Empirical calculation of the optimal tilt angle for solar collectors in northern hemisphere

ABSTRACT

Panel tilt angles (0°–90°) need to be in a proper position and location to get maximum productivity from solar energy. Values used in solar energy applications are generally computed by (global, diffuse, and direct) variation on horizontal surfaces calculated using isotropic sky and a mean albedo method. Being parallel to the available literature concerning such applications, this study focuses on the optimum solar panel angle. In this study, optimum solar panel angle value by months was determined for three sample provinces (Antalya, Kayseri, and Trabzon) first and North Hemisphere then. Capacity calculation of sample provinces was performed based on monthly, seasonal, and annual angle values and horizontal situation. Monthly and annual optimum angle values for Northern Hemisphere by 1° increase for between the latitudes of 1° N and 65° N. While the panel angle is at the highest level in autumn and winter (November-December-January and February) in annual process, the lowest angle is observed in spring and summer (May-June-July-August). Several different mathematical models have been developed for the sample provinces and Northern Hemisphere. While the variable of 12 different models that were developed for provinces is the Declination (δ) coefficient, the variable of 7 different models that were developed Northern Hemisphere is the latitude (Ø). Regional values in literature with estimation results of models were analyzed based on NASA and PVGIS data color scale. There was created a possibility of comparison by aligning all the optimum solar panel angle values of related location via a scale whose values vary by 1 and 10. Moreover, all the models were verified by statistical analysis methods. R² (determination coefficient) in 19 different estimation equations is pretty close or equal to 1. However, the best among them is Eq. 32 (0.9979) for sample provinces and Eq. (33) (1) for the Northern Hemisphere; developed models are less-than-stellar. Other statistical data of these equations are MBE (−0.0616), RMSE (1.1176), t-sat (0.1830), Bias (1). For Eq. (32); MBE (1.96), RMSE (2.75), t-sat (8.13), MPE % (3.98), MAPE (5.87), SSRE (0.27), and RSE (0.06) for Eq. (33). The statistical analyzes indicate that all regression models are applicable in Turkey and Northern Hemisphere. Developed all correlations are recommended for academic and industrial users.

KEYWORDS:

• Photovoltaic
• tilt angle
• latitude
• correlations
• optimum
• northern

Additional information

Notes on contributors

Mehmet Ali Kallioğlu

Mehmet Ali Kallioğlu obtained his B.E. (Mechanical Engineering) and M.E. (Energy Engineering) from the Erciyes University (ERÜ), Kayseri, Turkey, in 2010 and Nigde Omer Halisdemir University (OHU), Niğde, Turkey, in 2014 respectively. He is currently a research scholar and Ph.D. student at Technology Faculty of Batman University (BATÜ), Batman, Turkey. His major research interests are solar energy conversion, optimum insulation thickness, CFD, renewable energy and heat transfer.

Aydın Durmuş

Aydın Durmuş is presently working as Professor & Head Rector of Mechanical Engineering, Faculty of Engineering & Technology and Batman University, Turkey. He has more than 33 years of teaching and research experience. His research interest is Renewable Energy Systems; Clean Energy Systems, Heat and Mass Transfer, Energy Conservation, Solar Energy Applications; CFD, Environmental Engineering & Management.  He has published more than 100 papers in International / National Journals and conferences.

Hakan Karakaya

Hakan Karakaya is M.Sc. and the Ph.D. degree in Mechanical Engineering from Fırat University, Institute of Science and Technology. Currently Works as an Assistant Professor at Batman University, Faculty of Engineering and Architecture. Major research interests are energy conversion, optimum insulation thickness, solar energy applications and heating-cooling load of buildings.

Adem Yılmaz

Adem Yılmaz is M.Sc. and the Ph.D. degree in mechanical training from Gazi University, Institute of Science and Technology Institute. Currently Works as an Assistant Professor at Batman University, Faculty of Technology. Major research interests are renewable energy, fuel cell, biogas systems, solar energy applications, air conditioning and heating-cooling systems.