Lifetime, degradation and P-values

Everything on this page turns a single first-year energy figure into the numbers a project is actually financed against: output in year 30, and output at a probability a lender will accept. Two degradation inputs set the decline, one lifetime input sets how far the forecast runs, and one uncertainty figure plus three exceedance probabilities set the confidence band.

None of it changes the layout. These are all post-processing on the energy result, so a change here needs the energy calculation run again and nothing more.

Degradation

What the two figures represent

They describe two physically different things, which is why they are two fields and not one.

1st year degradation is the initial step down that a module takes in its first weeks and months of operation and then does not repeat — chiefly light-induced degradation, LID, the drop that occurs when a cell is first exposed to sunlight. A datasheet quotes this separately from the long-term rate for the same reason. It is applied once.

Annual degradation is the steady long-term decline that follows: encapsulant ageing, cell and interconnect wear, slow optical losses. It compounds, so it is applied to the previous year's figure rather than to the original one. A module warranty normally states this as a maximum annual rate, and the warranted rate is the defensible input.

The relations

Year 1 energy       = capacity_kWp × specific yield          (before LID)

Year 1 (actual)     = Year 1 energy × (1 − first_year_deg%)

Year n  (n ≥ 2)     = Year 1 (actual) × (1 − annual_deg%)^(n−1)

The exponent is the part that gets misread. Year 2 is Year 1 (actual) reduced once, not twice — the first-year step and the first annual step are not both applied to year two.

The defaults, worked through

On the shipped defaults — 1.0 % first year, 0.4 % annually — the multipliers on Year 1 energy are:

Year 1  (actual) = 0.99
Year 20          = 0.99 × 0.996^19 = 0.99 × 0.9267 = 0.9174
Year 30          = 0.99 × 0.996^29 = 0.99 × 0.8903 = 0.8813

So a plant on the defaults is modelled at about 91.7 % of its pre-degradation first-year output in year 20, and about 88.1 % in year 30. Check those two multipliers against the warranty you have been given: a module warranted to hold 87 % at year 30 is consistent with these inputs, and one warranted to hold 80 % means the inputs are optimistic against the product being bought.

Plant lifetime

Plant lifetime sets how many years the multi-year forecast runs for, and nothing else. It ships at 30 years and accepts 1 to 50.

It has no effect on the first-year figure, on the capacity factor, or on any exceedance probability — those are all year-one quantities. What it does control is the length of the year-by-year table carried into the report's energy pages, and therefore the lifetime energy total. Match it to the term the project is being modelled over: the tariff term, the debt tenor, or the module warranty period, whichever the report is answering.

The summary header says 25yr whatever the lifetime is

The lifetime total reaches the summary table in a column headed 25yrP50(MWh), and that header is fixed text. Unlike the three probability headers, which are generated from the fields behind them, this one does not follow Plant lifetime. The value under it is the sum of every year from 1 to Plant lifetime, scaled to the first exceedance probability — so on the shipped lifetime of 30 years, the column headed "25yr" holds a 30-year total.

Two things follow. Read the column as the lifetime total at the first exceedance probability, not as a 25-year figure — it is only a 25-year figure when the lifetime is actually set to 25. And when the number leaves the application, state the lifetime beside it, because the header will otherwise misreport it to whoever receives the table.

Probabilistic yield

A single energy figure is a central estimate, and a lender does not finance a central estimate. Probabilistic yield restates the same result as the output the plant will beat with a stated probability.

Exceedance probability

An exceedance probability — the P in P50, P75, P90 — is the probability that the actual annual energy comes out at or above the stated figure.

• P50 is the median: half of years land above it, half below.
• P90 is the figure the plant exceeds in 90 % of years. It is a lower number than P50, and it is lower precisely because it is more likely to be beaten.
• The higher the P number, the more conservative and the smaller the energy figure. P99 is a small number you are almost certain to exceed; P10 is a large one you will usually fall short of.

The single most common error in reading these figures is treating a higher P as a better plant. It is the same plant, described with more confidence.

Combined uncertainty

One sigma, σ, is the width of the distribution: on a normal distribution about 68 % of years fall within one sigma of the median. It is entered as a percentage and used as a fraction — 5.0 % is 0.05 in the relations below.

It is a combined figure, which conventionally bundles together everything that makes one year differ from the long-run expectation: year-to-year variation in the solar resource itself, the uncertainty in the irradiance dataset used, transposition and yield model uncertainty, and uncertainty in the loss and degradation assumptions. The application takes it as one number and does not decompose it, so what it covers is what you decide it covers — and that decision belongs in the report alongside the figure.

The two relations

P75 = P50 × (1 − 0.674 × σ)

P90 = P50 × (1 − 1.282 × σ)

The multipliers are not tuning constants. They are the standard normal deviates — the number of standard deviations below the median at which the chosen fraction of the distribution lies above. Look up the standard normal distribution: 75 % of the area sits above −0.674σ, and 90 % of it sits above −1.282σ. The relations are the standard normal quantile applied to the median, which is why the same two numbers appear in every yield assessment you will be shown.

On the shipped σ of 5.0 %:

P75 = P50 × (1 − 0.674 × 0.05) = P50 × 0.9663
P90 = P50 × (1 − 1.282 × 0.05) = P50 × 0.9359

The P50 column takes no multiplier, because the deviate at 50 % exceedance is zero.

The three exceedance fields

All three are yours to set. There is no fixed P50/P75/P90 triple in the application — 50, 75 and 90 are the shipped values, and each field accepts anything from 1.0 to 99.9.

The summary column headers are built from these values, so they rename themselves when you change them. Set the third field to 95 and the third column reports at 95 % exceedance under a heading that says so. Nothing else in the summary announces the change.

The columns sit at the right-hand end of the summary table, alongside the capacity factor and the lifetime energy total — see Summary columns.

Capacity factor

CUF = Year 1 (actual) / (capacity_kWp × 8760) × 100 %

The capacity utilisation factor, CUF, is first-year output as a percentage of what the plant would generate running flat out at its full DC capacity for every one of the 8 760 hours in a year. It is a normalised figure, so it is what makes two plants of different sizes, or on different sites, comparable at a glance — and it is the figure tenders and regulators most often ask for.

Two things to hold on to when quoting it:

• It is computed after the first-year degradation step, from Year 1 (actual), so it is a year-one figure. It declines over the plant's life in the same proportion as the energy does.
• It is referenced to DC capacity here. A capacity factor quoted elsewhere against AC capacity is a different, larger number. State which base you are using.

Which figure to quote where

Quote the exceedance probability with the number every time, and quote the uncertainty that produced it. A P90 without its σ is not a checkable figure — the same plant yields a different P90 at 5 % and at 10 % uncertainty, and the reader has no way to tell which they have been handed. See The PDF report for where these figures land in the document you issue.

Where to go next