Solar Energy Yield and Degradation Formulas
Solar PV yield formulas: the yearly energy from array size, peak sun hours and performance ratio, the output after degradation and the energy over 25 years.
The formulas
| To find | Formula |
|---|---|
| Yearly energy before degradation | E0 = kWp × PSH × 365 × PR |
| Specific yield | E0 / kWp, in kWh per kWp |
| Energy in year n | En = E0 × (1 − d1) × (1 − d)^(n − 1) |
| Energy over N years | ΣEn, for n = 1 to N |
kWp is the array size at standard test conditions, PSH the peak sun hours per day (the daily irradiation in kWh/m², with 1 kW/m² as the reference), PR the performance ratio that covers the losses of the temperature, the dirt, the cables and the inverter, d1 the loss in the first year and d the loss in each later year. The first-year loss of 2% and the later loss of 0.5% a year are example values, and the module data sheet gives the warranty figures. The sun hours and the performance ratio come from the site data and the design, and the values here are examples.
Worked example: 10 kWp at 5.2 peak sun hours a day and a performance ratio of 0.8
- E0 = 10 × 5.2 × 365 × 0.8 = 15,180 kWh a year
- The specific yield is 15,180 / 10 = 1,518 kWh per kWp
- Year 1 with a loss of 2%: 15,180 × 0.98 = 14,880 kWh
- Year 25: 15,180 × 0.98 × 0.995^24 = 13,190 kWh
- Energy over 25 years = 350,500 kWh
Output by year for the 10 kWp array
| Year | Output share of E0 | Energy |
|---|---|---|
| 1 | 98% | 14,880 kWh |
| 5 | 96.05% | 14,580 kWh |
| 10 | 93.68% | 14,220 kWh |
| 15 | 91.36% | 13,870 kWh |
| 25 | 86.89% | 13,190 kWh |
Frequently asked questions
What is the performance ratio?
The ratio of the energy that the plant delivers to the energy that it would deliver at its rating with no losses. A value near 0.75 to 0.85 is common for a well-built plant.
Why does the output fall each year?
The cells slowly lose power, and the first year is often the worst because of the light-induced loss. The data sheet gives a warranty line.
What are peak sun hours?
The daily irradiation in kWh/m² read as the hours at 1 kW/m². A site with 5.2 kWh/m² a day has 5.2 peak sun hours.
Is the yield the same every year?
No. The weather changes from year to year, so a plan uses a typical year and treats a bad year as a risk.
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