modelPVTransmissionFactors

Calculation of direct, diffuse and albedo transmission factors of incident rays on a photovoltaic module

Information

Hypothesis and equations

This model allows the use of analytical formulas for evaluating optical losses due to reflection on the three components of the solar flux : direct, diffuse and reflected by the ground (albedo).

This model is a improvement of the model developed by ASHRAE which is not valid for angles of incidence higher than 80°.

- The expression of the transmittance factor for the direct incidence is given by :

FT_B(theta_S)=T_dirt/T_clean*(1-(exp(-cos(theta_S)/a_r)-exp(-1/a_r))/(1-exp(-1/a_r)))

theta_S : sun rays angle of incidence on the module.

T_dirt/T_clean : module relative transmittance due to its degree of dirt.

a_r : coefficient characterizing the dirt of the module ( a_r values are related to the values of the relative transmittance).

Note : The formula used is not exactly the one that can be found in the literature, the multiplicative factor of relative transmittance can be included in the transmission factor as shown in equation (20.49) of the "Handbook of Photovoltaic Science and Engineering", P936.

- For diffuse radiation, the expression is :

FT_D(beta)=1-exp(-1/a_r*(c_1*(sin(beta)+(pi-beta*pi/180-sin(beta))/(1+cos(beta)))+c_2*(sin(beta)+(pi-beta*pi/180-sin(beta))/(1+cos(beta)))^2))

- And for albedo radiation, the expression is :

FT_R(beta)=1-exp(-1/a_r*(c_1*(sin(beta)+(beta*pi/180-sin(beta))/(1-cos(beta)))+c_2*(sin(beta)+(beta*pi/180-sin(beta))/(1-cos(beta)))^2))

c_1=4/(3*pi) : constant coefficient.

c_2 : coefficient linearly dependent of dirt coefficient a_r (automatically calculated in the model).

beta : module tilt angle.

Instructions for use

none

Bibliography

Handbook of Photovoltaic Science and Engineering, Antonio Luque & Steven Hegedus, Wiley, 2003, pp. 934-936

Martin N., Ruiz J, Solar Energy Materials & Solar Cells 70, 25-38, 2001

Known limits / Use precautions

The values of the dirt parameter a_r have not been studied, validations have been made only considering a clean module.

Validations

Model validated by simulation - Sergeï Agapoff (stagiaire Benoît Braisaz) 08/2012

--------------------------------------------------------------
Licensed by EDF under a 3-clause BSD-license
Copyright © EDF 2009 - 2023
BuildSysPro version 3.6.0
Author : Sergeï AGAPOFF, EDF (2012)
--------------------------------------------------------------

Parameters

Type	Name	Default	Description
Boolean	use_incl_in	false	Prescribed or fixed PV panel tilt
Boolean	use_azimut_in	false	Prescribed or fixed PV panel azimut
Modelica.Units.NonSI.Angle_deg	incl	30	PV panel tilt relative to the horizontal (0° upward, 180° downward)
Modelica.Units.NonSI.Angle_deg	azimut	0	PV panel azimuth - orientation relative to the South (S=0°, E=-90°, W=90°, N=180°)
Integer	salete	0	0 - Clean panels, 1 - Slightly dirt panels, 2 - Intermediately dirt panels, 3 - Very dirt panels

Connectors

Type	Name	Description
BuildSysPro.BoundaryConditions.Solar.Interfaces.SolarFluxInput[10]	G	Solar flux: {DIFH, DIRN, DIRH, GLOH, t0, CosDir[1:3], Solar azimuth angle, Solar elevation angle}
Modelica.Blocks.Interfaces.RealOutput	FT_B	Direct transmission factor
Modelica.Blocks.Interfaces.RealOutput	FT_D	Isotropic diffuse transmission factor
Modelica.Blocks.Interfaces.RealOutput	FT_A	Albedo reflexion transmission factor
Modelica.Blocks.Interfaces.RealInput	incl_in	PV panel tilt relative to the horizontal (0° upward, 180° downward)
Modelica.Blocks.Interfaces.RealInput	azimut_in	PV panel azimuth - orientation relative to the South (S=0°, E=-90°, W=90°, N=180°)

Revisions

Agapoff Sergeï 04/2012 : Model creation

Stéphanie Froidurot 07/2019 : Adding the possibility to use fixed (parameter) or prescribed (input) tilt and azimut, controlled by booleans (use_incl_in and use_azimut_in).