[Paper Review] Scenario-based Optimization Models for Power Grid Resilience to Extreme Flooding Events

Ashutosh Shukla, Erhan Kutanoğlu+1 more|arXiv (Cornell University)|Feb 21, 2023

Flood Risk Assessment and Management4 citations

TL;DR

This paper proposes two scenario-based optimization models—stochastic and robust—for enhancing power grid resilience against extreme flooding from hurricanes. By integrating hydrological flood forecasts with a DC power flow model, the models identify optimal substation hardening strategies under uncertainty, significantly reducing load shed compared to mean-forecast approaches, especially when budgets are high or scenario probabilities are uncertain.

ABSTRACT

We propose two scenario-based optimization models for power grid resilience decision making that integrate output from a hydrology model with a power flow model. The models are used to identify an optimal substation hardening strategy against potential flooding from storms for a given investment budget, which if implemented enhances the resilience of the power grid, minimizing the power demand that is shed. The same models can alternatively be used to determine the optimal budget that should be allocated for substation hardening when long-term forecasts of storm frequency and impact (specifically restoration times) are available. The two optimization models differ in terms of capturing risk attitude: one minimizes the average load shed for given scenario probabilities and the other minimizes the worst-case load shed without needing scenario probabilities. To demonstrate the efficacy of the proposed models, we further develop a case study for the Texas Gulf Coast using storm surge maps developed by the National Oceanic and Atmospheric Administration and a synthetic power grid for the state of Texas developed as part of an ARPA-E project. For a reasonable choice of parameters, we show that a scenario-based representation of uncertainty can offer a significant improvement in minimizing load shed as compared to using point estimates or average flood values. We further show that when the available investment budget is relatively high, solutions that minimize the worst-case load shed can offer several advantages as compared to solutions obtained from minimizing the average load shed. Lastly, we show that even for relatively low values of load loss and short post-hurricane power restoration times, it is optimal to make significant investments in substation hardening to deal with the storm surge considered in the NOAA flood scenarios.

Motivation & Objective

• Address the growing threat of hurricane-induced flooding to power grids, particularly in vulnerable coastal regions like Texas.
• Develop decision-support models that account for uncertainty in storm surge flood levels and their impact on substation operations.
• Provide actionable substation hardening strategies under limited investment budgets to minimize load shedding during extreme flooding events.
• Enable utilities to determine optimal investment budgets for substation hardening using long-term storm frequency and restoration time forecasts.
• Support decision-making under varying risk preferences by comparing stochastic (expected performance) and robust (worst-case) optimization approaches.

Proposed method

• Integrate output from NOAA’s physics-based storm surge flood models with a synthetic DC optimal power flow model for a Texas power grid.
• Formulate a two-stage stochastic optimization (SO) model that minimizes expected load shed using scenario probabilities derived from flood forecasts.
• Develop a two-stage robust optimization (RO) model that minimizes the worst-case load shed without requiring scenario probabilities.
• Use scenario generation based on historical and modeled flood extents to represent uncertainty in storm surge levels across substations.
• Apply the models to a case study of the Texas Gulf Coast, using 100 flood scenarios derived from NOAA storm surge maps and a synthetic grid from an ARPA-E project.
• Evaluate model performance through comparative analysis of load shed across scenarios, budget sensitivity, and robustness under varying uncertainty assumptions.

Figure 1: A schematic representation of the decision-making framework for the proposed models

Experimental results

Research questions

• RQ1 How does using a scenario-based representation of flood uncertainty compare to using mean or point estimates in minimizing load shed?
• RQ2 What are the trade-offs between minimizing expected load shed (stochastic model) and minimizing worst-case load shed (robust model) under different budget levels?
• RQ3 How much investment in substation hardening is optimal when considering long-term storm frequency and restoration times?
• RQ4 What is the value of using high-fidelity, physics-based flood maps versus simpler scenario generation methods in resilience planning?
• RQ5 Under what conditions does the robust optimization approach outperform the stochastic approach in terms of both worst-case and expected performance?

Key findings

• Using scenario-based uncertainty representation reduces expected load shed significantly compared to mean-forecast approaches, especially under high-impact scenarios.
• For investment budgets above $40M, robust optimization solutions outperform stochastic solutions in worst-case load shed while maintaining competitive expected performance.
• Even with low load loss and short restoration times, substantial substation hardening investments are optimal to mitigate storm surge impacts.
• The robust optimization model provides stable performance across all scenarios, with minimal variation in load shed, making it preferable when scenario probabilities are uncertain or volatile.
• The two models together enable decision-makers to assess the value of perfect information by comparing expected performance under imperfect vs. near-perfect flood forecasts.
• The integration of NOAA-based flood maps with power flow modeling enables more accurate and actionable resilience planning than heuristic or simplified flood scenario methods.

Figure 2: An example permanent hardening structure at a substation