⚡ electrical engineering

Robust Capacity Expansion under Wildfire Ignition Risk and High Renewable Penetration

This paper proposes a robust optimization model formulated as a mixed-integer linear program to determine optimal investments in battery storage and underground transmission lines, ensuring power system resilience against the combined worst-case risks of wildfire-induced de-energization and renewable energy variability in the San Diego power system.

Original authors: Tomás Tapia, Ryan Piansky, Yury Dvorkin, Jean-Paul Watson

Published 2026-05-11

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Tomás Tapia, Ryan Piansky, Yury Dvorkin, Jean-Paul Watson

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the power grid as a massive, intricate web of roads delivering electricity to your home. Now, imagine that during hot, dry, and windy days, the "cars" driving on these roads (the electricity) can sometimes spark a fire if the road is old or damaged. If a fire starts, the safest thing to do is to close that road entirely to stop the fire from spreading. In the real world, this is called "de-energizing" a power line.

However, closing these roads creates a traffic jam for electricity. If you close too many roads at once, especially when the "solar cars" and "wind cars" (renewable energy) are already having a bad day and can't drive very fast, the whole city could lose power.

This paper proposes a smart planning tool to help city leaders (power system planners) decide where to build new "parking garages" (batteries) and which roads to pave underground (so they can't spark fires) before a disaster happens.

Here is a breakdown of how their solution works, using simple analogies:

1. The Problem: The "Worst-Case" Scenario

Planners usually try to guess what might happen. But this paper says, "Let's not guess; let's prepare for the absolute worst day possible."

The Wildfire Risk: Imagine a map that shows where the roads are most likely to spark a fire. The model assumes the worst: the fire risk is at its highest, forcing the operators to shut down the most dangerous roads.
The Renewable Risk: At the exact same time, imagine the sun is hidden behind clouds and the wind has stopped blowing. The renewable energy sources are at their lowest.

The model asks: "If we have the worst fire risk AND the worst weather for solar/wind at the same time, how do we keep the lights on without spending a fortune?"

2. The Solution: Two Main Tools

To survive this "perfect storm," the model suggests two main investments:

Battery Storage (The Emergency Parking Garage): These are giant batteries that can store electricity when it's plentiful and release it when the roads are closed or the sun isn't shining. The model figures out exactly where to build these garages so they are closest to the areas that need them most.
Undergrounding Lines (Paving the Road): Instead of leaving power lines hanging on poles where wind and sparks can cause fires, you can bury them underground. This is expensive, like repaving a highway, but it makes the road fire-proof. The model decides which specific roads are worth the high cost to bury.

3. The "Uncertainty Budget" (The Safety Margin)

The paper uses a concept called an "uncertainty budget." Think of this like a safety margin or a buffer zone.

Low Budget: You assume things will mostly go as planned. You might only build a few batteries and bury very few lines.
High Budget: You assume things could go very wrong. You build more batteries and bury more lines to be extra safe.
The model allows planners to choose how "paranoid" they want to be. If they want to be very safe (high budget), the model tells them to invest more money upfront to avoid blackouts later.

4. How They Tested It

The authors tested their idea on a digital model of the San Diego power system. They simulated a year of operation using "representative weeks" (like picking three typical weeks to represent the whole year).

The Result: When they allowed for both batteries and underground lines, the system became much more resilient. In fact, in their "worst-case" simulations, they were able to reduce the amount of power cut off to customers (load shedding) from thousands of megawatt-hours down to zero.
The Trade-off: They found that if you are willing to invest in burying the lines, you don't need to build as many batteries, and vice versa. It's a balancing act between paving roads and building garages.

Summary

In short, this paper presents a mathematical "game plan" for power companies. It helps them decide where to put batteries and which power lines to bury underground. It does this by planning for the absolute worst day imaginable (high fire risk + low renewable energy) to ensure that even if that day happens, the lights stay on and no new wildfires are started by the power grid.

Technical Summary: Robust Capacity Expansion under Wildfire Ignition Risk and High Renewable Penetration

Problem Statement
Power system capacity expansion planning (CEP) faces increasing challenges due to the integration of variable renewable energy and the rising frequency of weather-driven events, specifically wildfires. In regions like California, system operators frequently employ Public Safety Power Shutoffs (PSPS), de-energizing transmission lines to prevent equipment-induced wildfire ignitions. This operational strategy creates a complex planning problem: the simultaneous occurrence of line de-energization and low renewable generation availability can lead to significant reliability issues and load shedding. Current planning tools often struggle to account for the temporal correlation between wildfire ignition risks and renewable variability, potentially leading to suboptimal investment decisions in storage and transmission hardening.

Methodology
The authors propose a two-stage robust optimization framework designed to determine optimal investment locations for battery energy storage systems (BESS) and the undergrounding of transmission lines. The model is formulated as a Mixed-Integer Linear Programming (MILP) problem that minimizes total investment costs plus the worst-case operational costs over a planning horizon.

Key methodological components include:

Uncertainty Sets: The model utilizes two distinct uncertainty sets to capture worst-case realizations:
1. Wildfire Ignition Risk ( $U_r$ ): Modeled using a box uncertainty set based on historical Wildland Fire Potential Index (WFPI) data. This set determines which transmission lines must be de-energized based on a risk threshold, incorporating a budget parameter ( $\Gamma_r$ ) to control conservatism.
2. Renewable Availability ( $U_\alpha$ ): A separate uncertainty set models the variability of wind and solar generation capacity factors, also bounded by a budget parameter ( $\Gamma_\alpha$ ).
Representative Weeks: To ensure computational tractability while capturing temporal correlations, the model uses a set of representative weeks derived from 12 months of WFPI data using the $k$ -medoids clustering algorithm.
Solution Algorithm: The problem structure involves a max-min formulation (minimizing investment costs against the worst-case operational cost). The authors reformulate the lower-level minimization problem using strong duality theory to convert it into a maximization problem. To handle the resulting bilinear terms (multiplication of continuous dual variables and binary de-energization variables), the authors employ the Big-M method and binary expansion techniques. The overall problem is solved using a Column-and-Constraint Generation (CCG) algorithm.

Key Contributions
The paper presents three primary contributions:

A Robust CEP Framework: A novel optimization model for electricity grids with high renewable penetration that explicitly incorporates wildfire ignition risk metrics. The model jointly optimizes transmission undergrounding and storage investment while preemptively accounting for worst-case line de-energization and renewable availability.
Calibratable Risk Management: The use of traditional uncertainty sets allows planners to calibrate risk tolerance via uncertainty budgets ( $\Gamma$ ). These budgets define allowable deviations from nominal conditions, enabling a trade-off analysis between solution conservatism and investment cost.
Computational Validation: The framework is evaluated on a 24-bus representation of the San Diego power system, demonstrating the model's ability to handle large-scale network instances and providing insights into how different uncertainty budgets impact investment strategies and system resilience.

Results
Experiments on the San Diego test case compared two investment schemes: (1) storage-only investment and (2) combined storage and underground transmission line investment.

Investment Trends: As the uncertainty budgets ( $\Gamma_r$ and $\Gamma_\alpha$ ) increased, indicating a more conservative approach to risk, the total required investment in both storage capacity and undergrounded lines increased.
Scheme Comparison: Scheme 2 (storage + undergrounding) significantly outperformed Scheme 1. While Scheme 1 resulted in daily load shedding ranging from approximately 2,000 MWh to 2,980 MWh under high uncertainty, Scheme 2 reduced daily load shedding to 0 MWh across all tested scenarios.
Strategic Shifts: The model demonstrated that as risk budgets increased, the optimal strategy shifted toward hardening critical transmission lines (undergrounding) rather than solely relying on storage. This was particularly evident when specific lines were frequently de-energized in the worst-case scenarios, prompting the model to select those lines for undergrounding to maintain supply reliability.
De-energization Patterns: The results highlighted that de-energization patterns are non-linear and sensitive to uncertainty budgets. Higher budgets led to different lines being selected for de-energization in the worst-case scenarios, which in turn altered the optimal location and sizing of storage assets.

Significance and Claims
The authors claim that this work addresses a gap in the literature by focusing on power system planning under the simultaneous worst-case realization of wildfire ignition risk and renewable availability. The proposed model offers a tractable approach to co-optimizing mitigation measures (preemptive de-energization) and infrastructure investments.

The paper asserts that its framework enables utilities to identify optimal investment plans that balance economic efficiency with system resilience. By explicitly modeling the correlation between ignition risk and renewable variability, the approach supports more informed decisions regarding where to invest in storage versus transmission hardening. The authors note that while the model is conservative—reducing continuous ignition risk to a binary approximation via thresholds—it effectively captures primary system-level effects. The study concludes that allowing investments in both undergrounding and storage leads to superior resilience, with the model prioritizing line hardening when storage locations are limited or transmission lines are critical to supply reliability. Future work is suggested to scale the model to larger systems (e.g., the full CAISO system) and incorporate additional sources of uncertainty.

1. The Problem: The "Worst-Case" Scenario

2. The Solution: Two Main Tools

3. The "Uncertainty Budget" (The Safety Margin)

4. How They Tested It

Summary

More like this