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

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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 Contents

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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 earths atmosphere and surface a. Earths 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, CO 2 and O 2 ) 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.

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Clear Sky Beam Radiation Beam Radiation Diffuse Radiation Diffuse Radiation Reflected Radiation Reflected Radiation Global Radiation Global Radiation TopographyShadowsAlbedo Real sky ExperimentalData Experimental Data Introduction

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Define a new sequence until level m m applying a derefinement algorithm Two derefinement parameters h and a 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 j1 with the 4-T Rivaras algorithm The number of levels m of the sequence is determined by the degree of discretization of the terrain,

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Solar beam direction Solar altitude and Solar azimuth Sun declination Day angleHour angle Terrain surface mesh and shadows

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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 xy The incidence solar angle exp is then computed for each triangle Check for each triangle of the mesh, if there exists another that intersects and is in front of it, i.e., the z coordinates of the intersection points with are greater than those of .

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

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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 ri 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.

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Solar radiation equations for clear sky Solar radiation types ReflectedDiffuseBeam Solar radiation modelling

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G b0c = G 0 exp{0.8662T LK m R (m)} Solar radiation equations for clear sky Solar constant Extraterrestrial irradiance G 0 normal to the solar beam Correction factor Beam irradiance normal to the solar beam h 0 : the solar altitude angle L f : the lighting factor exp : the incidence solar angle Beam irradiance on an inclined surface Beam irradiance on a horizontal surface Linke atmospheric turbidity factor Relative optical air mass Beam radiation G bc (0) = G b0c L f sin h 0 G bc ( ) = G b0c L f sin exp Solar radiation modelling

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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 surfaces h o 0.1 h o < 0.1 Shadowed surfaces Diffuse radiation Solar radiation modelling

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

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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 G c (0) with the clear sky index k c If some measures of global radiation G s (0) are available at different measurement stations, the value of the clear sky index at those points may be computed as Then k c may be interpolated in the whole studied zone Solar radiation modelling

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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 tted to third grade Fourier series Solar radiation modelling

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Typical meteorological year (TMY) Means Solar radiation modelling Medians

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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/m 2 per day in December 25.6 MJ/m 2 per day in June Results

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

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

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

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Beam radiation map (J/m 2 ) December 2006 82 87% of the mean global irradiation Results EXAMPLE

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Diffuse radiation map (J/m 2 ) December 2006 13 18% of the mean global irradiation EXAMPLE Results

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Reflected radiation map (J/m 2 ) December 2006 0 0.5% of the mean global irradiation Results EXAMPLE

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

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

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

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

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Results Influence of the trade winds:

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Results SIMULATIONS: Monthly average Real Sky radiation JanuaryApril

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Results SIMULATIONS: Monthly average Real Sky radiation JulyOctober

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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 Real Sky Irradiance Solar PV Model Solar Thermal Model Electric Power Generation Clear Sky Irradiance

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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

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Improve the interpolation procedure used for processing such data Optimal selection of the warning points for detecting the shadows Fully parallelise the calculations 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 Calculate the optimal orientation and inclination of solar collectors for each location Future research

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