1. A solar radiation model for photovoltaic and solar thermal
power exploitation
F. Díaz, G. Montero, J.M. Escobar, E. Rodríguez, R. Montenegro

2. Contents 1. Introduction
2. Terrain surface mesh and detection of shadows
3. Solar radiation modelling
-Solar radiation equations for clear sky
Beam radiation
Diffuse radiation
Reflected radiation
-Solar radiation for real sky
-Typical meteorological year (TMY)
4. Results
5. Conclusions

3. Introduction
Solar power is one of the most appreciate renewable energies in the world
Three groups of factors determine the interaction of solar radiation with the earth’s atmosphere and surface
a. Earth’s geometry, revolution and rotation (declination, latitude, solar hour angle)
b. Terrain (elevation, albedo, surface inclination/orientation, shadows)
c. Atmospheric attenuation (scattering, absorption) by
c.1. Gases (air molecules, ozone, CO2 and O2)
c.2. Solid and liquid particles (aerosols, including non-condensed water)
c.3. Clouds (condensed water)
Correct estimation needs an accurate definition of the terrain surface and the produced shadows. Previous works.
A typical meteorological year (TMY) for each available measurement stations has been developed.

4. Introduction Topography Shadows Albedo Beam Radiation
Diffuse Radiation
Reflected Radiation
Global Radiation
Clear Sky
Experimental Data
Real sky

5. Terrain surface mesh and shadows
Build a sequence of nested meshes from a regular triangulation of the rectangular region, such that the level j is obtained by a global refinement of the previous level j−1 with the 4-T Rivara’s algorithm
The number of levels m of the sequence is determined by the degree of discretization of the terrain,
Define a new sequence until level m’ ≤ m applying a derefinement algorithm
Two derefinement parameters εh and εa are introduced and they determine the accuracy of the approximation to terrain surface and albedo, respectively.

6. Terrain surface mesh and shadows
Day angle
Hour angle
Sun declination
Solar altitude and Solar azimuth
Solar beam direction

7. Terrain surface mesh and shadows
Construct a reference system x’, y’ and z’, with z’ in the direction of the beam radiation, and the mesh is projected on the plane x’y’
The incidence solar angle δexp is then
computed for each triangle
Check for each triangle Δ of the mesh, if there exists another Δ’ that intersects Δ and is in front of it, i.e., the z’ coordinates of the intersection points with Δ’ are greater than those of Δ.

8. Terrain surface mesh and shadows
12:00 hours
14:00 hours
14:00 hours
12:00 hours
16:00 hours
18:00 hours
16:00 hours
18:00 hurs

9. Solar radiation modelling
General aspects:
Use of adaptive meshes for surface discretization and a new method for detecting the shadows over each triangle of the surface.
This solar radiation model is based on the work of Šúri and Hofierka
Calculations flow:
We first calculate the solar radiation under the assumption of clear sky for all the triangles of the mesh.
Typical Meteorological Year (TMY) is evaluated for all the involved measurement stations.
Solar radiation values are corrected for a real sky by using the TMY from the available data of the measurement stations in each time step along an episode.
Steps 1 and 3 are repeated for each time step and finally, the total solar radiation is obtained integrating all the instantaneous values in each triangle.

10. Solar radiation modelling
Solar radiation equations for clear sky
Solar radiation types
Beam
Diffuse
Reflected

11. Solar radiation modelling
Solar radiation equations for clear sky
Solar constant
Beam radiation
Extraterrestrial irradiance G0 normal to the solar beam
Correction factor
Linke atmospheric
turbidity factor
Beam irradiance normal to the solar beam
Gb0c = G0 exp{−0.8662TLKmδR(m)}
Relative optical air mass
Beam irradiance on a horizontal surface
h0: the solar altitude angle
Lf: the lighting factor
Gbc(0) = Gb0c Lf sin h0
Beam irradiance on an inclined surface
δexp: the incidence
solar angle
Gbc(b) = Gb0cLf sin δexp

12. Solar radiation modelling
Solar radiation equations for clear sky
Diffuse radiation
Diffuse transmission
Diffuse radiation on horizontal surfaces
Diffuse radiation on inclined surfaces
Function depending on the solar altitude
Sunlit surfaces
ho ≥ 0.1
ho < 0.1
Shadowed surfaces

13. Solar radiation modelling
Solar radiation equations for clear sky
Reflected radiation
Mean ground albedo

14. Solar radiation modelling
Solar radiation under real-sky
Values of global irradiation on a horizontal surface for real sky conditions G(0) are calculated as a correction of those of clear sky Gc(0) with the clear sky index kc
If some measures of global radiation Gs(0) are available at different measurement stations, the value of the clear sky index at those points may be computed as
Then kc may be interpolated in the whole studied zone

15. Solar radiation modelling
Typical meteorological year (TMY)
To obtain accurate real sky values of global irradiation, the evaluation of a TMY is needed to avoid results based on a particular year weather conditions
We compute the daily typical meteorological year of maximums, means, medians, variance and percentiles of 90% and 75% series of values using weight means to smooth the irregular data.
TMY series were fitted to third grade Fourier series

16. Solar radiation modelling
Typical meteorological year (TMY)
Means
Medians

17. Results
The studied case corresponds to Gran Canaria, one of the Canary Islands in the Atlantic Ocean at latitude and −15.25 longitude.
The UTM coordinates (metres) that define the corners of the considered rectangular domain including the island are (417025, )
and (466475, ), respectively.
TMY (1998 – 2008) for all the stations in Gran Canaria Island were obtained for every month.
The average global radiation (real sky), varies from:
10.6 MJ/m2 per day in December
25.6 MJ/m2 per day in June

18. Geolocation of different stations on
Results
Geolocation of different stations on
Gran Canaria Island
Elevation map of Gran Canaria

19. Results Albedo map of Gran Canaria Macaronesic laurisilva 0.05
Salt mine
0.6
Albedo map of Gran Canaria

20. Results Intermediate mesh 5866 nodes 11683 triangles
Triangular mesh adapted to topography and albedo

21. Beam radiation map (J/m2)
Results
EXAMPLE
82 − 87% of the
mean global
irradiation
Beam radiation map (J/m2)
December 2006

22. Diffuse radiation map (J/m2)
Results
EXAMPLE
13 − 18% of the
mean global
irradiation
Diffuse radiation map (J/m2)
December 2006

23. Reflected radiation map (J/m2)
Results
EXAMPLE
0 − 0.5% of the
mean global
irradiation
Reflected radiation map (J/m2)
December 2006

24. Results Clear sky global radiation map (J/m2)
December 2006
Real sky global radiation map (J/m2)
December 2006

25. Results
Annual evolution of the computed monthly average per day (TMY) for both, clear sky and real sky global radiation DE DE

26. Percentage decrease from the computed radiation: Real sky to clear sky
Results
Percentage decrease from the computed radiation: Real sky to clear sky
TRADE WINDS
Months

27. Influence of the trade winds: Annual Wind Rose for Canary Islands
Results
Influence of the trade winds:
Annual Wind Rose for Canary Islands
Frequency (%)

28. Influence of the trade winds:
Results
Influence of the trade winds:

29. Monthly average Real Sky radiation
Results
SIMULATIONS:
Monthly average Real Sky radiation
January
April

30. Monthly average Real Sky radiation
Results
SIMULATIONS:
Monthly average Real Sky radiation
July
October

31. Solar Power Generation: Photovoltaic and Solar Thermal
Results
Solar Power Generation:
Photovoltaic and Solar Thermal
Hourly Clear Sky radiation calculation for all days
Numerical Integration
Clear Sky Index and Interpolation
Irradiation and Energy for
Real Sky conditions
Clear Sky
Irradiance
Real Sky
Irradiance
Solar PV
Model
Solar Thermal
Electric Power
Generation

32. Conclusions
The adaptive triangulation related to the topography and albedo is essential in order to obtain accurate results of shadow distribution and solar radiation
Adaptive meshes lead to a minimum computational cost, since the number of triangles to be used is optimum.
Statistical treatment of data is necessary to reach accurate conclusions about the possible behaviour of the radiation distribution values
Typical meteorological year (TMY) is the departure point to estimate the real sky radiation values
The model allows to choose the most suitable zone in the island for a solar power station
Rectangular collectors can be included in the model as composed by two triangles in the same plane

33. Future research
Improve the interpolation procedure used for processing such data
Calculate the optimal orientation and inclination of solar collectors for each location
Optimal selection of the warning points for detecting the shadows
Determinate the shadow boundary using ref/deref and mesh adaption by moving nodes
Define an error indicator to ref/deref the mesh attending to daily real global radiation
Fully parallelise the calculations

34. A solar radiation model for photovoltaic and solar thermal
power exploitation
F. Díaz, G. Montero, J.M. Escobar, E. Rodríguez, R. Montenegro