A solar radiation model for photovoltaic and solar thermal power exploitation

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



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


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


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



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



Reflected radiation


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


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


Typical meteorological year (TMY)

Means


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

A solar radiation model for photovoltaic and solar thermal power exploitation

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