Total uncertainty of AEP in wind projects: decomposition and spread to P90

The P50 of AEP is the number that the lender uses to calculate whether the project covers the debt. It is not the P50 — the central energy estimate — but the estimate that is 90% likely to be exceeded throughout the life of the project. The difference between P50 and P90 is entirely determined by the total uncertainty of the analysis: the greater the uncertainty, the greater the gap, the worse the DSCR, the more difficult the financing.

Understanding how total uncertainty is built—which components make up it, how it spreads and what dominates the result—is what separates a resource report that closes funding from one that generates previous conditions or is returned for review.This note presents the methodology of decomposition and propagation of uncertainties applied in wind reports of Renewene, with the typical values observed in onshore projects in Brazil.

Uncertainty vs. variability: the distinction that matters

The first common misconception in the interpretation of P50/P90 is to confuse uncertainty (epistemic) with natural variability (random). These are distinct origins with different statistical treatment:

• Interannual variability It is the natural fluctuation of the wind resource year by year — caused by variations in climate patterns, ENSO, NAO and large-scale teleconnections. It is real, it exists in the physical world and cannot be eliminated with more data or better methodology. It contributes to long-term uncertainty because we do not know in which years the project will operate within its useful life.
• Measurement uncertainty It is the lack of knowledge about the true value of a greatness — caused by limitations of the instrument, calibration method, or representativeness of the campaign. It can be reduced with better instrumentation, longer campaigns and more rigorous methodology.
• Model uncertainty It is the difference between model and reality — caused by simplifications in wake models, power curve, shearing. It can be partially reduced with more sophisticated models, but never eliminated.

In practice, the three contribute to P90 in a combined manner via uncertainty propagation (RSS). Interannual variability is invariably the dominant component — meaning that increasing measurement accuracy beyond a certain point has a decreasing return if P50-P90 gap is mainly determined by climate.

Quadratic Sum Propagation (RSS)

The industry standard method for combining independent uncertainties is the quadratic sum of roots (Root Sum of Squares — RSS), as described in the Guide to the Expression of Measurement Uncertainty (GUM, BIPM/JCGM 100:2008). For uncertainties expressed as standard deviation (1σ) of each component i:

σ_total = √(σ12 + σ22 + σ32 + ... + σn2)

The implicit hypothesis is that uncertainties are independent and not correlated. In practice, some correlations exist — for example, a year of meteorologically atypical measurement affects both the resource estimate and the MCP — and the RSS can both underestimate and overestimate total uncertainty depending on the correlation signal. Conservative reports treat correlations explicitly; basic reports assume total independence.

Once calculated σ_total, the relationship between P-values is immediate by normal distribution:

P90 = P50 × (1 − 1.282 × σ_total) P75 = P50 × (1 − 0.674 × σ_total) P99 = P50 × (1 − 2.326 × σ_total)

The 1.282 factor is the 90 percentile of the standard normal distribution (z0.90). The validity of the normal distribution for AEP — rather than an asymmetric distribution — is justified by the central limit theorem when many independent components combine, and is the convention universally adopted by the industry.

The ten components of uncertainty

The uncertainty decomposition of AEP can be organized into four groups. The values below represent typical ranges observed in onshore projects in Brazil (σ, 1 standard deviation, in % of estimated AEP). Each project will have specific values depending on the quality of the campaign and the complexity of the site:

From P50 to P90: the complete distribution

With σ_total = 7.35%, the distribution of AEP around the estimated P50 determines all relevant values for financing. P90 results in 90.6% of P50 — a difference of 9.4 percentage points which, for a project of 300 GWh/year of P50, represents 28.2 GWh of gap between the central estimate and the value for DSCR purposes.

Sensitivity: what matters most to narrow the gap

As each component contributes to the gap P50−P90 proportionally to its variance (σi2), not to its standard deviation (σi), the component with greater σ has disproportionately greater contribution to the square. For a hypothetical project with P50 = 300 GWh/year:

P50 - P90 = 300 × 1.282 × 0.0735 = 28.2 GWh/year

The contribution of each component to these 28.2 GWh is proportional to σi2/σ_total2. The tornado graph below shows these contributions in GWh — the format that makes the conversation about concrete uncertainty for investors and lenders:

How to reduce the gap P50−P90

The decomposition in FIG. 3 has direct implications for where to invest resources in the campaign:

1. Long campaign (≥ 3 years) is the most profitable investment. The annual variability reduces in the proportion of 1/√N, where N is the number of campaign years. A campaign of 3 years versus 1 year reduces this component from ~6.5% to ~3.8%, saving ~8 GWh from P90 in a project of 300 GWh/year. No other investment in quality has comparable return.
2. Wake modeling with explicit uncertainty is the second largest return. Wake loss is the second component (14.5% of the total). High fidelity models (LES, RANS) reduce the uncertainty of the model from 2.8% to ~1.5-2.0%, saving ~2-4 GWh from P90.
3. Choice and validation of the MCP (NT.02). The uncertainty of MCP of 2.3% can be reduced to ~1.5% with set of two reanalysis and concurrent period of 3+ years. See NT.02 For detailed methodology.
4. Instrumentation and QA/QC (NT.01, NT.03) have low marginal return From a certain level — these added components account for less than 4% of the total gap. Improving QA/QC beyond the normative minimum does not significantly move P90.

Documentation required in the resource assessment report

In order for a P90 to be bankable, the report must present the decomposition of uncertainty explicitly and traceable — not only the final number of P90. Lenders and ITAs check:

• Table of uncertainties with all components, values of σ in % of AEP and justification for each adopted value;
• Methodological reference for each component (e.g., interannual variability estimated by the Charter et al. 2002 method or equivalent);
• – Sensitivity test showing how P90 would change if each component diverged ±30% around the adopted value;
• Demonstration that the components are sufficiently independent for RSS application — or, where correlations exist, explicit correction;
• Explicit calculation of P50, P75, P90 and P99, with declared corresponding z factors.

The absence of the decomposition is equivalent to a black box for due diligence purposes: the number can be reasonable, but cannot be verified.