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A solar radiation model for photovoltaic and solar thermal power exploitation. F. Díaz, G. Montero, J.M. Escobar, E. Rodríguez, R. Montenegro. Contents. 1. Introduction 2. Terrain surface mesh and detection of shadows 3. Solar radiation modelling -Solar radiation equations for clear sky - PowerPoint PPT Presentation
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A solar radiation model for photovoltaic and solar thermal
power exploitation
F. Díaz, G. Montero, J.M. Escobar, E. Rodríguez, R. Montenegro
1. Introduction2. Terrain surface mesh and detection of shadows3. Solar radiation modelling
-Solar radiation equations for clear skyBeam radiationDiffuse radiationReflected radiation
-Solar radiation for real sky-Typical meteorological year (TMY)
4. Results5. Conclusions
Contents
• Solar power is one of the most appreciate renewable energies in the world
Introduction
• 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.
Clear Sky• Beam Radiation• Diffuse Radiation• Reflected Radiation• Global Radiation
TopographyShadowsAlbedo
Real sky
Experimental Data
Introduction
• 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.
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,
Solar beam direction
Solar altitude and Solar azimuth
Sun declination
Day angle
Hour angle
Terrain surface mesh and shadows
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.
14:00 hours
16:00 hours
12:00 hours
18:00 hours
12:00 hours14:00 hours
16:00 hours18:00 hurs
Terrain surface mesh and shadows
General aspects:
1. We first calculate the solar radiation under the assumption of clear sky for all the triangles of the mesh.
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
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.
Solar radiation modelling
Calculations flow:
2. Typical Meteorological Year (TMY) is evaluated for all the involved measurement stations.
3. 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.
Solar radiation equations for clear sky
Solar radiation types
ReflectedDiffuseBeam
Solar radiation modelling
Gb0c = G0 exp{−0.8662TLKmδR(m)}
Solar radiation equations for clear sky Solar constant
Extraterrestrial irradiance G0 normal to the solar beam
Correction factor
Beam irradiance normal to the solar beam
h0: the solar altitude angleLf: the lighting factor
δexp: the incidence solar angle
Beam irradiance on an inclined surface
Beam irradiance on a horizontal surface
Linke atmosphericturbidity factorRelative optical air mass
Beam radiation
Gbc(0) = Gb0c Lf sin h0
Gbc(b) = Gb0cLf sin δexp
Solar radiation modelling
Solar radiation equations for clear sky
Diffuse radiation on horizontal surfaces
Diffuse transmission
Function depending on the solar altitude
Diffuse radiation on inclined surfaces
Sunlit surfacesho ≥ 0.1
ho < 0.1
Shadowed surfaces
Diffuse radiation
Solar radiation modelling
Solar radiation equations for clear sky
Reflected radiation
Solar radiation modelling
Mean ground albedo
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
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 conditionsWe 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
Solar radiation modelling
Typical meteorological year (TMY)
Means
Solar radiation modelling
Medians
TMY (1998 – 2008) for all the stations in Gran Canaria Island were obtained for every month.
The studied case corresponds to Gran Canaria, one of the Canary Islands in the Atlantic Ocean at 28.06 latitude and −15.25 longitude. The UTM coordinates (metres) that define the corners of the considered rectangular domain including the island are (417025, 3061825)and (466475, 3117475), respectively.
The average global radiation (real sky), varies from:• 10.6 MJ/m2 per day in December• 25.6 MJ/m2 per day in June
Results
Elevation map of Gran Canaria
Geolocation of different stations on Gran Canaria Island
Results
Albedo map of Gran Canaria
Results
Macaronesic laurisilva
0.05
Salt mine
0.6
Intermediate mesh5866 nodes11683 triangles
Triangular mesh adapted to topography and albedo
Results
Beam radiation map (J/m2) December 2006
82 − 87% of the mean global irradiation
Results
EXAMPLE
Diffuse radiation map (J/m2) December 2006
13 − 18% of the mean global irradiation
EXAMPLE
Results
Reflected radiation map (J/m2)December 2006
0 − 0.5% of the mean global irradiation
Results
EXAMPLE
Clear sky global radiation map (J/m2)December 2006
Real sky global radiation map (J/m2)December 2006
Results
Results
Annual evolution of the computed monthly average per day (TMY) for both, clear sky and real sky global
radiation
1 3 5 7 9 110
5000000
10000000
15000000
20000000
25000000
30000000
Real sky
Trend (Real sky)
Clear sky
Trend (Clear sky)
Months
(MJ/
m2)
DEDE
Results
Percentage decrease from the computed radiation: Real sky to clear
sky
1 3 5 7 9 110.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
Decrement RS to CS
Trend
Months
TRADE WINDS
Results
Influence of the trade winds: Annual Wind Rose for Canary Islands
0
1
0
20
30
40
50
N
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
W
WNW
NW
NNW
Frecuencia (%)Frequency (%)
Results
Influence of the trade winds:
Results
SIMULATIONS:Monthly average Real Sky radiation
January April
Results
SIMULATIONS:Monthly average Real Sky radiation
July October
Results
Solar Power Generation:Photovoltaic and Solar Thermal
Hourly Clear Sky radiation calculation for
all days
Numerical Integration
Clear Sky Index and Interpolati
on
Irradiation and Energy for
Real Sky conditions
Real Sky Irradiance
Solar PVModel
Solar ThermalModel
Electric Power Generation
Clear Sky Irradiance
• Statistical treatment of data is necessary to reach accurate conclusions about the possible behaviour of the radiation distribution values
• Adaptive meshes lead to a minimum computational cost, since the number of triangles to be used is optimum.
• The adaptive triangulation related to the topography and albedo is essential in order to obtain accurate results of shadow distribution and solar radiation
• 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
Conclusions
A solar radiation model for photovoltaic and solar thermal
power exploitation
F. Díaz, G. Montero, J.M. Escobar, E. Rodríguez, R. Montenegro
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