Comparisons of two-stage models for flood mitigation of electrical substations
Brent Austgen, Erhan Kutanoglu, John J. Hasenbein, Surya Santoso
TL;DR
This paper tackles the problem of protecting electrical substations from imminent hurricane-induced flooding using two-stage stochastic programming and robust optimization. It develops three adapted PF recourse models (DC and two LPAC variants) with a feasibility indicator to ensure relatively complete recourse and applies the formulations to realistic Hurricane Harvey and Tropical Storm Imelda case studies, quantifying the influence of mitigation budget and uncertainty perspective on optimal strategies. The study finds that the mitigation budget and the chosen uncertainty perspective materially affect solutions, while the choice between DC and LPAC recourse has little impact on decisions (though LPAC can affect computation time). Validation against an AC power-flow model shows that the proposed approaches yield effective mitigation despite approximation errors, supporting the practical use of Tiger Dam™ barriers for flood resilience. The work suggests directions for future enhancements, including multi-period modeling and convex AC relaxations to bound solution performance under more realistic dynamics.
Abstract
We compare stochastic programming and robust optimization decision models for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. In our models, the first stage captures the deployment of a fixed quantity of flood mitigation resources, and the second stage captures the operation of a potentially degraded power grid with the primary goal of minimizing load shed. To model grid operation, we introduce adaptations of the DC and LPAC power flow approximation models that feature relatively complete recourse by way of an indicator variable. We apply our models to a pair of geographically realistic flooding case studies, one based on Hurricane Harvey and the other on Tropical Storm Imelda. We investigate the effect of the mitigation budget, the choice of power flow model, and the uncertainty perspective on the optimal mitigation strategy. Our results indicate the mitigation budget and uncertainty perspective are impactful whereas choosing between the DC and LPAC power flow models is of little to no consequence. To validate our models, we assess the performance of the mitigation solutions they prescribe in an AC power flow model.