🤖 machine learning

Predicting Estimated Times of Restoration for Electrical Outages Using Longitudinal Tabular Transformers

This paper introduces the Longitudinal Tabular Transformer (LTT), an axial-attention model that reformulates electrical outage restoration time prediction as a longitudinal task by leveraging historical revision data, achieving significant error reductions and improved customer satisfaction across six utility companies compared to existing methods.

Original authors: Bogireddy Sai Prasanna Teja, Valliappan Muthukaruppan, Carls Benjamin

Published 2026-09-10

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Bogireddy Sai Prasanna Teja, Valliappan Muthukaruppan, Carls Benjamin

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

When a storm knocks out power, the most urgent question for a family with a medical device, a business with frozen inventory, or a city planning a warming center is not just when the lights will come back on, but when they can expect them to. Utility companies provide this answer as an Estimated Time of Restoration, a promise that guides critical decisions about safety and survival. For decades, the industry has treated these outages as static events, like taking a single photograph of a broken wire and calculating a repair time based on that one moment. This approach ignores the reality that a power outage is a living, changing story. It begins with a crew being assigned, moves to them arriving at the scene, and evolves as they report damage, get redirected to higher-priority jobs, or begin partial repairs. Every one of these steps is recorded as a new update, a revision that changes the expected remaining time, yet traditional methods often discard the history of these updates to focus only on the latest snapshot.

A team of researchers at Exelon Corporation has developed a new way to handle this complexity by treating an outage not as a single event, but as a sequence of revisions. They built a specialized computer model that learns from the entire history of an outage as it unfolds. Instead of guessing the repair time once, this model issues a refined estimate at every single step of the process, using the information from all previous updates to improve its prediction. By analyzing data from nearly 243,000 storm-related outages across six different utility companies, involving over ten million recorded updates, the researchers found that this approach significantly outperforms the current standard methods used by utilities. The new model reduced the error in time estimates by a median of nearly 37 percent compared to the official estimates published by the utilities during the same storms. It also improved upon the best existing computer learning methods by more than 11 percent, proving that listening to the full story of an outage, rather than just its final chapter, leads to more accurate and reliable predictions for customers.

The core of this improvement lies in how the model processes information. In the past, systems would look at the most recent status of an outage and ignore the path taken to get there. The new system, called a Longitudinal Tabular Transformer, pays attention to the flow of time. It understands that a crew arriving at a site changes the outlook differently than a crew being suspended and sent to another job. The model tracks these changes continuously, learning that the more updates it sees, the more precise its estimate becomes. This is particularly important because the biggest errors in prediction happen right at the beginning, when there is little history to rely on. As the outage progresses and more data accumulates, the model's accuracy improves steadily, mirroring the way human dispatchers gain confidence as they gather more facts.

The researchers tested this system against the actual estimates released by utility companies during real storms, using a metric that weighs errors based on how many customers are affected and for how long. This is crucial because a wrong estimate for a small neighborhood is less damaging than a wrong estimate for a large area where thousands of people are waiting. The results showed that the new model not only reduced the average time error but also did so while avoiding a common pitfall of the old systems. Traditional utility estimates often lean toward being overly conservative, promising a longer wait time than necessary just to ensure they do not miss their deadline. While this strategy might make customers feel slightly more satisfied in the short term, it leads to large errors in the actual duration. The new model found a better balance, providing estimates that were both more accurate and more trustworthy, reducing the root mean squared error—a measure of how far off the predictions were—across all six companies studied.

One of the most significant findings was that the improvement did not come simply from updating the estimates more frequently. The researchers compared their model to other advanced computer programs that also updated their predictions at every step of the outage. Even when these competing models were given the same opportunity to update as often as the new system, the Longitudinal Tabular Transformer still performed better. This suggests that the advantage comes from the way the model understands the sequence of events, not just the speed of its updates. The study also confirmed that the model works well even when the data is messy or incomplete, a common reality in storm response where information can be delayed or missing. By explicitly accounting for missing information rather than guessing it, the model maintains its reliability.

The impact of this work extends beyond just better numbers on a screen. For the millions of customers who rely on these estimates to make decisions about their health, food, and safety, a more accurate prediction means less uncertainty and better preparation. The study covered a vast range of conditions, from small, quick outages to massive storms that lasted for days, and the model performed consistently well across all of them. While there is still room for improvement, as no prediction can be perfect, this research demonstrates a clear path forward. By shifting the focus from a single static view to a dynamic, evolving understanding of an outage, utility companies can provide their customers with the most reliable information possible, turning a chaotic and stressful experience into one where the timeline is known with greater certainty.

Technical Summary: Predicting Estimated Times of Restoration for Electrical Outages Using Longitudinal Tabular Transformers

Problem Formulation
Utilities provide Estimated Times of Restoration (ETRs) to customers during storm outages, a metric critical for decision-making regarding medical equipment, food safety, and relocation. Prior research has treated ETR prediction as a static tabular regression task, where each outage is characterized by a single feature vector and predicted once. This approach discards the longitudinal nature of outage management, where an outage evolves through a sequence of revisions (e.g., crew assignment, dispatch, damage assessment, suspension, partial restoration). Each revision updates the expected remaining duration, yet existing models typically ignore the trajectory of these updates, relying only on the final or latest state.

The authors reformulate ETR prediction as a longitudinal tabular regression problem. The goal is to predict the remaining time to restoration ( $y_{i,j}$ ) at every revision $j$ of an outage event $i$ , conditioned on the history of preceding revisions. The target is defined as the remaining time rather than an absolute timestamp to remove deterministic components related to calendar position and storm timing, ensuring the target is invariant to when the outage occurred.

Methodology: Longitudinal Tabular Transformer (LTT)
The paper introduces the Longitudinal Tabular Transformer (LTT), an axial-attention model designed to consume the stream of revisions preceding a prediction.

Tokenization and Embedding: Features are embedded independently. Continuous features are linearly projected, while categorical features are mapped via learned embeddings. Missingness is handled explicitly by adding a learned vector rather than imputing values, preserving the informational value of absent data (e.g., no crew assigned yet).
Architecture: The model employs a dual-axis attention mechanism:
1. Intra-revision Axis: A Transformer block processes the feature tokens within a single revision, using a learned pooling token to aggregate feature information.
2. Inter-revision Axis: A sequence of revisions is processed using cross-attention against static features and system context. The model incorporates a temporal encoding using learned periodic representations to capture irregular operational intervals (e.g., elapsed time, hour of day, time since storm onset).
3. Masking: The model uses a sliding window of size $W=20$ revisions. Padding is applied to the leading slots of the window for early revisions. Crucially, the model uses bidirectional attention within the window because all positions in the window $W(i,j)$ refer to timestamps $t_{i,j'} \le t_{i,j}$ , ensuring no temporal leakage.
Output Head: The model predicts ordered quantile levels ( $Q = \{1/2, 5/6, 9/10\}$ ) as a base plus non-negative increments. This ensures monotonicity ( $\hat{y}^{(1)} \le \hat{y}^{(2)} \le \hat{y}^{(3)}$ ) and non-negativity. The primary operational estimate corresponds to the $5/6$ level.
Objective Function: The training objective is a piecewise penalty function derived from internal customer satisfaction analysis. It heavily penalizes underprediction (restoration arriving later than promised) and moderately penalizes overprediction. The loss is Huber-smoothed to facilitate training with gradient-based methods. A stability term penalizes large jumps in the predicted timestamp between consecutive revisions.

Data and Experimental Setup
The study utilizes data from six operating companies (OPCO-1 to OPCO-6) of a single holding company, covering 242,928 storm-attributed outages and approximately 10 million revisions.

Cohort: The dataset includes standard and SCADA-detected customer outages, excluding momentary interruptions, planned outages, and cancelled events.
Evaluation: Metrics are weighted by customer-hours of exposure to prioritize accuracy on large, long-running events. Key metrics include Weighted Asymmetric Error (WAE), Root Mean Squared Error (RMSE), and a Customer Satisfaction Index (CSI) that reflects the asymmetric penalty structure.
Baselines: The LTT is compared against:
- The incumbent utility OMS estimates (published during the same storms).
- A climatological predictor.
- Static and lag-flattened boosted tree models (LightGBM, XGBoost, CatBoost).
- Recurrent neural networks (GRU, LSTM).
- A "lag-flattened" baseline that concatenates recent revisions as features to test if the benefit comes from feature engineering rather than architecture.

Key Results

Performance vs. Incumbent: The LTT reduces the customer-weighted asymmetric error (WAE) by a median of 36.9% (range 10.0–54.0%) compared to the estimates published by the utilities during the same storms across all six companies.
Performance vs. Learned Baselines: LTT reduces WAE by a median of 11.3% (range 6.2–19.2%) against the strongest learned baseline at each company.
Satisfaction and Error Trade-off: The incumbent OMS often achieves a competitive CSI through systematic overprediction (conservatism), which a rate-based statistic like CSI fails to penalize. LTT is the only method that improves upon the incumbent's CSI at all six companies while simultaneously reducing RMSE at all six.
Revision Trajectory: Error analysis shows that LTT error is largest at the first revision (where no history exists) and decreases monotonically as revisions accumulate, confirming the model's ability to leverage the outage trajectory.
Cadence Independence: The performance gain is not solely due to the LTT issuing more frequent updates. When the LTT is scored using only the most recent prediction available at the time of an OMS update, it still retains a median gain of 34.2% over the incumbent.

Significance and Claims
The paper claims novelty in three specific areas:

Formulation: It is the first work to model the revision stream of an outage as a longitudinal sequence rather than a static snapshot.
Benchmarking: It provides a benchmark against actual customer-facing utility estimates with an explicit cadence-matched control, rather than comparing only against other machine learning models.
Architecture: It contributes the LTT architecture and demonstrates its efficacy across six distinct operating environments.

The authors conclude that treating outages as sequences of revisions significantly improves ETR accuracy. However, they remain modest, noting that substantial error remains at every company and that characterizing the irreducible portion of this error, along with chronological evaluation, is the subject of ongoing work.

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