# Operator-Theoretic Resilience Calculations (ORC)

*Develop generalizable, calculable, data-driven resilience metrics, along with these calculation procedures, using the Koopman operator. *

###### PI: Sai Pushpak Nandanoori,saipushpak.n@pnnl.gov

This project is developing generalizable resilience metrics that can be calculated in real-time and thereby used for making operational decisions, not just for post-hoc analysis.

In FY 2021, the project connected changes in our ability to observe and control a system to resilience and showed how they could be mathematically formulated for evaluating resilience at different stages of a disruptive event. The derived metrics for resilience are: (1) changes in controllability under loss of actuators, (2) changes in observability under loss of sensors, and (3) resilience ratio, which combines the first two metrics. To enable metric calculation in real-time, the computation procedure utilized a structured, data-driven technique (operator-theoretic methods) to transform the nonlinear dynamical system into a linear representation and then employed existing linear theory and methods. The project also demonstrated the feasibility of the computational approach by applying the resilience metrics to a 123-bus islanded microgrid model. The results show the criticality (as defined by the metrics) of each of the generators and sensors (voltage, speed, and real power) at different locations in the system.

In FY 2022, the project will further validate the metrics with higher-fidelity data from the Thrust 1 testbed and will develop additional metrics to address other types of threats or effects. The project will also formalize the timescale separated Koopman operator formulation to capture CPS behavior at different timescales and coordinate with the other Thrust 2 projects to demonstrate the use of resilience metrics to inform resilient control decisions.

- Goal I: Employ proof-of-concept utilization of resilience metrics for system evaluation and control design.
- Goal II: Demonstrate metric effectiveness using data from the Thrust 1 123-node feeder microgrid testbed.