stability feature of the cyber-physical system could be reshaped to a multimodal shape, which injects inharmonious energy from the cyber network into the physical system.