comparative study of grid connected photovoltaic arrays by t

8/13/2019 Comparative Study of Grid Connected Photovoltaic Arrays by T

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COMPARATIVE STUDY OF GRID CONNECTED PHOTOVOLTAIC ARRAYS

A Thesis

Presented to the

Faculty of

San Diego State University

In Partial Fulllment

of the Requirements for the Degree

Master of Science

in

Physics

by

Tyler N. Otto

May 2009


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SAN DIEGO STATE UNIVERSITY

The Undersigned Faculty Committee Approves the

Thesis of Tyler N. Otto :

COMPARATIVE STUDY OF GRID CONNECTED PHOTOVOLTAIC ARRAYS

Alan Sweedler, ChairDepartment of Physics

Michael BromleyDepartment of Physics

Fletcher MillerDepartment of Mechanical Engineering

Approval Date


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c Copyright 2009

by

Tyler N. Otto


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ABSTRACT OF THE THESIS

COMPARATIVE STUDY OF GRID CONNECTED PHOTOVOLTAIC ARRAYSby

Tyler N. OttoMaster of Science in Physics

San Diego State University, 2009

As renewable energy becomes more prevalent, more information on how differenttechnologies will behave needs to be available. While the underlying physics of solar cells iswell understood, wiring many cells together to form a panel, and then many panels together toform an array, makes the system behavior more complicated. This research involvescollecting data on temperature, solar radiation, and the performance of ve different

photovoltaic arrays. The ve different arrays used include single crystal, multicrystal andamorphous silicon arrays, which are the most commonly installed types. These arrays, eachrated for approximately 2,000W of power output, are located on the roof of the physicsbuilding at San Diego State University. By creating a model which predicts the power outputas a function of solar radiation and temperature, a side-by-side comparison of different arrayscan be made. Current predictive models are not useful for a grid connected system, which islimited to operate at the maximum power point, thus adaptations to previous models havebeen made. This model accurately predicts the power output of different silicon based solararrays. The measured performance data is t to the model through use of a least squaresprogram. The program returns t parameters, which are related to the reduced power outputcaused by increased temperature, as well as the effect of non-linear absorption of solarradiation on power output. Data was collected for a 200 day period from 16 August 2008 to28 February 2009. This research is important because it exposes weaknesses of different typesof panels, and allows for a direct comparison of different panels. This research shows that thecurrent rating system is not the best indication of performance for a deployed, grid connectedsystem. Specically, this research shows that temperature has a different affect on the poweroutput of each array. The the size of this affect appears to be much smaller for amorphoussilicon arrays than crystalline based silicon arrays leading to a larger reduction in efciencyfor crystalline arrays.


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TABLE OF CONTENTS

PAGE

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

CHAPTER

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 3

SEMICONDUCTOR THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3INTERACTION OF LIGHT WITH SEMICONDUCTORS . . . . .. . . . . .. . . . . .. . . 7

PHYSICS OF PN JUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

THE EFFECT OF TEMPERATURE .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 LITERATURE REVIEW AND NOVEL DEVICES .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 14

THEORETICAL EFFICIENCY LIMITATIONS .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 14

CURRENT TECHNOLOGY AND NOVEL DEVICES .. .. .. .. .. .. .. .. .. .. .. .. 15

RELATED RESEARCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 EXPERIMENTAL PROCEDURES. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

EXPERIMENTAL SETUP.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

MEASUREMENT ACCURACY AND ERRO ANALYSIS .. . . .. . . . . .. . . . . .. . . 25

DATA REJECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 RESULTS . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

7 FURTHER RESEARCH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40APPENDIX

MANUFACTURER DETAILS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42


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LIST OF TABLES

Table 1. Initial Model Coefcients With and Without Cell Temperature Correc-tion . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Table 2. Improved Model Coefcients With Uncertainties and Reduced 2 val-ues . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Table 3. Comparison of Rated Conditions with Higher Temperature Values. . . . . . . . . . . . . . . . 36

Table 4. Photovoltaic Manufacturer Details. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 43

Table 5. Support Equipment Details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Table 6. Metrics with Associated Rated Uncertainty .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 43


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LIST OF FIGURES

Figure 1. Fermi-Dirac distribution of available states for different temperatures . . . . . . . . . . 4

Figure 2. Energy vs. momentum diagram for direct and indirect bandgap form = 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . 5

Figure 3. Measured absorption coefcient, , for silicon crystal [1] . . . . . . . . . . . . . . . . . . . . . . . . 8

Figure 4. (a) Carrier concentration (b) Charge (c) Electric eld (d) Potentialacross pn junction [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Figure 5. Current vs voltage for an un-illuminated diode and an illuminateddiode (from Eqn 22) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Figure 6. Power vs voltage for an illuminated pn junction ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 12

Figure 7. Example of single crystal silicon cell in panel (photo by Tyler Otto) . . . . . . . . . . . . . 15Figure 8. Example of multicrystal Si cell in panel (photo by Tyler Otto) . . . . . . . . . . . . . . . . . . . 16

Figure 9. Example of amorphous Si cell in panel (photo by Tyler Otto) . . . . . . . . . . . . . . . . . . . . 17

Figure 10. SDSU physics building roof orientation showing photovoltaic arrays(courtesy of Mark Hatay) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 11. View of array setup looking east (photo by Tyler Otto) . . . . .. . . . . .. . . . . .. . . . . .. . . 22

Figure 12. Signal conditioners and voltage transducers (photo by Tyler Otto) . . . . . . . . . . . . . . 23

Figure 13. DC/AC power inverter (photo by Tyler Otto) .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 24

Figure 14. Attached T-type thermocouple (photo by Tyler Otto) . . . . . . .. . . . . .. . . . . .. . . . . .. . . 25

Figure 15. Pyranometer (photo by Tyler Otto) .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 26

Figure 16. Data logger (photo by Tyler Otto) and Schematic of Data Acquisition . . . . . . . . . 26

Figure 17. Power output versus clock time on 18 August 2008. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . 28

Figure 18. Measured radiation versus clock time for different days of the year . . . . . . . . . . . . 29

Figure 19. Current at maximum power point versus measured solar radiation(Every 15th point is plotted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Figure 20. Voltage at maximum power point versus measured solar radiation(Every 15th point is plotted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Figure 21. Power output at maximum power point versus measured solar radia-tion for 120W Mc-Si array (Every 15th point is plotted). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Figure 22. Array efciency vs. temperature at maximum power point forKC120W array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32


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Figure 23. Modeled power output vs. measured power at maximum power point(Every 5th point is plotted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Figure 24. Normalized error of improved model as function of measured solar radiation . 34

Figure 25. Modeled power output versus measured power including ideal tline (Every

5th point is plotted) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35


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ACKNOWLEDGMENTS

I would like to thank my advisor, Alan Sweedler, for all of his patient advice and

constant perspective, without which I would nd myself tilting at windmills. I would also liketo thank Fletcher Miller, whose sagacious advice was invaluable throughout this project. I

would also like to thank Michael Bromley, whose advice and critical eye, was particularly

helpful with formatting, this thesis. Mark Hatay was able to provide a great deal of insight

into many of the problems encountered with the experimental design of the project. A special

thanks is due to Bill Lekas, without whom this project would not have been possible. Bills

desire for SDSU to be a model green campus has lead to many photovoltaic arrays

(including these), solar thermal installations, a cogeneration plant, and other projects. Pablo

Bryant was kind enough to install all of the measurement devices used for this project. I

would also like to thank my wife for putting up with my up and down moods based upon how

well my research was going. Julie was always there with a hug and a kind word of support.

As alternative energy is a very hot topic right now, there was never a dearth of advice on what

interesting topic I should look into. To all of these people, and others not mentioned, thank

you.


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CHAPTER 1

INTRODUCTION

Solar cell technology has been around since the 1950s when it was rst discovered at

Bell Labs. Initially selenium was being researched for use as a remote power source. It was

later discovered that adding impurities to silicon, much more efcient power could be

generated. Initially 4% of sunlight could be converted into electrical power, but the efciency

soon reached nearly 10%, from there an industry was born [3].

There was a large investment in renewable energy, particularly solar energy in the

1970s and early 1980s when an oil embargo was enacted by OPEC nations [4]. However,

when the oil embargo ended, so did this nations emphasis on renewable and local energy.

However, today we are faced with less temporary problems. Global warming and the global

war on terror have made not only the United States, but the entire world take a second look at

local, clean and sustainable energy. As we try to reduce our dependence on foreign oil, and

fossil fuels in general, we must nd a way to compensate for the large void left behind. This is

where photovoltaics can play a large role.

Solar technology, is a mature technology. Much of the solar electricity is generated

from silicon-based solar cells. There are many companies producing silicon based

photovoltaics, and with so many different companies there needs to be simple methods of

discerning one product from another. The ofcial rating system for solar panels is currentlyvery basic. It is a simple one-point measurement. The companies measure the panel power

output under a lamp-simulated 1000 W/m 2 , a cell temperature of 25 C,and a relative air massof 1.5. Relative air mass is an indication of the thickness of the atmosphere. There are several

problems with this system, most notably, it does not answer the question of how the panel, or

better yet an entire array, will perform under different conditions. Another problem, is that

only in some of the sunniest places on earth do we ever see such high radiation, San Diego

happens to be one such place. The other problem is that a cell temperature of 25 C is almostnever seen, with operating temperatures more frequently in the 40 50 C range. Researchneeds to be done to model how entire arrays behave under different conditions.

There has been a great deal of research in this area [5, 6, 7, 8, 9, 10, 11]. There are two

types of experiments that are frequently performed. The rst type of experiment is done in the

lab. Articial lights are used to simulate solar radiation, and an individual cell is placed on a

heating surface that can precisely vary the temperature of the cell. Solar cell performance can

be measured under varying temperature and lighting conditions. This is very important


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research; it models the behavior of a single cell, the building block of a solar panel. However,

to create a panel, these cells are wired in series, schottcky diodes are added and the cells are

encapsulated in varying materials, which could change the behavior.

This is where the second line of research comes in. Individual panels are placed in

outdoor test facilities [5, 6, 7, 8, 9, 10, 11]. The panels are not used to generate electricity; animportant fact that will be made clear later. The operating conditions are now dictated by the

weather instead of being precisely varied in a laboratory. Solar radiation and panel

temperature must be measured. To collect a large enough data sample, this research generally

requires a great deal of time. This line of research is one step closer to how deployed panels

are used, but it is still a couple of steps away. There are some advantages to this type of

research. Since the panels are not wired for power generation, the researcher can obtain an

entire current-voltage curve for the panel, this will be discussed in more detail later. Models

created from this line of research generally rely heavily on measured values that are

unobtainable by panels used for power generation.A new line of research is where this study comes in. A side-by-side analysis of ve

different solar arrays has been performed. A solar array is created by wiring many panels in

series and in parallel to generate a larger amount of power. An array can vary in capability

from a few hundred watts to a megawatt or more. This is how an installation on a home or

business would look. The different arrays included in the study represent the different, widely

available, silicon based technologies: single crystal, multicrystal, and amorphous silicon. The

differences in these technologies will be discussed later. This research is similar to the

research performed on single panels, in that it requires a large data collection period and thevarying conditions are dictated by the weather. This research creates some unique challenges.

Because the different arrays are being used to produce power, it is important to maximize the

electrical power generated. The impact of this will be made clear in later sections. However,

sufce to say that maximizing the power, limits the changes that can be made to the system,

and is the main main reason why little research has gone into modeling the output from grid

connected arrays. This important limitation requires modifying previous models to work with

metrics pertinent to grid connected systems. Specically, this research focused on modeling

the power output of grid connected, photovoltaic arrays as cell temperature and solar radiation

vary.


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CHAPTER 2

THEORY

SEMICONDUCTOR THEORYTo create a meaningful model of how photovoltaic arrays behave, one must understand

the underlying physics. Semiconductor physics will allow for a qualitative understanding of

the impact of temperature and solar radiation on solar array performance. In a semiconductor,

the probability of an electron occupying an available state is given by the Fermi-Dirac

distribution:

f (E ) = 1

1 + eE E f

k b T

(1)

where E f is the Fermi energy, or the chemical potential, T is the temperature, and kb is theBoltzmann constant. The Fermi-Dirac distribution applies to particles which obey the Pauli

exclusion principle, which prevents multiple electrons from occupying the same state [12].

The distribution also accounts for the fact that if an electron is excited into a higher energy

state, there must be a corresponding vacancy left behind. At absolute zero, the Fermi-Dirac

distribution implies that all electrons will be below the Fermi energy. With no states available

at higher energy, and all states below the Fermi energy lled, there is no state for which an

electron can move, meaning no conduction electrons. As the temperature is increased, more

states are available to electrons, causing an increase in conduction. Figure 1 shows thedistribution of states, f (E ) for different temperatures, noticing that as temperature increases,more states are available to conduction electrons.

As has already been mentioned, when an electron is excited from the valence band

into the conduction band, it must leave behind a vacancy. This vacancy is a positively charged

region called a hole. Thus, in semiconductors there are two particles that contribute to

conduction and current; the electrons that have been excited, and the positive holes left behind.

Both are capable of responding to an external electric eld by moving in opposite directions.

To look at how the electron moves in the conduction band, and the hole in the valence

band, the excess energy above the conduction band, or below the valence band, is assumed to

be converted into kinetic energy. This leads to an energy-momentum relationship for both

particles:

E E c = P 2

2meand E v E =

P 2

2mh, (2)

where E c is the lowest energy state in the conduction band, E v is the highest energy state inthe valence band, P is the electron or hole momentum, and me and mh are the effective mass


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0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2

f ( E ) ( D i s t . A v a

i l . S t a t e s )

Energy (units of E f)

T1T2>T1

T3>T2

Figure 1. Fermi-Dirac distribution of available states for different temperatures

of the electron and hole respectively. The effective mass will be discussed shortly. This

relationship assumes that the transition from the valence band to the conduction band is

direct. In other words, there is no change in momentum required to excite the electron. If a

change in momentum is required, through phonon absorption/transmission, then we can

re-write the above formulas more generally as [13]

E E c = (P P 0)2

2meand E v E = (P P

0)2

2mh. (3)

Indirect bandgap semiconductors are extremely important in photovoltaics. Two examples are

Si and Ge, where P 0 = 0 and P 0 = 0 . Figure 2 shows plots of the energy momentumrelationship for both a direct and indirect bandgap. From the gure for the indirect bandgap

(P > 0), one can see that in-order for an electron to transition from the valence band to theconduction band with the minimum amount of energy, the electron must increase its

momentum through the absorption of a phonon.

The effective mass is the mass the electron or hole appears to have when considered in

a classical theory. In order to determine the value for the effective mass, one only needs to

think of the Hamiltonian for a free particle and associate the Hamiltonian with the total energy

[14]:

H = E = P 2

2m =

( k)2

2m

1 2

d2E dk2

= 1m

. (4)

Once the probability of a state being occupied is known, the number of available states

must be determined using the density of states. The density of states, is the density of


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-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

E n e r g y

( A r b

i t r a r y

U n i

t s )

Momentum (Arbitrary Units)

Conduction Band, E c=1, P 0= 0Valence Band, E v=0

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

E n e r g y

( A r b

i t r a r y

U n i

t s )

Momentum (Arbitrary Units)

Conduction Band, E c=1, P 0> 0Valence Band, E v=0

Figure 2. Energy vs. momentum diagram for direct and indirect bandgap form = 12

available states for a given energy. For an electron, the density of states is given by [14]:

g(E ) = 122

2me 2

3/ 2

E E c. (5)

To determine the total density of electrons in the conduction band and holes in the

valence band, the density of states is multiplied by the probability of the state being occupied,

and integrated over all energies in the conduction band. The electron density in the

conduction band, n, is given by [13]:

n =

E cg(E )f (E )dE = 2

2m ekbT h2

3/ 2

eE f E c

k b T N ceE f E c

k b T , (6)

and similarly for holes in the valence band,

p = N veE v E f

k b T . (7)

An intrinsic semiconductor is one in which the number of electrons and holes is

strictly given by the above relationships. No additional electrons or holes have been added,

the material has not been doped. For intrinsic semiconductors, any electron that is excited to

the conduction band must leave behind a hole, thus n = p = n i , and from this the law of massaction is dened. The law of mass action allows one to determine the number holes or

electrons, by knowing the number of the other. The law of mass action gives the equilibrium

condition for electrons and holes at a given temperature:

n2i = np = N cN ve E g . (8)

where 1/k bT and E g E c E v is the size of the energy bandgap. At room temperature,silicon has an indirect bandgap of 1.11eV [15]. From Eqn. 8, an expression for the Fermi

energy can be obtained.

E f = 12

(E c + E v) + kT

2 n

N vN c

(9)


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For an intrinsic semiconductor the number of electrons equals the number of holes, nulling

the second term in Eqn. 9. When this is the case, the Fermi energy is located in the middle of

the bandgap. The position of the Fermi energy can be adjusted by changing the ratio of the

number of holes to electrons. This is achieved by doping the semiconductor, or introducing

impurities to the semiconductor. If an impurity atom is added which adds additional electrons,the semiconductor is n-type. Impurity atoms which add holes create p-type semiconductors.

As previously mentioned, doping a semiconductor changes the position of the Fermi

energy. For an n-type semiconductor the Fermi energy is shifted towards the conduction band.

While for a p-type semiconductor, there are more holes than electrons, shifting the Fermi

energy towards the valence band. Both doping processes increase the conductivity of a

semiconductor. This can be seen by looking at the distributions in gure 1. For temperatures

greater than zero, there is some nite probability of nding electrons with energy greater than

the Fermi energy (E=1 in the plot). However, if the energy lies in the bandgap region, there is

no state in which the electron can exist. If however, the Fermi energy is shifted toward theconduction band, there is a better chance of the electron nding a state to occupy. Thus, an

electron in an n-type semiconductor, will have more states readily available than an electron

in an un-doped semiconductor at the same temperature. Not all impurities have a positive

effect on the conduction of semiconductors. In fact, other than a select few, most impurities

degrade the performance of semiconducting devices [13]. This will be discussed further later.

There are two ways in which charge can travel in a semiconductor, both are important

in the behavior of photovoltaic cells. The rst method of transport is drift. Drift is the motion

of the carrier caused by an applied electric eld. The velocity of an electron under theinuence of an electric eld is as follows:

vd = at = qtrme

, (10)

where is the strength of the electric eld, q is the charge and tr is the average time betweencollisions for all electrons. From this point the carrier mobility and current density can be

dened as

e = vd

= qtrme

, h = qtrmh

, (11)

J e = qnvd = qen, J h = qh p. (12)

Similar expressions exist for holes in the valence band [13]. From the expression for current

density, the conductivity can be determined, showing a contribution from both the electrons in

the conduction band, as well as the holes in the valence band

= J

= qen + qh p. (13)


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where E p is the phonon energy, A is a constant. For transitions that involve phononabsorption , the absorption coefcient is given by [16]:

a = A (h E g + E p)2

exp E pkT 1. (20)

The indirect absorption coefcient changes very rapidly (several orders of magnitude) over

the visible range of light (Figure 3). This need for an electron to simultaneously absorb/emit a

phonon when a photon is absorbed, means that in order to absorb most (90%) of the light, an

indirect bandgap material such as crystalline silicon, requires a thickness of nearly 100 m .Amorphous silicon is a form of silicon that lacks crystalline structure, like glass. Amorphous

silicon is a direct bandgap, meaning it does not require the absorption or emission of a

phonon, and can more readily absorb the light. The thickness of amorphous silicon required

to absorb most of the incident light is only a few microns [3].

100

1000

10000

100000

1e+06

400 450 500 550 600 650 700 750 800 850

A b s o r p t

i o n

C o e

f f i c i e n

t ( c m

- 1 )

Photon Wavelength (nm)

Figure 3. Measured absorption coefcient, , for silicon crystal [1]

While the absorption of light leads to the creation of electron-hole pairs, the creation

of electron-hole pairs is a reversible process. The recombination of the pairs can occurthrough different pathways. Being able to effectively use the electron-hole pairs before

recombination occurs is essential for efcient solar cell devices. The rst method of

recombination is simply the reverse process of light absorption. An electron, which has been

elevated to the conduction band, drops back to the valence band, recombining with a hole.

The energy of recombination is given off in the form of radiation [16]. This type of radiation

occurs more rapidly in direct bandgap semiconductors because the simultaneous absorption or


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Figure 4. (a) Carrier concentration (b) Charge (c) Electric eld (d) Potential across pn junction [2]

exposed to light.

V 0 = kbT

q n

N cN vn2i

, (21)

where N c and N v are given by 6. To determine the ow of charge through the device, thedevice can be divided into two regions, the depletion region (or space-charge region) and the

quasi-neutral region. Also, for the uniformly doped, quasi-neutral region, the ow of majority

carriers (electrons in n-type) ow is negligibly small, and the minority carriers ow mainly bydiffusion [13]. Under these conditions, the number of holes in the n-type region decays

exponentially with increased distance from the depletion region. The current in the depletion

region for an illuminated pn junction is given by the illuminated diode law [13];

I = I 0 eqV 1 I sc , (22)

I 0 = AqDen p0

Le+

qDh pn 0Lh

, (23)

I sc = qAR(Le + W + Lh ), (24)

where Dh/e is the diffusion constant, and Lh/e is the diffusion length , representing the meandistance which the charge carriers will diffuse under no illumination or external potential

difference. A is the cross sectional area of the pn device, R is the rate which charge carriers

are created via illumination and W is the width of the depletion region. This equation gives

the important voltage-current characteristics for solar cells (gure 5).


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C u r r e n t

( A )

Voltage (V)

Un-illuminated diode, I 0=1,Beta q=10, I L=0illuminated diode, I 0=1,Beta*q=10, I L=10

Figure 5. Current vs voltage for an un-illuminated diode and an illuminated diode (fromEqn 22)

Figure 5 gives some information about photovoltaic performance. Compare the plot

for the un-illuminated diode and the illuminated diode. One can observe that by illuminating

the diode (an increase in R in Eqn. 22), there is a signicant increase in the current, while the

voltage only increases slightly. Thus, the current is heavily affected by a change in the amount

of radiation, while the voltage is less affected.

From the illuminated diode equation, Eqn. 22, we can derive an a formula which

corresponds to the maximum current output for an amount of radiation, R. The maximum

current can be generated when the voltage is zero. Setting V=0 in the equation, one nds that

the maximum current is I sc , otherwise called the short-circuit current .The open-circuit voltage , V oc, is the maximum voltage that can be generated by a solar

cell for a given radiation, R. this occurs when the current is zero. V oc can be found by takingEqn. 22 and setting the current to zero and solving for the voltage.

V oc = kT

q n

I scI 0

+ 1 (25)

I sc and V oc are the maximum current and voltage the solar cell is capable of producing,respectively. However, the cells are only capable of producing these values when the power

output is zero ( P = IV ). As voltage is increased from zero, the current decreases from I sc ,increasing the power from zero until reaching a maximum (the maximum power point, at V mpand I mp ). Upon reaching the maximum power point, continuing to increase the voltage,further reduces the current, until reaching zero at V oc, where again, the power is zero (Figure6). The maximum power point values are of great importance for grid connected solar panels,

which typically operate at these values. Looking at Eqn. 22 for an illuminated diode, it can be

observed that the current is a function of temperature and illumination. This means that the


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maximum power point is also changing with temperature and solar radiation, thus it must be

tracked in real time in order to extract the maximal power from the system.

P o w e r

( W )

Voltage (V)

Illuminated diode, I 0=1,Beta*q=10, I L=10

Figure 6. Power vs voltage for an illuminated pn junction

THE EFFECT OF TEMPERATUREAnother way of writing I sc that is very intuitive, but gives less insight into the physics

involved, is to state that I sc is the incident photon current for a specic wavelength of light,N (), times the fundamental unit of charge, e, multiplied by the efciency, (), at which thephotons generate an electron-hole pair [10]:

I sc = ()eN ()d. (26)This is how the spectral response of a photocell is measured [10]. While much of the physicsbehind what causes a change in I sc is hidden in this equation, it is particularly convenient formeasuring how the current is affected by a change in temperature. Any photon with energy

less than the bandgap will have an efciency of zero. The bandgap of silicon can be

approximated to rst order by [14]:

E g(T ) E g(300) + dE gdT T =300 K

(T 300K ). (27)

dE gdT |T =300 K = 2.3x10

4 eV/K for crystalline silicon [10]. The negative value of dE gdT implies

that the bandgap will get smaller as the temperature increases, implying more photons can be

absorbed, which in-turn increases the short circuit current.

V oc is also affected by a change in temperature. The change in V oc can beapproximated by [10]

dV ocdT

= (E g(T 0)/e ) V oc(T 0)

T 0

3ke

(28)


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14

CHAPTER 3

LITERATURE REVIEW AND NOVEL DEVICES

THEORETICAL EFFICIENCY LIMITATIONSThere is extensive literature on the subject of modeling the behavior and limitations of

photovoltaic devices. Many attempts have been made to place an upper limit on the efciency

of photovoltaic devices. The most widely accepted limit was derived in 1961 by William

Shockley and Hans Queisser [17]. The analysis provides a great deal of insight into where

improvements can be made.

In order to determine the maximum achievable efciency, certain quantities must be

taken to an ideal limit. The rst such quantity is the absorption coefcient of photons. All

photons incident upon the solar cell with an energy greater than the bandgap will be absorbed,

creating an electron-hole pair. All photons with energy less than the gap will not be absorbed.

Moreover, all photons with a large enough energy will have the same effect on the material. In

other words, a photon with an energy equal to twice that of the bandgap, will produce an

electron-hole pair with the same energy as that of a photon with just enough energy to create

the pair (thermalization in current devices makes this a fair approximation).

The next assumption, is that radiative recombination is the only pathway to

electron-hole recombination allowed. Radiative recombination sets an upper limit on the

mean lifetime of the carriers [16]. Using the assumptions mentioned before, a maximumtheoretical efciency can be determined. The efciency is a function of the bandgap, the solar

cell temperature, the solar spectrum and the solid angle subtended by the sun [17].

Initially, only a single bandgap device was assumed during the derivation of the

maximum efciency. In a single bandgap device, all of the electron-hole pairs are separated

by an internal voltage determined by the type of semiconductor (i.e.. the bandgap). This

means that photons with large energy have the same effect as a lower energy photon.

However, several p-n junctions with differing bandgaps and internal voltages can be stacked

to allow photons of high energy to create electron-hole pairs separated by a larger voltage, and

thus produce more power. By creating a multi-bandgap device, the maximum efciency can

be further increased [18]. The number of cells can be increased, theoretically to innity, but

2-4 is common. For light normally incident on 1,2,3,4 and stacked cells, theShockley-Queisser limits are 31%, 42.5%, 48.6%, 52.5% and 68.2% respectively [19].

The dependence of the efciency on the solid angle leads to some interesting

consequences. A solar cell that is placed in direct sunlight, receives light from the sun, which


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subtends a solar angle related to the diameter of the sun, and the distance of the sun to the

earth. By focusing this light two changes are made. First, there is an increase in the solar

intensity received. This increase in solar radiation, simply changes the amount of solar

radiation per unit area. The second change is an increase in the solid angle which the solar

cell receives light. This occurs by changing the ratio of the diameter and distance away of thesource of radiation, which is now the focusing optics. This increase in solid angle leads to an

increase in the maximum efciency [18]. For maximally concentrated light on 1,2,3,4 and stacked cells, the Shockley limits increase to 40.8%, 55.5%, 63.2%, 67.9% and 86.8%

respectively [19].

CURRENT TECHNOLOGY AND NOVELDEVICES

The dominant material currently used in the photovoltaic industry is silicon. Silicon

based solar cells come in different forms. Single crystal silicon has the highest efciency witha maximum reported cell efciency of 24.7% in the lab [20]. However, there are many

problems with this. The process used to grow single crystal ingots requires a great deal of

energy and the trimming of the ingot wastes a large amount of silicon [21]. Also, being an

indirect bandgap material, a relatively thick piece of silicon is required to absorb all of the

incident light (100 m). These factors lead to single crystal silicon panels being relativelyexpensive when compared to other silicon based technologies.

Figure 7. Example of single crystal silicon cell in panel (photo by Tyler Otto)


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Multicrystalline silicon (m-Si) is created by worrying less about having large single

crystals with few imperfections and focusing on reducing manufacturing costs. To make these

cells, the silicon material is poured into larger sheets instead of growing large ingots and

cutting them down. This leads to smaller crystals with a large number of grain boundaries.

These grain boundaries are sites for increased electron-hole recombination, which decreasesthe efciency. The most efcient m-Si cell is 20.3% in the lab [20].

Figure 8. Example of multicrystal Si cell in panel (photo by Tyler Otto)

The next common use of silicon for solar cells is amorphous silicon (a-Si).

Amorphous silicon is very different from the crystalline forms. The two crystalline types have

distinct crystalline structure, and an indirect bandgap of 1.1eV. Amorphous silicon does not

have a distinct crystal structure and has a direct bandgap of 1.7eV. Both of these differences

have important effects. The larger bandgap means that a larger number of low energy photons

are not absorbed. The direct bandgap means that far less material is required to absorb the

incident solar radiation (several m). As manufacturing of panels is streamlined, and thefabrication cost is decreased, the material cost will become a larger fraction of the total cost.

Panels which require a smaller amount of silicon stock, could become more competitive thanthose with thicker cells.

The lack of regular crystalline structure leads to many of the performance issues

associated with a-Si. With bond angles and lengths varying, there is an increased chance of

dangling bonds. These dangling bonds are essentially electrons that have not bound to

another Si atom. These are sites where electron-hole pairs can recombine, reducing the

efciency. To reduce the effects of these recombination sites, hydrogen gas is infused through


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angle over which light is absorbed, as well as the increasing the solar intensity. Most tandem

cells are only a few square centimeters in area, but have the light focused on them by

concentrating mirrors. It should be noted that the most efcient cells created follow this

method. While the value is constantly changing, the most efcient cell created to date, is

40.7%. This cell uses three sub-cells and operates under 240 suns [20].There are a couple problems with concentrating the solar radiation. First, diffuse solar

radiation cannot be focused. This has two important consequences. First, the system must

always be pointed directly at the sun, which means expensive tracking devices must be used to

ensure the sunlight is normally incident upon the mirrors. Next, on cloudy days, days where

all or most of the light received is diffuse, the system is not able to generate any energy. This

is in contrast to a typical at plat array which is capable of generating energy from both the

direct and diffuse portion of the sunlight. Another problem is associated with the tracking

device. To ensure the sun can be tracked throughout the day, all year long, the space between

different arrays must be great to prevent shadowing.A different method for breaking the spectrum up is to use a single bandgap material

and add a large amount of impurities. As previously noted, different impurities have different

effects on the performance of solar cells. The impurities add available states in the forbidden

bandgap region. Typically this makes for an efcient recombination pathway. However, if a

large bandgap semiconductor is used, and a great deal of impurities are added, an intermediate

band can be created. The impurity added must be specially chosen to lie at a specic point

within the bandgap. The idea is that this intermediate band is large enough that it can now

accept electrons from the valence band and donate them to the conduction band. The limitingefciencies are the same as the efciencies previously mentioned for tandem cells [19].

Another type of device being researched is a device that up and/or down converts

photons. Typically, when a photon with an energy twice that of the bandgap is absorbed, a

single electron-hole pair is generated. The excess energy of the pair is given up through

thermal interactions with the lattice. Thus, the excess energy is converted to heat. A device

that down converts photons absorbs a photon with energy twice that of the bandgap, and then

emits two photons with energy equal to the bandgap. A device that up converts photons

absorbs two photons with half the required energy and generates a single photon with the

proper energy [19]. Both of these methods increase the maximum efciency of a singlebandgap PV cell to 36.7% under normal sunlight [22]. Other researchers are trying to avoid

the conversion of the photons and simply create devices that generate multiple electron-hole

pairs directly.

These are just some of the changes being made to realize an improvement in

efciency. Most of the previous methods mentioned are based on well known semiconducting


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materials. There is a great deal of fundamental research taking place trying to create new

semiconducting materials. Conducting polymers is a huge area of research and lead to a

Nobel Prize in Chemistry in 2000. Another large area of interest is the area of

nano-technology. Nanowires and nanodots show great promise for future uses. Most of these

novel materials rely on physics that is not well developed or understood at this time. There isno longer a discussion of bandgap and electron-hole pairs, now we discuss excitions, and

lowest unoccupied shell and highest occupied shell. Currently the most efcient polymer

based solar cell is only 5.4% [23], while that of nano based photovoltaics is less than a couple

of percent. Both types of cells typically suffer from short life-spans [24]. The appeal of these

novel materials is the possibility of very low cost materials, ease of mass production and the

reduced dependence on scarce materials with large processing costs.

RELATED RESEARCH

While new types of solar cells are being researched and developed, there is still a greatdeal of room for improvement in the current silicon based panels that dominate the market.

Improving existing models and expanding them to be applicable for a wider variety of panels

is necessary. Also, researching how specic panels behave under general conditions leads to

improvements in current technology.

Many of the existing models are designed to model parameters of a single solar panel

that is not connected for power generation. These models require measurement of metrics that

are inaccessible to a typical installation, such as the short circuit current and open circuit

voltage [5, 6, 7, 8, 11]. This makes it difcult to compare model performance, to the

performance of an entire array of panels operating at maximum power point. Some of the

models previously created are very intuitive, and thus more readily adapted for other uses

[7, 8]. Some are exceedingly complex and provide a great deal of information, but are

impossible to adapt to a grid connected array [5, 6].

One model in particular was very readily adapted from a model which is designed to

work for a non-grid connected panel, to an entire grid connected array. This model starts with

the idea that the power output is linear with respect to an increase in radiation. As mentioned,

light of different wavelengths is absorbed differently. Thus, as the solar spectrum changes, the

performance of the solar cell is going to change. In order to account for this change in solarspectrum, instead of using the measured solar radiation, an effective radiation is used. The

effective radiation is obtained by measuring the short circuit current, I sc . The effectiveradiation is affected by a change in temperature, solar radiation and the solar spectrum. As

discussed previously, the power output decreases with an increase in temperature. This

decrease in power is approximately linear with temperature. With this information, a Power

Temperature Coefcient Model (PTCM) was created, normalizing the model to the standard


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conditions; 1000 W/m 2 and 25 C cell temperature [8]:

P PTCM = P 0Ref R0

[1 + (T 25)], (29)

Ref R0 I sc

I sc 0 [1 + (T T 0)]. (30)

P 0 is the panel rated power under standard conditions, Ref is the effective radiation,R0 = 1000W/m 2, I sc 0 is the short circuit current under standard conditions, and T is the celltemperature. Both and represent constants which determine the impact of temperature onthe power output, and effective radiation respectively.

Equation 29 works fairly well at high radiation, but tends to overestimate the power

output at lower radiation values. Experimentally it has been seen that solar panels are not as

efcient at lower radiation [8]. The uneven absorption across all radiation values was taken

into account by turing Eqn. 29 into a piecewise model, having a low and high radiation

region, as well as including higher order radiation terms. It was found that the addition of a

fourth order radiation term below 200 W/m 2, and an additional linear term above 200 W/m 2

signicantly improves the model effectiveness [8]. This additional term can be thought of as a

power expansion of the fundamental physics equations for current and voltage, Eqn. 22.

P model =P 0

R ef R 0 [1 + (T 25)] 1 1

Ref 200

4 if Ref 200W/m 2

P 0R ef R 0 [1 + (T 25)]

R 0 R ef R 0 200 if Ref > 200W/m

2,(31)

where determines the size of the higher order radiation term [8]. This model, accuratelytakes into account the reduced efciency of the solar panel at lower radiation. It should be

noted that dening the low radiation region as being below 200 W/m 2, as well as the orderof the additional radiation terms, are experimental results.

The main problem with this model, is the use of the effective radiation. As mentioned

earlier in the section, the purpose of the effective radiation is to account for the spectral

response of the solar panel. The relationship between the effective radiation and the actual

solar radiation are not clear, especially when a temperature correction is added to the effective

radiation. Using the temperature dependent, effective radiation, makes it difcult to make a

direct comparison of results obtained from the model. Also, the effective radiation cannot be

obtained for a grid connected array operating at maximum power point, as the short circuit

current cannot be measured, and thus renders the model incompatible.


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CHAPTER 4

EXPERIMENTAL PROCEDURES

EXPERIMENTAL SETUPIn order to perform this scale of experiment, a fairly large setup is required. Seven

different PV arrays were installed a few years ago, along with some data collection capability.

The arrays, along with the data monitoring system, was installed by campus Physical Plant,

and some minor monitoring was being done by campus Field Stations. Only ve of the arrays

were included in this study due to data collection issues early on (arrays 2-6 in Figure 10).

The ve photovoltaic arrays included in the study include three multicrystal silicon arrays,

one amorphous silicon array, and one single crystal silicon array. The experimental setup is

located on the physics building at San Diego State University. The building is located

approximately 32.5 North of the equator, at an elevation of 425ft ASL. The building and

arrays are oriented approximately 15 East of South, which is close to ideal (directly

South)(Figure 10). There are no buildings signicantly taller in the near vicinity, which is

important to prevent shading.

Figure 10. SDSU physics building roof orientation showing photovoltaic arrays(courtesy of Mark Hatay)


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Figure 11. View of array setup looking east (photo by Tyler Otto)

The amorphous silicon array (A-Si) is composed of 16 panels, each with a rated power

of 116W, and is manufactured by Unisolar (array 2). This array has a rated power of 1,856W.

It should be noted that the rated power for the amorphous panels is the stabilized value

reached after the initial Staebler-Wronski effect has degraded the power. The rst

multicrystalline silicon (mC-Si) array is composed of 16 panels rated at 125W and is

manufactured by Kyocera (array 3). This array is rated to output 2,000W. The next mC-Si

array is also manufactured by Kyocera. There are 16 panels rated at 120W for an array power

of 1,920W (array 4). The nal mC-Si array is manufactured by BP Solar. The array iscomposed of 12 panels, each rated at 160W (array 5). This array is rated to output 1,920W.

The nal array is the single crystal (C-Si), which is manufactured by Sharp Solar. The array is

composed of 12 panels rated at 175W, for an array power of 2,100W (array 6). For a list of

arrays and ratings see the appendix.

Each array is angled approximately 14 from horizontal, which is relatively at. To

maximize power produced throughout the year, the angle should be the same as the latitude

(rule of thumb). While this is not ideal for power output, the behavior is not affected by this.

The arrays were also cleaned off with a hose approximately once a week to prevent the

buildup of dirt, which can be substantial. While dirt buildup is a reality for all installations,

the amount and composition of buildup will vary with location and is difcult to parameterize.

To determine the efciency with which the solar arrays convert solar power to

electrical power, the area of each array must be determined. To determine the area of the

array, the entire area of a single panel was measured, including the framework. The total area

of the array was dened as the area of a single panel multiplied by the number of panels.


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Dening the area this way, as opposed to the active power generating surface, means that if a

manufacturer includes a large unusable area, the apparent efciency will be reduced. This also

leaves single crystal arrays at a disadvantage due to the way in which the ingots are shaped

(see gure 7). The area of a single amorphous panel is 1.869m 2. The area of a single panel of

both of the Kyocera multicrystal panels is 0.929m2

. The area of a single BP multicrystal panelis 1.258m 2. The area of a single crystal panel is 1.300m 2. See the appendix for a list of array

sizes.

In order to obtain data about the DC voltage and current, a voltage transducer and

signal conditioner were added to the output of each array (Figure 12) (See the appendix for

manufacturer details). The voltage transducer takes the relatively large voltage of the array,

and reduces it to a more manageable 0-5V. The voltage transducer is an Ohio Semitronics

model VT7, which measures a maximum voltage of 600V. The signal conditioner relies on the

Hall effect to measure the large current from the arrays. A probe is placed around the output

wires, and the signal conditioner creates a voltage output of 0-5V. The signal conditioner usedis the Ohio Semitronics CTL-5135 paired with the CTA 201RX5 Hall effect probe. This

measures a maximum current of 35A. The very linear response of both devices allows one to

convert the voltage back to the appropriate metric.

Figure 12. Signal conditioners and voltage transducers (photo by Tyler Otto)

Each array is connected to its own dedicated power inverter with maximum power

point tracking (See the appendix for manufacturers details). The power inverter used is the

Sunny Boy 1800u (Figure 13). This power inverter is designed for grid-tied photovoltaics.

The power inverter has a maximum efciency of 93.6%. An important point to note, is that


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the efciency of the DC/AC power conversion varies with respect to the DC power input.

Thus, to prevent confusing the behavior of the inverter with the behavior of the arrays, the AC

power was not considered.

Figure 13. DC/AC power inverter (photo by Tyler Otto)

In order to obtain information about the cell temperature, T-type thermocouples were

added to each array. The thermocouples were epoxied to the back-side, center of each array

with the use of an epoxy with high thermal conductivity and low electrical conductivity

(Figure 14). The thermocouple wires were then run varying lengths to the data logger. The

data logger uses a built-in thermistor as a reference temperature for reporting the temperature

from the thermocouples.

There are two LI-200 pyranometers installed on the roof (Figure 15). The LI-200 is a

silicon based pyranometer, which means that it does not have the same sensitivity to all

wavelengths of light. Fortunately however, it absorbs light in a similar fashion to the solar

panels (which are also composed of silicon). The calibration on one of the pyranometers is

slightly out-of-date, and is being used strictly as a check on the calibrated one. Both

pyranometers are placed at the same angle as the panels. The new pyranometer is located inthe center of the ve arrays, while the one with the expired calibration is located at the East

end of the roof in Figure 10. The two pyranometers were cleaned at the same time as the

photovoltaic arrays. An Eppley global helionometer has also been installed on the roof top.

This is a highly accurate device which measures the total radiation from all angles and all

wavelengths. This device was also used as a check for the new LI-200, to ensure the data is

reliable.


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Figure 14. Attached T-type thermocouple (photo by Tyler Otto)

The output of the previous devices, was then sent to two Campbell Scientic data

loggers (Figure 16a). The data loggers measure the input values, and then store the

information online. The data loggers measure each of the values every 5 seconds, and then

average over a 15 minute period. Thus one data point is collected every 15 minutes, which is a

result of an average reading. The data can then be collected online. Data was collected for a

200 day period from 16 August 2008 to 28 February 2009. A diagram of the data acquisition

setup can be found in Figure 16b.

MEASUREMENT ACCURACY AND ERROANALYSIS

The LI-200 pyranometer used to measure the incident solar radiation, was purchased

shortly before beginning data collection. The device was factory calibrated, and the

calibration is certied for one year. The LI-200 is a cosine corrected device, which means that

it accurately measures the solar radiation for all solar angles. This is important when trying to

include both diffuse and direct solar radiation, as well as radiation at low solar angles. Under

natural sunlight conditions, the rated error of the pyranometer is 5%.The signal conditioner and voltage transducers are responsible for measuring the DC

current and voltage respectively. As mentioned in the previous section, much of the setup was

installed years before. Using a handheld multi-meter, the output from the arrays was directly

measured and compared with the values obtained from the signal conditioner and voltage

transducer. It was determined that the devices needed to be re-calibrated. Thus Signal

Conditioners and Voltage Transducers were accurately calibrated with the use of a very


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Figure 15. Pyranometer (photo by Tyler Otto)

Figure 16. Data logger (photo by Tyler Otto) and Schematic of Data Acquisition

precise, high current and high voltage, variable source. The rated accuracy of the current

measurements are 0.5%. The rated accuracy of the voltage measurements are 0.25%. Thecalibration of these devices are valid for one year.

For T-type thermocouples, ANSI standards state that the wires must be capable of

measuring the temperature to 1 C , or 1.5% whichever is greater [25].

The data loggers are responsible for measuring the output values from the previouslymentioned devices. The pyranometer, signal conditioner and voltage transducer have an

output of 0-5V. The data logger measures voltage in this range with a rated accuracy of

5mV. The data logger is capable of reporting the temperature from the thermocouple to anaccuracy of 0.5 C . All of the uncertainties are summarized in the appendix.


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CHAPTER 5

RESULTS

Data was collected for two hundred days. Over this time period, not only was

modeling data obtained, but data about the solar resource in the inland San Diego region was

also obtained. Figure 17 shows the power output versus the time of day for 18 August 2008, a

typical sunny day. The power output from each array clearly follows the trend of radiation,

being scaled differently depending on the power output of the array. It should be noted that

this plot will be different each day, depending on cloud cover and the time of year.

-200

0

200

400

600

800

1000

1200

1400

1600

1800

0 4 8 12 16 20 24

P o w e r o u

t p u t

( W )

Time of Day

Amorphous ArrayMulticrystal125Multicrystal120MulticrystalBPSingle Crystal

Solar Radiation (W/m 2)

Figure 17. Power output versus clock time on 18 August 2008

Information about when the most solar radiation is available, can also be determined

for different months the year. Figure 18 show the measured incident solar radiation available

on a sunny day during different months of the year. The exact shape of each plot will differ on

a daily basis depending on cloud cover. These plots give some indication for the need of modeling PV arrays as the radiation varies over a large range throughout the day and the year.

Figure 19 show plots of current vs. radiation at the maximum power point for each of

the different arrays, while Figure 20 show plots of voltage vs. radiation at the maximum

power point. These gures give an indication of what parameters are being most affected by

the environment. The gures for current vs. radiation are very linear with radiation and have


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0

200

400

600

800

1000

0 4 8 12 16 20 24

S o l a r

R a d

i a t i o n

( W / m

2 )

Time of Day

16 January 200917 March 2008

15 May 200815 September 2008

Figure 18. Measured radiation versus clock time for different days of the year

very little observed deviation which could be caused by an increase in temperature, consistent

with expectations. This is in contrast to the voltage vs. radiation plots. Above around

200 W/m 2 the voltage changes very little with radiation, and conrms the expectation that thismay be the dominant metric being affected by temperature.

There are some outliers observed in the plots for the single crystal array, even using

the data rejection methods described. The outlier values are consistent however. The current

always appears lower than expected, while the voltage always appears larger than expected.

These are consistent with values measured at lower radiation. This array is the closest to theedge of building, and the furthest from the pyranometer, it is possible the are times when the

array is partially shaded, and not being caught by the pyranometers, however this seems

unlikely.

Figure 21 shows a plot of power output at maximum power point as a function of the

measured solar radiation for the KC120W multicrystal array. This plot is representative of

how the power output plots look for the other arrays in the study. This data shows the power

output increasing fairly linearly with an increase in solar radiation.

Figure 22 shows a plot of the maximum power point array efciency versus cell

temperature. The efciency is dened as the power output per unit of area, divided by the

measured solar radiation. From this gure, one can observe that the efciency, and in turn the

power output, has a linear dependance on the cell temperature. It should be noted, that the

efciency does have some radiation dependence, which causes some of the spreading in the

gure. Also, from this plot, the arguments made during the discussion on temperature seem

well justied, namely, that the power output at maximum power point decreases with an


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-1 0

1 2 3 4 5 6 7 8 9

0 200 400 600 800 1000

D C C u r r e n t

( A )


Amorphous Array

-1 0

1

2

3

4

5

6

7

0 200 400 600 800 1000

D C C u r r e n t

( A )


Multicrystal Kc125W Array

-1

0

1

2

3

4

5

6

7

0 200 400 600 800 1000

D C C u r r e n t

( A )


Multicrystal Kc120W Array

-1 0 1 2 3 4 5 6 7 8 9

0 200 400 600 800 1000

D C C u r r e n t

( A )


Multicrystal BP Array

-1 0 1 2 3 4 5 6 7 8 9

0 200 400 600 800 1000

D C C u r r e n t

( A )


Single Crystal Array

Figure 19. Current at maximum power point versus measured solar radiation (Every15th point is plotted)

increase in cell temperature. Also, since the increase in current with temperature is fairly

small when compared to the decrease in voltage, it can be assumed that the decrease in

efciency is mostly due to the linear decrease in voltage found in Eqn. 28.

With the plots for power (Figure 21), efciency (22), voltage (20) and current (19), the

models previously discussed can be fully justied. The models discussed previously use the

effective radiation, a term which cannot be obtained for a grid connected array. Thus, instead

of using the effective radiation, the actual solar radiation can be used in its place. This

modies the model in such a way that it can be used for grid connected arrays. There is a

trade off to doing this. As the effective radiation changes with the solar spectrum, by using thesolar radiation this spectral dependance is removed from the model. However, future work

could possibly include it explicitly. The rst mode, in its altered form is;

P model = P 0RR0

[1 + (T 25)], (33)

where R0 = 1000W/m 2, P 0 is the rated array power, R is the measured solar radiation, isthe temperature coefcient, and T is the cell temperature. The thermocouples (Figure 14) are


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0

50

100

150

200

250

0 200 400 600 800 1000

D C V o l

t a g e

( V )


Amorphous Array 0

50

100

150

200

250

300

0 200 400 600 800 1000

D C V o l

t a g e

( V )


Multicrystal KC125 Array

0

50

100

150

200

250

300

0 200 400 600 800 1000

D C V o l

t a g e

( V )


Multicrystal KC120 Array 20 40 60 80

100 120 140 160 180 200 220

0 200 400 600 800 1000

D C V o l

t a g e

( V )



0

50

100

150

200

250

0 200 400 600 800 1000

D C V o l

t a g e

( V )



Figure 20. Voltage at maximum power point versus measured solar radiation (Every15th point is plotted)

measuring the back-of-array temperature, not the cell temperature. To obtain the cell

temperature, an approximation must be used. To approximate the cell temperature, 2.5 C per1000W/m 2 is added to the measured back-of-array temperature [6]. It should be noted thatthis is an experimental result from other panels, and improved cell temperature data could

improve the accuracy of the model. The temperature coefcient for this model will be shown

with and without the added cell temperature correction to show its impact. The temperature

coefcient, is the fractional change in power output per degree Celsius, and is unique toeach array.

The use of a weighted least squares program was used to nd the best t of the data toEqn. 33 by adjusting the value of . The weighted t function of GNUPLOT was used forthis. GNUPLOT returns the value of as well as the asymptotic uncertainty in the value, andthe reduced 2 (See Table 1). From this table it can be seen that including the cell temperaturecorrection, the temperature coefcient is reduced, which makes sense as the apparent

temperature is increased. The reduced 2 values are also smaller with the cell temperaturecorrection added, implying that the data ts the model better that when the correction is


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This model works fairly well, considering it is fairly simplistic. However, it does have

some problems. Figure 23 shows a plot of the model predicted power output versus the actual

measured power output for the arrays. This gure shows that the model appears to work better

for large radiation than at low radiation. At low radiation, the model tends to overestimate the

power output. This is consistent with the observations previously noted.

0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

Measured DC Power

Amorphous Array

0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

Measured DC Power


0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

Measured DC Power


0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

Measured DC Power


0

400

800

1200

1600

0 400 800 1200 1600

M o d e

l e d D C P o w e r

Measured DC Power


Figure 23. Modeled power output vs. measured power at maximum power point (Every5th point is plotted)

The next model, was able to accurately account for this overestimate at low radiation

by including a higher order radiation term. The initial model assumed the power output was

linear with radiation, this assumption is only valid if the voltage changes little with radiation.This was seen to be the case from the current-voltage plots of Eqn. 22 (Figure 5. The voltage

changed little by increasing the radiation, while the current changed a great deal. Figure 20

shows that the behavior of the voltage at maximum power point is actually very complicated.

Unfortunately there are no general equations for maximum power point voltage to justify the

plot. Above 200 W/m 2, the voltage changes little with radiation, however below 200 W/m 2,


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the voltage rapidly increases from 0 to a maximum. This rapidly changing voltage at low

radiation means the assumption of a linear power output is no longer justied at low radiation.

The normalized error in Figure 24, shows that the error is maximized near 200W/m 2. Thisgure is what leads to the fourth order correction factor at low solar radiation. The nal model

is

P model =P 0 RR 0 [1 +

(T 25)] k 1 1 R2004

if R 200W/m 2

P 0 RR 0 [1 + (T 25)] k R 0 RR 0 200 if R > 200W/m

2.(34)

-0.1

-0.05

0

0.05

0.1

0.15

0 200 400 600 800 1000 1200

( P m o d e l e d

- P m e a s u r e

d ) / P

0

Radiation (W/m 2)

Figure 24. Normalized error of improved model as function of measured solar radiation

Table 2 shows the values for the new temperature coefcient, and the additional higherorder radiation term,k , with the associated asymptotic error. Each value was returned by the

least squares tting program. Also included in the table are the reduced 2 values for eacharray. As a note, for this model the added cell temperature correction was included.

Table 2. Improved Model Coefcients With Uncertainties and Reduced 2 values

Array ( C 1) k k reduced 2

Amorphous -0.00185 2 10 5 0.0355 3 10 4 8.37Multicrystal125 -0.00997 1.5 10 5 0.0568 3 10 4 9.01Multicrystal120 -0.00820 1.7 10

5 0.0668 3 10

4 6.28MulticrystalBP -0.00754 3 10 5 0.0963 3 10 4 13.04Single Crystal -0.00920 3 10 5 0.0695 4 10 4 28.05

From Table 2, one can immediately start making observations of the behaviors of

different technologies. The amorphous array has a temperature coefcient which is

signicantly smaller than the other, crystalline based arrays. The amorphous array also has a


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smaller k value than the other arrays. These two facts indicate that the amorphous array

behaves in a more ideal fashion than do the crystalline based arrays. Ideal simply means

there is less of an effect of temperature on the power, and the radiation is absorbed more

effectively for all insolation values.

In gure 25 plots of measured power output versus model predicted power can befound for each of the arrays. These gures show how well the model ts the measured data. If

the model perfectly ts the measured data, 800W of measured power would be exactly

predicated by the model using the temperature and radiation information. This means the

plots should be a line with a slope of unity. This line has been added to each plot as a visual

reference. From this plot it can be observed that the model does accurately predict the power

output from each array for all radiation.

0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

( W )

Measured DC Power (W)

Amorphous Array

0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

( W )



0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

( W )



0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C P o w e r

( W )



0

400

800

1200

1600

0 400 800 1200 1600

M o d e l e d

D C

P o w e r

( W )



Figure 25. Modeled power output versus measured power including ideal t line (Every5th point is plotted)


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Immediately noticeable is the reduced power output from the crystalline based arrays

under an increase in temperature. The large temperature dependence leads to an

approximately 25% reduction in power for the crystalline based arrays for large solar

radiation. The 125 Mc-Si array went from the highest rated array, to having the lowest

operating efciency. The amorphous array is not nearly as affected by the temperature, andsees a relatively small reduction in power output. While the rated power of the amorphous

array is the smallest of the arrays, after including the effect of temperature, the array is now

the largest producer of power on the physics roof. While the power output of the amorphous

array is larger than the other arrays, the efciency is still not as large as the crystalline based

arrays, which is an important distinction, because it still requires a larger area to produce the

same amount of power as a crystalline based array.

There are some important points to note for the crystalline arrays. Looking at the

impact of temperature on the efciency at 1000 W/m 2 one can notice that the rated efciencyfor a panel is not necessarily the best indicator of what the operating efciency will be. Thethree crystalline based arrays, after the increase in temperature is factored in, have nearly the

same efciency . This is a very important point as, loosely speaking, the cost of a panel is

related to the expected efciency, with more efcient panels generally costing more than less

efcient ones.

Using this model, and the determined temperature coefcient and non-linear radiation

term, the power output from each array can now be predicted with accuracy. This can be done,

not only for a single unrealistic value, but under general operating conditions. Being able to

accurately predict the power output is very important for increased growth in the deploymentof photovoltaic systems.


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CHAPTER 7

FURTHER RESEARCH

The focus of this research has been on measuring the impact of solar radiation and cell

temperature on the power output of grid connected arrays. However, there is another

parameter which affects the power output from PV cells: the solar spectrum. The solar

spectrum is constantly changing throughout the day and year. This is caused by absorption

and re-radiation in the atmosphere. Photons of different wavelengths have differing impacts

on the power production of a solar cell. This is caused by the frequency dependence of the

absorption of light by the cell. Thus, as the solar spectrum changes so does the power output.

The solar spectrum is a difcult parameter to quantify and is typically done by looking at the

change in relative air mass. The relative air mass changes with incident solar angle, the air

density and relative humidity. The impact of the change in solar spectrum is not typically

studied, and to my knowledge, not included in any predictive models. Including a term that

considers the relative air mass could further improve the accuracy of the model studied, and

shed more light on the behavior of solar arrays.

The timeframe over which this research took place, is small enough that one can

assume the panels did not signicantly degrade. However, over the lifetime of the panels,

different panels will see different levels of degradation. This degradation will likely lead to a

change in the coefcients measured. This impact should be further studied.The coefcients obtained from the arrays appear to be consistent with values measured

by others for a single panel [8, 9]. However, other studies have been conducted with different

panel and using slightly different parameters, making a direct comparison impossible. Further

research needs to be done to compare the results for a single panel and arrays of different size.

This can be achieved by doing the same experiment for a single panel at the same time as an

array composed of the same panels. This research will determine if there is a size dependence

for the temperature dependence, i.e. is a single panel more/less affected by an increase in

temperature than a very large array?

The position of the physics roof prevents shading of the different arrays. However not

all installations are so fortunate. Shading creates two issues for power production. First, a

portion of the array is no longer generating power, which will clearly lead to a reduction in

power output. The second problem arises from wiring many cells together. If one of the cells

in a string is shaded, the current generated by that cell is zero (the voltage is not). This cell is

now acting like a current limiting point for all of the cells before this point. Bypass diodes can


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be added to reduce this problem, but it is still an issue. Studying the effect of shading on an

entire array is important to understand what issues a tree in the yard may cause.

Also, Table 1 shows that the temperature coefcients are affected by the

approximation used for the cell temperature. Improving the data for cell temperature can

improve the accuracy of the coefcients. It is possible to drill into the back of a panel anddirectly attach a T/C to a PV cell, but this would void the warranty, and likely cause other

issues. More research should go into improving the cell temperature measurements, by

including information about wind speed and direction, which would clearly have an impact on

how much cooling takes place, and in turn the cell temperature.


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BIBLIOGRAPHY

[1] Edward D. Palikeditor, editor, Handbook of Optical Constants of Solids , AcademicPress, 1998.

[2] Wikipedia, Depletion region (2009), URLhttp://en.wikipedia.org/wiki/Depletion zone .

[3] K. Zweibel, Harnessing Solar Power The Photovoltaics Challenge , Plenum Press, 1990.

[4] Energy Information Administration, Annual Energy Review .

[5] D. K. et al, Temperature Coefcients for PV Modules and Arrays: MeasurementMethods, Difculties and Results, in 26th IEEE Photovoltaic Specialists Conference ,Sandia National Laboratories, 1997.

[6] D. K. et al, Field Experience With a New Performance Characterization Procedure ForPhotovoltaic Arrays, in 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion , Sandia National Laboratories, 1998.

[7] W. et al, Application and Validation of a New PV Performance CharacterizationMethod, in 26th IEEE Photovoltaic Specialists Conference , Sandia NationalLaboratories, 1997.

[8] B. Marion, Comparison of Predictive Models for Photovoltaic Module Performance,in 33rd IEEE Photovoltaic Specialists Conference , NREL, 2008.

[9] E. Radziemska, Renewable Energy , 28, 112 (2003).

[10] E. Radziemska and E. Klugmann, Energy Conversion & Management Management , 43,18891900 (2002).

[11] Sandia National Laboratories, Photovoltaic Module and Array PerformanceCharacterization Methods for All System Operating Conditions .

[12] M. Kardar, Statistical Physics of Particles , Cambridge University Press, 2007.

[13] M. A. Green, Solar Cells , Prentice-Hall, Inc., 1982.

[14] R. Brown, Solid State Physics , El Corral Publication,

comparative study of grid connected photovoltaic arrays by t

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