Dean A. Jones

Robust optimization for fleet planning under uncertainty

We create a formulation and a solution procedure for fleet sizing under uncertainty in future demands and operating conditions. The formulation focuses on robust optimization, using a partial moment measure of risk. This risk measure is incorporated into the expected recourse function of a two-stage stochastic programming formulation, and stochastic decomposition is used as a solution procedure. A numerical example illustrates the importance of including uncertainty in the fleet sizing problem formulation, and the nature of the fundamental tradeoff between acquiring more vehicles and accepting the risk of potentially high costs if insufficient resources are available.

Investment Planning for Electric Power Systems Under Terrorist Threat

Access to electric power is critical to societal welfare. In this paper, we analyze the interaction between a defender and a terrorist who threatens the operation of an electric power system. The defender wants to find a strategic defense to minimize the consequences of an attack. Both parties have limited budgets and behave in their own self-interest. The problem is formulated as a multi-level mixed-integer programming problem. A Tabu Search with an embedded greedy algorithm for the attack problem is implemented to find the optimum defense strategy. We apply the algorithm to a 24-bus network for a combination of four different defense budgets, three attack budgets, and three assumptions as to how the terrorists craft their attacks.

Logistics planning under uncertainty for disposition of radioactive wastes

The US Department of Energy (DOE) faces an enormous environmental remediation challenge involving highly radioactive wastes at former weapons production facilities. The purpose of this analysis is to focus on equipment acquisition and fleet sizing issues related to transportation of wastes from remediation sites to disposal sites. Planning for the transportation of these wastes must be done with recognition of important uncertainties related to overall quantities of waste to be moved, the rate at which the wastes will be prepared for transport, and the certification of suitable transportation containers for use in the effort. However, deadlines for completion of the effort have already been set by the political process, without much regard for these uncertainties. To address this fleet sizing problem, we have created a robust optimization model that focuses on equipment investment decisions. Through this robust optimization, we illustrate how modeling can be used to explore the effects of uncertainty on the equipment acquisition strategy. The disposition of radioactive wastes from DOE sites is an important illustration of a category of problems where equipment investments must be made under conditions of considerable uncertainty. The methodology illustrated in this paper can be applied to this general class of problems.

Conceptual Framework for Developing Resilience Metrics for the Electricity, Oil, and Gas Sectors in the United States

This report has been written for the Department of Energy’s Energy Policy and Systems Analysis Office to inform their writing of the Quadrennial Energy Review in the area of energy resilience. The topics of measuring and increasing energy resilience are addressed, including definitions, means of measuring, and analytic methodologies that can be used to make decisions for policy, infrastructure planning, and operations. A risk-based framework is presented which provides a standard definition of a resilience metric. Additionally, a process is identified which explains how the metrics can be applied. Research and development is articulated that will further accelerate the resilience of energy infrastructures. Conceptual Framework for Developing Resilience Metrics for US Electricity, Oil, and Gas Sectors September, 2014 4 SAND2014-18019 ACKNOWLEDGMENTS The authors of this paper wish to acknowledge the many experts that provided invaluable effort and information for this document. Dan Ton from the Department of Energy Office of Electricity Delivery and Energy Reliability and Rima Oueid and Kate Marks, from the Department of Energy Office of Energy Policy and Systems Analysis. Thanks is given for their tremendous leadership in formalizing the development of resilience concepts and bringing ideas to fruition. Acknowledgment is also given to Henry Willis from the Rand Corporation, who provided instrumental feedback and guidance. From the Sandia Corporation, thanks to Eric Vugrin for providing foundational help in establishing this document. Thanks to Lori Parrott and Steve Conrad for both having leveraged significant accomplishments via their long-standing contributions in NISAC. Further appreciation is given to Abe Ellis for his work in electric power resilience activities and Jason Stamp for providing leadership through the development of the Energy Surety Microgrid and design methodologies. And acknowledgement is also given to Bob Hwang for his continuous efforts and guidance. We appreciate all of your efforts and look forward to collaborating in the future. Conceptual Framework for Developing Resilience Metrics for US Electricity, Oil, and Gas Sectors SAND2014-18019 5 September, 2014 CONTENTS Executive Summary ...................................................................................................................... 11 Conclusions and Recommendations ...................................................................................... 15 1. Introduction .............................................................................................................................. 17 2. What is Resilience? .................................................................................................................. 19 2.1 Literature Review .......................................................................................................... 19 2.2 Defining Resilience ....................................................................................................... 19 3. Resilience Analysis Process ..................................................................................................... 23 3.1 Define Resilience Goals ................................................................................................ 24 3.2 Define System and Resilience Metrics ......................................................................... 24 3.3 Characterize Threats ..................................................................................................... 24 3.4 Determine Level of Disruption ..................................................................................... 24 3.5 Define and Apply System Models ................................................................................ 25 3.6 Calculate Consequence ................................................................................................. 25 3.7 Evaluate Resilience Improvements ............................................................................... 25 4. Resilience Metrics .................................................................................................................... 27 4.1 Metrics: Measures of Resilience ................................................................................... 27 4.1.1 The Metric Is in Terms of Threat ..................................................................... 27 4.1.2 The Metric Is Based on Performance ............................................................... 27 4.1.3 The Metric Measures Consequence ................................................................. 28 4.1.4 The Metric Accounts for Uncertainty .............................................................. 28 4.1.5 The Metric Effectively Captures Resilience .................................................... 28 4.1.6 The Metric Is Not a Value Judgment ............................................................... 29 4.1.7 Multiple Metrics Are Often Necessary ............................................................ 29 4.1.8 System-Level Models in Resilience Metric Computation ............................... 29 4.2 Resilience Analysis Use Cases ..................................................................................... 30 5. A Framework for Developing Resilience Metrics ................................................................... 33 6. Populating Metrics ................................................................................................................... 35 7. Simplified, Anecdotal Use Case .............................................................................................. 37 7.1 Define Resilience Goals ................................................................................................ 37 7.2 Define System and Resilience Metrics ......................................................................... 37 7.3 Characterize Threats and Determine Level of Disruption ............................................ 38 7.4 Define and Apply System Models ................................................................................ 38 7.5 Calculate Consequence ................................................................................................. 39 7.6 Evaluate Resilience Improvements ............................................................................... 39 7.7 Incorporating the Resilience Improvement Process ...................................................... 40 8. Advanced Use Case Summaries .............................................................................................. 41 8.1 Electricity ...................................................................................................................... 41 8.2 Petroleum ...................................................................................................................... 41 8.3 Natural Gas ................................................................................................................... 42 9. What can be simplified today .................................................................................................. 43 9.1 How we can prepare for a more resilient framework .................................................... 43 Conceptual Framework for Developing Resilience Metrics for US Electricity, Oil, and Gas Sectors September, 2014 6 SAND2014-18019 10. Research & Development ...................................................................................................... 45 10.1 Furthering Resilience ................................................................................................... 45 10.1.1 Characterize Threats ....................................................................................... 45 10.1.2 Determine Level of Disruption ....................................................................... 45 10.1.3 Define and Apply System Models .................................................................. 46 10.1.4 Calculate Consequence ................................................................................... 46 10.1.5 Evaluate Resilience Improvements ................................................................. 46 11. Moving Forward .................................................................................................................... 47 11.1 Identifying Specific Metrics that Could Be Generally Applied Across Many Different Systems ......................................................................................................................... 47 11.2 Stakeholder and Buy-In Process .................................................................................. 47 11.3 Development of Sector-Specific System Models ......................................................... 49 11.4 Consequence Quantification ........................................................................................ 49 11.5 Conclusions and Recommendations ............................................................................. 50 Appendix A: Reliability and Other Complementary Metrics ...................................................... 53 A.1 Resource Adequacy ...................................................................................................... 54 A.1.1 Loss of Load Probability (LOLP) .................................................................... 54 A.1.2 Loss of Load Expectation (LOLE) .................................................................. 55 A.1.3 Expected Unserved Energy (EUE) or Loss of Energy Expectation (LOEE) .. 55 A.1.4 Effective Load Carrying Capability (ELCC) .................................................. 55 A.2 Transmission Reliability Indices and Measures ..............................................

Transmission and Generation Expansion to Mitigate Seismic Risk

This paper develops a two-stage stochastic program and solution procedure to optimize the selection of capacity enhancement strategies to increase the resilience of electric power systems to earthquakes. The model explicitly considers the range of earthquake events that are possible and, for each, an approximation of the distribution of damage to be experienced. This is important because electric power systems are spatially distributed; hence their performance is driven by the distribution of damage to the components. We test this solution procedure against the nonlinear integer solver in LINGO 13 and apply the formulation and solution strategy to the Eastern Interconnect where the seismic hazard primarily stems from the New Madrid Seismic Zone. We show the feasibility of optimized capacity expansion to improve the resilience of large-scale power systems with respect to large earthquakes.

Physical Security and Vulnerability Modeling for Infrastructure Facilities

A model of malicious intrusions in infrastructure facilities is developed, using a network representation of the system structure together with Markov models of intruder progress and strategy. This structure provides an explicit mechanism to estimate the probability of successful breaches of physical security, and to evaluate potential improvements. An example of an intruder attempting to place an explosive device on an airplane at an airport gate illustrates the structure and potential application of the model.

Approximate Solution Procedure for Dynamic Traffic Assignment

This paper proposes an approximate dynamic traffic assignment algorithm for the analysis of traffic conditions in large-scale road networks over several days. The time-dependent origin-destination trips are assumed to be known. A case study for evacuation of the New Orleans metropolitan area prior to the landfall of Hurricane Katrina is presented to test the efficiency and effectiveness of the proposed procedure. The model results are compared to the traffic counts collected during the evacuation and then further tested by the mesoscopic simulation-based model, DynusT. The study shows that the traffic pattern produced by the proposed procedure is a good approximation to traffic count data and that the algorithm provides a good approximation to the computations performed by DynusT.

Routing of Hazardous Material Shipments Under the Threat of Terrorist Attack

Approximately 800,000 shipments of hazardous materials (hazmat) move daily through the U.S. transportation system [41] and approximately one truck in five on U.S. highways is carrying some form of hazardous material [40]. The modeling tools that have been developed over the last 30 years for the identification of routes and schedules for hazmat shipments emphasize the tradeoffs between cost minimization to the shipper and carrier and controlling the “natural” consequences that would stem from an accident. As the terrorist threat has grown, it has become clear that a new perspective, which allows for the representation of the goals and activities of terrorists, must be incorporated into these routing and scheduling models. This paper develops a non–cooperative two–person non–zero sum game to represent the interaction of the shipper/carrier and the terrorist for the movement of hazardous materials. It also develops an effective solution procedure for this game. Finally, it illustrates the methodology on a realistic case study.

Seismic Retrofit for Electric Power Systems

This paper develops a two-stage stochastic program and solution procedure to optimize the selection of seismic retrofit strategies to increase the resilience of electric power systems against earthquake hazards. The model explicitly considers the range of earthquake events that are possible and, for each, an approximation of the distribution of damage experienced. This is important because electric power systems are spatially distributed and so their performance is driven by the distribution of component damage. We test this solution procedure against the nonlinear integer solver in LINGO 13 and apply the formulation and solution strategy to the Eastern Interconnection, where seismic hazard stems from the New Madrid seismic zone.

Optimization-Based Probabilistic Consequence Scenario Construction for Lifeline Systems

The construction of a suite of consequence scenarios that is consistent with the joint distribution of damage to a lifeline system is critical to properly estimating regional loss after an earthquake. This paper describes an optimization method that identifies a suite of consequence scenarios that can be used in regional loss estimation for lifeline systems when computational demands are of concern, and it is important to capture the spatial correlation associated with individual events. This method is applied to a realistic case study focused on the highway network in Memphis, Tennessee, within the New Madrid Seismic Zone. This case study illustrates that significantly fewer consequence scenarios are needed with this method than would be required using Monte Carlo simulation.