On a utility-scale project, the lender does not size debt on the P50 in your model. It sizes it on a downside percentile — and if you built that percentile by subtracting a fixed margin, the independent engineer will take it apart. The discount from P50 to P90 is not a market convention: it is 1.282 × σ, and σ belongs to your site, your data and your assessment period.
This article is for the engineer who has to produce that number and defend it, and for the analyst who turns it into debt. It is not an introduction to percentiles.
In one screen
- The P50→P90 discount is
1.282 × σ. Published total uncertainty for a well-documented assessment is around 6.5 % (IEA-PVPS Task 13), so roughly −8 % — but with 20 years of measured in-plane irradiance the same report puts total uncertainty as low as 4.55 %, and with short satellite series as high as 14.9 %.- Seven assessors, the same inputs, the same site produced P50 values from 1,095 to 1,405 kWh/kWp — σ ≈ 9.7 % between assessors. The spread between people exceeded the uncertainty budget any one of them declared.
- Assuming a symmetric distribution is optimistic by construction: Sandia’s modelling guide states that when input distributions are treated as symmetric, “energy yield forecasts tend to be overstated, and financial risk understated”.
- Fleet data agrees: P99 outcomes are occurring about five times more often than expected — roughly one year in 20, not one in 100 — and 17 times more often once the optimism in the P50 itself is included, i.e. about one year in six (kWh Analytics, 2023).
- The one-year P90 and the tenor P90 are different numbers. Only the interannual term divides by √N; model bias does not.
The two percentiles a lender actually uses
The mechanism is simple and worth stating precisely, because it is where most reports lose credibility. The lender takes the cash available for debt service in a downside production case, applies a target DSCR to it, and the result caps the debt service the asset can carry. Pivotal180’s project-finance course describes the operating rule: run the cash flows in more than one production case and, period by period, take the lesser of cash available divided by the target DSCR — that is the binding constraint, and the sculpting follows the more conservative case (Pivotal180, 2024; educational material, not a survey of transactions).
Which percentile is applied, and at what DSCR, is a matter of negotiation, jurisdiction and contract — not a constant you can print in a report. Some structures pair a P50 case at a higher DSCR with a downside case near 1.00× (Renewables Valuation Institute, also teaching material). What is documented from the lending side is that P99 estimates are used in both debt and tax-equity sizing (kWh Analytics, Solar Risk Assessment 2023, p. 10). If you have been told there is a universal “1.25× on P90”, treat it as hearsay until your lender says it.
So: the deliverable is not one number. It is a distribution with auditable provenance, from which any percentile can be read.
Where the discount comes from, and why a fixed margin is wrong
The quantile factors are not in dispute:
| Percentile | Met or exceeded in | z factor | Energy at P50 = 170 GWh, σ = 6.5 % |
|---|---|---|---|
| P50 | 50 % of years | 0.000 | 170,000 MWh |
| P75 | 75 % of years | 0.675 | 162,540 MWh |
| P90 | 90 % of years | 1.282 | 155,830 MWh |
| P95 | 95 % of years | 1.645 | 151,820 MWh |
| P99 | 99 % of years | 2.326 | 144,300 MWh |
Factors as published by Solargis; the energy column is an illustrative case, not a project. If any of these terms is new, start with the glossary entries for P50, P90 and P99, DSCR and DSCR-sculpted debt sizing.
Everything therefore rides on σ, and σ is not a property of the technology — it is a property of how well you know the site. IEA-PVPS Task 13 publishes the range explicitly: a reference case of 20 years of satellite data in the horizontal plane carries 8.7 % uncertainty; shorter series push it to 14.9 %; 20 years of measured in-plane irradiance bring it down to 4.55 %, and the report notes P90 values “which could be up to 20 % higher for the case with reduced uncertainty” (IEA-PVPS T13-18:2020, Fig. 16).
Apply that to the same P50:
| Same P50 (170 GWh) | Total σ | P90 | Real discount |
|---|---|---|---|
| 20 years of measured in-plane irradiance | 4.55 % | 160,100 MWh | −5.8 % |
| Well-documented assessment | 6.5 % | 155,830 MWh | −8.3 % |
| Short satellite series | 14.9 % | 137,500 MWh | −19.1 % |
A fixed 8 % margin overstates the P90 on the poorly characterised site and understates it on the well-measured one. In the first case you are promising the bank energy your own uncertainty does not support; in the second you are leaving cheap debt on the table. And note the direction of the incentive: the money spent on a ground station is not an expense against the report, it is leverage.
The uncertainty budget, item by item
This is the table an independent engineer wants to see reconstructed. IEA-PVPS Task 13 publishes one worked example (courtesy Fraunhofer ISE), with uncertainty per step of the chain:
| Step | Uncertainty | Effect on energy |
|---|---|---|
| Global horizontal irradiation | 4.0 % | 1,248 kWh/m² |
| Transposition to plane of array | 2.5 % | +16.0 % |
| Near-shading between rows | 2.0 % | −1.7 % |
| Shading by objects | 3.0 % | 0.0 % |
| Soiling | 0.5 % | −0.5 % |
| Reflection / IAM | 0.5 % | −2.7 % |
| Spectrum | 0.5 % | −1.0 % |
| Irradiance dependence | 0.8 % | −1.5 % |
| Temperature | 1.0 % | −2.5 % |
| Mismatch, DC wiring | 0.5 % each | −1.6 % |
| Inverter | 1.5 % | −1.2 % |
| Curtailment, AC, transformers | 0–0.5 % each | −1.6 % |
| Total | 6.5 % | PR 86.6 % |
Two things are easy to miss. First, the report states the combination method and its condition: the total is the root-sum-square of the relative uncertainties, “only valid if all distributions are assumed as normal and independent from each other”. Second — and this matters for the next section — this table contains no interannual variability and no degradation: the specific yield is an average over the operating period.
Interannual variability is a separate term, and a regional one. The same report defines it as the ratio of standard deviation to long-term average GHI and reports that in Europe it “can range from ca. ±4 % up to ca. ±7 % for more complex conditions like e.g. near coastal areas”, while noting the resource over Africa varies considerably less. PV output amplifies it: in Solargis’s worked case for Almería, GHI variability is ±2.6 % while PV output variability is ±3.2 %.
The finding that should change how you read any yield report
If the budget above is followed carefully, total uncertainty lands near 6.5 %. So here is the uncomfortable measurement, from the same IEA-PVPS report: a blind exercise gave five to seven professional assessors identical inputs for the same plant and compared their results.
| Site | P50 range (kWh/kWp) | P90 range | σ between assessors | Measured |
|---|---|---|---|---|
| Bolzano, Italy | 1,095 – 1,405 | 997 – 1,274 | 9.7 % | 1,275 (2010–2019) |
| Alice Springs, Australia | 1,757 – 1,985 | 1,631 – 1,819 | 3.9 % | 2,075 initial, 1,926 at 10 years |
And the mechanism behind the spread is the detail worth keeping: the GHI→in-plane transposition alone ranged from +18.8 % to +24.6 % “even if the yield assessors all claimed to have used the Perez model”.
Read that again: the same model name, the same input data, a six-point spread in the first step of the chain. The uncertainty between assessors, on complex terrain, exceeded the uncertainty budget any single assessor declared. If you are comparing two reports on your project and they disagree, the software brand is not the first place to look — the assessor’s decisions are. The assessor’s decisions are where two yield estimates on the same site come apart.
The distribution is not a bell curve, and the direction of the error is known
Two independent strands say the same thing.
From the modelling side, Sandia’s PV Performance Modeling Guide is explicit: annual insolation “is commonly modelled by a normal distribution for convenience”, but PV energy yield “is likely to be asymmetric about the P50”, and “when input distributions are treated as symmetric, energy yield forecasts tend to be overstated, and financial risk understated” (PVPMC, uncertainty quantification). NREL measured the size of that effect in SAM: computing P90 from a fitted normal instead of the empirical distribution of 30 historical years gave a P90 1.72 % too high for fixed tilt, 2.91 % for single-axis tracking and 2.98 % for CPV (Dobos, Gilman & Kasberg, NREL/CP-6A20-54488, 2012). The same paper adds a warning about the input file everyone uses: because TMY files exclude the potential worst-case years, they “may be more appropriate for preliminary analysis of a system design than for financial decisions” — and in all three of their cases the TMY run came out above the P50.
From the operating fleet, kWh Analytics reviewed 25 independent-engineer reports against a dataset of more than 200 utility-scale plants and over 600 plant-years, adjusted for weather and curtailment. The result: “P99 outcomes are happening 5 times as often as would be expected, even after removing the effect of optimistic P50 estimates” — about one year in 20 instead of one in 100. Keep the two numbers apart, because they answer different questions: five times is the uncertainty problem alone, with the P50 assumed correct; 17 times — roughly one year in six — is what projects actually experience, once the optimism in the P50 is included. Their named root cause is a gap in the budget, not a failure of statistics: none of the reports reviewed incorporated uncertainty due to equipment performance, and the real performance-index distribution is “strongly left skewed compared to the normal distribution typically assumed”, driven by recurring inverter failures, ground faults and manufacturing defects (Solar Risk Assessment 2023, p. 10).
IEA-PVPS saw the same failure from a third direction, comparing modelled bands against 10 years of measurements at Alice Springs: “it appears that the modelled uncertainty bounds were taken too small, with the measured yield hitting or exceeding the P10 to P90 boundaries”.
Three sources, three methods, one conclusion: symmetric uncertainty and an incomplete budget produce a P90 that is too high. That is the number the debt rests on.
One year or the tenor: two P90s, and only one of them averages out
This is the distinction that separates a report that survives due diligence from one that gets sent back.
Interannual variability is aleatory: natural, irreducible year-to-year weather noise. Over N years it averages, and the standard error of the mean falls as σ/√N — the method Solargis publishes for exactly this calculation. Model and data bias is epistemic: it comes from incomplete knowledge, and Sandia notes it “can be reduced” with better information — but crucially it does not dilute with time. If your satellite dataset reads 2 % high at your site, it reads 2 % high every year of the loan.
So the arithmetic splits:
- One-year P90 → governs whether there is cash in a given year, so it drives the annual DSCR test. Here the full interannual term applies.
- Tenor P90 (10 years, or the debt term) → sizes the loan. The interannual term is divided by √N; the systematic term stays put. IEA-PVPS states it plainly: over a 20-year-plus horizon “the interannual variability is essentially cancelled out”, and “the P90/P50 ratio will decrease due to the decrease in uncertainty”.
Worked through the Almería example, an interannual ±3.2 % at one year becomes ±1.0 % over ten, and total uncertainty drops from 6.9 % to about 6.2 % — moving the P90 discount from −8.9 % to −7.9 % (our arithmetic applied to Solargis’s published components, not a published result). The effect looks small precisely because the systematic term dominates, and that is the lesson: if you want a materially better tenor P90, reduce model and data bias, not the number of years you average.
One caveat we should state rather than bury: σ/√N assumes independent, identically distributed years. Multi-year autocorrelation and resource drift violate it. Long-term in-plane irradiance in Germany rose about 1.1 %/year over 2008–2018 across 44 systems — brightening large enough that measured yields rose despite module degradation (Müller & Kiefer, 2019, doi:10.13140/RG.2.2.16442.54721; figures as reported in IEA-PVPS T13-18:2020). A TMY built on a different decade is not a neutral reference.
What the independent engineer checks
From the sources above, the checklist is not a matter of taste:
- P50 and P90 both stated, and the P90 given for one year and over the debt tenor.
- The uncertainty budget broken out by source, with the combination method stated — and its independence assumption acknowledged.
- Equipment-performance uncertainty included. This is the gap kWh Analytics found in 25 of 25 reports; including it is now a differentiator.
- Resource provenance: which dataset, over how many years, validated how, and whether it was site-adapted with ground measurement.
- Whether the percentile came from a fitted normal or an empirical/Monte Carlo distribution — and, if normal, the acknowledgement that this is optimistic in the tail by a couple of percent.
- Degradation and availability assumptions, stated and justified.
- Coherence above all: a P90 that cannot be reconstructed from the declared σ is a P90 the IE will cut.
How Heliosolve handles it, and what it does not do
Heliosolve derives P50/P90/P99 with a Monte Carlo that keeps the correlations between uncertainty sources, rather than a subtraction from the P50, and it reports the debt the downside case supports at a target DSCR you set. It separates the interannual term from the systematic one, so the one-year and tenor percentiles are different outputs rather than the same number relabelled. Every input is tagged as typed, estimated or taken from a catalogue, which is what makes the reconstruction the IE asks for possible.
What this does not mean: we have no track record of lender acceptance, our documented validation against measured data covers a single plant, and energy and financial results are estimates under the assumptions you enter. Nothing here removes the need for an independent review — the point of the traceability is to make that review faster, not to replace it.
If you want to see it on a project: talk to an engineer.
Frequently asked questions
What is the difference between P50 and P90 in a solar yield assessment?
The P50 is the median annual production, met or exceeded in half of years. The P90 is met or exceeded in 90 % of years. The developer evaluates the project on the P50; debt is sized on a downside percentile, because repayment depends on the weak years.
How do you calculate the P90 of a solar plant?
P90 = P50 × (1 − 1.282 σ) if you assume a normal distribution, where σ is total uncertainty combined by root-sum-square — or, better, from an empirical or Monte Carlo distribution. NREL measured the normal assumption to be optimistic by 1.7–3.0 % depending on technology.
Why is subtracting a fixed margin from the P50 wrong?
Because the discount is 1.282 × σ, and σ depends on your resource data and site. Published total uncertainty ranges from 4.55 % with 20 years of measured in-plane irradiance to 14.9 % with short satellite series — that is a P90 discount between roughly 6 % and 19 % for the same P50.
Why is the P99 breached more often than once a century?
Because the real distribution is left-skewed and the budget usually omits equipment performance. kWh Analytics found P99 outcomes occurring about five times more often than expected across more than 600 plant-years.
Is the P90 for one year the same as the P90 over the debt term?
No. Interannual variability averages out as σ/√N, so the tenor P90 sits closer to the P50; model and data bias does not average out at all. Reporting a single one-year P90 for both purposes is a common and expensive error.
How much can better resource data raise the P90?
IEA-PVPS Task 13 reports P90 values up to 20 % higher in its reduced-uncertainty case, where 20 years of measured in-plane irradiance replaces a short satellite series. The gain comes from lower σ, not from a higher P50.
Where to go next. If you want what a mis-stated P90 costs the financing, continue with the real cost of a PV simulation error. If you are choosing the tool that will produce this number, start with how to choose solar farm design software, or go straight to Heliosolve and PVsyst compared. And if you want to see how we derive the percentiles and what our validation does and does not cover, read the methodology and its limits.
Sources. IEA-PVPS Task 13, Uncertainties in Yield Assessments and PV LCOE, T13-18:2020 · Sandia PVPMC, PV Performance Modeling Guide, uncertainty quantification · Dobos, Gilman & Kasberg, NREL/CP-6A20-54488, 2012 · kWh Analytics, Solar Risk Assessment 2023 · Solargis knowledge base, P50/P90 scenarios · PVsyst documentation, P50–P90 evaluations · Pivotal180 and Renewables Valuation Institute (educational material) · Müller & Kiefer, 2019.