A Mathematical Framework for Digital Twins of Cyber-Physical Energy Systems

This paper introduces a mathematical framework for designing digital twins (DTs) for cyber-physical energy systems (CPESs). Hereby we move beyond ad-hoc methods by employing physics-informed dynamic models and state-space representations. The framework encompasses key DT functionalities: state and parameter estimation, forecasting, prognosis, control, and system design, all underpinned by mathematical formulations. The practical applicability of this framework is demonstrated through a case study of an industrial power grid within a business park in the Netherlands, thereby focusing on a battery energy storage system (BESS). The case study illustrates how the DT architecture facilitates error detection, system design considerations, and supervisory control strategies by analyzing real-world operational data and estimating crucial BESS parameters like charging/discharging efficiencies and self-discharge rates. The dynamic and iterative nature of the proposed DT architecture, continuously updated with new data, ensures a close replication of the physical twin (PT).