Risk-Based Dynamic Thermal Rating in Distribution Transformers via Probabilistic Forecasting

This paper proposes a probabilistic forecasting framework using clustered quantile regression on UK low-voltage transformer data to dynamically optimize thermal protection settings, achieving a 10–12% capacity increase while enabling risk-informed operational decisions through direct overheating risk quantification.

The Gist

Imagine your local electricity network is like a busy highway system, and the distribution transformers are the toll booths that step down high-voltage power to safe levels for your home.

For years, these toll booths have been run by very cautious, old-school managers. They have a rule: "If the traffic gets too heavy, we shut the gate immediately to be safe." This is called Static Protection. The problem is, these managers are so cautious that they often shut the gate even when the road is only 80% full, just to be absolutely sure no one crashes. This wastes a lot of potential capacity, and since buying new toll booths (transformers) is incredibly expensive and slow, we need a smarter way to use the ones we already have.

This paper proposes a Dynamic Thermal Rating (DTR) system. Think of it as upgrading those old managers to a team of AI-driven traffic controllers who can look at the weather, the time of day, and the road conditions to say, "Actually, it's a cold day, and the cars are cool, so we can safely let 20% more cars through without melting the asphalt."

Here is how the paper solves the problem, broken down into simple concepts:

1. The Problem: The "One-Size-Fits-All" Trap

Currently, the safety devices (relays) on these transformers are set to trip (shut off power) at a fixed limit. It's like having a speed limit sign that says "50 mph" even on a wide, empty, straight highway in perfect weather. It's safe, but inefficient.

• The Risk: If we just guess how much more power we can handle, we might accidentally overheat the transformer (like an engine overheating), which damages it.
• The Challenge: We can't have a human operator standing at every single transformer (there are hundreds of thousands!) to check the temperature every hour. We need an automated system.

2. The Solution: The "Crystal Ball" Approach

The authors created a system that predicts the future to set the safety limit before the day begins.
Instead of guessing the load and then calculating the safety limit (which is like trying to guess the weather by looking at a single cloud), they built a model that directly predicts the safety limit (the "Scale Factor").

• The Analogy: Imagine you are packing for a trip.
  • Old Way: You guess the temperature, guess the humidity, guess the wind, and then try to calculate what jacket to wear. If you get one guess wrong, your whole outfit is wrong.
  • New Way: You ask a super-accurate AI, "Based on all the data, what is the exact jacket I need to wear to stay comfortable but not freeze?" The AI gives you the answer directly.

3. The Secret Sauce: "Grouping" and "Probabilities"

The researchers didn't just build one model for all 644 transformers. That would be like trying to teach one student to be a doctor, a mechanic, and a chef all at once.

• Clustering: They grouped similar transformers together (like grouping all "small town" transformers vs. "busy city" transformers). This helps the AI learn the specific habits of each group.
• Probabilistic Forecasting (The Risk Dial): This is the most important part. The system doesn't just give one number; it gives a range of possibilities with a "risk dial."
  • If the utility company wants to be super safe (like a parent driving a car with a nervous child), they turn the dial to the 2nd percentile. This means there is only a 2% chance of overheating.
  • If they want to maximize capacity (like a race car driver pushing the limits), they turn the dial to the 95th percentile. This allows for much more power, but there is a 5% chance the transformer might get too hot.

4. The Results: More Power, Less Risk

The study tested this on real transformers in the UK during a cold winter (when demand is highest).

• The Gain: By using this smart, risk-aware system, they unlocked an extra 10–12% capacity. That's like adding 100 extra cars to a highway without building a new lane.
• The Safety: Because the system uses probabilities, the utility company knows exactly how risky they are being. If they choose the "2% risk" setting, they can be mathematically confident that the transformer will not overheat 98% of the time.
• The Comparison: They tried a "multi-step" method (guessing the load first, then the limit), but it failed because errors piled up like a house of cards. Their "direct prediction" method was much more stable and accurate.

The Big Picture

This paper is a blueprint for smart, automated asset management. It tells utility companies: "You don't need to buy expensive new transformers right now. Instead, upgrade your software to be a 'risk-aware' traffic controller. You can safely squeeze more power out of your existing equipment, save money, and keep the lights on, all while knowing exactly how much risk you are taking."

It turns a rigid, fear-based safety system into a flexible, data-driven optimization tool.

Technical Summary

Here is a detailed technical summary of the paper "Risk-Based Dynamic Thermal Rating in Distribution Transformers via Probabilistic Forecasting."

1. Problem Statement

Low Voltage (LV) distribution transformers are facing accelerating demand growth (forecasted to increase by 50–100% by 2050) while replacement lead times and costs rise. Consequently, maximizing the utilization of existing assets is critical.

• Current Limitation: Existing protection devices (PDs) in distribution transformers are typically static and conservative. They rely on fixed tripping thresholds (e.g., based on instantaneous current) rather than real-time thermal conditions. This constrains transformer capacity even when safe operating headroom exists.
• The Gap: While Dynamic Thermal Rating (DTR) allows for adjusting loading limits based on real-time conditions, it is rarely applied to LV transformers due to a lack of monitoring and simple protection hardware. Furthermore, existing methods for optimizing relay settings often rely on deterministic load forecasts. This introduces error propagation (compounding uncertainties from load prediction to scale factor calculation) and fails to explicitly quantify the risk of transformer overheating.

2. Methodology

The authors propose a probabilistic, risk-based framework that directly forecasts the optimal scale factor ($k$) for adaptive numerical relays. This scale factor adjusts the tripping current threshold to maximize capacity while managing overheating risk.

A. Thermal and Protection Modeling

• Thermal Model: The study utilizes the IEEE thermal model to estimate the winding hotspot temperature ($\theta_H$). It accounts for ambient temperature, top-oil rise, and hotspot rise. Crucially, it addresses phase unbalance by splitting the load factor into winding ($K_w$) and top-oil ($K_o$) components.
• Protection Model: A dual time-constant model (ANSI 49) is used to calculate the tripping current ($I_{trip}$) based on the scaled rated current ($\hat{I} = k \times I_{rated}$).
• Target Variable: The "ground truth" for training is the optimal scale factor calculated retrospectively. This is the maximum $k$ that keeps the hotspot temperature below 140°C (the threshold for insulation bubble formation) given historical load and weather data.

B. Probabilistic Forecasting Framework

Instead of predicting load first and then calculating the scale factor (a multi-stage approach), the authors propose a direct forecasting approach:

1. Clustering: To overcome data scarcity (limited historical data per transformer) and capture fleet diversity, transformers are clustered using K-means on pre-processed features (historical load, metadata, and temperature). The optimal number of clusters is determined via Silhouette and Bayes Information Criterion scores.
2. Feature Engineering: Inputs include lagged per-phase loads, unbalance metrics, calendar data (day/holiday), and temperature features (including exponential weighted moving averages).
3. Model Training: LightGBM is used for Quantile Regression. Separate models are trained for each cluster and for specific percentiles (e.g., 5th, 50th, 95th).
   • Risk Control: Selecting the $p$-th percentile of the forecast corresponds to a $p\%$ probability of exceeding the hotspot limit.
4. Robustness Testing: The model was tested under "clean" (perfect weather) and "noisy" (realistic forecast errors, $\sigma \approx 1.12^\circ$C) temperature scenarios to ensure resilience.

3. Key Contributions

• Direct Probabilistic Forecasting: The paper introduces a novel method to directly predict the optimal relay scale factor, bypassing intermediate load forecasting steps. This eliminates the compounding of errors inherent in multi-stage approaches.
• Risk-Informed Decision Making: By using quantile regression, the method provides a direct mapping between the chosen prediction percentile and the probability of overheating. This allows Distribution Network Operators (DNOs) to tune the system based on their specific risk appetite (e.g., choosing the 5th percentile for a 5% risk of exceedance).
• Scalable Clustering: The use of clustering allows the model to generalize across a fleet of 644 transformers, capturing specific group characteristics without overfitting to individual, data-scarce units.
• Validation of Risk Metrics: The study demonstrates that the predicted percentiles are well-calibrated, meaning the actual frequency of hotspot exceedance matches the selected probability level.

4. Results

The methodology was validated using data from 644 UK LV transformers (25–1000 kVA) over 183 days during the winter of 2024/25.

• Capacity Gains: Compared to a standard static scale factor of 1.05, the proposed method achieved a 10–12% increase in mean maximum capacity.
  • Example: Using the 2nd percentile setting increased capacity by ~10.5% while maintaining a hotspot exceedance risk of only 2%.
• Model Calibration:
  • The Direct Approach achieved a 90% coverage rate (the true scale factor fell within the 5th–95th prediction interval 90% of the time), indicating excellent calibration.
  • The Multi-Stage (Load-based) Approach failed significantly, achieving only 17% coverage due to error compounding and the inability to capture phase correlations.
• Robustness to Forecast Errors: The model remained robust even when realistic temperature forecast errors (within 2°C) were introduced. Sensitivity analysis showed that temperature errors resulted in minimal scale factor deviations (0.017–0.03), which can be absorbed by selecting a more conservative percentile.
• Temperature Training: Training with a single exact temperature value outperformed training with multiple perturbed values, suggesting that synthetic data augmentation did not improve generalization in this context.

5. Significance

This paper provides a practical, automated pathway for DNOs to unlock significant capacity in existing distribution networks without requiring new hardware investments (other than potentially retrofitting numerical relays).

• Operational Impact: It shifts protection policy from static, conservative limits to dynamic, risk-aware limits.
• Economic Value: By deferring costly transformer upgrades and replacements, DNOs can manage the surge in LV demand (driven by EVs and heat pumps) more effectively.
• Safety: The probabilistic framework ensures that capacity gains are not achieved at the expense of asset safety; the risk of insulation failure is explicitly quantified and controllable by the operator.

In conclusion, the proposed framework successfully bridges the gap between advanced thermal modeling and operational protection settings, offering a scalable solution for maximizing the utilization of LV distribution assets in the face of uncertain future demand and weather conditions.