Industry: Utilities Product: ModelRisk Application: Day-Ahead Load Forecasting and Reserve Sizing
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.
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.
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:
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.
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.
The curve quantifies the reliability the operator is buying:
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.
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.
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.
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.