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formulae.txt
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formulae.txt
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-----------------
electricity production
-----------------
solar (photovoltaïcs)
electricity production in watt, per day = solar irradiation per hour (in watt, per m²) x hours of direct sunlight per day x PV panel efficiency
standard PV panel sizes are:
65 x 39 inch = 165,1 x 99,06 cm = 16354,8 cm² = 1,63548 m²
75 x 39 inch = 198,2 x 99,06 cm = 19633,7 cm² = 1,96337 m²
(bio)fuel
liters of fuel in tank x kWh per liter of fuel = potential energy in tank (in kWh)
potential energy in tank (in kWh) x engine (or fuel cell + electric engine) efficiency = actual available energy
hydro
height (in meter) x flow (in liter/second) x gravity (9,81) x turbine efficieny rate = electricity production
wind
electricity production per second = 0,5 x swept area (in m²) x air density (=1,23) x velocity (in meter/second)³
--------------
energy storage
--------------
batteries:
power (in watt) = electric potential (in volt) x electric current (in ampère)
also see the other repo
hydro
weight (in Newton) x height (in meter) x 0,0000002 = energy stored (in kWh)
Notes
For the electricity production (solar):
for the solar irradiation per day: you can get this data from http://globalsolaratlas.info
for the hours of direct sunlight: you can use the data from https://en.wikipedia.org/wiki/List_of_cities_by_sunshine_duration ;
alternatively you can calculate it by subtracting the sunrise hour from the sunset hour
the STC (Standard Testing Conditions) power output mentioned on PV panels are theoretical values and only useful for comparing
PV panels (the STC is calculated on peak solar irradiation -1000 W/m²- x the PV panel efficiency mentioned elsewhere on the PV
panel label (typically between 5 and 20%)
Also note that besides using solar tracking, you should also keep PV panel temperature between 15 and 35°C (ideally 25°C), if
it gets hotter or colder than that, it will negatively affect efficiency
For the electricity production (fuel):
you can get energy density data for various fuels from
https://en.wikipedia.org/wiki/Energy_density#Energy_density_in_energy_storage_and_in_fuel
For the electricity production (wind):
swept area is calculated by (rotor diameter/2)² x 3,14
air density is 1,23 only at sea level
the "system efficiency" will typically be very poor (say 25%) due to the Betz limit and other losses
For the energy storage (hydro):
if you want to culaculate a weight of water expresssed in m³, know that 1 m³ = 1000 liter water = 1000 kg
the weight in Newton can then be calculated by multiplying the weight in kg x 9,81
The 0,0000002 comes from the fact that 1 kWh = 3600000J
References
http://zebu.uoregon.edu/disted/ph162/l4.html
http://ecgllp.com/files/3514/0200/1304/2-Solar-Radiation.pdf
https://livingonsolarpower.wordpress.com/2013/03/23/basic-solar-energy-math/
https://solarpowerrocks.com/solar-basics/how-much-electricity-does-a-solar-panel-produce/
http://www.reuk.co.uk/wordpress/wind/calculation-of-wind-power/
http://www.reuk.co.uk/wordpress/hydro/calculation-of-hydro-power/