Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.
As system of systems (SoS) models become increasingly complex and interconnected a new approach is needed to capture the effects of humans within the SoS. Many real-life events have shown the detrimental outcomes of failing to account for humans in the loop. This research introduces a novel and cross-disciplinary methodology for modeling humans interacting with technologies to perform tasks within an SoS specifically within a layered physical security system use case. Metrics and formulations developed for this new way of looking at SoS termed sociotechnical SoS allow for the quantification of the interplay of effectiveness and efficiency seen in detection theory to measure the ability of a physical security system to detect and respond to threats. This methodology has been applied to a notional representation of a small military Forward Operating Base (FOB) as a proof-of-concept.
System-of-systems modeling has traditionally focused on physical systems rather than humans, but recent events have proved the necessity of considering the human in the loop. As technology becomes more complex and layered security continues to increase in importance, capturing humans and their interactions with technologies within the system-of-systems will be increasingly necessary. After an extensive job-task analysis, a novel type of system-ofsystems simulation model has been created to capture the human-technology interactions on an extra-small forward operating base to better understand performance, key security drivers, and the robustness of the base. In addition to the model, an innovative framework for using detection theory to calculate d’ for individual elements of the layered security system, and for the entire security system as a whole, is under development.