arxiv: 2605.07880 · v1 · submitted 2026-05-08 · 🧮 math.OC · cs.SY· eess.SY

Recognition: no theorem link

Robust Capacity Expansion under Wildfire Ignition Risk and High Renewable Penetration

Tom\'as Tapia , Ryan Piansky , Yury Dvorkin , Jean-Paul Watson

Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:11 UTC · model grok-4.3

classification 🧮 math.OC cs.SYeess.SY

keywords robust optimizationcapacity expansionwildfire ignition riskbattery energy storagetransmission undergroundingrenewable integrationmixed-integer linear programmingpower system resilience

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The pith

A robust optimization model finds optimal battery storage placements and transmission line undergrounding to handle worst-case wildfire de-energization combined with renewable variability.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper builds a robust optimization framework that selects where to add battery energy storage and which transmission lines to underground when power systems face both wildfire ignition risks and high renewable penetration. It models the joint worst-case outcomes of line de-energization from fires and low renewable output, then solves for the least-cost investments that keep the system reliable. Representative weeks and uncertainty sets capture how these risks unfold over time. A reader would care because utilities already de-energize lines during fire season and renewables add variability, so better planning tools can reduce blackouts and expensive emergency measures.

Core claim

The paper formulates a two-stage robust capacity-expansion problem as a mixed-integer linear program that simultaneously optimizes storage capacity and line undergrounding decisions against the worst-case realization of ignition-induced line outages and renewable generation shortfalls, using duality theory and binary decomposition to linearize the model and a column-and-constraint generation algorithm to solve it; numerical results on a San Diego system instance show the method produces investment plans that improve resilience.

What carries the argument

Two-stage robust optimization model with polyhedral uncertainty sets for ignition risk and renewable availability, discretized via representative weeks, converted to MILP by duality and binary decomposition, and solved by column-and-constraint generation.

Load-bearing premise

Representative weeks and the chosen uncertainty sets are sufficient to represent the temporal correlations and extreme joint scenarios of ignition risk and renewable output.

What would settle it

Running the San Diego instance with the model's recommended investments against a held-out set of actual historical wildfire days and renewable traces that lie outside the uncertainty sets and observing whether load shedding still occurs or costs exceed the planned budget.

Figures

Figures reproduced from arXiv: 2605.07880 by Jean-Paul Watson, Ryan Piansky, Tom\'as Tapia, Yury Dvorkin.

**Figure 2.** Figure 2: Illustration of three representative weeks. Each [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Storage capacity investment (red dots) solutions under investment Scheme 1. Largest circle equating to 100 MWh of [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Line hardening (colored lines) and storage capacity investment (red dots) solutions under investment Scheme 2. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Worst-case wildfire ignition risk for two lines under [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: Worst-case wildfire ignition risk for two lines under [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 8.** Figure 8: Worst-case case realization for W1 capacity factor [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: Worst-case case realization for W2 capacity factor [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

read the original abstract

In power systems, the risk of wildfire ignition has increased significantly in recent years. The impact and severity of these events on energy dispatch, as well as their societal ramifications, make wildfire prevention critical for power system planning and operation. A common intervention by system operators is to de-energize transmission lines to mitigate the risk of fire caused by equipment failures. With the growing integration of variable renewable generation, managing and preparing the system to de-energization under wildfire risk has become even more challenging. In this context, mitigation decisions such as installing battery energy storage systems and undergrounding transmission lines can reduce the risk and adverse effects associated with de-energization and renewable generation variability. This paper presents a robust optimization model to determine the optimal location of battery storage and undergrounding of transmission line investment, utilizing representative weeks and uncertainty sets to capture the temporal relationship of uncertain variables. Specifically, this paper addresses: (i) the worst-case realization of ignition risk leading to the de-energization of transmission lines, combined with the worst-case realization of renewable energy availability, and (ii) the optimal investment decisions for energy storage capacity and undergrounding of transmission lines that are exposed to ignition risk. The proposed model is formulated as a mixed-integer linear programming (MILP) problem, employing duality theory and binary decomposition to address nonlinearities, and is solved using a column-and-constraint generation algorithm. The proposed framework is evaluated on a model of the San Diego power system, demonstrating its practical effectiveness in improving the resilience to wildfire risk.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This applies standard robust optimization with column-and-constraint generation to wildfire de-energization plus renewable uncertainty for storage and undergrounding decisions, but the representative-week approach may miss the joint extremes that matter most.

read the letter

The paper takes established robust optimization techniques and applies them to decide battery storage locations and which transmission lines to underground when facing both ignition-driven line outages and variable renewable output. It builds uncertainty sets from representative weeks, formulates the problem as an MILP, uses duality and binary decomposition to handle the nonlinearities, and solves it via column-and-constraint generation on a San Diego system model. That specific combination for capacity expansion under wildfire risk is not in the prior literature they cite, so the application itself is the incremental contribution. The formulation is clean and the choice of a real grid instance lets readers see concrete investment trade-offs rather than abstract examples. The evaluation shows the framework can be solved and produces sensible-looking plans, which is useful for practitioners. The soft spot is the scenario construction. Wildfire ignitions are weather-driven and low-probability; their overlap with low wind or solar output determines the real worst-case cost. If the week-selection rule does not explicitly include or weight those joint tail events, the uncertainty sets will only cover milder combinations. The column-and-constraint generation will then certify robustness only to the scenarios that made it into the weeks, not to the events the abstract claims to address. That is a standard concern with representative-period methods and it lands here because the paper's central claim is about worst-case ignition-plus-renewable realizations. Readers working on power-system resilience in high-fire-risk regions or on robust infrastructure planning will find the worked example helpful. It is not a theoretical advance, so it is not for optimization specialists looking for new algorithms. The work is coherent on its own terms and engages the relevant literature, so it deserves a serious referee who can check the week-selection details, the uncertainty-set construction, and the numerical results in the full manuscript.

Referee Report

2 major / 2 minor

Summary. The paper proposes a robust optimization model for power system capacity expansion planning under wildfire ignition risk and high renewable penetration. It determines optimal investments in battery energy storage and undergrounding of transmission lines exposed to ignition risk by modeling worst-case joint realizations of line de-energization (from ignition) and renewable availability. The approach selects representative weeks, constructs uncertainty sets around these uncertainties, formulates the problem as a MILP using duality theory and binary decomposition to handle nonlinearities, solves it via a column-and-constraint generation algorithm, and demonstrates the framework on a model of the San Diego power system.

Significance. If the uncertainty sets and representative weeks adequately capture the relevant joint extremes, the framework could provide a practical tool for resilient investment decisions in power systems facing increasing wildfire and renewable variability risks. The application of standard robust optimization techniques (duality reformulation and C&CG) to this combined problem is appropriate and timely; the real-world San Diego test case adds practical value. The paper correctly employs off-the-shelf algorithmic components without introducing self-referential parameters.

major comments (2)

[§3 (representative weeks)] Section describing representative week selection (likely §3): The week-selection procedure does not explicitly ensure inclusion of periods where high ignition probability coincides with low renewable output. This is load-bearing for the central claim of addressing combined worst-case realizations, because the uncertainty sets are built around the selected weeks; omission of these joint tail events would mean the column-and-constraint generation produces decisions robust only to milder scenarios present in the weeks, not the actual extremes the model claims to handle.
[§4 (uncertainty sets)] Uncertainty set construction (likely §4): The bounds on ignition risk and renewable availability are free parameters without reported sensitivity analysis or validation against historical joint distributions of high-ignition and low-renewable periods. This directly affects whether the robust investment decisions (storage capacity and undergrounding) remain optimal under the paper's stated worst-case objective.

minor comments (2)

The abstract states that the model is evaluated on the San Diego system and demonstrates practical effectiveness, but the provided text does not include specific quantitative metrics (e.g., cost reductions, resilience improvements, or comparison to deterministic baselines); adding these in the results section would strengthen the demonstration.
Notation for the MILP formulation (variables, sets, and parameters) should be collected in a single table or dedicated subsection for clarity, especially given the use of duality and binary decomposition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We have reviewed each major comment carefully and provide point-by-point responses below, indicating the revisions we plan to implement.

read point-by-point responses

Referee: [§3 (representative weeks)] Section describing representative week selection (likely §3): The week-selection procedure does not explicitly ensure inclusion of periods where high ignition probability coincides with low renewable output. This is load-bearing for the central claim of addressing combined worst-case realizations, because the uncertainty sets are built around the selected weeks; omission of these joint tail events would mean the column-and-constraint generation produces decisions robust only to milder scenarios present in the weeks, not the actual extremes the model claims to handle.

Authors: We appreciate the referee pointing out this critical requirement for capturing joint extremes. Our representative week selection procedure, detailed in Section 3, relies on clustering historical data to represent variability across load, renewables, and ignition probabilities while preserving temporal correlations within each week. However, we acknowledge that the current approach does not include an explicit criterion to guarantee inclusion of weeks exhibiting simultaneous high ignition risk and low renewable output. To address this, we will revise Section 3 to incorporate a targeted selection step or augmentation that prioritizes such joint tail events (e.g., via a weighted scoring or conditional sampling from historical records). This will ensure the uncertainty sets are constructed around scenarios that better align with the paper's worst-case joint realization objective, and we will add supporting discussion and validation metrics. revision: yes
Referee: [§4 (uncertainty sets)] Uncertainty set construction (likely §4): The bounds on ignition risk and renewable availability are free parameters without reported sensitivity analysis or validation against historical joint distributions of high-ignition and low-renewable periods. This directly affects whether the robust investment decisions (storage capacity and undergrounding) remain optimal under the paper's stated worst-case objective.

Authors: The uncertainty set bounds were derived from statistical summaries of historical wildfire ignition data and renewable generation records specific to the San Diego region, cross-referenced with relevant literature on California power system risks. We agree that the absence of explicit sensitivity analysis and joint-distribution validation limits the interpretability of the results. In the revised manuscript, we will add a dedicated subsection (or appendix) to Section 4 that includes: (i) a sensitivity analysis varying the key bounds on ignition probability and renewable availability, (ii) comparison of selected bounds against empirical joint distributions from historical data where available, and (iii) discussion of how the optimal investment decisions (storage and undergrounding) respond to these variations. Any data limitations will be noted transparently. revision: yes

Circularity Check

0 steps flagged

No circularity; standard robust optimization applied to capacity expansion

full rationale

The derivation chain consists of a standard two-stage robust optimization formulation (minimax over uncertainty sets for ignition-driven line de-energization and renewable output), discretized via representative weeks, converted to MILP via duality and binary decomposition, and solved by column-and-constraint generation. None of these steps reduce to self-definition, fitted parameters renamed as predictions, or load-bearing self-citations. Representative-week selection and uncertainty-set construction are modeling choices whose validity can be checked externally against historical data; they do not tautologically force the investment decisions. The paper's claims about optimal storage and undergrounding locations therefore retain independent content relative to its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on standard robust optimization assumptions for power systems; no new physical entities are postulated and free parameters are limited to uncertainty set definitions.

free parameters (1)

Uncertainty set bounds for ignition risk and renewable availability
Parameters defining worst-case scenarios; chosen or calibrated to data but not specified in abstract.

axioms (1)

domain assumption Representative weeks and uncertainty sets capture temporal relationships of uncertain variables
Invoked to model worst-case de-energization and renewable variability while keeping the problem tractable.

pith-pipeline@v0.9.0 · 5589 in / 1250 out tokens · 59300 ms · 2026-05-11T02:11:06.850690+00:00 · methodology

discussion (0)

Reference graph

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