Rachel A. Davidson

Estimating the spatial distribution of power outages during hurricanes in the Gulf coast region

Hurricanes have caused severe damage to the electric power system throughout the Gulf coast region of the US, and electric power is critical to post-hurricane disaster response as well as to long-term recovery for impacted areas. Managing power outage risk and preparing for post-storm recovery efforts requires accurate methods for estimating the number and location of power outages. This paper builds on past work on statistical power outage estimation models to develop, test, and demonstrate a statistical power outage risk estimation model for the Gulf Coast region of the US. Previous work used binary hurricane-indicator variables representing particular hurricanes in order to achieve a good fit to the past data. To use these models for predicting power outages during future hurricanes, one must implicitly assume that an approaching hurricane is similar to the average of the past hurricanes. The model developed in this paper replaces these indicator variables with physically measurable variables, enabling future predictions to be based on only well-understood characteristics of hurricanes. The models were developed using data about power outages during nine hurricanes in three states served by a large, investor-owned utility company in the Gulf Coast region.

Post-Earthquake Restoration Planning for Los Angeles Electric Power

This paper describes the application of a new discrete-event-simulation model of the post-earthquake electric power restoration process in Los Angeles. The findings are that (1) Los Angeles residents may experience power outages lasting up to 10 days; (2) what we call the power rapidity risk (the joint probability distribution of restoration of a specified number of customers in a specified amount of time) varies throughout the area; (3) there is a relatively high likelihood that more repair materials than are currently available will be required if a large earthquake occurs; and (4) there are ways to reduce the expected duration of earthquake-initiated power outages and they should be subjected to cost-benefit analysis. These results should be useful to utilities and emergency planners in Los Angeles. The new simulation modeling approach could be used in other seismically active cities to gain insights into the restoration process that other modeling approaches cannot provide.

Statistical models of the effects of tree trimming on power system outages

This paper develops statistical models for estimating the impacts of tree trimming on electric power system outages under normal (nonstorm) operating conditions. The models are based on an extensive data set from Duke Power, a company in the southeastern U.S., and the models used are a negative binomial generalized linear model and a Poisson generalized linear mixed model (GLMM). The results show that: 1) increasing tree trimming frequency does lead to a decrease in the number of outages on the electric power distribution system; 2) the effects of tree trimming on different circuits can be differentiated and measured; and 3) the Poisson GLMM provides a good fit to the data in this situation. In particular, the results of the model show that for the Duke Power system, one would have expected, on average, 0.9 fewer outages per circuit over the 43-month data recording period if the time between tree trimming cycles was decreased by 1 yr across the whole system. These models could be applied to other power systems, and the results should be useful for power managers in setting tree trimming frequencies and in focusing on the most frequent trimming efforts on those circuits for which trimming will have the greatest benefit.

Optimizing Regional Earthquake Mitigation Investment Strategies

Regional mitigation analysis is a systematic procedure to determine how much to spend on mitigation versus post-event reconstruction and to prioritize alternative mitigation strategies. It requires at least the following information: magnitude and character of the regional risk, costs and benefits associated with all possible mitigation alternatives, available budget, and specific regional objectives for risk management. Currently available loss estimation models provide increasingly comprehensive estimates of regional risk, but offer little guidance about how to use that information to make mitigation resource allocation decisions. This paper describes a linear program developed to support systematic regional earthquake mitigation analysis, and illustrates its application through a case study in Los Angeles County. Results suggest which buildings—by structural type, occupancy type, and census tract location—should be upgraded so as to minimize total mitigation and expected post-earthquake reconstruction costs.

Discrete event simulation of the post-earthquake restoration process for electric power systems

This paper describes a discrete event simulation model of the post-earthquake restoration process for electric power systems. The model explicitly represents the real-life restoration process, enabling development of geographically disaggregated, quantitative restoration curves with uncertainty bounds, a dynamic map showing the spatial distribution of outages changing over time, and information on how personnel and repair materials are used throughout the process. The new restoration modelling approach is applied to the Los Angeles Department of Water and Power electric power system. Simulation results for the 1994 Northridge earthquake indicate that the model is capable of accurately estimating the restoration time and spatial sequence of the recovery process. The model aims to help improve the quantitative restoration time estimates that are required to estimate economic losses due to business interruption caused by power outages, and identify and compare the effectiveness of different ways to improve the restoration process in future earthquakes.

Fire Following Earthquake—Reviewing the State-of-the-Art of Modeling

Models for estimating the effects of fire following earthquake (FFE) are reviewed, including comparisons of available ignition and spread/suppression models. While researchers have been modeling FFEs for more than 50 years, there has been a notable burst of research since 2000. In particular, borrowing from other fire modeling fields and taking advantage of improved computational power and data, there is a new trend towards physics-based rather than strictly empirical spread models; and towards employing different simulation techniques, such as cellular automata, rather than assuming fires spread in an elliptical shape. Past achievements include identification of the factors affecting FFE, documentation of historical events, and years of FFE model use by practitioners. Opportunities for future advances include continued development of physics-based spread models; better treatment of slope, water and transportation system functionality, and suppression by fire departments; and more validation and sensitivity analyses.

Bilevel Optimization for Integrated Shelter Location Analysis and Transportation Planning for Hurricane Events

Responding to hurricanes is an exceedingly complex task, the effectiveness of which can significantly influence the final effects of a hurricane. Despite a lot of progress, recent events and unchecked population growth in hurricane-prone regions make it clear that many challenges remain. Hurricane Katrina has shown that having appropriate shelter options and an appropriate shelter evacuation plan are very important for hurricane evacuations. This paper proposes a scenario-based shelter location model for optimizing a set of shelter locations among potential alternatives that are robust across a range of hurricane events. This model considers the influence of changing the selection of shelter locations on driver route-choice behavior and the resulting traffic congestion. The state of North Carolina is used as a case study to show the applicability of the model.

Simulation of post-earthquake water supply system restoration

This paper describes a discrete event simulation model of post-earthquake restoration for the Los Angeles Department of Water and Power water supply system. It mimics the real-life process in detail, simulating the movement of different types of crews as they inspect, reroute around, isolate, and repair system damage. For any given earthquake, the model provides restoration curves with uncertainty bounds, maps showing the spatial distribution of outages over time, and crew and repair material usage information. Results for the 1994 Northridge earthquake suggest the model is capable of accurately estimating the time and spatial sequence of the restoration. It can be useful for loss estimation and resilience assessment, evaluating the effectiveness of hypothetical restoration strategies, and improving understanding of the restoration process and its key determinants. This is the first application of discrete event simulation to post-disaster water supply restoration, and one of the first for any infrastructure system.

Application of regional earthquake mitigation optimization

A linear program was developed to help seismically active communities decide: (1) how much to spend on pre-earthquake mitigation that aims to reduce future losses versus waiting until after an event and paying for reconstruction, and (2) which of the many possible mitigation activities to fund so as to minimize overall risk. The mitigation alternatives considered are structural upgrading policies for groups of buildings. Benefits of mitigation are losses avoided in future earthquakes, including structural, non-structural, contents, and time-related losses, and casualties. The model is intended to be used as a tool to support the public regional mitigation planning process. In realistic applications, the model includes millions of variables, thus requiring a special solution method. This paper focuses on two efficient solution algorithms to solve the model-a Dantzig-Wolfe decomposition algorithm and a greedy heuristic algorithm. A comprehensive numerical study compares the two algorithms in terms of solution quality and solution time. The study shows that, compared to the Dantzig-Wolfe algorithm, the heuristic algorithm is much faster as expected, and provides comparable solution quality.

Identification of Optimization-Based Probabilistic Earthquake Scenarios for Regional Loss Estimation

We develop a method to estimate long-term earthquake hazard for use in regional loss estimation. The method includes formulation of a linear program that selects a small subset of earthquake scenarios from a library of such events and estimates hazard-consistent annual occurrence probabilities so that their combined effect on the region of interest approximates that described by r-year return period maps that account for all possible events while preserving recurrence relationships based on geological and seismological data. The method is reproducible, computationally tractable, and results in easily understood earthquake scenarios. We apply it to identify earthquake scenarios for Tehran, Iran.