A practical guide to probabilistic load forecasting for distribution operators

The buffer in a point-forecast workflow is an informal estimate of how wrong the forecast may be. Operators receive one number for tomorrow's peak, add a margin based on experience, and procure against the result. Probabilistic forecasting makes that uncertainty visible and measurable.

What P10, P50, and P90 actually represent

A probabilistic output describes a demand distribution rather than supplying only one estimate. P10, P50, P90 are quantiles of a demand distribution. P50 = median, meaning there is an equal probability of demand landing above or below it. P10 means there is a 10% chance demand falls at or below this value. P90 means there is a 10% chance demand exceeds this value.

For reserve sizing, P90 is the operationally significant number. Procuring enough generation for P90 demand should cover approximately 90% of dispatch periods. The remaining question concerns the other 10%: is the cost of occasionally being short justified by avoiding excess procurement during the 90% of periods when demand stays below P90?

A point forecast does not offer that choice. It gives you a single value, leaving you to create a buffer heuristic from historical errors. A probabilistic forecast includes the uncertainty characterisation in its output.

Why the band width matters as much as the median

Two systems can return the same P50 while producing very different P10 to P90 ranges. A narrow band signals that the model expects demand within a relatively tight interval. A wide band indicates greater uncertainty, often because conditions differ from the training data or because the input signals are noisy.

For a distribution operator, a wide P10-to-P90 band is also an operational alert. It indicates that the duty engineer should not rely on the median alone. With a narrow band, procurement can sit closer to P50, with a smaller reserve margin.

That is the practical information missing from a point forecast. A persistence model might return 280 MW for tomorrow's peak. A probabilistic model could return a P50 of 274 MW, a P10 of 251 MW, and a P90 of 298 MW. The P90 of 298 MW becomes the actionable procurement ceiling rather than the single-point estimate. These numbers are a synthetic illustration only.

What probabilistic forecasts require from the underlying model

Producing P10/P50/P90 labels does not automatically mean a model is producing calibrated probabilities. In a calibrated forecast, the stated quantile probabilities correspond to observed frequencies. If a model says P90 is 300 MW, actual demand should exceed 300 MW about 10% of the time. A poorly calibrated system may use the correct labels while consistently making its bands too wide or too narrow, which makes the probabilities misleading.

Calibration should be a standard part of evaluating any probabilistic forecasting system. Backtesting needs a long enough period to produce dependable frequency counts, typically a full year at minimum to capture seasonal variation. Ask a vendor for its P90 coverage rate on its validation set. That result should be close to 10%. Coverage rates significantly above 10% mean the model is being overly conservative. Coverage rates significantly below 10% mean the band is too narrow and the stated uncertainty is not real.

The eZap model uses a gradient-boosted quantile regression approach, calibrated against held-out feeder data across different seasons. We track coverage rates as a routine quality metric. An uncalibrated probabilistic forecast can be worse than a point forecast because it creates confidence in a level of precision the model has not earned.

Where probabilistic forecasting falls short

Probabilistic forecasting cannot resolve demand events that are fundamentally unpredictable. Grid faults, sudden industrial shutdowns, and unexpected public events that move large populations toward air conditioning at the same time can all sit outside the distribution learned by the model. Such low-frequency, high-magnitude events are difficult for any forecasting system.

A wide P10-to-P90 band on an unusual day represents appropriate uncertainty, not a tail-event predictor. It does not identify which tail event will occur. Our claim is narrower: probabilistic forecasts improve procurement decisions on typical high-variance days, including temperature-driven peaks, demand transitions at season boundaries, and weekday-versus-weekend transitions. They do not replace operational judgment in genuinely novel conditions.

Resolution is another constraint. A feeder-level probabilistic forecast needs sufficient history from that feeder to learn a reliable conditional distribution. Feeders with sparse metering history or frequent topology changes will produce wide, uninformative bands until enough data accumulates. Newly commissioned feeders show this pattern clearly: the first season of probabilistic output can resemble a wide uniform distribution until the model has enough examples of that feeder's demand shape to form a useful estimate.

A practical note on presenting probabilistic output to operators

During early integration work, we found that probabilistic output asks readers to use a different mental model. Duty engineers accustomed to a single-number forecast may initially find a band difficult to interpret. "So what number do I actually use?" is a common first reaction.

The clearest framing we have found is P90 as the "safe procurement level" and P50 as the "expected outturn." Reserve margin is then the difference between what you procure and what P50 predicts. On a narrow-band day, that margin may be small. On a wide-band day, it should be larger. This language matches how experienced operators already assess risk, even when their existing process uses point forecasts and intuitive buffers.