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The PV Model is part of the SIMONA Simulation framework and represented by an agent.
Parameters
Attributes, Units and Remarks
Please refer to {doc}PowerSystemDataModel - PV Model <psdm:models/input/participant/pv> for Attributes and Units used in this Model.
Implemented Behaviour
Output visualization
Calculations
The energy produced by a photovoltaic (pv) unit in a specific time step is based on the diffuse and direct radiation provided by the used weather data. The following steps are done to calculate (= estimate) the power feed by the pv.
To calculate the overall feed in of the pv unit, the sum of the direct radiation, diffuse radiation and reflected radiation is needed. In the following, the formulas to calculate each of these radiations are presented and explained. The sections end with the formula to calculate the corresponding power feed in.
Caution: all angles are given in radian!
The azimuth angle $\alpha_{E}$ starts at negative values in the East and moves over 0° (South) towards positive values in the West. Source
Declination Angle
The declination angle $\delta$ (in radian!) is the day angle that represents the position of the earth in relation to the sun. To calculate this angle, we need to calculate the day angle $J$. The day angle in radian is represented by:
$$
J = 2 \pi(\frac{n-1}{365})
$$
with n = number of the day in the year (e.g. 1 January = 1, 20 February = 51)
Based on $J$ the declination angle $\delta$ (in radian!) can be calculated as follows:
The hour angle is a conceptual description of the rotation of the earth around its polar axis. It starts with a negative value in the morning, arrives at 0° at noon (solar time) and ends with a positive value in the evening. The hour angle (in radian!) is calculated as follows
The hour angles at sunrise and sunset are very useful quantities to know. These two values have the same absolute value, however the sunrise angle ($\omega_{SR}$) is positive and the sunset angle ($\omega_{S}$) is negative. Both can be calculated from:
with $\alpha_e$ = sun azimuth $\alpha_s$ = solar altitude angle $\gamma_e$ = slope angle of the surface $\delta$ = the declination angle $\phi$ = observer's latitude $\omega$ = hour angle
References:
* :cite:ts:`Quaschning.2013`
* :cite:ts:`Maleki.2017` p. 18
Air Mass
Calculating the air mass ratio by dividing the radius of the earth with approx. effective height of the atmosphere (each in kilometer)
* :cite:ts:`Zheng.2017` p. 53, formula 2.3b
* :cite:ts:`Iqbal.1983`
Beam Radiation on Sloped Surface
For our use case, $\omega_{2}$ is normally set to the hour angle one hour after $\omega_{1}$. Within one hour distance to sunrise/sunset, we adjust $\omega_{1}$ and $\omega_{2}$ accordingly:
Please note:$\frac{1}{180}\pi$ is omitted from these formulas, as we are already working with data in radians.
with $\delta$ = the declination angle $\phi$ = observer's latitude $\gamma$ = slope angle of the surface $\omega_1$ = hour angle $\omega$ $\omega_2$ = hour angle $\omega$ + 1 hour $\alpha_e$ = sun azimuth $E_{dir,H}$ = beam radiation (horizontal surface)
Reference:
* :cite:ts:`Duffie.2013` p. 88
Diffuse Radiation on Sloped Surface
The diffuse radiation is computed using the Perez model, which divides the radiation in three parts. First, there is an intensified radiation from the direct vicinity of the sun. Furthermore, there is Rayleigh scattering, backscatter (which lead to increased in intensity on the horizon) and isotropic radiation considered.
A generator correction factor (depending on month surface slope $\gamma_{e}$) and a temperature correction factor (depending on month) multiplied on top.
It is checked whether proposed output exceeds maximum ($p_{max}$), in which case a warning is logged. If output falls below activation threshold, it is set to 0.