Solar irradiation

The sun delivers energy to the earth by means of electromagnetic radiation. For our purposes we can assume that the radiation flows evenly distributed from a surface which is close to spherical. The sunlight covers a broad range of wavelengths from roughly 250 nm (UV) over the visible range (400-700 nm) up to several thousands of nm (IR). The radiation density is decreasing with the sqare of the distance. At the average distance of the earth from the sun the flux of energy amounts to 1366 W/m² which is called the solar constant.

On the way through the atmosphere the properties of the irradiation are slightly changed; e.g. the UV light is absorbed by the ozone layer, some parts of the IR are absorbed by water vapour and carbon dioxide. Depending on the latitude of the observer, the irradiation density is still lower due to the longer path of sunlight through the atmosphere, e.g. to below 1000 W/m² in Central Europe.

The total irradiated energy per year, including seasonal changes, times of overcast sky, and night time, amounts to about 1000 kWh/m²*year in Central Europe (corresponding to 2 to 3 hours of ideal sunshine each day). The map below illustrates the worldwide distribution of the irradiation density.

Figure 1: Solar irradiation map (Source: MySolar)

For the conditions of central Europe a PV system of 1 kW_p (say an area of 10 m² and an efficiency of 10%) will produce approximately 900 kWh of electric energy. The expression W_p is a power rating for solar cells and modules and gives the output power under standard test conditions (AM1.5 Spectrum with 1000 W/m² and a cell temperature of 25^oC).

The average electricity consumption of a 4-person family is about 4000 kWh, thus, solar energy has the potential to supply the average amount of energy, even in the moderate climate of Central Europe.

Two serious drawbacks arise: The storage and the required area. Daily and seasonal availability of solar energy is often contrary to the customers needs and not every family has access to 40 m² for mounting their solar modules. Nevertheless, storage solutions are beeing developed and if existing buildings were equipped with solar systems a considerable amount of energy could be produced even without consumption of additional area.

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Some more numbers:

We can estimate the total radiated power of the sun with the law of Stefan and Boltzmann.

P = 4 p r² s e T⁴ = 3.9^.10²⁶ W

T is the temperature (about 5800 K, see next section), r the radius of the sun (6.9^.10⁸ m) and s e the Boltzmann constant (5.67^.10^-8 W/m²K⁴) and e is the emissivity of the surface (assumed to be one). The power is created by nuclear fusion processes inside the core. Due to Einsteins famous law E = mc² about fourty thousand tons of matter are converted to energy every single second!

The solar energy irradiated to the Earth is 5^.10²⁴ Joule per year. This is 10 000 times the present worldwide yearly energy consumption which is estimated to 5^.10²⁰ Joule (as of 2004). In the literature the energy consuption is frequently given in terms of Quads. The Quad is 10¹⁵ (one quadrillion) British Thermal Units (BTUs), where a BTU is1055 Joule (the BTU is defined as the amount of energy which increases the temperature of one pound of water by one degree Fahrenheit). Therefore, the annual global consumption is 500 Quads.