Annual kWh from a fixed-tilt array — with the performance ratio written out term by term,
so you can see exactly which losses you are accepting. Screening-grade, in your browser,
nothing uploaded.
What this calculator does
Answers "how many kWh a year will this array make" at the same fidelity you would get from
a napkin an experienced designer would actually accept: irradiance on the tilted plane, a
transparent performance ratio, an explicit clipping allowance, and a degradation schedule
you can defend. It will not pretend to the precision of an hourly simulation — and it says so.
The calculation
GTI = GHI × TF(tilt, lat) × AF(azimuth)
PR = [1 + γ(T_cell − 25)] × η_inv × (1−s)(1−m)(1−dc)(1−ac) × availability
E₁ = kWp × GTI × PR × (1 − clipping)
Eₙ = E₁ × (1 − degradation)^(n−1)
TF is the tilt transposition factor — annual irradiance on the tilted plane relative to
horizontal — from an isotropic-sky model with 0.2 ground albedo, tabulated by latitude and
interpolated. AF penalises azimuth offset from equator-facing. T_cell uses an irradiance-weighted lift above annual mean air temperature
(6 °C + GHI/280, plus 0.8 °C per degree above 20 °C mean for hot climates), which approximates
a NOCT-style cell temperature without pretending to hourly resolution.
Where the 8–10 % uncertainty comes from
- Annual averaging hides cloudy-year variance (±5 % year to year in temperate climates).
- Transposition model is isotropic; real skies have horizon brightening and circumsolar
glare, worth a few percent at high tilt in clear climates.
- Temperature model is an annual shortcut; hot-clear climates (Phoenix, Riyadh) run
a little worse than modelled, cool-cloudy ones a little better.
- City GHI values are approximate annual totals in the Global Solar Atlas range —
pull your own value from PVGIS for the site.
Worked example
100 kWp, Madrid, 35° tilt, due south, DC/AC 1.2, default losses:
GHI 1780 × TF(35°, 40°) 1.127 × AF 1.000 → GTI ≈ 2005 kWh/m²/yr
T_cell = 15 + 6 + 1780/280 ≈ 27 °C effective → temp loss −0.8 %
PR = 0.992 × 0.975 × 0.98 × 0.98 × 0.985 × 0.995 × 0.99 ≈ 0.90
E₁ = 100 × 2005 × 0.90 × 0.995 ≈ 180 000 kWh/yr → ≈ 1800 kWh/kWp
1800 kWh/kWp in central Spain is exactly the band published monitoring studies report for
well-built fixed-tilt systems there. If a proposal quotes 1950 kWh/kWp for the same roof,
you now know to ask which loss they skipped.
What this tool does not do. No hourly simulation, no shading geometry, no economics.
Near shading (chimneys, trees, neighbouring roofs) can cost far more than any loss line here;
row-pitch and horizon studies are a separate exercise. For financing-grade numbers use PVGIS,
Solargis or a PVSyst study with measured met data.
Sources & further reading
- Global Solar Atlas — World Bank/Solargis maps and city data.
- EU PVGIS — free hourly time series for Europe, Africa, Asia.
- NREL PVWatts — the reference hourly model this screening approach mirrors.
- Transposition: Liu & Jordan isotropic model with HDKR-style annual corrections; albedo 0.2.
Frequently asked
What is performance ratio?
Delivered energy ÷ energy at STC with the same irradiance. Bundles temperature, inverter, wiring, soiling, mismatch and outage losses. Healthy systems land at 0.75–0.85; quotes above 0.90 deserve a question about which losses were skipped.
What tilt should I use?
Roughly latitude for maximum annual energy. Lower tilt trades winter energy for summer self-consumption; higher tilt sheds snow. In the tropics, tilt barely matters — 5–10° for rain cleaning is enough.
Does a bigger DC/AC ratio help?
Up to ~1.2–1.3, marginally: more hours at the inverter's efficient point, ~1 % clipping. Past 1.4 clipping grows faster than the morning/evening gain pays back.
East–west roofs: how bad is it?
About 10–15 % annual energy vs equator-facing at mid-latitudes, but output flattens across the day — often worth more per kWh where self-consumption drives the economics. Set the azimuth offset accordingly.
How accurate is this?
Typically within 8–10 % of an hourly simulation for unshaded fixed-tilt systems. Use it to compare options; use PVGIS/PVSyst for contracts.
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