Model Description¶

So far only two simple models are provided but there will improvements and a larger variety in future version hopefully with the help of the github community.

PV Model¶

The pv model is based on the pvlib library. http://pvlib-python.readthedocs.org/en/latest/

Solar Position and Incident Angle¶

To calculate the position of the sun the ephemeris model of the pvlib is used (pvlib.solarposition.get_solarposition). A lot of weather data sets contain the hourly mean of each parameter. The algorithms that calculate the position of the sun will do that for the given time. Therefore the feedinlib calculates the hourly mean of the sun angles based on 5-minute values.

To avoid nan-values the feedinlib cut values that are lower than 0° and higher than 90°.

Base on the position of the sun and the orientation of the module the angle of incident is determined (pvlib.irradiance.aoi).

In Plane Irradiation¶

The pvlib needs the direct normal irradiation (dni) so the feedinlib uses a geometric equation to calculate it from the direct horizontal irradiation (dirhi) provided by the weather data set and the zenith angle ( $\alpha_{zenith}$ ).

$dni=\frac{dirhi}{\sin\left(\pi/2-\alpha_{zenith}\right)}$

Small differences between the solar position model and the weather model (or measurement) can cause a big deviation for dni if the sun is near the horizon $(\alpha_{zenith}>88°)$ . caused by a very small denominator in the equation above. Assuming that the irradiation near the horizon is low and the effect on the in-plane-irradiation is very small, the dni is set to dirhi $(dni=dirhi)$ for zenith angles greater than 88°.

To determine the diffuse radiation from the sky the Perez Model is used. Therefore the following functions from the pvlib are used:

pvlib.irradiance.extraradiation

pvlib.atmosphere.relativeairmass

pvlib.irradiance.perez

To calculate the ground reflection the pvlib.irradiance.grounddiffuse is used.

The global in plane function sums up the different fractions (pvlib.irradiance.globalinplane).

Electrical Output¶

The next step calculate the electrical output is to determine the temperature of the solar cell (pvlib.pvsystem.sapm_celltemp). Knowing the cell temperature the feedinlib uses the Sandia PV Array Performance Model (SAPM) to determine the electrical output of the module (pvlib.pvsystem.sapm).

Wind Model¶

The wind model is a simple model based on the cp-values of a specific type of a wind turbine. The cp-values are provided by the manufacturer of the wind turbine as a list of cp-values for discrete wind speeds in steps of 0.5 or 1 m/s. The feedinlib makes an linear interpolation of these values to get a continuous cp-curve over the wind speeds.

$P_{wpp}=\frac{1}{8}\cdot\rho_{air,hub}\cdot d_{rotor}^{2}\cdot\pi\cdot v_{wind,hub}^{3}\cdot cp\left(v_{wind,hub}\right)$

with $d_{rotor}$ the diameter of the rotor in meters, $\rho_{air,hub}$ the density of the air at hub height, $v_{wind,hub}$ the wind speed at hub height and $cp$ the cp-values against the wind speed.

The wind speed at hub height is determined by the following equation, assuming a logarithmic wind profile.

$v_{wind,hub}=v_{wind,data}\cdot\frac{\ln\left(\frac{h_{hub}}{z_{0}}\right)}{\ln\left(\frac{h_{wind,data}}{z_{0}}\right)}$

with $v_{wind,hub}$ the wind speed at the height of the weather model or measurement, $h_{hub}$ the height of the hub and $h_{wind,data}$ the height of the wind speed measurement or the height of the wind speed within the weather model.

The density of the air is calculated assuming a temperature gradient of -6.5 K/km and a pressure gradient of -1/8 hPa/m.

$T_{hub}=T_{air, data}-0.0065\cdot\left(h_{hub}-h_{T,data}\right)$

with $T_{air, data}$ the temperature at the height of the weather model or measurement, $h_{hub}$ the height of the hub and $h_{T,Data}$ the height of temperature measurement or the height of the temperature within the weather model.

$\rho_{air,hub}=\left(p_{data}/100-\left(h_{hub}-h_{p,data}\right)*\frac{1}{8}\right)/\left(2.8706\cdot T_{hub}\right)$

with $p_{data}$ the pressure at the height of the weather model or measurement, $T_{hub}$ the temperature of the air at hub height, $h_{hub}$ the height of the hub and $h_{p,data}$ the height of pressure measurement or the height of pressure within the weather model.

Weather Data¶

The weather data manly used by the oemof developing group is the coastDat2 of the Helmholtz-Zentrum Geesthacht

http://wiki.coast.hzg.de/pages/viewpage.action?pageId=4751533

Due to licence problems we are not allowed to ship the dataset with the feedinlib. Please contact the Helmholtz-Zentrum Geesthacht (HZG), the data set for Europe might be free for non commercial use. If you have a licence agreement with the HZG for the coastDat2 data set we might be able to provide a ready-to-use database dump for a postgis database (about 70 GB).