# Power density

Physical size
Surname area-related power density
Formula symbol ${\ displaystyle I, \, S, \, E, \, M, \, q, \, \ psi}$
Derived from Performance per area
Size and
unit system
unit dimension
SI J · s -1 · m -2 M · T −3
Physical size
Surname volumetric power density
Formula symbol ${\ displaystyle \ phi}$
Derived from Performance per volume
Size and
unit system
unit dimension
SI J · s -1 · m -3 M · L −1 · T −3
Physical size
Surname gravimetric power density, specific power
Derived from Power per mass
Size and
unit system
unit dimension
SI J · s -1 · kg -1 L 2 · T −3

The power density (or also the power density quotient ) describes in physics the distribution of contained or deliverable power over a certain quantity and consequently always has the shape ${\ displaystyle P}$${\ displaystyle X}$

${\ displaystyle {\ frac {\ mathrm {d} P} {\ mathrm {d} X}}}$

Different physical quantities are referred to as power density depending on the application :

• Surface power densities : For transport and operations flow area-related performance measures with the unit W / m 2 is used. These include a general size, the intensity I , as a special electromagnetic power density sizes S and Poynting vector , irradiance E , emittance M , heat flux q , energy flux density ψ and sound intensity I .${\ displaystyle {\ vec {S}}}$
• Volume power density: If the power is related to the volume in which it is implemented, the size has the dimension W / m 3 and can also be referred to as volume-related power φ or volumetric power density . This size is of particular interest in technical energy converters (insofar also in energy storage systems , there in addition to the energy density ), e.g. B. in steam generators, reactors or batteries.
• Mass power density : The power can also be referred to its mass , especially for the characterization of energy converters and storage systems, i.e. the power density can be specified in W / kg. Special terms are specific power or gravimetric power density . This variable is particularly relevant for vehicles and mobile devices and has recently played an important role in electromobility, for example .
• Spectral power density : In vibration processes, the distribution of power within the relevant frequency or wavelength range is often considered. For this purpose z. B. in communications engineering the spectral power density S ν or S λ , whichformsa power density spectrum specified for all frequencies or wavelengths.

## Radiation physics (surface power density)

The figure describes the power density S of electromagnetic radiation, which decreases with the square of the distance

In the field of radiation physics ( thermal radiation , electromagnetic waves ) the power density S corresponds to the amount of the Poynting vector . In the case of a point source, the power density decreases with the square of the distance. After all, the same power has to be distributed over an ever larger area A with increasing distance. This is also known as clearance attenuation .

The power drawn from the wave can be determined from the power density of the incident wave and the antenna effective area.

## Energy converter

In nuclear engineering , the volume power density is a measure of the heat released per unit volume in a reactor. Here, calculations are usually made in the unit kW / l (1000 watts / liter). The unit kW / kg heavy metal is used to describe the fuel element load. The last-mentioned unit is also called specific power.

In the case of fuel cells , accumulators or capacitors , the volume power density determines the size of the cells, the mass power density ( W / kg ) the weight. This plays an essential role in electromobility . A Ragone diagram relates them to the energy density .

In the use of solar energy and wind energy, an area-related power density is used; this is the radiant power radiated in per area or the power of the wind that flows through an area. This power density of an energy source indicates how much power is converted into watts per unit area in square meters. The higher this value, the smaller z. B. a power plant can be designed. Conversely, low power density means higher material costs.

Comparison of power densities:
Energy source Power density
in kW per m²
Geothermal energy 0.00006
Tidal current (medium) 0.002
Wind flow (wind speed 6 m / s, air pressure 1000 hPa, temperature 20 ° C) 0.128
Solar radiation ( solar constant ) <1.37
Oil (boiler) 20-30
Water flow (6 m / s, density 1,000 kg / m³) 108
Coal (in the steam generator combustion chamber of
a power plant)
500
Uranium (on the fuel element cladding) 650

## Power density in the application of renewable energies

The power density in renewable energies is mostly related to the area, da

• the part of renewable energies that depends directly (solar thermal, photovoltaic, biomass), indirectly (wind) or partially (near-surface geothermal) on global radiation from the sun, is meaningfully related to the area and
• Even with deep geothermal energy, it makes sense to refer to the area, as this energy is released from the inside of the earth via the spherical surface to the outside / above.
system Power density
in watt / m²
comment
Input
Solar constant 1,367 Intensity of solar radiation outside the earth's atmosphere on the earth's orbit, based on a flat disc with an area of ​​1 m² which is perpendicular to the direction of the radiation, source of renewables
Solar constant / 4 341 The power radiated onto the cross-sectional area of ​​the globe is distributed over the four times larger spherical surface
mean global radiation in Germany 125 Consideration of the geographical latitude and the attenuation in the atmosphere through backscattering and absorption
comparison
Mining coal seams with a total thickness of 30 m over 100 years 400 calculated with an energy density of the coal of 40 GJ / m³ and based on the area of ​​the mining area
Primary energy requirement in Germany based on the area of ​​Germany 1.2 According to the Federal Ministry of Economics and Technology, Germany's primary energy requirement in 2008 was 13 EJ / year, corresponding to 431 GW, based on the area of ​​Germany of 357,112 km²
Power density of the mean power requirement for final energy 0.8 According to the Federal Ministry of Economics and Technology, Germany's final energy demand in 2008 was 9 EJ / year, corresponding to 286 GW, based on the area of ​​357,112 km² in Germany
Power density of the mean power requirement for electrical energy 0.17 According to the Federal Ministry of Economics and Technology, the average power consumption for electricity from all consumers (industry, trade, commerce, services, households) in Germany in 2008 is 542 TWh / a = 62 GW
output
Electricity generation from hydropower 10 - 60 z. B. Lac des Dix has a power density of ~ 60 watt / m², Itaipú 10 watt / m²
Implementation of global radiation in a roof solar thermal system 40
Implementation of global radiation in a parabolic trough power plant in Spain 21st VDI Nachrichten 15-07-2011 Page 18 "Solar thermal large-scale power plants: Hope with a dark side"
Implementation of global radiation in a photovoltaic system 10 to 15 The mean value at the moment is ~ 10 watts / m² at the network connection point, good new systems achieve around 12 to 15 watts / m²
Implementation of global radiation in an open-space photovoltaic system 3.7 53 MW photovoltaic power plant in Lieberose / Brandenburg
Wind farm 0.7 to 4.5 Values ​​for USA and UK. The area under the wind turbines can be used twice for agricultural cultivation. According to simulations, a maximum of 1 W / m² for extensive use.
Biomass 0.2 to 0.5 For biogas plants, up to 50,000 kWh / (m² year) are achieved today
near-surface geothermal energy 0.12 A mixture of heat extraction through the heating of the ground by solar radiation and the geothermal heat flowing in from the earth's interior.
deep geothermal energy 0.09 good heat flow outside of volcanic areas, in tectonically shaped areas with rising hot deep waters, much more can be achieved.