Determining Global Solar Radiation Incident on Tilted Surfaces with Different Tilt Angles at the Department Of Physics Makerere University

ABSTRACT Solar radiation data at horizontal level, tilted surfaces and in the atmosphere is an important feature in solar energy applications such as photovoltaic systems for electricity generation, solar collectors for heating and passive solar devices. This study presents an investigation of the dependence of global solar radiation incident on a tilted surface on some meteorological parameters for different tilt angles based on measured meteorological data of sunshine, relative humidity and temperature at Makerere University. Empirical models relating global solar radiation on tilted surfaces and meteorological data were formulated using data of six months. The proposed empirical model for the estimation of daily global solar radiation on the tilted surfaces assessment based on the statistical analysis with the Mean Bias and Root Mean Square difference that is in good agreement with the measured data on a tilted surface is = -0.2614 - 0.2386(RH) + 1.5822 (Tmax) + 0.1065 (Tmax) Hap 65 Tmin In comparison with the other tilt angles the model yielded a RMSE of 4.2654, with a low (poor) correlation coefficient of 0.3743 at a 95% confidence interval and MBE of 1.5801. Analysis of data for a period of 3 years, towards the verification of Akoba's (2009) model, the study recommends a new model = -0.9227 - 0.1405 (!.::.) - 0.0335(RH) + 3.2826 (Tmax) that capitulated a RMSE of Hap N 65 2.5985, with a correlation coefficient of 0.8863 at a 95% confidence interval and MBE of 2.3391.

 TABLE OF CONTENTS 

DECLARATION A 

DECLARATION B ii 

DEDICATION iii 

ACKNOWLEDGEMENTS iv 

TABLE OF CONTENTS V 

LIST OF TABLES ix 

LIST OF FIGURES X 

ABSTRACT xiii 

PARAMETER AND VARIABLE DEFINITIONS xiv 

ACRONYMS xvi 

DEFINITION OF TERMINOLOGIES xvii 

CHAPTER ONE 1 

INTRODUCTION 1 

1.1 Background of the Study 1 

1.2 Statement of the Problem 6 

1.3 General Objective 7 

1.4 Specific Objectives 7 

1.5 Significance 8 

1.6 Justification 8 

1.7 Scope of the Study 9 

CHAPTER TWO 10 

LITERATURE REVIEW 10 

2.1 The Sun 10 

2.1.1 The Nature of Solar Radiation 11 

2.1.2 Sun - Earth Relationships 12 

2.2 Radiation on an Inclined Surface 16 

2.2.1 Beam (Direct) Radiation 16 

2.2.2 Diffuse Radiation 17 

2.2.3 Albedo Radiation 18 

2.3 Solar Time 19 

2.4 Global Solar Radiation 

2.4.1 Extraterrestrial Solar Radiation 

2.4.2 Extraterrestrial Solar Spectral Irradiance 

2.4.3 Solar Constant 

2.4.4 Extraterrestrial Solar Radiation on a Horizontal Surface 

2.4.5 Extraterrestrial Solar Radiation on an Inclined Surface 

2.5 Estimation of Global Solar Radiation on a Tilted Surface 

2.6 Empirical Correlations of Global Solar Radiation on a Tilted Surface  

2.7 Comparison of Global Insolation on a Tilted Surface with the Corresponding values on 

a Horizontal Surface 32 

3 .1 Study Area 35 

3.2 Data Structure 35 

3.3 Data Collection 35 

3.3.1 Measurement of Global Solar Radiation 35 

3.3.1.1. Pyranometer 35 

3.3.1.2 Radiation Sensors 36 

3.3.1.3 Kipp and Zonen Pyranometers 36 

3.3.1.4 Classification of Pyranometers 37 

3.3.1.5 Sensitivity and Spectral Range of a CM6B Pyranometer 37 

3.3.1.6 Principle of Operation 38 

3.4 Measurement of Global Solar Radiation on a Titled Surface 39 

3.5 Measurement of Global Solar Radiation on a Horizontal Surface 40 

3.6 Parameters Used in the Estimation and Analysis of Global Solar Radiation 41 

3.7 Collection of Meteorological Data 42 

3.7.1 Measurement of Sunshine Hours 42 

3.7.2 Units and Scales 43 

3.7.3 Meteorological Requirements 43 

3.7.4 The CSDl Sunshine Duration Sensor 44 

3.7.5 Specifications of the CSDl Sunshine Duration Sensor 45 

3.7.6 Installing the CSDl Sunshine Duration Sensor 45 

3.7.7 Radiation Measurement 47  

3.7.7 CSDl Sunshine Duration Sensor and Measurement of Sunshine Duration 47 

3.8 Measurement of Temperature 48 

3.9 Measurement of Relative Humidity 49 

3.9.1 The Sling Psychrometer and the Humidity Slide Rule 49 

3.10 Data Analysis 

CHAPTER FOUR: PRESENTATION AND DISCUSSION OF RESULTS 

4.1 Distribution of Global Solar radiation on a Horizontal and tilted surfaces 

4.2 Distribution of Ambient Temperature 

4.3 Distribution of Relative Humidity 

4.4 Distribution of Sunshine Hours 

4.5 Variations of Global Solar Radiation on a Tilted Surface with Sun Shine Hours,  

Temperature and Relative Humidity. 56 

4.5.1 Variation of the ratio clearness index with the measured global radiations received 

on the different tilt angles. 62 

4.6 Model Formulation 

4.7 Validation of Empirical Models Developed 

4.8: Comparison of Global Solar Radiation on a Tilted Surfaces With the Measured on a 

Horizontal Surface 72 

4.9 Analysis of the angle of tilt p = 22. 50 for a period of three years 74 

4.9.1 Regression Coefficients for the Justification of Akoba's (2009) Model Using Developed 

Models in Section 4.6 76 

4.9.2 Model Validation using monthly data averages of the angle of tilt ~=22.5° for a 

period of three years 78 

CHAPTER FIVE: CONCLUSIONS AND RECOMMENDATIONS 83 

5.1. Conclusions 

5.2. Recommendations 

REFERENCES  

Appendix 1: Code for computing Parameters Used in the estimation and Analysis of Global 

Solar Radiation, for the Julian days and angles 15°, 22.5° and 30° for a period of Six Month. 90 

Appendix 2: Daily Values of the extraterrestrial Parameters 

Appendix 3: Table of results: Measured data 

Appendix 4: Table of results: Calculated