The overarching goal of the proposed research is to derive critical information and characterization of large scale generic nonlinear dynamical systems using limited observables. In the present state-of-the-art in data-driven dynamical system analysis, all the underlying state measurements and the time evolution of these states are required. Access to all of the dynamical states measurements in real-world is impossible or expensive. The objective of the proposal is to develop data-driven tools for dynamic system identification, classification and root-cause analysis of dynamic events, and prediction of system evolution. The research team will specifically conduct research on using available measurements to perform near real-time applications for various dynamic events that occur in electric power systems. The data analytics proposed are applicable to general non-linear dynamic systems and can be easily applied to other cyberphysical systems (CPS). More broadly, there is a large effort in the CPS and control community to model real world systems that we all interact with on a daily basis (such as transportation systems, communication networks, world wide web, etc.) as dynamical systems and thus, the theory and techniques developed through this project will enable online monitoring of these critical systems, allowing operators to quickly analyze these systems for any unstable/anomalous behavior from minimal data streams. The project will promote various educational and outreach activities including developing new courses, short courses, activities in schools, and scholarships for women and underrepresented minority students. 

Overview: The goal of this proposal is to develop operator theoretic data analytics techniques for dynamic systems with limited measurements to identify the underlying non-linear dynamical system and characterize their behavior such as causal interactions between constituent components, stability monitoring, identifying targets for control. The proposed research is in the domain of "Technology for cyber-physical systems". The novelty of the proposed methods is that they do not require the dynamic states but can utilize system outputs, making it applicable to real-world dynamical systems. Power systems are rapidly evolving with increased deployment of sensors like the phasor measurement units (PMUs) that have high accuracy and high sampling frequencies (up to 120 Hz). These measurements will be used to develop an equivalent linear representation in a higher dimensional function space that can be used for online identification and characterization of nonlinear dynamics of the power grid. Further, machine learning techniques will be formulated to learn effective dictionary functions for the scalable deployment of proposed method. Using the proposed system identification method, the project will develop the theory and methodology for data-driven Information Transfer based causality mapping for detection and localization of system stress and dynamic coupling between the systems components. Specific applications for power grids will include stability monitoring, trajectory prediction and identification of targets for controlling adverse dynamic behavior. The methods are evaluated by an integrated power-cyber co-simulator (IPCC) that integrates power transmission, distribution and communication systems to generate synthetic sensor data for large systems under various dynamic scenarios. The IPCC will be able to model intermediate communication networks that cause measurement inconsistencies like delays, packet drop, etc. The Iowa State University's hardware in the loop cyber-physical testbed will be used to validate and evaluate some of the online applications like stability monitoring and trajectory prediction for large power grid topologies.