Simulation of tracking systems for solar towers

DISSERTATION Simulation of Tracking Systems for Solar Towers ausgeführt zum Zwecke der Erlangung des akademischen Grades eines Doctors der technischen Wissenschaften unter der Leitung von a.o Univ-Prof Dr Karl Ponweiser Institut für Energietechnik und Thermodynamik eingereicht an der Technischen Universität Wien Fakultät für Maschinenwesen und Betriebswissenschaften von Dipl.-Ing Nguyen Quoc Long e1129460 Kantnergasse 48-5 A-1210 Wien Wien, im March 2016 ACKNOWLEDGMENT I would like to express my deep appreciation and gratitude to my Supervisor, Prof Dipl.-Ing Dr.techn Karl PONWEISER for his guidance and encouragement during my study I also gratefully acknowledge Prof Dipl.-Ing Dr techn Markus HAIDER, who firstly gave me an opportunity to work in Vienna University of Technology and has helped me to overcome the difficulties of the whole research process I wish to thank Mr Georg BRUNAUER for his dedicated guidance of the dissertation theory and his kindness for helping me in the most difficult moment of my life in Vienna A special thank is also for Mr Michael LAUERMANN Without his instructions of MATLAB software, the dissertation will not be a sufficient result Above all, I deeply grateful my family for their lovely encouragement during my study time in Vienna and in my life as well ii ABSTRACT Thermal energy, which is created from a conversion of solar radiation, is then converted into mechanical energy The efficiency of this procedure is highly dependent on the temperature at which the thermal energy is available Because of the low energy density of solar radiation, the temperature of a not cooled surface and the temperature of the environment are nearly the same This problem leads to the necessity of a concentrated solar radiation If the energy density of the radiation is higher, the temperature a solar energy earning device can reach is higher as well As a result, the higher the temperature of the thermal energy, the higher is the efficiency of a device which is converting the thermal energy into mechanical energy However, since the sun is moving in relation to the earth, concentrating devices have to be moved to follow the sun by applying solar trackers to concentrate sun energy to target plane This study aims to establish new equations for tracking systems calculation suitable for realistic conditions Based on this calculation, MATLAB software is used to simulate trackers for solar tower systems By use of two methods of solar trackers: azimuth-elevation method and spinning-elevation method, formulas for calculating two rotation angles on two axes of the heliostat are established to ensure that incident sunrays which are hitting the heliostat are reflected to the target plane Accordingly, defining the equations of sunrays tracking is a significant section of this research In the solar tower systems, the distance between the mirror (heliostat) and the receiver (target plane) is longer than in other concentrating systems In this case, the tracking accuracy range has to be a few miliradians (mrad) on the axes of the sun tracking system to maintain the great performance of concentration on the target plane It is the purpose to investigate the errors of the heliostat systems to describe the real position of a heliostat and establish the formulas of the errors of the tracking angles in reality by use of the measurement tools In another method, the error angles can be calculated by measuring the solar elevation angles and the solar azimuth angles during the time of sun tracking at three different times via recording the image of the sun by using a camera The outcome of this method is more accurate than those of using the measurement tools Then the calculation of received energy on the target plane is achievable iii KURZZFASSUNG Thermische Energie, die durch Konversion von solarer Strahlung erzeugt wurde, kann teilweise in mechanische Energie umgewandelt werden Der Wirkungsgrad dieser Umwandlung ist stark von der Temperatur abhängig, bei der die thermische Energie verfügbar ist Aufgrund der geringen Energiedichte der Solarstrahlung ist die Temperatur einer bestrahlten, ungekühlten Fläche nahe der Umgebungstemperatur Dieses Verhalten führt zur Notwendigkeit, die Solarstrahlung zu konzentrieren Je höher die Konzentration, desto höher die Temperatur und somit auch der mögliche Wirkungsgrad der Umwandlung von thermischer in mechanische Energie Da sich die Sonne relativ zur Erde bewegt, müssen Einrichtungen, die die Solarstrahlung auf eine Absorberfläche konzentrieren, der Sonne nachgeführt werden Im Zuge der gegenständlichen Arbeit wurden Gleichungen entwickelt und in MATLAB implementiert, die die Nachführung von Heliostaten für Turmkraftwerke unter realistischen Bedingungen beschreiben Es wurden die Azimuth-Elevation-Method und die Spinning-Elevation-Method betrachtet und verglichen In Solarturm-Systemen sind die Abstände zwischen den Reflektoren und dem Receiver viel grưßer als in anderen konzentrierenden Systemen Deshalb muss die Genauigkeit der Nachführung innerhalb von wenigen Milliradianten sein, um einen hohen Wirkungsgrad erzielen zu können Um das reale System beschreiben zu können, sind die Winkelfehler der Heliostaten zu untersuchen Diese können durch Messung ermittelt werden Eine andere Methode der Winkelfehlerbestimmung besteht darin, zu drei verschiedenen Zeitpunkten im Tagesverlauf die Position der Sonne, beispielsweise mit Hilfe einer Kamera zu bestimmen Diese Methode ist genauer und erlaubt eine genauere Bestimmung des auf den Receiver auftreffenden Energiestroms iv Table of Contents ACKNOWLEDGMENT ii ABSTRACT iii KURZZFASSUNG iv NOTATION xix Chapter INTRODUCTION 1.1 Background and Motivation 1.2 Solar tracking application 1.3 Objective of the Thesis 1.4 Thesis Organization Chapter THEORETICAL BACKGROUND 2.1 Structure of the sun 2.2 The earth 2.3 The relevant geometry between Earth and sun 2.3.1 Distance earth-sun 2.3.2 The geometric relationship of the solar radiation rays 2.4 2.3.2.1 The local hour angle (): 2.3.2.2 Angle of declination ( ): 10 2.3.2.3 Equation of Time (EoT): 12 2.3.2.4 Solar Elevation (s) and Azimuth (s) angles: 13 Controller theory 16 Chapter SOLAR TOWER SYSTEMS AND TRACKING HELIOSTATS 19 v 3.1 Solar tower systems 19 3.2 Tracking methods 21 3.2.1 Active tracking 21 3.2.2 Passive tracking 22 3.3 Methods description 24 3.4 Equations for tracking systems 24 3.4.1 Equations for tracking azimuth-elevation method 25 3.4.1.1 Formulas for the calculation of the tracking angles, using the azimuth-elevation method 26 3.4.1.2 Calculation of the tracking angles, using the azimuth-elevation method 31 3.4.2 Equations for the tracking spinning-elevation method 33 3.4.2.1 Formulas for the calculation of the tracking angles, using the spinning-elevation method 34 3.5 3.4.2.2 Calculation of the tracking angles, using the spinning-elevation method 41 Equations for tracking the sunrays of tower systems 43 3.5.1 Tracking sunrays by use of the azimuth-elevation method 46 3.5.1.1 Equations, describing the tracking of sunrays by use of the azimuth-elevation method 46 3.5.1.2 3.5.2 Applying the equations of the azimuth-elevation method 55 Tracking sunrays by use of the spinning-elevation method 56 vi 3.5.2.1 Equations, describing the tracking of sunrays by use of the spinning-elevation method 56 3.5.2.2 Chapter Applying the equations of the spinning-elevation method 66 ERRORS OF THE HELIOSTAT SYSTEMS 68 4.1 Mathematical Background 68 4.2 The geometric relation of the solar radiation sunrays 71 4.2.1 The sun’s vector relative to the earth centre .71 4.2.2 Solar tracking angle errors 74 4.2.2.1 The various location of the coordinate system 75 4.2.2.2 The coordinates vector of the incident sunrays 77 4.2.3 4.3 Applying the equation to calculate the solar tracking angle 80 Equations for errors of tracking systems 84 4.3.1 Equations for errors of tracking systems which are using the azimuth- elevation method .85 4.3.1.1 Formulas for the calculation of the errors of the tracking angles, using the azimuth-elevation method 86 4.3.1.2 Calculation of the tracking error angles, using the azimuth- elevation method 89 4.3.2 Equations for the errors of tracking systems which are using the spinning- elevation method .92 4.3.2.1 Formulas for the calculation of the errors tracking angles, using the spinning-elevation method 93 vii 4.3.2.2 Calculation of the errors of the tracking angles, using the spinning-elevation method 94 4.4 Conclusion 98 Chapter ACCURACY IMPROVEMENT OF THE SUN TRACKING SYSTEMS 99 5.1 Error formulas establishment 99 5.2 The calculation of the three error angles 100 5.3 Integration of the formulas into the sun tracking systems 108 5.4 Simulation of the tracking angles 109 5.4.1 Simulation of the tracking angles by using the azimuth-elevation method 110 5.4.2 Simulation of the tracking angles by using the spinning-elevation method 115 5.5 Conclusions 119 Chapter CALCULATION AND SIMULATION OF RECEIVED ENERGY ON THE TARGET SURFACE 120 6.1 Solar tower system layout 120 6.2 Heliostats system losses 122 6.2.1 The mirror reflectivity (mir) 122 6.2.2 Cosine efficiency (cos) .122 6.2.3 Shadowing efficiency (sh) and blocking efficiency (bl) .125 6.2.4 Atmospheric transmittance efficiency (at) 127 6.3 Integration of the formulas to calculate the efficiency of the heliostats system 127 viii 6.3.1 Efficiency applied for a heliostat per day 127 6.3.2 Annual efficiency applied for a heliostat 129 6.3.3 Efficiency applied for all heliostats system per day 131 6.3.4 Annual efficiency applied for all heliostats system 133 6.4 Distributions of energy on the target surface 135 6.4.1 Position of the images 136 6.4.2 Distribution of energy flux on the target surface 139 6.5 Distribution of temperature on the target surface 147 6.6 Calculation of energy received on the target surface 157 6.7 Conclusion 157 Chapter CONCLUSIONS 158 7.1 Concluding remarks 158 7.2 Future works 159 References 161 ix List of figures Figure 1-1: Single axis tracker use for solar parabolic trough [43] Figure 1-2: Dual axis tracker of solar thermal disk [43] Figure 2-1: Surface of the sun [21] Figure 2-2: Structure of the Sun [21] Figure 2-3: Variation of the earth-sun distance [21] Figure 2-4: Distance between sun and earth as a function of time Figure 2-5: Local hour angle of a day 10 Figure 2-6:Declination angle of the year [15] 11 Figure 2-7: Variation equation of the time of the year [15] 13 Figure 2-8: Relations of the solar angles [18] 13 Figure 2-9: Geocentric of sun angles [18] 14 Figure 2-10: Geocentric to top centric coordinate transform 15 Figure 2-11: Azimuth angle and elevation angle of the sun 17 Figure 2-12: Azimuth angle and elevation angle of the sun 18 Figure 3-1: Molten salt power tower system 19 Figure 3-2: Schematic of a solar tower system 20 Figure 3-3: Active tracking use sensors to operate the tracker 21 Figure 3-4: Passive tracking compressed gas to operate the tracker 22 Figure 3-5:Two kinds of sun tracking with heliostats 24 x ... vector of the incident sunrays 77 4.2.3 4.3 Applying the equation to calculate the solar tracking angle 80 Equations for errors of tracking systems 84 4.3.1 Equations for errors of tracking. .. sun tracking systems 108 5.4 Simulation of the tracking angles 109 5.4.1 Simulation of the tracking angles by using the azimuth-elevation method 110 5.4.2 Simulation of the tracking angles... calculation, MATLAB software is used to simulate trackers for solar tower systems By use of two methods of solar trackers: azimuth-elevation method and spinning-elevation method, formulas for calculating