Calculation model

1. Location and irradiation

Your postcode maps via its first two digits to one of 95 irradiation regions. Each region carries the long-term annual sum of global horizontal irradiation in kWh/m²·a and a representative latitude.

The German range runs from about 980 kWh/m²·a in the north-west to roughly 1,200 kWh/m²·a in the Alpine foreland. That 25 percent difference feeds straight into the yield.

2. Solar geometry

For each month a representative day is chosen and computed hour by hour. Declination, latitude and hour angle give the zenith angle and the angle of incidence on the tilted module plane.

The clear-sky daily curve only supplies the shape. The absolute level comes from the measured monthly sum, so the annual result agrees with the measurements.

3. Splitting beam and diffuse

The ratio of measured global irradiation to extraterrestrial irradiation gives the clearness index. The Erbs correlation then yields the diffuse fraction — about 55 percent as a German annual mean, and over 85 percent in December.

This split is decisive: beam radiation benefits strongly from correct orientation, diffuse radiation hardly at all. Without it, north-facing arrays come out systematically too poor and south-facing ones too good.

4. Transposition to the module plane

Both components are transposed onto the tilted plane with the anisotropic sky model of Hay and Davies. It treats the circumsolar share of diffuse light as beam, and therefore represents the gain of tilted surfaces more realistically than a purely isotropic model.

Ground reflection is included with an albedo of 0.2 — relevant above all for vertical mounting on a balcony railing.

5. Losses

• Cell temperature via the NOCT model, temperature coefficient −0.36 %/K, with monthly mean ambient temperatures.
• Soiling, mismatch, reflection and wiring losses as separate factors depending on system type.
• Inverter efficiency and, for plug-in devices, clipping at the output limit — computed hourly rather than as a flat deduction.
• Shading in four steps, from 0 to 35 percent annual loss.

6. Load profile and self-consumption

Your annual consumption is spread across an hourly profile derived from the H0 standard load profile and fanned out into three occupancy patterns. Heat pump and electric car are added as separate profiles.

Self-consumption is the hourly intersection of generation and load. Because typified daily curves are smoother than reality, the result is corrected by a volatility factor of 0.93; the energy balance stays closed.

7. Battery simulation

When a battery is present, the daily cycle is run twice so the state of charge settles. Surplus charges up to the usable capacity, deficit discharges — each with the square root of the round-trip efficiency per direction, and a power limit.

8. Economics

The energy flow becomes a payment stream. For each year the benefit is escalated by the price increase and reduced by degradation, net of operating cost and any replacement investment.

Payback is interpolated within the year. Net present value discounts at your chosen rate. The internal rate of return is found by bisection as the root of the net present value.

9. Heat demand and heat pumps

Heat demand follows from floor area and the building's condition: a specific demand per square metre is applied, and that figure differs by more than a factor of five between an unrenovated older building and a passive house. Hot water is added on top, and it scales with the number of occupants rather than with the area.

The heat pump's electricity demand follows from the heat demand through the seasonal performance factor — how many kilowatt hours of heat come out of one kilowatt hour of electricity. It depends above all on the flow temperature: underfloor heating reaches considerably more than an old radiator.

The existing heating system is calculated with its own efficiency: the heat demand gives the fuel input, and the fuel input gives the cost. The comparison sets both annual costs side by side, each at the price you entered.

10. Charging an electric car

Distance and consumption per hundred kilometres give the energy that actually reaches the wheels. What has to be charged is more than that: charging loses energy in the charger and in the battery, proportionally more at an AC post than at a DC rapid charger.

The electricity demand is split across the four places you charge — at home, at work, at a public AC post and at a rapid charger — and each share is priced separately. A share taken from your own solar array is deducted from household electricity and valued at its generation cost rather than at the retail price.

The combustion engine is derived from consumption per hundred kilometres and the fuel price. Only energy costs are compared; servicing, tax and insurance are left out because they depend too heavily on the individual vehicle.

Accuracy and limits

Data sources

• Deutscher Wetterdienst — irradiation maps, long-term means.
• PVGIS, European Commission, Joint Research Centre — irradiation and yield benchmarking.
• BDEW — H0 standard load profile, electricity price analysis.
• Bundesnetzagentur — monitoring report, feed-in tariff rates.
• Federal Statistical Office — energy prices, consumption structures.
• German Environment Agency — emission factors of the German electricity mix.