Abstract
This paper proposes the best tilting case for Sakarya city, Turkey. The main contribution of this work is the correlation of the tilt angle and the output of a photovoltaic (PV) module mathematically. For this purpose, new diffuse solar radiation equations are developed using existing equations in three groups: (i) group 1: the diffuse fraction (K d ) calculated by the clearness index (K t ); (ii) group 2: the diffuse fraction calculated by the sunshine fraction (K n ); and (iii) group 3: the diffuse fraction calculated by both the clearness index and the sunshine fraction. The most suitable equation of new and existing equations is selected for the city on the basis of different statistical indicators. This equation is used to predict the monthly average daily diffuse, beam, and total solar radiation for the city. Using the predicted data, optimum tilt angles of solar surfaces for different time periods are established. Finally, a PV module is modelled in Matlab and output of the module tilted at optimum tilt angles is evaluated.
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Abbreviations
- H :
-
Monthly average daily global solar radiation (kWh/m2/day)
- H 0 :
-
Monthly average daily extraterrestrial solar radiation (kWh/m2/day)
- H d :
-
Monthly average daily diffuse solar radiation (kWh/m2/day)
- H t :
-
Monthly average daily total solar radiation (kWh/m2/day)
- H b :
-
Monthly average daily beam solar radiation (kWh/m2/day)
- S :
-
Sunshine hours (h)
- S 0 :
-
Maximum sunshine hours (h)
- K t :
-
Monthly average daily clearness index
- K n :
-
Monthly average daily sunshine fraction
- K d :
-
Monthly average daily diffuse fraction
- G sc :
-
Solar constant (=1361 W/m2)
- n day :
-
Number of the day of the year
- w s :
-
Sunrise hour angle for horizontal surface (°)
- ϕ :
-
Latitude (°)
- δ :
-
Solar declination (°)
- β :
-
Tilt angle (°)
- w s’ :
-
Sunrise hour angle for tilted surface (°)
- R b :
-
Tilt coefficient for the beam solar radiation
- R d :
-
Tilt coefficient for the diffuse solar radiation
- ρ g :
-
The ground reflectivity coefficient
- MBE :
-
Mean bias error (MJ/m2)
- MAPE :
-
Mean absolute percentage error (%)
- MABE :
-
Mean absolute bias error (MJ/m2)
- RMSE :
-
Root mean square error (MJ/m2)
- R 2 :
-
Coefficient of determination
- t :
-
t statistics
- I ph :
-
Photocurrent (A)
- I s :
-
Diode saturation current (A)
- n :
-
Diode quality factor
- R s :
-
Lumped series resistance (Ω)
- R sh :
-
Lumped shunt resistance (Ω)
- V T :
-
kT/q
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Acknowledgements
The authors would like to thank Sakarya University Scientific Research Projects Unit for their support within the project 2015-50-02-028.
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Aksoy Tırmıkçı, C., Yavuz, C. Determining optimum tilt angles of solar surfaces in Sakarya, Turkey. Theor Appl Climatol 133, 15–22 (2018). https://doi.org/10.1007/s00704-017-2174-x
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DOI: https://doi.org/10.1007/s00704-017-2174-x