Ying Yu Thesis

8/6/2019 Ying Yu Thesis

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TRACKING ALIGNMENTS FOR A PHOTOVOLTAIC

CONCENTRATING SYSTEM

by

Ying Yu

A thesis submitted to the Faculty of the University of Delaware in partial fulfillment ofthe requirements for the degree of Master of Science in Electrical and Computer Engineering

Fall 2009

Copyright 2000 Ying Yu

All Rights Reserved


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TRACKING ALIGNMENTS FOR A PHOTOVOLTAIC

CONCENTRATING SYSTEM

by

Ying Yu

Approved: _________________________________________________________

Charles Ih, Ph.D.Professor in charge of thesis on behalf of the Advisory Committee

Approved: _________________________________________________________

Kenneth E. Barner, Ph.D.Chair of the Department of Electrical and Computer Engineering

Approved: _________________________________________________________Michael J. Chajes, Ph.D.Dean of the College of Engineering

Approved: _________________________________________________________

Debra Hess Norris, M.S.Vice Provost for Graduate and Professional Education


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ACKNOWLEDGMENTS

This study would not have been possible without the permission from the ECE department,

University of Delaware.

First and foremost I want to thank my supervisor Dr. Charles Ih. He is always an awesome

advisor, gave the help when I was in the most difficult situation. Also he gives the patient and

useful suggestions not only for the research but also for my life.

The thanks are to people who have helped me in life and in thesis for the past one and one-half

years. Ge Gan and Xu Wang who are my best friends in University of Delaware, encourage me

and help me how to begin the compiler and programming, took care of me during my daily life. I

will always appreciate the help from them. Dr. Cook in Department of Mathematical Sciences

gave me many help when I was in the difficult time, also keep in touch for some precious

suggestions, Jing Li, Yuanqu Lin, Tom and other friend give me a lot of help during the study

and life.

This thesis would not have been possible without the love and encouragement of my parents. I

love them so much.


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CONTENTS

LIST OF FIGURES vi

LIST OF TABLES .vii

ABSTRACT..viii

Chapter 1 Introduction......................................................................................................... 1

1.1 Importance of the solar energy ............................................................................ 1

1.2 Known CPV systems ......................................................................................... 3

1.3 Contributions.................................................................................................... 5

Chapter 2 The Photovoltaic System ...................................................................................... 8

2.1 The typical photovoltaic system .......................................................................... 8

2.2 New Concentrator Photovoltaic (PV) systems (CPV) ........................................... 12

Chapter 3 System Description ......................................................................................................... 16

Chapter 4 Alignment Mathematical DERIVATION ............................................................... 19

4.1 Mathematical Derivation....................................................................................... 19

4.2 Critical Parameters ............................................................................................... 28

4.2.1 Solar Position ............................................................................................ 29

4.2.2 Solar Azimuth and Altitude.......................................................................... 34

4.2.3 Local Solar Time (LSoT) ............................................................................ 36

4.2.4 Important Dates ......................................................................................... 38

4.2.5 Declination angle ....................................................................................... 39

4.3 Azimuth, altitude, declination calculator.................................................................. 41

4.4 Alignment calculator ............................................................................................ 42

Chapter 5 Alignment Analysis ............................................................................................ 43

5.1 Precise Local Solar Time....................................................................................... 43

5.2 Accurate Angular Distance .................................................................................... 47

Chapter 6 Heat-RECOVER ................................................................................................ 51

6.1 Heat recovery for hot water heating system ............................................................. 54

6.1.1 Water heating system necessity .................................................................... 54

6.1.2 Water heating system structure [36, 37] ......................................................... 54

6.2 Heat Recovery Simulation..................................................................................... 57

6.2.1 Create Geometry in Gambit [46] ................................................................ 58


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Conclusion....................................................................................................................... 68

APPENDIX...70

References.72


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vi

LIST OF FIGURES

Figure1.1 Different Latitude of Solar Radiation2

Figure1.2 Grid-Connected PV system with optional storage........................................................................5

Figure2.1 Concentrator Photovoltaic Arrays...9

Figure2.2 Three commonly used reflecting schemes for concentrating solar energy...............................10

Figure2.3 Proposed Concentrator Photovoltaic Arrays.........................................................................13

Figure2.4 PV system configuration with heat recovery...............................................................................15

Figure3.1 Panel assembly with the coarse tracking ....17

Figure4.1~4.4 Alignment Diagram.................................................................................................................21~27

Figure4.5 Hourly Sun-path............................................................................................................................30

Figure4.6 Annual Path of the Sun on a hemispheric View.........................................................................31

Figure4.7 For each 5 of latitude giving the altitude and azimuth of the sun-path diagrams.33

Figure4.8 Azimuth and Altitude Angle..........................35

Figure4.9 How solar declination varies through out of the year.........................40

Figure5.1 The Local Standard Time Meridian (LSTM)..44

Figure5.2 Equation of Time..46

Figure6.1 Typical Annual Space and Water Heating Costs52

Figure6.2 Panel assembly with the pipe system53

Figure6.3 Water heating system55

Figure6.4 Circular pipe58

Figure6.5 Four vertices...60

Figure6.6 Rectangular edges and faces created60

Figure6.7 Meshed rectangular61

Figure6.8 Solver and the residual monitors set63

Figure6.9 Residuals for each iteration...64

Figure6.10 Axial velocity for the centerline result......65

Figure6.11 Static Temperature in the pipe66


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LIST OF TABLES

Table2.1 The residential solar PV systems cost...12

Table4.1 LSTM for North America..38

Table4.2 Important dates relevant to solar position...39

Table5.1 The difference between the standard angular distance and specific angular distance48


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ABSTRACT

A novel concentrator has recently been proposed by Dr. Charles Ih [1]. The concentrator can

greatly reduce the cost of the grid-tied photovoltaic system by only using a simple 1-D tracking

system. In the new system, the number of solar cells used is reduced. The panel structure and

tracking mechanism are simplified as they take advantage of the special properties of the small

frame Fresnel lens and a special tracking arrangement. The great cost reduction is the result of

eliminating the N-S tracking completely, and more important, the tracking error tolerance is

improved. The techniques are unique to the proposed concentrator but not effective in the more

conventional 2-D concentrators. Since the proposed concentrator is effective for the silicon cells,

it can meet or exceed the SAI goal in the near future, i.e making the cost equal to or lower than

that of conventional sources. The immediate benefits are, reducing silicon usage (cost) by 95%,

increasing collecting efficiency by 20% and reducing the system cost by two thirds [1]. These

advantages will help to accelerate the popularization of photovoltaic systems and let people

enjoy the benefit of the photovoltaic energy system. The system is much easier to maintain and

repair, as most of the materials can be recycled. The system also has the capability of being

upgraded when efficiency cells become generally and economically available in the future.

Unlike other concentrating systems, a special tracking methodology is needed. This thesis

describes the special tracking arrangement and alignment for the operation. This system is also

more adaptable for solar heat recovery. The heat recovery is described and discussed in this

thesis.

Key Words: Photovoltaic Concentrator, Fresnel Lens Concentrator, heat recovery.


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CHAPTER 1

INTRODUCTION

In this chapter, the background information is introduced. It is organized

as the following: section 1.1 is a brief introduction about the importance of using solar

energy. The common CPV (Concentrator Photovoltaic) systems are presented in

section 1.2. The main contributions of this thesis are presented in section 1.3.

1.1 Importance of the solar energy

With the current high cost of energy as a result of production interruptions

and global competitions from limited resources, it is painfully aware that the cost of

these fuels keeps rising by huge amounts, not only the gasoline for our cars, but also

our utility bills for gas and electricity and, in many states, the oil or coal for heating, it

is important to use more renewable resources. The solar energy is directly from the

Sun. As we know, most of the lives around the world cannot depart from the sun. Heat

and light from the sun, along with solar-based resources such as wind and wave

power, etc are account for most of the available flow of renewable energy. As global

warming and accelerated environment harmful gas emissions to continue, the use of

environmental friendly energy source, such as photovoltaic systems, become even

more urgent and attractive. Unfortunately, the cost of the photovoltaic electrical power

is still too high to be used in significant proportion to supplement the conventional

electrical power source.


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The amount of energy from the sun that falls on Earths surface is

enormous. All the energy stored in Earth's reserves of coal, oil, and natural gas is

matched by the energy from just 20 days of sunshine. Outside Earth's atmosphere, the

sun's energy contains about 1,300 watts per square meter. Close to the earths surface,

the energy in sunlight has fallen to about 1,000 watts per square meter at noon on a

cloudless day. Averaged over the entire surface of the planet, 24 hours per day for a

year, each square meter collects the approximate energy equivalent of almost a barrel

of oil each year, or 4.2 kilowatt-hours of energy every day [2].

Figure 1.1 Different latitude of solar radiation


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Figure 1.1[3] shows how solar radiation at the top of the earth's

atmosphere varies with latitude. For example, in North America, the average

insolation at ground level over an entire year (including nights and periods of cloudy

weather) lies between 125 and 375 W/m (3 to 9 kWh/m/day).[4] At present,

photovoltaic panels typically convert about 15 percent of incident sunlight into

electricity; therefore, a solar panel in the contiguous United States, on average,

delivers 19 to 56 W/m or 0.45 - 1.35 kWh/m/day [5].

The solar energy can be converted into many other forms of energy, such

as heat and electricity. Today, the solar energy can be used for the water heating,

space heating, air conditioner, electricity, etc. It can be converted to electricity by

using Photovoltaic (PV devices) or solar cells-changing sunlight directly into

electricity.

1.2 Known CPV systems

Typical solar energy system includes: (1) Solar panel; (2) Optional storage

battery; (3) Inverter; (4) Installation site or roof. Figure 1.2 shows a PV concentrator

system. The key part is the solar collector (solar panel) which intercepts the incoming

sunlight and changes it into a useable energy to meet the specific demands.

Traditionally, most of the collectors use the flat-plate PV (photovoltaics)

which produces electricity directly from the sunlight striking the silicon panel.


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However, the expensive solar cells and the installation cost limit the popularization of

the solar technology.

In order to reduce the high cost of the solar cell, a concentrator is added to

make use of relatively inexpensive materials such as plastic lenses or glass to capture

the solar energy shining on a fairly large area and focus that energy onto the solar cell.

The primary advantage to use concentrators is to be able to use less solar cell material

in a PV system, because PV cells are the most expensive components of a PV system.

However, CPV systems must be pointed directly at the sun because they work by

focusing sunlight onto solar cell, and therefore require trackers which follow the suns

trajectory throughout the day. Since CPV systems require less semiconductor material

to capture a given amount of sunlight, it's still cost-effective to use more expensive

and higher efficiency cells to increase the electricity generated from a given collection

area [48].

The use of concentrators in principles can reduce the cost. Concentrators

in different configurations have been evaluated and tested. The most recent R/D has

been on high concentration ratio because the expected very high cost of high

efficiency solar cells. The FLATCON [11] modules require a quite massive precision

tracking system. Thus they are not cost effective. The main reason is that the cost of

supporting structure and the required precision tracking system can easily offset the

savings on the solar cells. Systems with very high concentration ratio require high

precision and complicated 2-D external mechanical tracking system. The whole rigid

assemble is moved in a 2-D fashion precisely to track the sun during the day and

through the year such as the FLATCON [12].


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Figure 1.2 Grid-Connected PV system with optional storage


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1.3 Contribution

As described above, the limitation for the traditional CPV system is the

high cost of the solar concentrator and the tracking system is more complicated. In

order to use the tracking system effectively, the physical structure needs to be aligned

to the real north which needs to consider the magnetic field of the earth, the latitude

and the position on the earth. Whats more, the position of the sun changes every day

and every season, the receiving angle is also different. How to align it automatically to

track the sun is the most important for the design.

Dr. Ihs group in ECE department, University of Delaware proposed a

new CPV system, which can greatly reduce the cost, and improve the limitations

described above. In this thesis, the alignment both in hardware and theory are

investigated.

For the hardware, the proposed system utilizes the special properties of

the Fresnel lens, and replaces the costly 2-D with a simple 1-D tracking. The

combination can cut the cost and even can reach the low cost of conventional sources.

It can also meet the requirement of recycling, repairing, and easy maintenance .

From the theory, the proposed alignment software makes the alignment

easy to use. When the local longitude and latitude are known, the local time can be

easily calculated, and the suns location and angle can be deduced from the software .

In general, the direction of the house has an angle with respect to the true south. A


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precise device can be used to measure the angle, and compare it to the suns angle, if

they are the same, the houses location is direct to the true south, or else, the

difference will be the angle between the houses location and the true south. It can

easily deduced by the developed software.

The main advantages are: 1) Proposing an easy but effective way to track

the alignment to the true south; 2) Reducing system cost by more than 3 times by

eliminating 2-D tracking; 3) Reducing silicon usage by 95%; 4) Increasing collecting

efficiency by 20%; 5) Can be Upgraded to high efficiency cells and even VHESC in

the future; 6) Most of the materials can be recycled; 7)Capable meeting and exceeding

SAIs goals in a shorter time; 8)Getting the high efficiency heat recovery from the

new system [1].

The thesis is presented as the following: the first chapter gives the preview

of the project; the second chapter describes the Photovoltaic system; the third chapter

explains the mathematical deduction; the fourth chapter is the hardware design; the

fifth chapter gives the result and the analysis; the sixth chapter expresses the idea for

the heat recovery; the last chapter is the conclusion and the future work.


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CHAPTER 2

THE PHOTOVOLTAIC SYSTEM

In chapter 1, it is stated that solar energy is a very important energy source

for residential and commercial use and also has the benefit of minimizing the air

pollution. Unfortunately, as mentioned earlier, the solar collectors used now are not as

popular as expected because of the high cost. In this chapter, an overview of the

research project is presented, and the target is to make the photovoltaic cell system

more cost effective. This chapter is organized as the following: in section 2.1, the

traditional photovoltaic system is presented; the new photovoltaic concentrator system

is introduced in section 2.2.

2.1 The typical photovoltaic system

Photovoltaic (PV) systems use solar electric panels to directly convert the

sun's energy into electricity, as shown in Figure 2.1 [50]. The single module of the

solar cell cannot produce enough power for practical use. To increase power output,

inter-connected solar cells form the PV panel which is framed in aluminum frames

suitable for mounting, which can be further interconnected to form an array. The array

refers to the entire generating system, which is made up of thousands panels as thearray size needed. The PV array can increase the total power output (voltage and

current) for practical application [9]. For example, the converted electrical power from

the Sun reaching the earth is typically about 1,000 Watts per 6 square meters. The

maximum energy is from the hot and dry locations (like California) and is more than


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six kilowatt-hour per day per square meter. The average in the U.S. is closer to 3.6

kilowatt-hour per day per square meter with an efficiency of 15%.

In order to increase the cost-effectiveness, the Concentrating Photovoltaic

(CPV) systems are used to reduce the cost for the solar panel materials. But most

concentrators can only concentrate the parallel insolation coming directly from the

suns disk [49], and most of them need the 2-D tracking system, as shown in Figure

2.2.

Figure 2.1 Concentrator Photovoltaic Arrays


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A recent commercial CPV system by SolFocus will be in the form of

molded glass tile including lenses and mirrors. These panels still need 2-D tracking.

The tracking accuracy is reduced to about 2

, a great achievement[6]. With the

greatly relax tracking accuracy, this system has the potential to be installed in large

scale at a reasonable cost. However, the panel itself is quite complicated and includes

lenses and mirrors. Its cost is probably quite high. It is not clear how the precision

laminated high reflectance mirrors can be made at low cost. Because of high cost of

the panels, even using a moderate 2-D tracking system, the overall system is probably

still high. They are only suitable for large scaled installation and using high efficiency

cells. They only predict a modest cost reduction now and promise a great cost

reduction in the future [7].

Figure 2.2 Three commonly used reflecting schemes for concentrating solar

energy


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Entech has been a leader in CPV system particularly for apace (satellite)

applications using linear Fresnel lenses and has recently turn their attention to

terrestrial applications [8]. They have installed many 20kW (expandable to 100kW)

systems for large scaled utility applications. The panel itself is quite massive and

strong to support their proper operations. Because of the very high cost (200X), the

current high efficiency cells (multi-junction) (by Spectralab) still require 2-D

concentrators. Entech has recently developed the Mini-Dome Lens Module (2-D

concentrator) claimed to have large tolerances for assembly, alignment and sun

tracking and concluded that it has no clear advantages over their linear system [10]. It

is believed that the Mini-Dome Lens Module is similar in concept of the SolFocuss

system with a different implementation [10].

The typical cost for installing PV system is shown in Table2.1 [15]. This

investment is like paying for years of electricity bill all at once. The electricity bill

will reduce monthly after the system has paid for itself. The formula below uses the 16

cents per kWh utility rate to estimate the monthly savings [14].

2, 424 16 / $388 /kWh kWh year (2.1)

Take the studio for example, the installation price is $16500, the annual

saving fee is $388, so after 42 years, the payment can be made up by saving using the

PV system. However, the typical lifetime of the PV system is only 25 years.


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Table 2.1 The residential solar PV systems cost

Direct Grid-Tie (net metering)

Solar PV System The Studio The Cottage The Family Family Plus The Estate

1.5kW grid-tie 2.6 kW grid-tie 3.7 kW grid-tie 4.5 kW grid-tie 6 kW grid-t ie

Estimated monthly energy output (KWH)*

Monthly Ave 140 250 355 425 570

Summer Peak 200 350 505 605 810

Winter Low 60 100 150 180 240

System Components

Inverter PVP 2500 PVP 2500 PVP 3500 PVP 4800 PVP 5200

Modules 9 Sharp 167 14 Sharp 187 20 Sharp 187 24 Sharp 187 36 Sharp 167

String Sizing 1x9, 1503W 2x7, 2618W 2x10, 3740W 2x12, 4488W 3x12, 6012W

Estimated Total Installed Cost

Installed Price $16,500 $23,500 $31,500 $36,000 $46,500

2.2 New Concentrator Photovoltaic (PV) systems (CPV)

As explained above, the payback period is still too long for family to use,

which also limits the spread of the solar energy system. On the other hand, the suns

position, altitude and azimuth, depend on the location, time and date and the

relationship among these variants is quite complicated. But all the 2-D concentrators

reported in the literatures need to accurately track these changes during the day and

throughout the whole year. Obviously it is neither practical nor cost effective to

accurately track the sun with a single joint for a concentrator with a size much larger

than 1m2 [18, 19]. For instance, at the latitude of N 40, the suns altitude can change

from 28to 74

from 7am to 5pm during summer time and from 7

to 27

from 8am to


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4pm in winters respectively. For large sizes, a massive tracking structure is required,

for instance FLATCON [18].

In order to overcome these disadvantages of the traditional CPV systems,

in this thesis, the new proposed system uses the Fresnel lens to collect and concentrate

the sunlight onto photovoltaic cell. As shown in Figure 2.3 [16], the PV concentrator

module consists of solar cells with electrical isolation and thermally conducting

contacts and Fresnel lenses.

It is known that severe optical aberrations will result if images are formed

off axes of a simple lens or mirror. Because of these severe image aberrations, the

traditional concentrator systems must point directly at and follow the sun accurately.

These limitations are eliminated in the new system.

8 ' 3"

2 ' 3"

4"

Figure 2.3 Proposed Concentrator Photovoltaic Arrays


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By using the optical concentrators to focus direct sunlight onto solar cells,

the cell area, and consequently the cost, can be reduced by 95%. The solar-cell cost

constitutes between 5% and 10% of total concentrator system cost. Unlike other

concentrating systems, the cost of the tracking system is also low. So the total system

is cost effective.

The concentrator should track the suns position and fix the collector to

the south orientation. In this thesis, the new simple position and angle calculator is

presented to give the exact angle adjustment for the CPV system installation which

can highly improve the precision and efficiency of the system. Accordingly, it can

largely reduce the installation cost dramatically. More important, in this design, as

shown in Figure 2.4, the heat recovery system is included. The heat can be used for

the water heating and space heating, save a lot of cost such as hot water, electricity for

the air-conditioner and so on.


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Heatexchange(Preheat)

Pump

Hotwatertank

Expansiontankwithpressureequalization

Radiator(whichmaybelinkedtoaheatpumpfortheheatrecovery)

Coldwater

Hot water

Figure 2.4 PV system configuration with heat recovery


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CHAPTER 3

SYSTEM DESCRIPTION

In this Chapter, the new CPV system is outlined. The heat recovery tubes

are embedded in the back panel. This Chapter is to describe how to apply the theory

on the application to make the solar concentrator more cost effective.

Typical PV system configuration is shown in Chapter 2. The PV array

consists of a number of individual photovoltaic modules connected together to give

the required power with a suitable current and voltage output. The system occupies a

large area and costs a lot accordingly. Typical modules have a rated power output of

around 75 - 120 Watts peak (Wp) each [1].

The proposed system uses Fresnel lenses as the concentration elements,

and the collector for the heating system is in fact also the concentrator. The basic

panel is constructed in the form of a thin box, the enclosure, as shown in Figure 2.2

in last chapter[1]. The system includes many PV panels, and each of the PV panels is

fixed on an axis, as shown in Figure 3.1. The panels can be adjusted along X and Z

axis, and also can do tracking around rotating axis to follow the suns position.

Meanwhile, water tubes are embedded in the back panel for the heat recovery, which

can take away the heat for the hot water usage, and also lower the temperature of the

panel to improve the efficiency since the PV panels are more efficient at a lower

temperature.


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The size of the panel is approximate 2 '' 8'and the aperture of the

linear Fresnel lens is 2'' (wide) and there are 12 lenses in each panel. In order to make

the panel light and strong, the top and bottom plates are made with supporting

Figure 3.1 Panel assembly with the coarse tracking mechanism


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beams and/or ridges. Because of the supporting beams, we can use relatively thin

glass plate on which silicon Fresnel lenses are molded or use thin molded Fresnel

lenses. The supporting back plates have ridged structures to increase the physical

rigidity and heat radiation area.


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CHAPTER 4

ALIGNMENT MATHEMATICAL DERIVATION

In Chapter 2 and 3, a brief description of proposed photovoltaic

concentrator system is outlined. The hardware design for the proposed PVC system is

also explained and a large cost reduction for the new system can be expected. How to

get the exact installation angel and how to get the true north orientation will be

discussed in this Chapter. This Chapter is organized as follows: in section 4.1, the

mathematical derivation is described; the critical parameters are explained in the

section 4.2; then the calculator software for the azimuth, altitude, declination and

alignment is discussed in section 4.3 and 4.4, more details are given in Appendix A

and B.

4.1 Mathematical Derivations

As shown in Figure 3.1, the real tracking frame may not be exactly facing

the true south. In order to make the PVC solar panel to be aligned, the tracking frame

needs to be adjusted along the new X-Z direction and the panel in the new Y-Z

direction. We need to decide the adjustment angles based on the local latitude,

longitude and solar time and so on. In the actual installation, the tracking frame of the

system will rotate an angle from the true north. The details will be given in the

following deductions to realign to the North Pole. In order to simplify the deductions,

the adjustment angles are projected in the new rectangular coordinates system after the

rotation.


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Firstly, a system of rectangular coordinates axis is established. It is

assumed that 0OV

is the original vector in the 3-D coordinates, with the tracking

frame points to a fixed orientation, as shown in Figure 4.1. Its angle with respect to

the Z axis is . Let 0OV

=a and the coordinate of 0V

is 0 0 0( , , )x y z

.

To simplify the calculation, it is assumed that vector 0OV

is in the x-z

plane, so the coordinates of 0V

are,

0 0 0 0( , , ) ( sin ,0, cos )V x y z a a

(4.1)

The equation of the line0

OV

is,

0 0 0

x y z

x y z

(4.2)


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The center is fixed as'O , radius as

'

0O V

, then a circle is drew at the

plane of

'

Z OO

, where 0V

is rotated along the circle to new a spot 1 1 1 1( , , )V x y z

, the

spotsO and 1V

are connected to get a new vector 1OV

, the angle between 0'O V

and

1'O V

is , actually it is the rotation from plate'

0O V O

to plate'

1O V O

around the z-

axis. The angle between the two plates is , which is the rotation angle between the

tracking bar direction and true north. As shown in Figure 4.2.

Figure 4.1


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The equation of the line 1OV

1 1 1

x y z

x y z

(4.3)

If the new system is rotated clockwisedegrees about the z-axis, the new

coordinates become:

Figure 4.2


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0 0 01

1 0 0 0 0

1 0 0

cos sincos sin 0

sin cos 0 cos sin0 0 1

z

x x yx

y R V y y xz z z

(4.4)

For the plane contains z-axis and 1OV

, the normal of the plane passing

through V1 is:

0 1 0 1 0

1 1 0

0 0 x y z

x y

a a a

z y z a x z a

x y z

(4.5)

The equation of the new plane can be expressed as:

1 0 1 1 0 1( ) ( ) 0y z x x x z y y (4.6)

1 1 1 1( ) ( ) 0y x x x y y (4.7)

From0

V

, a vertical line can be drawn to plane containing z-axis

and 1OV

, as shown in Figure 4.3.


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The equation of the vertical line is:

0 0

1 1

x x y y

y x

(4.8)

From (4.6), (4.7), (4.8), the coordinate of the intersectingpoint 2V

2 2 2( , , )x y z can be calculated as the following:

Figure 4.3


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1 1 0 1 0

2 2 21 1

1 1 0 1 02 2 2

1 1

( )

( )

x y y x xx

x y

y y y x xy

x y

(4.9)

The equation of the vector 2OV

:

2 2 2

x y z x y z

(4.10)

In order to make the tracking axis back to the North Star, the new vector

need to be rotated by an angle of , and then back to the North Star by an angle of .

Assuming that the angle between the vector 1OV

and vector 2OV

is , that between the

vector 0OV

and vector 2OV

is , as shown in Figure 4.4, then:

2

1 0 1 0 0

2 2 2 2 2 2

0 0 0 1 1 0

cosx x y y z

x y z x y z

(4.11)

2

1 2 1 2 0

2 2 2 2 2 2

1 1 0 2 2 2

cosx x y y z

x y z x y z

(4.12)

2

2 0 2 0 0

2 2 2 2 2 2

0 0 0 2 2 2

cosx x y y z

x y z x y z

(4.13)


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Where:

1 0 0

1 0 0

1 0

cos sin

cos sin

x x y

y y x

z z

(4.14)

And

2

1 1 0 1 02 2 2

1 1

1 1 0 1 0

2 2

1 1

2 0

( )

( )

x y y x xx

x y

y y y x xy

x y

z z

(4.15)


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It is described the angle between either 2 vectors using0

V

0 0 0( , , )x y z .

Then we can check that these equations provide right answers at 2 special

conditions:

(1)When 0 , there is no rotation, then 0OV = 1OV = 2OV , the directionof the vector has no change.

(2)When

Figure 4.4


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2

(4.16)

1 0

1 0

1 0

x y

y x

z z

(4.17)

0 0 0 0 0

2 2

1 1

1 0 0 0 02 2

1 1

0

( )0

( )0

y x y x yx

x y

y x y x yy x y

z z

(4.18)

So 2OV

is on the z-axis, then if it want to go back to the 0OV

direction, the

rotate angle is equal to.

For the position of the sun is changing constantly, if the latitude and the

initial angleis fixed, the rotate angleis to be estimated.


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4.2 Critical Parameters

The theory of alignment has been described above. The more importance

thing is to get the true north for the alignment. When the true north is determined, the

accurate alignment angles can be set. For more accurate alignment, the parameters to

calculate the angle are described here.

4.2.1 Solar Position

In order to make the concentrator face the sun directly all the time, it is

important to track the sun position. The position of the sun varies continually during

the day (as shown in Figure 4.5 [21, 22]) and also changes with seasons during the

whole year (as shown in Figure 4.6 [21, 22]). How to determine the sun position is

critical for the calculations for the given latitude and longitude of a local position.

More complexity is added because of the tilted angle of the earth and its

elliptical orbit around the sun. It is often much simpler and quicker to get the sun

positions directly from a sun-path diagram for any time of the day and day of the year,

a unique summary of solar position can be provided when the designer consider the

shading requirements and design option. However, it is not very accurate (as shown in

Figure 4.7 [22, 23]). In this thesis, an accurate calculation method is provided.


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Figure 4.5 Hourly Sun-path


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Figure 4.6 Annual path of the Sun on a hemispheric view


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On the charts, a point corresponding to the projected position of the sun is

determined from the heavy lines corresponding to declination and solar time. To find

the solar altitude and azimuth:

1. Select the chart or charts appropriate to the latitude2. Find the solar declination corresponding to the date3. Determine the true solar time4. Read the required altitude and azimuth at the point determined by

the declination and the true solar time

It should be emphasized that the solar altitude determined from these

charts is the true geometric position of the center of the sun. At low solar elevations

terrestrial refraction may considerably alter the apparent position of sun. Under

average atmospheric refraction the sun will appear on the horizon when it actually is

approximately 34' below the horizon; the effect of refraction decreases rapidly with

increasing solar elevation [23].


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Figure 4.7 For each 5 of latitude (except 5 ,15 , 75 ,85 ) giving thealtitude and azimuth of the sun-path diagrams


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4.2.2 Solar Azimuth and Altitude

The solar azimuth angle is often defined as the angle between the line

from the observer to the sun projected on the ground and the line from the observer

due north.

The solar altitude is the angular height of the sun measured from the

Horizon. Above the horizon is positive, below is negative. The solar altitude for the

sun directly in the center of the sky is 90 degrees. Solar altitude is a measure in a

horizontal coordinate system. The horizontal coordinate system takes the observation

point as the origin and fixes the sun's position by giving a compass direction

(Azimuth) and elevation above the horizon (Altitude), as shown in Figure 4.8 [21,

22].

When the sun is to the east of the south, the azimuth angle is positive

while the azimuth angle is negative when the sun is to the west of the south. The

Azimuth angles

can be calculated to a good approximation, using the following

formula [21, 24]:

sinh cossin

coss

s

(4.19)


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The solar azimuth angle can also be approximated using the following two

formulas. However, because these formulas utilize cosine, the azimuth angle will

always be positive, and therefore, should be interpreted as the angle to the east of the

south when the hour angle, h, is negative (morning) and the angle to the west of the

south when the hour angle, h, is positive (afternoon) [21, 24].

cosh cos sin sin coscos

coss

s

(4.20)

Figure 4.8 Azimuth and Altitude angle


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sin sin sin

cos

cos cos

ss

s

(4.21)

Where

s is the solar elevation angle;

h is the hour angle of the present time.

is the current sun declination.

is the local latitude.

In the thesis, the solar azimuth and altitude can be calculated by the

calculator described in Appendix A by inputting the latitude, local time zone, and

the day number. They will be more accurate if the local solar time is more accurate

known or can be more accurately calculated. The determination of the Local Solar

Time is described below.

4.2.3 Local Solar Time (LST)

Local solar time is a system of astronomical time in which the sun crosses

the true north-south meridian at 12:00 pm, and which differs from local time

according to longitude, time zone, and equation of time. In order to calculate sun

angles and other solar variables, the local solar time must be calculated to account for

time zones, daylight savings time adjustments, and earth's motion around the sun. In

most locations, the local solar time and the local time may be different. Solar time is

determined by the position of the Sun. At noon it is directly overhead, with sunrise

and sunset occurring at symmetrical times either side of noon. Local (or clock) time is

determined by the local time zone and is taken at a reference longitude.


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There is a 4 minute time difference for each degree of difference in

longitude between the actual and reference. Thus, to convert solar time to local time,

we can use the following formula [21]:

[( ) 4]local solar ref

T T Longitude Longitude (4.22)

4min*( ) LSoT LST LSTM LL EoT (4.23)

The reference longitude (Longitude) refers to the longitude at which the

time-zone is calculated and also can be worked out by multiplying the time zone

hourly offset by 15 degrees. For example, at the time zone of 10 hours would have a

reference longitude of 150 degree. So the local solar time can be easily gotten by the

following steps [21]:

1. Determine the local standard time, LST which is clock time, adjustedfor daylight savings time if necessary.

2. Determine the local standard time meridian, LSTM.3. Determine the local longitude, LL.4. Determine the equation of time, EoT, adjustment in minutes.

There are 2 points should be paid more attention to:

1: If the site is east of the LSTM, the (LSTM - LL) factor should be a

positive number, and if it is west it should be negative.

2: The "4" in the equation is the quotient of 60 minutes of time and the 15

degrees of longitude that the earth rotates in that time.


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Table 4.1 LSTM for North America [25]

Atlantic Standard Time = 60 West longtitudeEastern Standard Time = 75 West longtitude

Central Standard Time = 90 West longtitude

Mountain Standard Time = 105 West longtitude

Pacific Standard Time = 120 West longtitude

Yukon Standard Time = 135 West longtitude

Alaska-Hawaii Standard Time = 150 West longtitude

4.2.4 Important Dates

The aim of the good design is to utilize the cyclical movement of the Sun

through the sky to the best advantage - usually for complete exclusion in summer and

maximum exposure in winter. Given this cyclical nature, there are four important

dates to remember when considering solar position, as shown in Table 4.2.

The altitude of the noon sun at the equinox is determined by the latitude of

the site. At noon on the solstices, the altitude of the Sun at noon is given as [21]:

Mid-Summer: 90 ( 23.45 ) Altitude latitude (4.24)

Mid-Winter: 90 ( 23.45 ) Altitude latitude (4.25)

Where the vertical lines around the latitude denotes the values.


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Table 4.2 Important dates relevant to solar position [21]

NAME Nth.Hem. DESCRIPTIONSummer Solstice 22 Jun. Sun at its highest noon altitude

Autumn Equinox 21 Sep. Sun rises due east, sets due west

Winter Solstice 21 Dec. Sun at its lowest noon altitude

Spring Equinox 21 Mar. Sun rises due east, sets due west

4.2.5 Declination angle

Solar Declination is a measure of how many degrees North (positive) or

South (negative) of the equator that the sun is when viewed from the centre of the

earth. This varies from approximately +23.5 (North) in June 21th to -23.5 (South) in

December 22th, as shown in Figure 4.9 [26].


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Using the day number, according to the formula [24]:

23.45*sin[360/ 365*(284 )]N (4.26)

Where = declination, which is the angular distance of the sun north or

south of the earths equator, N=Day Number, January 1=day1, and so on

In the thesis, it can be easily calculated by using the first calculator in

Appendix A.

Figure 4.9 How solar declination varies through out of the year


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4.3 Azimuth, altitude, declination calculator

In the first calculator in Appendix A, the input day number is compared to

January 1st, the input latitude and the angular distance are accordingly from the

meridian of the observer. For example, the Newark, Delaware is at the 75

according to the meridian, so the time zone will be -5, calculate the altitude and the

azimuth of the sun, according to the following formula [27]:

sin sin sin cos cos cosa (4.27)

sin cos cos / cosa a (4.28)

Where:

a = altitude of the sun (angular elevation above the horizon)

= latitude of the observer

= declination of the sun

= hour angle of sun

= azimuth of the sun (measured eastward from north)

From the Equations (4.27) and (4.28) it can be seen that the altitude and

azimuth of the sun are functions of the latitude of the observer, the time of day (hour

angel), and the date (declination).


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4.4 Alignment calculator

The next step is inputting the latitude, longitude and to get from the

first step, the aligned angle and aligned length based on the mathematical deduction.

For the convenience, the calculator is designed for three formats which are the

ordinary format, in minute format, in second format. The Calculator is in the

Appendix A.

Theazimuth, altitude, and also the local solar time are the most important

variables for the solar alignment. The alignment parameters, such as rotation angle

and adjustment angle need to be calculated easily and quickly for practical

applications. In order to make the alignment easier, the calculator is designed to be

user friendly and easy to use.

From the first calculator, we input day number N and use the formula

(4.26) to get the declination of the sun and then use it as the input data. We then input

the observers latitude, Local Time Zone into the purple cells to get the output of

altitude and azimuth of the sun in the yellow cells.

For the second calculator, the local longitude and latitude are the input

data. The elevation angle can be easily got as the complementary angle of latitude.

According to the mathematical deduction above, the adjustment angles can be

calculated from the calculator.


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CHAPTER 5

ALIGNMENT ANALYSIS

5.1 Precise Local Solar Time

As mentioned in Chapter 4, local solar time is critical in the proposed

alignment system. Twelve noon local solar time (LST) is defined as when the sun is

highest in the sky. Local Time (LT) usually varies from LST because of the

eccentricity of the Earth's orbit, and because of human adjustments such as time zones

and daylight saving time, etc.

The Local Standard Time Meridian (LSTM) is a reference meridian used

for a particular time zone and is similar to the Prime Meridian, which is used for

Greenwich Mean Time [29]. The LSTM is illustrated in Figure 5.1 [28].


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The (LSTM) is calculated according to the equation [28]:

15 GMT LSTM T

(5.1)

where GMTT is the difference between the Local Time (LT) from

Greenwich Mean Time (GMT) in hours. 15= 360/24 hours.

Figure 5.1 The Local Standard Time Meridian (LSTM)


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The equation of time (EoT) (in minutes) is an empirical equation that

corrects for the eccentricity of the Earth's orbit and the Earth's axial tilt [28].

2o sin(2 ) 2 sin 4 sin cos 2 ( / 2) sin(2 )E T y B e M ey M B y M

(5.2)

Where:

Suns mean longitude:

360( 81)365B d (5.3)

2tan ( / 2) y obl , obl = obliquity of the ecliptic

e = eccentricity of the Earths orbit

M = Suns mean anomaly

The time correction EoT is plotted in the Figure 5.2 [30] below:


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The net Time Correction Factor (in minutes) accounts for the variation of

the Local Solar Time (LST) within a given time zone due to the longitude variations

within the time zone and also incorporates the EoT above [28]:

4( )TC LSTM Longitude EoT (5.4)

Figure 5.2 Equation of Time


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The factor of 4 minutes comes from the fact that the Earth rotates 1 every

4 minutes.

The Local Solar Time (LST) can be found by using the previous two

corrections to adjust the local time (LT) [28]:

60

TC LST LT (5.5)

5.2 Accurate Angular Distance

In the calculation, all of the input parameters include the longitude and

latitude of the observer, day number, are normally accurately know. However the hour

angle of sun is the uncertain factor for the inaccuracy. This is the hour angle of the

Sun with respect to the meridian of the observer. That is the difference between the

current local sidereal time (LST) and the right ascension of that of the object (Sun)

[31].

object objectHA LST (5.6)

For example, if the sun had an hour angle of 2.5 hours, it transited across

the local meridian 2.5 sidereal hours ago, is currently 37.5 degrees west of themeridian. An hour angle of zero means the object is currently on the local meridian.

For every time zone there is a 15 degree difference. If the place is defined,

the time zone is an integer, for example, for University of Delaware, the time zone is -

5, that means the local time zone taken at a longitude for Newark, Delaware is -75


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degree. Actual longitude of Newark is -75.74229, but Detroit, MI which is in the same

time zone as Newark, DE, should take the same local time zone as a longitude of -75

degree, but actual longitude of Detroit is -83.09 degree. Will the difference between

the real longitude and local time zone taken longitude affect the accuracy very much?

We can use the mathematical way to deduce the difference of the adjustment.

Table 5.1 The difference between the standard angular distance and specific

angular distance

Time Zone of -5 Newark, DE

Take day number N 100(From 1st, Jan) 100(From 1

st, Jan)

Latitude 39.69 degree 39.69 degree

Angular distance from themeridian of the observer

-75 degree -75.74229 degree

Altitude of the sun 25.69 24.56

Azimuth of the sun 80.43 79.58

53.31 53.31

40.73 39.67 52.25 52.06


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Time Zone of -5 Detroit, MI

Take day number N 100(From 1st, Jan) 100(From 1st, Jan)

Latitude 42.4 degree 42.4 degreeAngular distance from themeridian of the observer

-75 degree -83.09 degree

Altitude of the sun 26.11 19.59

Azimuth of the sun 81.73 76.2

47.6 47.6

38.65 32.96 48.95 45.82

As the examples shown above, although Newark, DE and Detroit, MI both

deviate some angular distance from -75 degree, the final adjust lengths is only

0.04~0.1, there is no big differences between the standard one and the local one.

(Please clarify these statements and also what is the unit, inches or centimeters.

Otherwise delete these sentences).

Meanwhile, the system is designed to tolerate a tracking error of 0.7or

1.5 and with a concentration ratio of 20 or 10. The E-W tracking system increases

the collection efficiency by 20% year average with collection efficiency nearly 100%

during the spring, fall and winter and about 94% during the summer [32, 33]. There is

some shading effect of tracking arrangement. The above calculations have taken the

shading effect into consideration. Once the tracking is reduced from 2-D to 1-D, the

heavy 2-D joint or pivots are no longer needed [1]. The large solar panels can be


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supported on pivots on both ends. The result is a lighter, stronger, and simple

supporting structure. The alignment method is accurate and also practical.


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CHAPTER 6

HEAT-RECOVERY

The residential and commercial buildings consume 39% of the energy

used in the United States today. Close to 20% of the total U.S. energy consumption

goes for heating homes and other buildings, public and private. The home heating

costs shown in the chart are based on the amount of gas used to heat the average

natural gas-heated home. The average home is about 1200 square feet and uses a mid-

efficiency furnace and conventional gas water heater. The heating costs may differ due

to a range of factors, such as weather, type of heating equipment, insulation levels, air

tightness, and lifestyle, as shown in Figure 6.1 [34].

In order to conserve the fossil fuels, the Energy Research and

Development Agency has made announcement to encourage the use of as much as

possible the clean energy, especially the solar energy. Unfortunately, the current PV

systems covert no more than 20% of the solar energy into electrical energy and the

rest is lost as the heat. The average efficiency of the PV system using now is around

15%. Almost 85% of the energy collected from the panel is converted into heat.


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In the proposed PVC system, the cooling down system (water pipes) is

added to recover the heat from the Photovoltaic panels, as shown in the Figure 6.2

[1], a typical solar heating system. When the panels collect the solar light and begin toconvert it into heat, water will be pumped through the pipes embedded in the back

panels and become hot. After the heat is transferred to the storage tank, the water is

recycled. It will take out the heat, cool down the panel. The savings for using the

Figure 6.1 Typical Annual Space and Water Heating Costs


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solar heated water for the home can be just as dramatic and effective. Moreover, it will

increase the conversion efficiency of a photovoltaic cell at the lower temperature.

Figure 6.2 Panel assembly with the pipe system


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6.1 Heat recovery for hot water heating system

6.1.1 Water heating system

Important usages for the heat recovery system are for the supplement hot

water and space heating which can provide considerable savings for the family. So the

main need for central heating is at night when there is no sunlight and in winter when

solar gain is lower. Therefore solar water heating for washing and bathing is often a

better application than central heating because supply and demands are better

matched.

About 50%-80% of domestic hot water can be provided by a well

designed solar system (less in winter, more in summer). There should be 10-15 square

feet of solar collector area for each person in the household. The storage tank should

hold 20-30 gallons per person. Also there should be no shade on the collectors during

the hours from 9:00 AM to 3:00 PM. The collectors and storage tank should be in

close proximity to the backup system and house distribution system to avoid excessive

pipe losses. The pipes need to be well insulated. Mixing valves or thermal shutoff

devices should be employed to protect from excessively high temperatures.

6.1.2 Water heating system structure [36, 37]

In the design as shown in Figure 6.3 [40], there are five major

components in active solar water heating systems: Collector(s) to capture solar energy;

Circulation system to move a fluid between the collectors to a storage tank; Storage

tank; Backup heating system; Control system to regulate the overall system operation.


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The pump is activated by the controller when the temperature in the

collectors is higher than the temperature in the storage tank. As mentioned before, the

concentrator has a high efficiency when the temperature is not too high (about 38

degrees), in order to keep the efficiency high for the collector. When the temperature

is higher than 38 degrees and the collectors are hotter than the storage tank, the valve

will purge the water and allows the system collectors to refill and the heating

operation resumes [39].

Figure 6.3 Water Heating System


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If the system is exposed outside of the room, it needs to use antifreeze

fluids to verify its viability. Oil or refrigerant circulating fluids are sealed into the

system and will not require maintenance. The drain-back system typically uses

distilled water as the collector circulating fluid. The collectors in this system will only

have water in them when the pump is operating. This means that in case of power

failure as well as each night, there will be no fluids in the collector that could possibly

freeze or cool down and delay the startup of the system when the sun is shining.

The water that is circulated into the collectors is separated from the heated

water which can be used for the home by using a heat exchanger. The heat exchanger

is used to transfer the heat from the circulating water through the solar collector to the

water used for the home. Since in order to prevent the freeze in the collector during

the winter time, the fluids in the collector maybe the mixture of water, oil, and

antifreeze fluids, so during the heat exchange process, the home-use water should be

separated to prevent the contamination.

The water from the collector can reach very high temperatures in good

sunshine, or if the pump fails. Designs should allow for relief of pressure and excess

heat through a heat dump. In sunny, warm locations, where freeze protection is not

necessary, a batch type solar hot water heater can be extremely cost effective. In

higher latitudes, there are often additional design requirements for cold weather,

which add to system complexity. This has the effect of increasing the initial cost (but

not the life-cycle cost) of a solar hot water system, to a level much higher than a

comparable hot water heater of the conventional type. In the proposed design, a solar

controlled pump is added. When it is sunny, it will start to work and the water will be

pumped into the compressed system. When the weather is not fine, it will stop


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pumping water into system and there will be no water left in the panel. There is no

need to worry about the frozen.

6.2 Heat Recovery Simulation

Consider the water flowing through a circular pipe (as shown in Figure

6.4) embedded in the panel for the heat recovery. As an example for illustration, the

pipe diameter D=2 '' and length L = 8' . Consider the velocity to be the constant

velocity Vin = 1m/s, the fluid exhausts into the ambient atmosphere which is at a

pressure of 1 atm. Take density 1 kg/liter and coefficient of viscosity

32 10 kg/(ms). The Reynolds number Re based on the pipe diameter is:

100avg

e

V DR

(6.1)

avgV is the average velocity at the pipe, set as 1 m/s in this case as

convenience for solving the problem in FLUENT [45, 46]. We can plot the centerline

velocity, wall skin-friction coefficient, and velocity profile at the outlet.


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6.2.1 Create Geometry in Gambit [46]

If the profile of the pipe is the rectangle, the first step is to create the

vertices at the four corners. We can then join the adjacent vertices by straight lines to

form the edges of the rectangle and create a face corresponding to the area

enclosed by the edges.

We first specify and create the mesh to be used with the FLUENT 6.0.

Then from the Main Menu > Solver > FLUENT 5/6, the boundary types that can be

defined as,

0 ,02

Dr x L , (6.2)

where r and x are radial and axial coordinates respectively.

L

D=0.2

Figure 6.4 Circular Pipe


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Create Vertices

From the Operation Toolpad > Geometry Command Button > Vertex

Command Button > Create Vertex, the Create Vertex button has been selected by

default, and the four vertices are set as Figure 6.5.

Then the four vertices should be connected to form edges, from the

Operaion Toolpad > Geometry Command Button > Edge Command Button > Create

Edge, select pairs of vertices to make up the edge of the rectangle.

To form the face out of the area enclosed by the four lines, the four edges

should be selected to enclose the area. From the Operation, follow Toolpad >

Geometry Command Button > Face Command Button > Form Face, the final result is

shown in Figure 6.6.


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Figure 6.5 Four vertices

Figure 6.6 Rectangular Edges and Faces Created


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Mesh Geometry

For the created rectangular, a mesh is created on the face with 100

divisions in the axial direction and 5 divisions in the radial direction. So for each

horizontal edge of the rectangular, the interval count is set as 100, while the interval

count of vertical edge is set as 5. The meshed face is as shown in Figure 6.7.

Figure 6.7 Meshed Rectangular


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Specify the boundary types in Gambit as the following:

Edge Position Name Type

Left Inlet VELOCITY_INLET

Right Outlet PRESSURE_OUTLET

Top Wall WALL

Bottom Centerline AXIS

Check the grid size, it shows 1 cell zone, 5 face zones, 500 cells, 1105

faces, and 606 nodes. We can then save the setting as the .msh file and export to

FLUENT6.

From the Main Menu > Define > Model, the initial energy is set as the

solar energy from the panel, with the panel size as:

8 2 '' 8 ' 8 2 2.54 8 30.48 9909.65 cm

2

(6.3)

For the North America, it is set as 4 hours as the direct receiving time.

The average energy for one m2 is 55.4 Calories/hour = 231.82 Joules/hour, so the total

average energy can be gotten from the sun for one day is:

55.4 0.99 4 219.41 Calories/day = 918 Joules/day (6.4)

The initial Velocity Magnitude is set to be 1 m/s, the Axial Velocity is set

as 1 m/s, the Radial Velocity is set to be 0 m/s, the Gauge Pressure is set to be 0


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pascal, the Pressure is set to be as the default, 0.3, and the Density is set to be as 1, the

set of the Solver and the Residual Monitors are shown in Figure 6.8:

We then start the calculation by running 100 iterations. The residual of

each iteration is printed out as well as plotted in the graphics window as in Figure

6.9:

Figure 6.8 Solver and the Residual Monitors set


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In order to analyze the results, the next step is to plot the variation for the

axial velocity along the centerline. Please make sure that the Position on X Axis is set,

under Options, to be 1 and Y to be 0 under Plot Direction. This tells FLUENT to plot

the x-coordinate value on the abscissa of the graph, the X Axis function and Y Axis

function describe the x and y axes of the graph, which should not be confused with the

x and y directions of the pipe. Finally, the plot graph is shown in Figure 6.10.

Figure 6.9 Residuals for each iteration


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As shown in the Figure 6.11, the temperature varies from 290K to 280k

respectively from the input part to output part. It means that the cold water is pumped

into the pipe from the input side, and the hot water coming out from the output side.

For the convenience of calculation, the average temperature output is set at 290K, so

the average energy taken by the water can be calculated as:

4.2 10 4 0.99 =168 Joules (6.5)

Actually, in the summer, the water output temperature is much higher than

290K, the water can be heated as least to 320K. Then the energy taken by the hot

Figure 6.11 Static Temperature in the pipe


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water is as high as 4*168 Joules, or 672 Joules. Compared to the energy/day got from

the solar, 918 Joules, the heat recovery rate is at least 75%. When the water

temperature is heated as high as the limit of the efficient temperature mentioned

before for the solar panel, the rate can be as high as 87%. So it can be seen that most

of the heat received from the solar can be recovered for the residential use, instead of

heat lost in the air. It can supply most of the normal hot water ( 45) usage for the

average family.


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Chapter 7

CONCLUSION AND DISCUSSIONS

As described above, from the calculations and descriptions in the previous

chapters, the proposed concentrator uses the simple 1-D tracking technique to replace

of the costly 2-D tracking [1, 9]. In addition, the system can tolerate more tracking

errors. The concentrator can tolerate a tracking error of 1.5, at a concentration ratio

of 10 [1]. The system is designed to have the suns image in the middle of the solar

cell strip so that all the solar energy can be absorbed and converted into electric

energy.

For the hardware, the solar cells are enclosed in a long, narrow box

against the outside environment. They are made of common materials of low cost,

such as glass, aluminum, etc. These solar panels can then be installed / assembled very

easily without any special protection for the solar cells. Only a coarse 1-axial tracking

is needed to track the sun during the day and the whole year [1]. For the advantages

stated above, the entire system is of low cost and can be used for many applications.

In addition, they can be easily upgraded, repaired and much of the material recycled. It

helps to reduce the concentrator size, weight, and cost [9] with modern mass

production techniques.

The calculator is designed to help the alignment of the concentrator.

Engineers and/or technicians can now easily install the system even in less than ideal

conditions. They only need to know the date, local longitude, and other parameters.

The align angles are calculated automatically saving a lot of time and cost.


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For the heat recovery, as analyzed before, the proposed system can

effectively recover up to 85% of the heat energy. The hot water recovered from the

system can meet the requirement of a typical American family. More important, it

saves the cost for the space heating system and makes the photovoltaic system more

efficient.

It is important to reduce the overall system cost. For example, the total

energy produced by one kW photovoltaic panel is 1 kW 360 days 4 hours = 1,440

kWh for a typical location in the US. It is higher in some of the western states and

lower in some for the northeastern states. At the current electrical cost of $0.15 per

kWh, this is equivalent to $216 per year. The expected useful time of the photovoltaic

system is 20 years. For the current fixed installation at $10,000 per kW, the payback

period is 46 years, clearly not cost effective. By reducing the cost by a factor 4, the

payback period is around 10. The system becomes cost effective and is considered to

have exceeded SAIs goals. When the cost is reduced by a factor of 6, the payback

period is less than 8 years. The system becomes very cost effective and far exceeds the

SAIs goals [1]. The above calculations are based on $0.15/kWh and average 4 hours a

day. In California and other western states, the numbers are more likely $0.18/kWh

and 5 hours a day. The payback periods are 33% shorter [1].

In summary, by reducing the overall system cost, the photovoltaic energy

can become a major energy source. Because of the cost benefit, a payback period less

than 10 year, residential installations will accelerate. If a large portion of household

and industry can install photovoltaic systems, it is essentially a large distributed power

system. The concentrators can be reconfigured suitable for utility companies for very

large photovoltaic system installations [1].


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APPENDIX A

AZIMUTH, ALTITUDE, DECLINATION CALCULATOR

In the form, the purple cells are the input parts, including latitude, local

time zone, and the day number. From the formula calculation above, the azimuth,

altitude, declination and the sun hour angle can be easily gotten, which will be the

input for the next step. It must be paid attention to the leap year when there is one day

more in February.

Engineers can choose the suitable format as they want, for example, if

they want to just input a data with specific degree, min, sec, they can select the third

one, and the output will be in the last format with accordingly same format.


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REFERENCES

[1]. Private communication with Dr. Ih.[2]. Agrafiotis, C.; Roeb, M.; Konstandopoulos, A.G.; Nalbandian, L.;

Zaspalis, V.T.; Sattler, C.; Stobbe, P.; Steele, A.M. (2005). "Solar water

splitting for hydrogen production with monolithic reactors". Solar Energy 79 (4):

409421. doi:10.1016/j.solener.2005.02.026.

[3]. "Natural Forcing of the Climate System". Intergovernmental Panel onClimate Change. http://www.grida.no/climate/ipcc_tar/wg1/041.htm#121.

Retrieved on 2007-09-29

[4]. NREL: Dynamic Maps, GIS Data, and Analysis Tools - Solar Maps[5]. National Renewable Energy Laboratory, US. Retrieved on 4 September

2006.

[6]. Chang-Kyu Song, Gyungho Khim, Improvement of Tracking Accuracyof Positioning Systems with Iron Core Linear DC Motors, International Journal

of Precision Engineering and Manufacturing Vol. 6, No.1, January 2005

[7]. Kh.S. Karimov, M.A. Saqib, P. Akhter, M.M. Ahmed, J.A. Chattha andS.A. Yousafzai, A simple photo-voltaic tracking system, Solar Energy Materials

and Solar Cells, Volume 87, Issues 1-4, May 2005.

[8]. Oapos;Neill, M.J.; McDanal, A.J.; Walters, R.R.; Perry, J.L, Recentdevelopments in linear Fresnel lens concentrator technology,including the 300 kW

3M/Austin system, the 20 kW PVUSA system, and theconcentrator initiative,

Photovoltaic Specialists Conference, 1991., Conference Record of the Twenty

Second IEEE Volume, Issue, 7-11 Oct 1991 Page(s):523 - 528 vol.1.


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[9]. Next Generation Photovoltaics - high efficiency through full spectrumutilization, edited by A Marti and A Luque, Institution of Physics Publishing,

Bristol and Philadelphia, 2004.

[10]. Mark J. ONeill, Entechs Stretched Lens Array (SLA) for NASAsMoon/Mars Exploration Missions, International Conference on Solar

Concentrators for the Generation of Electricity or Hydrogen, Scottsdale, May 1-5,

2005.

[11]. Advances in Color Mixing Lens/Multi Junction Cell (CML/MJC)Concentrators for Space and Ground Power, Mark O Neil, Fouth International

Conference on Solar Concentrators, El Escorial, Spain, March 12-16, 2007.

[12]. Mauk, M.G., P.E. Sims, and R.B. Hall, Feedstock for Crystalline SiliconSolar Cells, Proceedings of the First Conference on Future Generation

Photovoltaic Technologies (March 1997).

[13]. Solar Electricity Explained, Complete Guide To Solar electricitySystems

[14]. Buying a photovoltaic solar electric system, a consumer guide[15]. Residential Solar Photovoltaic systems[16]. EMCORE's Multi- Junction Solar Cell Technology Adapted to Terrestrial

Power Generation

[17]. Swanson, R.M., Straight Talk about Concentrators, Proceedings of theFirst Conference on Future Generation Photovoltaic Technologies (March 1997).

[18]. Kurtz, S.R., and D. Friedman, Recent Developments in TerrestrialConcentrator Photovoltaics, Proceedings of the 14th NREL Photovoltaics

Program Review, (November 1996).


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[19]. "The PV Concentrator Alliance Founding Position Paper," PVConcentrator Alliance, for the U.S. Department of Energy: April 1997.

[20]. David R. Mills, Graham L. Morrison, Compact Linear Fresnel Reflectorsolar thermal powerplants, Solar Energy, Volume 68, Issue 3, 3 March 2000.

[21]. AutoDesk, Polar position, http://squ1.org/wiki/Solar_Position.[22]. SunPosition. 2007, Dec 1. Sun and Shadow Position Modeling Retrieved

Dec 12, 2007, from 2. easily obtain the sun paths for a particular month.

http://www.sunposition.com/

[23]. C.G.Ramsey, H.R.Sleeper, John Wiley & Sons, Architectural GraphicStandards, N.Y. 1972.

[24]. Solar azimuth angle, http://en.wikipedia.org/wiki/Solar_azimuth_angle[25]. Time-Zone and Meridian Offset Reference Information, http://

www.VixenAmerica.com

[26]. Solar Declination http:// www. Sunli t design . com/ infosearch/declination. php? Indexref = 1.

[27]. Horizontal coordinate system , http:// en. wikipedia. org/ wiki/ Horizontal_ coordinate_system.

[28]. Local Standard Time Meridian (LSTM) http:// pvcdrom. pveducation. org/SUNLIGHT/SOLART.HTM.

[29]. Greenwich Mean Time (GMT) http://wwp.greenwichmeantime.com/.[30]. Equation of Time, http://en.wikipedia.org/wiki/Equation_of_time[31]. http://www.nationmaster.com/encyclopedia/Horizontal-coordinate-system[32]. Brian P. Dougherty, A.Hunter Fanney, Measured Performance of Building

Integrated Photovoltaic Panels - Round 2.


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[33]. King, D.L., Boyson, W.E., and Kratochvil, J.A, Photovoltaic ArrayPerformance Model,Sandia Report SAND2004-3535, Sandia National.

[34]. Typical Home & Water Heating Costs, Manitoba Hydro, February 2009,Rev 00.

[35]. The Promise of Concentrators, by Richard M. Swanson, Progress inPhotovoltaics: Research and Applications, vol. 8, 93-111 (2000).

[36]. Solar hot water, http://en.wikipedia.org/wiki/Solar_hot_water.[37]. Garboushian, V., D. Roubideaux, and S. Yoon, An Evaluation of

Integrated High-Concentration Photovoltaics for Large-Scale Grid-Connected

Applications, Proceedings of the Twenty-Fifth IEEE PV Specialists Conference,

Washington, D.C. (May 1996).

[38]. Gunn, J.A., and F.J. Dostalek, EPRI 25-kW High-ConcentrationPhotovoltaic Integrated Array Concept and Associated Economics, Proceedings

of the Twenty-Third IEEE PV Specialists Conference, Louisville, KY (May 1993).

[39]. Solar Hot Water Basics, http://www.homepower.com/basics/hotwater/.[40]. Solar Hot Water, Heating and Cooling Systems http:// www. greenbuilder.

com/ sourcebook/HeatCool.html.

[41]. Paul Allen Tipler, Physics for Scientists and Engineers, p614.[42]. Adolfo Bauchspiess, Joao Y. Ishihara, Felix Felgner, Lothar Litz, First-

Principles Structured Identification For Predictive HAVC control.

[43]. Heat Pump, http://hyperphysics.phy-astr.gsu.edu/Hbase/thermo/heatpump.html.

[44]. http://en.wikipedia.org/wiki/Water_heating.


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[45]. StudentFLUENT-Tutorial Library http:// www.fluent.com/software/sf_mesh_and _ tutorials/tutorial.htm.

[46]. FLUENT,http://web.njit.edu/topics/Prog_Lang_Docs/html/FLUENT/fluent/gambit/help/tutorial_guide/tg01.htm.

[47]. Entechs patents and/or publications, Development of TerrestrialConcentrator Modules Using High Efficiency Multi-Junction Solar Cells, M. J. O

Nail, A. J. McDanal, and P. A. Jaster, 20th IEEE photovoltaic Specialists

Conference, New Orleans, May 2002.

[48]. http://www1.eere.energy.gov/solar/concentrator_systems.html[49]. http://www.powerfromthesun.net/chapter1/Chapter1.htm


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yingyu

FW:Permissionofusingtheimages9messages

ChristineKalb Tue,Nov3,2009at1:54PMTo:"[email protected]"

Hello,Ying,

Yourrequest(includedbelow)hascometomeforresponse.Areyouinterestedinusingallthe

materialthatiscontainedonthepagestowhichyouveprovidedlinks,orjustspecificimages?Are

thematerialsrequestedforanycommercialpurposeoronlyinconnectionwithyouracademic

endeavor? Congratulations,bytheway,onpursuingyourmastersdegree.

Inthemeanwhile,Iwillneedtodeterminewhetherornotwearethecopyrightholderoftheimages

andmaterialsinquestion.

Thankyou,

Christine

ChristineKalbIPParalegal

CorporateLegal

Autodesk,Inc.

111McInnisParkway

Room42145B


86/91

SanRafael,California94903

Direct 4155076744

Fax 4155076128

Pleasedonotprintthisemailunlessabsolutelynecessary.

CONFIDENTIALITYNOTICE THISEMAILTRANSMISSIONANDANYDOCUMENTS,FILESORPREVIOUSEMAILMESSAGESATTACHEDTOIT

MAYCONTAININFORMATIONTHATISCONFIDENTIAL,PRIVILEGED,ANDEXEMPTFROMDISCLOSUREUNDERAPPLICABLELAW.IFYOU

ARENOTTHEINTENDEDRECIPIENT,ORAPERSONRESPONSIBLEFORDELIVERINGITTOTHEINTENDEDRECIPIENT,YOUAREHEREBY

NOTIFIEDTHATANYDISCLOSURE,COPYING,DISTRIBUTION,ORUSEOFANYOFTHEINFORMATIONCONTAINEDINORATTACHEDTOTHIS

TRANSMISSIONISSTRICTLYPROHIBITED.IFYOUHAVERECEIVEDTHISTRANSMISSIONINERROR,PLEASEIMMEDIATELYNOTIFYUSBY

REPLYEMAIL,[email protected](415)5076744ANDDESTROYTHEORIGINAL

TRANSMISSIONANDITSATTACHMENTSWITHOUTREADINGORSAVINGINANYMANNER.THANKYOU.

From:yingyu[mailto:[email protected]]

Sent:Tuesday,November03,200910:12AM

To:AnnaCecchettini

Subject:Permissionofusingtheimages

Hi,

IamthegraduatestudentinECEdepartment,UniversityofDelaware,Ineedsomeimagesfromyourwebsite

formyM.S.thesis:

http://squ1.org/wiki/sun_path_diagram

http://squ1.org/wiki/Solar_Position


87/91

Couldyoupleaseauthorizethecopyingpermissiontometouse?Thanksalot.

Best,

Ying

HappyHelen

yingyu Tue,Nov3,2009at2:13PMTo:ChristineKalb

HiChristine,

Thankyouforyouremail.Iamjustusingsomeoftheimagesformythesis, notallthematerialscontainedon

thepages,alltheimagesIneedareonlyforacademicbutnotcommercialpurpose. Thanksalot.

Best,

Ying

[Quotedtexthidden]

HappyHelen

ChristineKalb Tue,Nov3,2009at2:28PMTo:yingyu

Hi,

Isitpossibletoisolateandsendmeonlythoseimagesyouareinterestedinusing?

Thanks,

Christine



88/91


To:ChristineKalb

Subject:Re:FW:Permissionofusingtheimages

[Quotedtexthidden]


Sure,theattachedistheimagesIamusing,pleaseletmeknowanyquestionsyoumayhave.Thanksalot.

Best,

Ying

[Quotedtexthidden]

HappyHelen

.pd284K

ChristineKalb Tue,Nov3,2009at4:17PMTo:yingyu

Hi,againYing,

Thank you for contacting me again about your forthcoming thesis, and requesting to use images from our

Autodesk Ecotect web pages, the links to which you provided, and which are included below. We are

always interested and delighted to learn the various ways in which our software products are being used,

particularly in cases such as yours, where our software is nurturing your academic pursuits. To that end, please

review the below terms and guidelines.

PERMISSIONTOUSE/DISPLAYAUTODESKCOPYRIGHTEDMATERIALS:ScreenshotsaretheindividualscreendisplayscontainedwithinAutodesk

softwareapplicationsandonline


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services(ScreenShots). Ifyouwishtouseordisplay(a)screenshotsfromAutodesksoftwareand/or(b)

materialsand/orimagesfrominternetpagesorfromAutodesk.compagesthatcontainthirdpartycontent,

youshouldcontactthethirdpartycontentproviderdirectlyforpermission. [Theimagesyouhaverequested

onpage3oftheattachedpdfarenotAutodeskcopyrightedmaterial,butarefromabookbySteveSzokolay

(TheEnvironmentalDesignofBuildings),thereforeyoumustcontactMr.Szokolaytousehisimages.]

Pursuanttoyourrequest,youmayusealimitednumberofScreenShotsforpurelyeducationalorillustrative

purposes(e.g.,educationalguides,tutorials,howtobooks,trainingpresentations,productreviews,video

demonstrationsofthesoftware,Websites,etc.)providedyouadheretothefollowingguidelines:1. Yourusemaynotdirectlyorindirectlystateorimplysponsorship,affiliation,orendorsementofyour

product

or

service

by

or

with

Autodesk.

2. YoumaynotaltertheScreenShotsinanywayexcepttoresizetheScreenShotindirectproportiontotheoriginal.ScreenShotsmustbereproducedintheirentirety.

3. Youmayaddcommentaryorothertextanalysisaslongasitisveryclearlyattributabletoyou,andnottoAutodesk.

4. Asstatedabove,youmaynotuseScreenShotsthatcontainthirdpartycontentunlessyouseparatelyseekandobtainpermissionfromsuchthirdpartytodisplayitscontent.

5. YoumustincludethefollowingcopyrightattributionstatementonallmaterialscontainingAutodeskScreenShots:"SomeimagescourtesyAutodeskInc.2008.Allrightsreserved."

6. IfyourmaterialsincludereferencestoanAutodeskproduct,showinplaintextthefullnameoftheproductwithcorrespondingtrademarksymbolatthefirstand/ormostprominentmention(e.g.,

AutodeskEcotectinyourrequesteduse)insuchmaterials,andshouldincludeatrademark

attributionparagraphthatcorrectlylistsallAutodesktrademarksreferencedinyourmaterials,such

as,AutodeskandEcotectareregisteredtrademarksortrademarksofAutodesk,Inc.,and/orits

subsidiariesand/oraffiliatesintheUSAandothercountries.

7. YouruseofAutodesk'sScreenShotsmaynotbeincorporatedintoobsceneorpornographicmaterial,andmaynot,inAutodesk'ssoleopinion,bedisparaging,defamatory,orlibeloustoAutodesk,anyof

itsproducts,oranyotherpersonorentity.

8. YourmaterialsshouldnotbemostlyorsolelycomposedofAutodeskScreenShotsorotherAutodeskintellectualproperty.IfAutodeskScreenShotsorotherAutodeskintellectualpropertywouldrepresent

themajorityofthematerialyouwishtoreproduceand/ordistribute,pleaserespondwithadditional

detailsofthespecificmaterialsyouwishtouse.

Ifyouagreetotheaboveterms,youmayuseAutodeskcopyrightedmaterialsyouobtainfromthelinks

below:

http://squ1.org/wiki/sun_path_diagram

http://squ1.org/wiki/Solar_Position

Oryoumayuse,equally,imagesfrom:

http://ecotect.org/wiki/sun_path_diagram

http://ecotect.org/wiki/Solar_Position

Byreturnemail,kindlyconfirmyourunderstandingofandagreementtoadheretotheaboveguidelines. Of


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course,letmeknowifyouhaveadditionalquestionsorconcerns.

Withthanks,andkindregards,

Christine

ChristineKalbIPParalegal

CorporateLegal

Autodesk,Inc.

111McInnisParkway

Room42145B

SanRafael,California94903

Direct 4155076744

Fax 4155076128

Pleasedonotprintthisemailunlessabsolutelynecessary.

CONFIDENTIALITYNOTICE THISEMAILTRANSMISSIONANDANYDOCUMENTS,FILESORPREVIOUSEMAIL

MESSAGESATTACHEDTOITMAYCONTAININFORMATIONTHATISCONFIDENTIAL,PRIVILEGED,ANDEXEMPT

FROMDISCLOSUREUNDERAPPLICABLELAW.IFYOUARENOTTHEINTENDEDRECIPIENT,ORAPERSON

RESPONSIBLEFORDELIVERINGITTOTHEINTENDEDRECIPIENT,YOUAREHEREBYNOTIFIEDTHATANY

DISCLOSURE,COPYING,DISTRIBUTION,ORUSEOFANYOFTHEINFORMATIONCONTAINEDINORATTACHED

TOTHISTRANSMISSIONISSTRICTLYPROHIBITED.IFYOUHAVERECEIVEDTHISTRANSMISSIONINERROR,

PLEASEIMMEDIATELYNOTIFYUSBYREPLYEMAIL,[email protected]

TELEPHONEAT(415)5076744ANDDESTROYTHEORIGINALTRANSMISSIONANDITSATTACHMENTSWITHOUTREADINGORSAVINGIN

ANYMANNER.THANKYOU.


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[Quotedtexthidden]

[Quotedtexthidden]

YingPermission.pdf

284K


HiChristine,

Thanksalotforyourkindemail.Iundersta

Ying Yu Thesis

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