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Modeling Adversarial Wildfires for Power Grid Disruption

Matthew Brun, Xu Andy Sun, Jean-Paul Watson

Abstract

Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire models do not effectively describe worst-case, or even high-impact, fire behavior. To address this issue, we propose a mixed-integer conic program to characterize an adversarial wildfire that targets infrastructure while respecting realistic fire spread dynamics. We design a wind-assisted fire spread set based on the Rothermel fire spread model and propose principled convex relaxations of this set, including a new relaxation of the inner product over Euclidean balls. We present test cases derived from the recent Park, Eaton, and Palisades fires in California and solve models to identify the minimum time-to-outage of multiple-element contingencies and the maximum load shed associated with a sequence of element outages caused by a realistic wildfire. We use the minimum time-to-outage values to screen contingencies and construct security-constrained optimal power flow models that promote operational resilience against wildfire.

Modeling Adversarial Wildfires for Power Grid Disruption

Abstract

Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire models do not effectively describe worst-case, or even high-impact, fire behavior. To address this issue, we propose a mixed-integer conic program to characterize an adversarial wildfire that targets infrastructure while respecting realistic fire spread dynamics. We design a wind-assisted fire spread set based on the Rothermel fire spread model and propose principled convex relaxations of this set, including a new relaxation of the inner product over Euclidean balls. We present test cases derived from the recent Park, Eaton, and Palisades fires in California and solve models to identify the minimum time-to-outage of multiple-element contingencies and the maximum load shed associated with a sequence of element outages caused by a realistic wildfire. We use the minimum time-to-outage values to screen contingencies and construct security-constrained optimal power flow models that promote operational resilience against wildfire.
Paper Structure (27 sections, 7 theorems, 58 equations, 7 figures, 6 tables)

This paper contains 27 sections, 7 theorems, 58 equations, 7 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Contributions
  4. Notation
  5. An Optimization Model for Adversarial Wildfires
  6. Pointwise Wildfire Spread Models
  7. The Rothermel Fire Spread Model
  8. The Inner Product Spread Set
  9. The Shor Relaxation
  10. Second-Order Minor Constraints
  11. Rotated McCormick Inequalities
  12. Inner Product Spread Set Formulation
  13. Ball Spread Set
  14. Choosing a Relaxation
  15. Explicit Mixed-Integer Conic Formulations
  16. ...and 12 more sections

Key Result

Proposition 3.1

Fix some $\{x,w\} \subset \mathbb{R}^2$. Let $B \in [0,1]$ and $(C,V(x)) \geq 0$. Then, the set $\mathcal{S}^{\mathrm{r}}(w,x)$ can be written as the projection of a power conic set; specifically,

Figures (7)

  • Figure 3.1: Comparison of spread sets $\mathcal{S}^{\langle \rangle}(w,0_2)$ for each convex relaxation of the inner product. Wind velocity $w$ is fixed in each plot. We set $B = 0.9093$, $\overline{w} = 0_2$, and $\varepsilon = 50\ \text{mi/hr}$. Units are miles; arrows show the wind direction and relative magnitude.
  • Figure 3.2: Comparison of the Rothermel, relaxed, and ball spread sets. Wind velocity $w$ is fixed in each plot. We set $B = 1$, $\overline{w} = 0_2$, and $\varepsilon = 50\ \text{mi/hr}$. Units are miles; arrows show the wind direction and relative magnitude.
  • Figure 6.1: Synthetic power network topology musselman2025climate overlaid on the state of California. Final perimeters of the Park, Eaton, and Palisades fires are shown in orange, and lines in the selected contingency set are highlighted in red. The ignition location of each fire is marked by an asterisk. The union of the Rothermel spread sets over the first 24 hours of fire spread are shown with dotted lines.
  • Figure 6.2: WFPI data (top) and rate of spread regions (bottom) extracted from optimal classification trees for each fire.
  • Figure 7.1: Distribution of minimum time-to-outage values by fire, spread set, flexibility, and number of contingency elements.
  • ...and 2 more figures

Theorems & Definitions (12)

  • Proposition 3.1
  • proof
  • Theorem 1: wang2024semidefinite Sec. 4.1
  • Corollary 3.1
  • proof
  • Theorem 2
  • proof
  • Lemma 3.1
  • Proposition 3.2
  • proof
  • ...and 2 more