Publications

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Network segmentation of a power grid's communication system can make the grid more resilient to cyberattacks. We develop a novel trilevel programming model to optimally segment a grid communication system, taking into account the actions of an information technology (IT) administrator, attacker, and grid operator. The IT administrator is allowed to segment existing networks, and the attacker is given a budget to inflict damage on the grid by attacking the segmented communication system. Finally, the grid operator can redispatch the grid after the attack to minimize damage. The resulting problem is a trilevel interdiction problem that we solve using a branch and bound algorithm for bilevel problems. We demonstrate the benefits of optimal network segmentation through case studies on the 9-bus Western System Coordinating Council (WSCC) system and the 30-bus IEEE system. These examples illustrate that network segmentation can significantly reduce the threat posed by a cyberattacker.

Efficient restoration of the electric grid from significant disruptions – both natural and manmade – that lead to the grid entering a failed state is essential to maintaining resilience under a wide range of threats. Restoration follows a set of black start plans, allowing operators to select among these plans to meet the constraints imposed on the system by the disruption. Restoration objectives aim to restore power to a maximum number of customers in the shortest time. Current state-of-the-art for restoration modeling breaks the problem into multiple parts, assuming a known network state and full observability and control by grid operators. These assumptions are not guaranteed under some threats. This paper focuses on a novel integration of modeling and analysis capabilities to aid operators during restoration activities. A power flow-informed restoration framework, comprised of a restoration mixed-integer program informed by power flow models to identify restoration alternatives, interacts with a dynamic representation of the grid through a cognitive model of operator decision-making, to identify and prove an optimal restoration path. Application of this integrated approach is illustrated on exemplar systems. Validation of the restoration is performed for one of these exemplars using commercial solvers, and comparison is made between the steps and time involved in the commercial solver, and that required by the restoration optimization in and of itself, and by the operator model in acting on the restoration optimization output. Publications and proposals developed under this work, along with a path forward for additional expansion of the work, and summary of what was achieved, are also documented.

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.

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The goal of this work is to identify critical nodes in a bulk electric system for grid resilience to a specified threat. We present a cascading outage framework and an analytical framework for identifying electric grid failure trends and critical components. We create thousands of threat scenarios to be modeled in a dynamic electric grid cascading outage model. Each threat scenario determines which major grid components are removed from service due to the threat. The cascading outage model runs transient dynamic simulations which allow for secondary transients to affect the relays/protection leading to cascading outages. The results of the cascading model feed an analytics model to identify trends and critical components whose failure is more likely to cause serious systemic effects. Information on which system components are most critical to electric grid resilience can significantly assist grid planning and reduce grid consequences of large-scale disasters.

In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model.

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This report summarizes the activities performed as part of the Science and Engineering of Cybersecurity by Uncertainty quantification and Rigorous Experimentation (SECURE) Grand Challenge LDRD project. We provide an overview of the research done in this project, including work on cyber emulation, uncertainty quantification, and optimization. We present examples of integrated analyses performed on two case studies: a network scanning/detection study and a malware command and control study. We highlight the importance of experimental workflows and list references of papers and presentations developed under this project. We outline lessons learned and suggestions for future work.

In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model.

We present scalable stochastic optimization approaches for improving power systems' resilience to extreme weather events. We consider both proactive redispatch and transmission line hardening as alternatives for mitigating expected load shed due to extreme weather, resulting in large-scale stochastic linear programs (LPs) and mixed-integer linear programs (MILPs). We solve these stochastic optimization problems with progressive hedging (PH), a parallel, scenario-based decomposition algorithm. Our computational experiments indicate that our proposed method for enhancing power system resilience can provide high-quality solutions efficiently. With up to 128 scenarios on a 2,000-bus network, the operations (redispatch) and investment (hardening) resilience problems can be solved in approximately 6 min and 2 h of wall-clock time, respectively. Additionally, we solve the investment problems with up to 512 scenarios, demonstrating that the approach scales very well with the number of scenarios. Moreover, the method produces high quality solutions that result in statistically significant reductions in expected load shed. Our proposed approach can be augmented to incorporate a variety of other operational and investment resilience strategies, or a combination of such strategies.

Severe, wide-area power system emergencies are rare but highly impactful. Such emergencies are likely to move the system well outside normal operating conditions. Appropriate remedial operation plans are unlikely to exist, and visibility into system stability is limited. Inspired by the literature on Transient Stability Constrained Optimal Power Flow and Emergency Control, we propose a stability-incentivized dynamic control optimization formulation. The formulation is designed to safely bring the system to an operating state with better operational and stability margins, reduced transmission line overlimits, and better power quality. Our use case demonstrates proof of concept that coordinated wide-area control has the potential to significantly improve power system state following a severe emergency.

When faced with uncertainty regarding potential failure contingencies, prioritizing system resilience through optimal control of exciter reference voltage and mechanical torque can be arduous due to the scope of potential failure contingencies. Optimal control schemes can be generated through a two-stage stochastic optimization model by anticipating a set of contingencies with associated probabilities of occurrence, followed by the optimal recourse action once the contingency has been realized. The first stage, common across all contingency scenarios, co-optimally positions the grid for the set of possible contingencies. The second stage dynamically assesses the impact of each contingency and allows for emergency control response. By unifying the optimal control scheme prior and post the failure contingency, a singular policy can be constructed to maximize system resilience.

This paper presents a novel dynamic programming (DP) technique for the determination of optimal investment decisions to improve power distribution system reliability metrics. This model is designed to select the optimal small-scale investments to protect an electrical distribution system from disruptions. The objective is to minimize distribution system reliability metrics: System Average Interruption Duration Index (SAIDI) and System Average Interruption Frequency Index (SAIFI). The primary input to this optimization model is years of recent utility historical outage data. The DP optimization technique is compared and validated against an equivalent mixed integer linear program (MILP). Through testing on synthetic and real datasets, both approaches are verified to yield equally optimal solutions. Efficiency profiles of each approach indicate that the DP algorithm is more efficient when considering wide budget ranges or a larger outage history, while the MILP model more efficiently handles larger distribution systems. The model is tested with utility data from a distribution system operator in the U.S. Results demonstrate a significant improvement in SAIDI and SAIFI metrics with the optimal small-scale investments.

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This paper presents a multi-Time period two-stage stochastic mixed-integer linear optimization model which determines the optimal hardening investments to improve power system resilience to natural disaster threat scenarios. The input to the optimization model is a set of scenarios for specific natural disaster events, that is based on historical data. The objective of the optimization model is to minimize the expected weighted load shed from the initial impact and the restoration process over all scenarios. The optimization model considers the initial impact of the severe event by using electromechanical transient dynamic simulations. The initial impact weighted load shed is determined by the transient simulation, which allows for secondary transients from protection devices and cascading failures. The rest of the event, after the initial shock, is modeled in the optimization with a multi-Time period dc optimal power flow (DCOPF) which is initialized with the solution from the dynamic simulation. The first stage of the optimization model determines the optimal investments. The second stage, given the investments, determines the optimal unit commitment, generator dispatch, and transmission line switching during the multi-Time period restoration process to minimize the weighted load shed over all scenarios. Note, an investment will change the transient simulation result, and therefore change the initialization to the DCOPF restoration model. The investment optimization model encompasses both the initial impact (dynamic transient simulation results) and the restoration period (DCOPF) of the event, as components come back online. The model is tested on the IEEE RTS-96 system.

This simple Microgrid Design Toolkit (MDT) use case will provide you an example of performing microgrid sizing by identifying the types and quantities of technology to be purchased for use in a microgrid. It will introduce basic principles of using the MDT microgrid sizing capability by comparing the results of two microgrids in two different markets. Please reference the MDT User Guide (SAND2020-4550) for detailed instructions on how to use the tool.

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In this paper we report preliminary results from the novel coupling of cyber-physical emulation and interdiction optimization to better understand the impact of a CrashOverride malware attack on a notional electric system. We conduct cyber experiments where CrashOverride issues commands to remote terminal units (RTUs) that are controlling substations within a power control area. We identify worst-case loss of load outcomes with cyber interdiction optimization; the proposed approach is a bilevel formulation that incorporates RTU mappings to controllable loads, transmission lines, and generators in the upper-level (attacker model), and a DC optimal power flow (DCOPF) in the lower-level (defender model). Overall, our preliminary results indicate that the interdiction optimization can guide the design of experiments instead of performing a 'full factorial' approach. Likewise, for systems where there are important dependencies between SCADA/ICS controls and power grid operations, the cyber-physical emulations should drive improved parameterization and surrogate models that are applied in scalable optimization techniques.