A two-stage stochastic programming model for electric substation flood mitigation prior to an imminent hurricane

TL;DR

The paper addresses proactive flood mitigation for electrical substations facing an imminent, uncertain hurricane. It introduces a two-stage stochastic programming framework where first-stage discrete decisions allocate a fixed budget of temporary flood barriers (modeled with stacking and an unattainable level), and second-stage DC power-flow recourse evaluates grid performance under flood realizations via a linearized PF model. Key contributions include a novel mitigation deployment model, scenario-generation methods based on the National Water Model for two real storms (Tropical Storm Imelda and Hurricane Harvey) on a geographically anchored Texas grid, and a parametric greedy heuristic that yields near-optimal solutions within 5% of the optimum. The results reveal budget-sensitive, nonmonotone mitigation patterns driven by discrete decisions, emphasize greater resource allocation to urban substations, and show the value of higher-fidelity mitigation options while highlighting computational trade-offs. The work advances proactive resilience planning by linking discrete barrier deployment with physics-based grid operations and offers directions for extending to multi-period planning and equity-aware objectives, with practical implications for utility decision-making under time-critical hurricane forecasts.

Abstract

We present a stochastic programming model for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.

Figures (13)

• Figure 1: When a substation is flooded, its components and all adjacent transmission lines become inoperable. In this illustration, the substation shaded in light red is flooded, and the components shaded in red are consequently affected.
• Figure 2: A diagram of our two-stage model. First, a decision maker commits to a specific mitigation solution $\boldsymbol{x} \in \mathcal{X}$. For each scenario $\omega \in \Omega$, the load shed-minimizing grid operational response is computed via recourse problem $\mathcal{L}(\boldsymbol{x}, \boldsymbol{\xi}^\omega)$, a physics-based model that captures power flow limitations following mitigation solution $\boldsymbol{x}$ and flooding realization $\boldsymbol{\xi}^\omega$. The efficacy of the mitigation solution is measured by the probability-weighted sum of loss (i.e., the expected weighted combination of load shed and overgeneration) across all sample scenarios. The goal of our model is to identify the mitigation solution (red diamond) that minimizes the resulting expected load shed (yellow rectangle).
• Figure 3: Comparing (a) the full original grid with (b) the reduced grid, we observe the number of buses and branches are reduced by more than 50%. In (b), teal represents the parts retained from the original grid, and green represents the parts introduced by the reduction. The Texas-Gulf region, the area modeled in our streamflow simulations, is shaded yellow.
• Figure 4: The cross-sectional view of a stacked Tiger Dam™ flood barrier. The colors indicate the resources required to attain the next-highest level of resilience. Though level $r=3$ is illustrated here, we model this level as being unattainable (i.e., $\hat{r} = 3$) in our case studies.
• Figure 5: Tropical Storm Imelda scenario flood levels by scenario and by substation.