This article shows the results obtained in tables and graphs of the solar incidence of solar panels with different inclination angles. The monthly average solar radiation with different inclined surfaces is exposed, we see the influence that the inclination of the solar panels has on the capture of solar radiation with respect to a horizontal plane.
angle-inclination-solar-panelsWith the knowledge of having quantitative values of the incidence of solar radiation with optimal angle, these obtained data are very important to make future decisions in the design of photovoltaic solar radiation generators projects.
INTRODUCTION
The purpose of this article is to test or disseminate the theoretical and practical development of the solar incidence of solar panels with an optimal inclination for capturing solar radiation.
Although it is true that there are publications of tables and solar incidence software on the Earth's surface with different angles of inclination, referring to a latitude in the position where the solar panels would be found. But those of us who are interested in this type of research leave a gap in its literature, in order to find the optimal angle of inclination of the solar incidence on the Earth's surface.
The incidence of solar radiation on solar panels depends on the location area, position in the global system (latitude), environment (clear, partly cloudy, cloudy), solar season (winter, summer) and inclination. This article will try to explain the sequential intervention of the mathematical parameters that intervene in the development to calculate the angle that optimizes the capture of solar radiation with respect to a horizontal plane.
To calculate the estimate of solar radiation on a sloping surface, the diffuse radiation component was separated from the global radiation (Liu and Jordan isotropic model).
We must mention that in this work the obtaining of total solar radiation on an inclined plane was obtained from the sum of direct radiation and diffuse radiation (reflected radiation was not taken into account)
DEVELOPING
Location: Sinchi Roca Park, Comas Lima
Latitude: -11.9233 N masl: 139 Average Monthly Radiation, captured on a horizontal surface (kwh / m2 / day) Data extracted from data from the NASA meteorological space station
| β | JAN | FEB | SEA | APR | MAY | JUN | JUL | AUG | SEP | OCT | NOV | DEC |
| 0 ºC | 7.14 | 7.15 | 7.04 | 6.33 | 4.93 | 3.39 | 3.14 | 3.58 | 4.32 | 5.29 | 6.01 | 6.8 |
Solar Incidence Angle
Taking into account that the solar panels are oriented towards the geographic north, in addition to having an inclination angle (β), with respect to the horizontal. You can calculate the angle of solar incidence that is the angle between the normal surface and the sun's rays. This ratio of the solar angles can be calculated from the trigonometric equation below.
Cosθ = cos (Ф-β).cosρ.cosω + sin (Ф-β).senρ
θ = angle formed by direct solar incidence on the inclined panel and horizontal solar incidence. Ф = latitude β = angle of inclination ρ = angle of solar declination ω = solar angle
n = day of the year
360 * (284+ n)
ρ = 23.45 * Sen ()
365
Ho = (24 / π) * Gon
Ho = Monthly average daily extraterrestrial irradiation reaching the projected atmosphere on a horizontal surface.
Polynomial model according to Liu and Jordan
It is noted for the calculations of the solar contributions received from the solar radiation, they are monthly average daily values.
The fuzzy component can be found by the regression curves of the fuzzy fraction (Hd / H) versus the clarity index (k). The direct component can be calculated by the difference between Ht and Hd.
Hd / H = 1,390 - 4,027k + 5,531k 2 - 3,108k 3
k = H / Ho
k = Clarity index
Hd = Diffuse daily irradiation from the celestial vault
H = Global daily irradiation on a horizontal surface
Total radiation is the sum of direct, diffuse, and reflected solar radiation on an inclined surface
Ht = HbRb + HdRd + HδRr
Hb = direct irradiation
Rb = factor that relates the direct solar radiation on an inclined surface and the direct radiation on a horizontal surface.
Rd = factor that relates diffuse solar radiation on an inclined surface and diffuse radiation on a horizontal surface. δ = reflectance of the surrounding area
RESULTS OBTAINED
Table where the results obtained from the monthly average radiation are observed on a plane for different angles of inclination (β) in kw / m2, on a horizontal surface.
| β | Jan | Feb | Sea
|
Apr | may | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Annual Avg |
| 0º | 7.15 | 6.33 | 4.93 | 3.14 | 4.32 | 6.01 | 5.43 | ||||||
| 7.14 | 7.04 | 3.39 | 3.58 | 5.29 | 6.80 | ||||||||
| 2nd | 7.20 | 7.17 | 7.01 | 6.24 | 4.83 | 3.32 | 3.09 | 3.54 | 4.29 | 5.29 | 6.05 | 6.87 | 5.41 |
| 5th | 7.29 | 7.20 | 6.95 | 6.10 | 4.67 | 3.22 | 3.00 | 3.47 | 4.25 | 5.29 | 6.10 | 6.96 | 5.38 |
| 10th | 7.39 | 7.19 | 6.81 | 5.84 | 4.39 | 3.03 | 2.85 | 3.33 | 4.15 | 5.26 | 6.15 | 7.08 | 5.29 |
| 15th | 7.44 | 7.15 | 6.63 | 5.54 | 4.09 | 2.83 | 2.69 | 3.18 | 4.03 | 5.19 | 6.16 | 7.15 | 5.17 |
| 20th | 7.44 | 7.05 | 6.41 | 5.20 | 3.76 | 2.62 | 2.51 | 3.01 | 3.88 | 5.09 | 6.14 | 7.17 | 5.02 |
| 25th | 7.39 | 6.91 | 6.14 | 4.83 | 3.42 | 2.40 | 2.32 | 2.83 | 3.72 | 4.97 | 6.07 | 7.14 | 4.85 |
From figure 1 we can affirm that the profiles of solar radiation that affect an inclined plane vary according to the angle of inclination that the solar panels adopt.
It shows the solar radiation for different angles of inclination.
Figure Nº 2 shows minimum values, taken from the incidence table for different inclination angles, which correspond to the month of July. This quantification is important to measure the number of panels that a PV generator can have, for annual periods.
It shows minimum values of incident solar radiation on an inclined plane.
Figure 3 shows maximum data values, which correspond to the month of January, where the incidence of solar radiation on an inclined surface is greater. The quantification of these data is important since if we want to generate PV energy in seasonal periods, we would have to do it taking into account the months with the highest solar incidence.
Show maximum values of incident solar radiation on an inclined plane
CONCLUSIONS
The location of the solar panels will depend on the function in which the thermal or photovoltaic generation system is designed.
In the PV energy literature, there is an estimation rule for the inclination in solar panels that is latitude + 10º, where greater radiation will be obtained in the winter months and latitude - 10º, for greater radiation in the summer months..
We would have to consider and quantify for periods of solar radiation capture that are annual, seasonal or very short periods. Analyzing the data obtained in the table for different inclination angles, it can be affirmed that for the annual solar radiation capture the most recommended is 0º inclination, which is a horizontal plane.
For the summer period that is the months of December, January and February, the solar incidence is on an inclined plane:
| β | Dec | Jan | Feb | Average
(Kw / m2) |
| 0º | 6.80 | 7.14 | 7.15 | 7.03 |
| 2nd | 6.87 | 7.20 | 7.17 | 7.08 |
| 5th | 6.96 | 7.29 | 7.20 | 7.15 |
| 10th | 7.08 | 7.39 | 7.19 | 7.22 |
| 15th | 7.15 | 7.44 | 7.15 | 7.25 |
| 20th | 7.17 | 7.44 | 7.05 | 7.22 |
| 25th | 7.14 | 7.39 | 6.91 | 7.15 |
The monthly average solar incidence for an inclination angle of 15º north orientation is 7.25 kw / m2, which is a 3% greater solar incidence on a horizontal plane.
The solar radiation of the sample (Lima Comas), is not the most recommended, since during the year its climate is cloudy, only in the summer months the sky is clear and clear. But this modeling serves to find solar radiation at any point on the Earth's surface, obviously taking into account the geographical and climatic considerations of the environment.
Bibliography
Solar Energy Calculation, Jose Javier Garcia-Badell. Lapetra Technical and Scientific Editions, 2003.
Estimation of incident global solar radiation on inclined surfaces. Department of Physics, Universidad Heredia - Costa Rica
Research Work Influence of the Inclination Angle of a solar collector surface on incident radiation. Cuba Energy.
Research Work, Direct Radiation Models for the city of Bogotá from experimental data taken at the Francisco José de Caldas District University, 2004.
Alternative Energy Group, Universidad Distrital de Colombia.
WEBSITES
Global Solar Atlas: http://globalsolaratlas.info/
NASA Surface Meteorology and Solar Energy: https://eosweb.larc.nasa.gov/
Geographical Coordinates: http://dateandtime.info/es/citycoordinates.php?id=3936456
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