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Abstract
We present a two-stage stochastic programming model for determining the optimal deployment of temporary mitigation resources to protect electrical substations prior to an imminent hurricane. The first stage involves deciding how to deploy a limited supply of mitigation resources, and the second stage is an optimal power flow problem in which the controls are power generation and load shed. The objective is to minimize the expected load shed across a discrete set of flooding scenarios. To study the model, we introduce a test instance representative of Hurricane Harvey which wreaked havoc on the Texas coastline in 2017. Using this instance, we qualitatively assess and compare the optimal first-stage decisions that result from using the classical DC power flow approximation model and the more contemporary LPAC approximation model to comprise the second stage problem.
Keywords
stochastic programming, power flow, hurricane, flood
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1.Introduction
Over the last decade, the United States has been devastated repeatedly by extreme weather events. Though hurricanes are not as common as some other natural disasters, they cause a disproportionately large amount of damage and recovery is tremendously expensive and time-consuming. In 2017 alone, the U.S. coastal and island regions were ravaged by Hurricanes Harvey, Irma, and Maria, three of the five most costly hurricanes in U.S. history. All occurred within a 5-week interval and had estimated costs of $131B, $53B, and $95B, respectively [1]. These figures and others like them clearly motivate the goal of improving infrastructure resilience, and there is, in fact, a large and growing body of literature dedicated to decision models that integrate infrastructure logistics and the effects of extreme weather. Some examples include pre-hurricane power system inventory planning [2], pre-hurricane grid component hardening [3], pre-hurricane rescue and repair asset positioning [4], and post-disaster coordination of transportation and power network repairs [5].
We present a model similar to those developed in [2, 3] in that it is a scenario-based two-stage stochastic optimization model that incorporates a power flow model in the second stage. It is meant to guide the allocation of limited flood mitigation resources to electric substations such that expected load shed is minimized across the resulting topologies. Rather than incorporate the exact, nonconvex AC power flow model in our second-stage problem,...