Answer
Solar probability of exceedance describes the modeled chance that energy production meets or exceeds a stated value over a defined period. P50 is the median; P90 is a lower threshold with 90% exceedance probability. Under a normal distribution, P90 is approximately P50 minus 1.282 times the energy standard deviation.
Last updated: November 2026
A yield estimate is more useful when the report explains what could make actual output lower. Probability of exceedance gives that uncertainty a precise meaning, but only when the time period, energy boundary and statistical assumptions are stated. This guide connects the P50, P90 and P99 labels to the design inputs behind them.
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What Probability of Exceedance Means in Solar Design
Probability of exceedance is the modeled chance that production will equal or exceed a stated energy value over a defined period. P50 is the median: half of the modeled outcomes lie above it. P90 is a lower threshold with a 90% modeled probability of exceedance, not a guaranteed minimum.
State whether the report concerns one future year, a multi-year average or another period. A one-year P90 does not promise that exactly nine of the next ten calendar years will exceed that number. Nor is a long-term average P90 interchangeable with a single-year downside estimate.
The Sandia PVPMC uncertainty guide distinguishes model uncertainty and input variability and explains the relevance of the P90/P50 ratio to project risk. A narrow spread is useful only if the uncertainty assessment is complete; understating uncertainty can also produce an attractively narrow spread.
For designers, separate two questions: how much energy the layout is expected to deliver, and how well that estimate is known. Better measurements may reduce uncertainty without changing the hardware. A layout change may increase central yield while introducing a new loss mechanism that needs assessment.
Annual exceedance values do not size an inverter’s instantaneous rating or establish battery autonomy during a cloudy week. Those decisions need time-series and power checks. Likewise, a contractual production guarantee may contain weather adjustments, exclusions and a different assessment period, so its breach probability cannot be inferred from the P50 label alone.
The P-Values Designers Actually Use
The following values are calculated using a normal-distribution approximation. Other distributions or an empirical series may be appropriate; the method must be stated in the report.
| P-value | Probability of exceedance | Z-score | Typical design use |
|---|---|---|---|
| P50 | 50% | 0.000 | Median production case |
| P75 | 75% | 0.674 | Intermediate downside illustration |
| P90 | 90% | 1.282 | Downside case if accepted by the reviewer |
| P99 | 99% | 2.326 | More extreme annual-energy downside case |
The relationship between any P-value and P50 is:
P_xx = P50 − (z-score × σ_total)
Where σ_total is the total combined uncertainty expressed in the same units as energy yield. This equation applies when the modeled distribution is normal and P50 equals its mean. It is not a universal method for every yield distribution.
A designer does not need to memorize z-scores. But a designer does need to understand that the P90/P50 spread is not arbitrary. It depends on the assessed uncertainty, the distribution and the reporting horizon. Those assumptions need review alongside the ratio.
How Probability of Exceedance Is Calculated
Start with a defined output and time horizon, then build an uncertainty budget that matches them. The energy boundary should say whether output is DC, inverter AC or net energy at the revenue meter.
Step 1: Gather Long-Term Irradiance Data
Use weather data with a documented period, spatial coverage, version and validation basis. Global horizontal irradiance (GHI) is irradiance on a horizontal plane; direct normal irradiance (DNI) is the direct beam on a plane normal to the sun; diffuse horizontal irradiance (DHI) is the diffuse component on a horizontal plane.
A site measurement campaign can help evaluate a long-term resource dataset, but its duration alone cannot prove quality. Sensor calibration, maintenance, missing records and representativeness matter. Do not assign a universal uncertainty percentage to a dataset name without the provider’s location-specific evidence.
Step 2: Run the System Simulation
Combine the resource data with the actual layout, equipment and documented losses. A multi-year simulation can show weather-driven variation; a typical-year simulation gives one representative result. Neither automatically supplies every model or parameter uncertainty.
P50 is the median of the modeled production distribution. Mean and median coincide under a symmetric normal model, but they need not coincide for a skewed distribution. Label the statistic correctly instead of calling every average P50.
Step 3: Quantify Each Uncertainty Source
For independent contributions represented as standard deviations on the same basis, root-sum-square gives a combined standard deviation. Correlated inputs require covariance or another suitable propagation method. Avoid counting weather variation twice when it is already represented by a multi-year simulation.
| Contribution | Evidence to review | Common mistake |
|---|---|---|
| Resource estimate | Provider validation and local comparison | Treating a confidence interval as one standard deviation |
| Interannual variability | Multi-year weather or energy series | Inferring variability from one typical year |
| Model and equipment | Validation and parameter evidence | Assuming a datasheet tolerance is automatically a normal distribution |
| Local losses | Site measurements and operating assumptions | Hiding expected losses inside uncertainty |
| Long-term performance | Degradation method and reporting period | Applying a single-year method unchanged to a lifetime average |
The IEA PVPS report on yield-prediction uncertainty discusses uncertainty across weather, modeling and measurements. Use it as methodological context, not a table of default values for every project.
Step 4: Build the Distribution
Choose the statistical treatment and retain the reasoning. The PVsyst P50-P90 documentation describes a Gaussian approach and user-supplied uncertainty parameters. It also explains that its annual-variability tool has limits, including treatment of uncertainty in the long-term mean. Know which uncertainties a tool includes before copying its output into a finance report.
Step 5: Report and Act on the Results
Report the central yield, uncertainty components, combination method, horizon and resulting exceedance values. Identify the evidence that could change the conclusion. A reviewer should be able to trace a conservative energy case back to its inputs rather than accepting a round-number haircut.
Design Choices That Tighten Your P90/P50 Spread
The P90/P50 ratio is not fixed by climate alone. Design decisions can materially improve it. A defensible reduction in uncertainty may improve a financing assessment, but lender acceptance and financing terms remain project-specific.
Use site-measured irradiance data
A well-maintained ground measurement campaign can help assess bias and local conditions. Compare it with a sufficiently long resource record, and agree the required campaign scope with the reviewer. Do not promise a specific uncertainty reduction or financing result from a fixed number of months.
Minimize shading and inter-row losses
Shading is one of the largest controllable uncertainty sources. Poorly spaced rows, nearby structures, and vegetation create losses that are hard to estimate precisely. Use shadow analysis to validate assumptions. Tighter spacing may save land cost but widen the P50/P90 spread if row-to-row shading is not well-characterized.
Validate bifacial albedo and rear-side gain
Bifacial gain depends on rear-side irradiance, mounting geometry and albedo, the fraction of incident light reflected by the surface. A software default may not represent the actual ground or roof. Measure albedo seasonally or use conservative values. Document the evidence for the gain and its uncertainty separately.
Select proven equipment with tight tolerances
Use appropriate module parameters and inverter efficiency data, with evidence for their uncertainty. A lower temperature coefficient affects performance but does not by itself prove lower uncertainty. Identify any limited validation evidence and account for it transparently.
Optimize DC/AC ratio and clipping
A higher DC/AC ratio increases annual energy but also increases clipping losses. The optimal ratio depends on local irradiance distribution, not a universal rule. Clipping interacts with the weather distribution. Do not assume that its effect on P90 is a fixed percentage of its effect on central yield. Model the full loss cascade before finalizing the ratio.
Use trackers with validated backtracking
Single-axis trackers increase production but add mechanical availability and backtracking uncertainty. Ensure the tracker algorithm accounts for terrain slope and diffuse light conditions. Trackers that fail to backtrack correctly during low-sun angles can cause unexpected shading and widen the P50/P90 gap.
Common Design Mistakes That Widen Uncertainty
Some design practices increase the gap between P50 and P90 without improving actual production. These mistakes are expensive because they make the project look riskier to lenders.
Over-relying on TMY data alone
A Typical Meteorological Year (TMY) is a synthetic 8,760-hour year built from typical months. It does not contain the sequence of year-to-year variation. Use separate variability evidence or an appropriate multi-year analysis; the size of any error is project-specific.
Using aggressive soiling assumptions
Check soiling against the site, rainfall and planned cleaning. An optimistic expected-loss assumption biases the central estimate; adding an uncertainty margin is not a substitute for correcting that bias. A single disappointing year cannot reveal which input was wrong without operational evidence.
Ignoring inverter degradation and availability
Inverters fail. Transformer oil ages. Auxiliary loads change. An availability assumption needs a definition, maintenance plan and supporting evidence. Use manufacturer data and O&M records to set realistic availability assumptions.
Combining optimistic and pessimistic assumptions inconsistently
Some designers use conservative irradiance but optimistic losses, or vice versa. This produces a P50 number that looks conservative but a P90 number that is not. Every assumption should be documented and internally consistent.
Failing to update the model after commissioning
Once the plant operates, actual production data should refine the model. Operating data can refine performance and availability assumptions. The update may raise or lower the estimate; use the evidence rather than aiming for a preferred P90.
A Worked Example for a 2 MW Rooftop Project
This is an illustrative design calculation, not a measured Texas project. Assume a 2 MWp rooftop, a normal annual-energy distribution and independent one-standard-deviation contributions expressed as percentages of P50. All inputs below are assumptions, not recommended uncertainty defaults.
| Input | Assumed value |
|---|---|
| P50 annual net energy | 3,200 MWh |
| Irradiance estimate uncertainty | 3.0% |
| Model uncertainty | 3.5% |
| Interannual variability | 3.0% |
| Equipment uncertainty | 1.0% |
| Soiling uncertainty | 1.5% |
Combine uncertainties:
σ_total = √(3.0² + 3.5² + 3.0² + 1.0² + 1.5²) = √33.5 = 5.788%
Convert to energy: 0.05788 × 3,200 = approximately 185.21 MWh. With the rounded normal quantile 1.282, P90 is 3,200 - 1.282 × 185.21 = approximately 2,962.6 MWh, or 92.6% of P50. That ratio describes these assumptions; it is not a bankability certificate.
Now change only irradiance uncertainty from 3.0% to 4.5%:
σ_total = √(4.5² + 3.5² + 3.0² + 1.0² + 1.5²) = √44.75 = 6.690%
The energy standard deviation becomes approximately 214.07 MWh and P90 becomes approximately 2,925.6 MWh. The difference is about 37 MWh, not 21 MWh. The earlier calculation incorrectly summed the squared terms.
| Illustrative case | P50 | P90 | Total sigma |
|---|---|---|---|
| Resource sigma 3.0% | 3,200 MWh | 2,962.6 MWh | 5.788% |
| Resource sigma 4.5% | 3,200 MWh | 2,925.6 MWh | 6.690% |
- 3.0% resource sigma2,962.6
- 4.5% resource sigma2,925.6
Source: Illustrative example, not market data; normal model and independent uncertainties above, checked November 2026.
Do not multiply this P90 difference by project life and call it recovered revenue. Lower uncertainty is not additional physical generation, and a lifetime-average exceedance calculation has a different time basis. A measurement campaign’s value needs its own cost and decision analysis.
Key Takeaway
Check the squared-term sum before interpreting P90. Keep uncertainty reduction separate from an increase in expected physical output.
Review the model inputs before presenting downside yield
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Probability of Exceedance in Design Workflows
Use the statistical method that fits the design question. A single annual-energy percentile cannot represent every risk in a clipped, bifacial or storage-coupled system.
Clipping-Aware Assessment
Compare candidate DC/AC ratios using the same weather and loss assumptions. If clipping changes the shape of the energy distribution, check whether a normal approximation remains adequate. Do not infer downside production merely by applying a constant annual haircut to every simulated hour.
Bifacial and Tracker Assessment
Retain the geometry, albedo and tracker-control assumptions with the yield model. Separate expected rear-side production from uncertainty in that estimate. Additional modeled gain should have evidence behind it rather than automatically receiving the same confidence as better-characterized output.
Storage Coupling Changes the Question
Storage value depends on when energy is available, the load or price profile, operating limits and dispatch decisions. Annual P90 energy alone cannot establish reliable backup duration or a revenue percentile. Review the joint weather, operating and price scenarios required by the decision.
SurgePV supports energy-yield and financial modeling. Its published scope does not substantiate native probabilistic reporting, lender acceptance or automatic uncertainty selection. Use a demonstration to examine the supported workflow and identify the independent analysis required for the project.
When P90 Matters and When It Does Not
The need for formal exceedance analysis comes from the decision and its reviewer, not a universal project-size threshold. Ask the owner, lender or guarantor which horizon and energy boundary they require.
| Project context | Useful assessment | Question it answers |
|---|---|---|
| Residential proposal | Expected yield plus clearly labeled downside sensitivity | How might savings change in a lower-output year? |
| Financed commercial project | Reviewer-approved exceedance analysis | What downside energy case supports the finance model? |
| Utility project | Independent yield and uncertainty review | Are resource and loss assumptions suitable for the investment? |
| Off-grid or critical loads | Chronological reliability and energy-balance analysis | Can loads be served during specific shortages? |
| Solar plus storage | Dispatch and revenue scenarios | How do timing and controls affect service or value? |
Do not label an arbitrary percentage reduction P90. A conservative scenario can still be useful when it is honestly identified as a sensitivity. The probability label requires a statistical basis and a defined scope.
When explaining results in customer proposals, distinguish expected savings from a contractual guarantee. State the modeled period and the key uncertainty drivers in language the customer can understand.
How to Read a Yield Report as a Designer
Read the assumptions before judging the headline ratio. A useful report lets another reviewer reconstruct the path from resource data to net energy and then to the probability statement.
1. Irradiance Dataset and Period
Record the provider, version, years, spatial resolution and any site adjustment. Check gaps and time conventions. Ask why the record represents the site and whether its duration is sufficient for the stated purpose. Coverage differs across products; a provider’s name alone is not a validation result.
2. Loss Assumption Table
Every expected loss needs a basis. Review shading geometry, cleaning, availability, electrical losses and degradation separately. A warranty limit is not necessarily an expected degradation curve, and component reliability alone is not the full plant-availability assumption.
3. Uncertainty Breakdown
Check whether entries are standard deviations, confidence intervals or limits. Review dependence and double counting before combining them. Distinguish uncertainty in the central estimate from natural year-to-year variability, and explain how each behaves over the chosen reporting period.
4. Sensitivity Cases
Use sensitivity cases to identify which assumptions influence the decision most. A sensitivity is a changed input, not automatically a probability scenario. Retain both the central and changed assumptions so the engineering team can identify a useful measurement or design action.
Pro Tip: Put the time horizon beside P90
Write whether the result describes one year or a multi-year average, and identify the net-energy measurement boundary. This prevents a statistically correct number from answering the wrong question.
For a review of the design and energy-yield workflow, book a project demonstration. Bring the independent engineer’s reporting requirements so any additional uncertainty analysis is identified early.
Frequently Asked Questions
What is probability of exceedance in solar design?
It is the modeled chance that production meets or exceeds a stated energy value over a defined period. P50 is the median and P90 is a lower threshold with 90% modeled exceedance probability. Neither is a production guarantee.
How do you calculate P90 from P50 in solar?
For a normal energy distribution, P90 is approximately P50 minus 1.282 times the energy standard deviation. The uncertainty estimate must match the time horizon and energy boundary. Independent contributions can be combined in quadrature, while correlated contributions need additional treatment.
What is a good P90 to P50 ratio for solar projects?
There is no universal ratio that proves a project is bankable. The ratio depends on the resource, uncertainty method and reporting horizon. Review the uncertainty budget rather than selecting a target ratio first.
Does P90 mean exactly nine good years out of ten?
No, P90 is a modeled probability rather than a guaranteed sequence of annual outcomes. A single-year result and a multi-year-average result answer different questions. State the period and assumptions beside the value.
Can TMY data alone provide a P90 estimate?
A typical meteorological year alone does not describe interannual variability. A P90 assessment needs additional variability and uncertainty evidence or an appropriate multi-year analysis. A single simulation output is not automatically a complete probability distribution.
Should residential solar proposals include P90?
Use P90 when there is a defensible statistical assessment and a reason to show it. Otherwise a clearly labeled downside sensitivity can explain lower-output conditions. Do not attach a probability label to an arbitrary production reduction.
Do bifacial modules and trackers change exceedance analysis?
They introduce production inputs that need their own evidence and uncertainty treatment. Albedo, rear-side geometry, tracking and availability can affect the result. Additional expected energy does not automatically mean a narrower P50/P90 spread.
Where this fits
This article is part of SurgePV's Solar Design hub, which works through the topic from first principles to the decisions a project team actually has to make.
