| Vose Software

Industry: Utilities
Product: ModelRisk
Application: Day-Ahead Load Forecasting and Reserve Sizing


A Day-Ahead Peak Forecast of 8,935 MW Hides an 11.4% Chance of Beating Available Capacity

The control-room deterministic load forecast for tomorrow's 5pm coincident peak reads 8,935 MW. The system has 11,000 MW of committed capacity lined up — a comfortable-looking 2,065 MW of headroom. Yet when the same model is run as a distribution rather than a single number, the peak has a mean of 9,621 MW, a P99 of 12,972 MW, and an 11.4% probability of exceeding the 11,000 MW that has actually been scheduled. That is one summer afternoon in nine where the operator is short and buying into a scarcity-priced real-time market — or shedding load.

The gap is not a forecasting error. It is the difference between the expected peak and the tail of the peak. Air-conditioning load responds convexly to temperature, and tomorrow's peak temperature is itself a skewed forecast. A balancing authority rebuilt its day-ahead forecast in ModelRisk to size reserves against the distribution it actually faces, not the point estimate it had been committing to.

Day-ahead peak load distribution with capacity and reserve marks

The simulation runs 200,000 day-ahead futures. The deterministic forecast (the dotted line at 8,935 MW) sits well below the mean of 9,621 MW, because evaluating a convex temperature-to-load curve at the average temperature systematically underestimates the average load — Jensen's inequality, in MW. The right tail runs out to a P99 of 12,972 MW, almost 2,000 MW past the 11,000 MW committed line. The reserves the operator must hold are governed by that tail, not by the headline forecast.

Why a point forecast fails here

Load is the sum of a non-weather base, a weather-sensitive component, and a behind-the-meter solar offset. Each is uncertain, and the weather term is non-linear:

  • Peak temperature is a right-skewed forecast: a Normal central spread plus a one-sided Gamma heat surge. Mean 33.1 deg C, P99 of 41.1 deg C.
  • Temperature-to-load response is convex above an 18 deg C cooling balance point — a linear term (mean 200 MW per deg C) plus a quadratic A/C-saturation term — so a 1 deg C error near the top of the range costs far more MW than the same error near the balance point.
  • Base (non-weather) load carries a shared economic-activity multiplier so the aggregate keeps realistic spread instead of averaging away. Mean 6,400 MW.
  • Behind-the-meter solar offsets 5pm load by a mean of 743 MW, but is lower on the hottest, haziest days — a negative correlation that thins exactly when load is highest.

Evaluating that chain at central inputs returns 8,935 MW. Propagating the distributions returns a mean of 9,621 MW and the long upper tail above. The point estimate is not in the middle of the answer — it is below the bottom third of it.

Sizing the reserve against the tail

The decision is not "what is the peak" but "how much reserve to commit". The sweep below traces the probability that load exceeds committed capacity as a function of reserve held above the deterministic forecast.

Reserve sizing sweep shortfall probability versus reserve MW

The curve quantifies the reliability the operator is buying:

  • 2,181 MW of reserve above the deterministic forecast holds shortfall probability to 10%.
  • 4,037 MW is needed to reach a 1% shortfall night.
  • 6,006 MW is required for 0.1% — the cost of near-certainty rises steeply because it is buying down a thin tail.

Today's actual commitment — 2,065 MW above the deterministic forecast — corresponds to the 11.4% shortfall probability flagged on the headline chart. The sweep turns reliability from a slogan into a price.

What's driving the peak

Tornado chart of drivers of tomorrow peak load

Peak temperature dominates everything: its P10-to-P90 swing moves the peak by +/-1,211 MW — more than the next four drivers combined. The convex A/C-saturation term (+/-228 MW) and the temperature-to-load slope (+/-308 MW) amplify it. Base load (+/-312 MW), behind-the-meter solar (+/-262 MW) and forecast/telemetry error (+/-179 MW) are second order. The ranking tells the forecasting team where accuracy actually pays: tomorrow's temperature ensemble, not the load-model coefficients.

What the model changed

Committed headroom before and after Monte Carlo reserve sizing

The utility had been committing a flat 8% margin on the deterministic forecast — 9,649 MW. Against the simulated peak distribution that margin leaves a 44.8% probability of shortfall: the "before" histogram of committed headroom (capacity minus actual peak) sits squarely across the zero line. Re-sizing the commitment to the Monte-Carlo 1% target — 12,972 MW — pushes the headroom distribution cleanly positive, with a P10 headroom of +1,856 MW instead of -1,467 MW.

  • Reserve target switched from a flat 8% margin to a P(shortfall) = 1% reserve sized on the simulated peak distribution.
  • Temperature ensemble prioritised as the forecast input worth the most accuracy spend, on the strength of the tornado.
  • Convexity correction adopted: the day-ahead forecast now reports the distribution mean (9,621 MW), not the central-temperature evaluation (8,935 MW), ending the systematic low bias.
  • Behind-the-meter solar de-rated on high-heat days to reflect the negative correlation the deterministic offset was ignoring.

ModelRisk functionality used

  • Skewed temperature inputs — a Normal central spread plus a one-sided Gamma heat surge — to capture the fat upper tail of peak-day temperature that the deterministic forecast averaged away.
  • Convex temperature-to-load response combining linear and quadratic A/C-saturation terms, propagated through Monte Carlo so the peak distribution mean correctly exceeds the central-temperature evaluation.
  • Correlated behind-the-meter solar offset, negatively coupled to the heat surge, so the offset thins on exactly the days the peak is highest.
  • Reserve-sizing sweep of P(shortfall) against committed MW, turning a reliability target into a specific reserve quantity.
  • Tornado on the peak to rank where forecasting accuracy is worth buying — peak temperature first, by a wide margin.

The day-ahead forecast on the control-room screen is the mean of a distribution. The reserve the operator commits, the scarcity price the trading desk is exposed to, and the reliability the regulator measures all live in the tail of that distribution. Monte Carlo is what keeps the three numbers consistent.