How it works
An energy yield assessment estimates a plant's long-term annual output and the uncertainty around it. The uncertainty comes from year-to-year variation in the weather, from the estimate of the long-term resource itself, and from the modelling of losses. Independent sources combine as σ = √(σ_1^2 + σ_2^2 + … + σ_n^2), where each σ_i is one source's standard deviation as a share of P50. Assuming a normal distribution, P50 is the central estimate and P90 = P50 × (1 − 1.282 × σ). The factor 1.282 is the number of standard deviations below the mean that leaves 90% of outcomes above.
The period matters. A one-year P90 includes the full year-to-year swing in weather. Over ten years good and bad years partly cancel, so the weather term shrinks by a factor of √10 and the ten-year P90 sits closer to P50. The error in the long-term resource estimate stays the same every year, so it does not shrink. Lenders commonly test debt service against one-year values, such as a one-year P90 or P99.
Why it matters
The gap between P50 and P90 sets how much a project can borrow. If the lender sizes debt on P90, a P90 close to P50 means more debt against the same expected output. Better data narrows the gap. A year or more of on-site wind measurement can lower the uncertainty, and so raise debt capacity. Developers plan returns on P50, so an optimistic P50 inflates the IRR. Buyers with a volume guarantee in a PPA should check which value the seller has committed to.
A worked example
A wind farm has a P50 of 300,000 MWh a year. Its uncertainties are 6% for year-to-year wind, 5% for the long-term resource and 4% for losses and modelling. Combined, σ = √(6^2 + 5^2 + 4^2) = √77 = 8.8%. The one-year P90 is 300,000 × (1 − 1.282 × 0.088) = 300,000 × 0.887 = about 266,000 MWh. Over ten years the wind term becomes 6 ÷ √10 = 1.9%, σ = √(1.9^2 + 5^2 + 4^2) = 6.7%, and P90 rises to about 274,000 MWh.
Illustrative figures.